What Is an Element of Reality?

[vanesch]

I don't really understand this. I just don't know any details about formal Kolmogorov probability theory. In what way are the variables one "conditions on" there (I gather that's technically the wrong word, but I don't know what the right one is) different from regular variables in regular conditional probabilities?

Ok, I think this is crucial to all that follows. Maybe I got too much of a mouthful with "Kolmogorov" ; it is just standard probability theory. From the top of my head - correct me if I'm wrong - a probability measure according to Kolmogorov P is a mapping from a subset M of the power set of Omega into the interval of real numbers [0,1] such that:

P(Omega) = 1
P(empty set) = 0
P(A U B) = P(A) + P(B) if A and B disjoint

and some other, more subtle, properties making P into a measure,
see http://en.wikipedia.org/wiki/Kolmogorov_axioms

A, an element of M (and thus a subset of Omega), is called an "event", and P(A) is "the probability for the event A to happen".

For a finite set of elements Omega, M can be set equal to the powerset (the set of all subsets) of Omega.
These axioms define a standard probability distribution. Of course, for a given set Omega, there can be MANY DIFFERENT PROBABILITY DISTRIBUTIONS, and we can label some of them, with a PARAMETER SET a,b or L. But there is a difference between looking at different sets within one probability distribution, and looking at the probability of a set for different values of the parameter set, and that's the entire difference I tried to explain between the usage of | (which is WITHIN a single probability distribution), and the usage of ; which refers to swapping between different probability distributions.
As I said, in all considerations of "causality" and "locality" and "determinism" and so on, one has to ASSUME FREE CHOICE somehow, and depending on this free choice, we CHANGE THE PROBABILITY DISTRIBUTION. So all what depends on our free choice goes into parameters that tell us which probability distribution we are going to use. The free choice is the setting of Bob and Alice's analysers: they can decide that freely, and as a function of the choice they make, we have different probability distributions of how things will happen. ALL things that will happen. There is also an extra parameter included, which is the COMMON cause, L, and which can be seen as a free choice of some unknown individual (a little devil, if you want). It fixes the entire probability distribution.
However, an OUTCOME is not something that FIXES the probability distribution, it is part of what is described by that distribution. So it doesn't enter into any parameter list !

And how can it be that outcome independence is somehow built into the axioms of probability theory? What does this mean for OQM since that theory violates OI?

Ok, I formulated this badly, sorry. OI is not something that is "build into the axioms of probability theory", it is rather something that is well-defined within probability theory, but which I don't NEED. What I meant was, that P(A) and P(A|B) are two well defined quantities, meaning we can talk about P(A) without having to say that "it depends also on B or not".
In fact, P(A|B) is nothing else but P(A sect B) / P(B) ; so it is a derived concept. Saying that P(A|B) = P(A) just comes down to saying that
P(A sect B) = P(A) x P(B). We usually write P(A sect B) as P(A,B).
It makes perfectly sense to talk about P(A) and about P(A,B). These are numbers which are well defined if the probability distribution is well defined (meaning, the parameters which select the distribution from its family are fixed, in our case a, b and L).

I don't know now. You'll have to explain the difference between conditionalizing on a variable and regarding it as a parameter or whatever for
Kolmogorov.

As I said, the parameters select ONE of different probability distributions out of a family. Once we have our distribution, we can apply it to M. A conditional probability within this distribution is then nothing else but a shorthand for a fraction of two measures of this distribution.
You cannot write P(A ; a) = P(A and a) / P(a) if a is a parameter. You can however, write very well P(A |B ) = P(A sect B) / P(B) ; it is its very definition.

But as far as I know, Bell Locality is still the condition that

P(A|a,b,B,L) = P(A|a,L).

Which is to be re-written:
P(A|B ; a,b,L) = P(A ; a,L)

By definition, we have: P(A|B ; a,b,L) = P(A,B ; a,b,L) /P(B ; a,b,L)

Now, if we rewrite my "Bell condition" which is:
P(A,B ; a,b,L) = P(A ; a,L) x P(B ; b,L), together with the fact that P(B ; a,b,L) = P(B ; b,L) (does not depend on parameter a - that's information locality to me), and we fill it into the definition of P(A|B ; a,b,L) above,
we have:

P(A|B ; a,b,L) = P(A ; a,L) x P(B ; b,L) / P(B ; b,L) = P(A ; a,L) and we're home:

both statements are equivalent.

Just to repeat my request above, can you clarify how this applies to orthodox QM? Because sure in OQM, we don't have

P(A,B;a,b,L) = P(A;a,b,L) * P(B;a,b,L).

Right? Somehow you've got to "conditionalize" (or whatever) one of the two factors on the right on the other outcome (just like Bayes' rule requires). You seem to be saying that there is no need or ability to do this, yet OQM requires it...

I'm sorry that I misformulated this: I didn't mean to imply that in just any Kolmogorov system you have to have this factorisation of course ! What I meant to say (and I badly expressed myself) was:
P(A ; a,b,L) is perfectly well defined. You do not have to say that the expression is somehow "incomplete" because I didn't include B in the list to the right. I could have been talking about ANOTHER quantity P(A|B ; a,b,L) ; only, I didn't talk about it, I didn't need it, because I only wanted to demonstrate P(A,B | a,b,L) = P(A ; a,L) x P(B ; b,L).
That's a perfectly sensible statement, and the three quantities are well defined in just any Kolmogorov system (the equality, of course, is not always true and has to be demonstrated for the case at hand).
I could also talk about things like P(A|B ; a,b,L) and so on, but I simply didn't need to. It is not an ERROR to talk about P(A | a,b,L) and in doing so I do not make any assumption. That's what I put badly as "it is build into the axioms of probability theory".

I hate to make a fuss over terminology, but could you use the technical term "parameter independence" if that's what you mean? Or "signal locality" if that's what you mean? (And btw, these are not the same. Violating signal locality requires parameter-dependence *and* a sufficient control over the prepared initial state of the system.)

That is correct. There could be of course a conspiracy that L compensates for every change in a that I make. I assume of course same L.

Here you're sliding back and forth between "signal locality" and "what relativity requires." Remember, Bohmian Mechanics is also consistent with signal locality, yet somehow you (and most others) think that this theory is inconsistent with relativity. No double standards.

Ok, we've had this discussion already a few times. Because the statistical predictions of both theories are identical, there's no discrimination between both on those "black box" outcomes of course. It is a matter of esthetics of the inner workings. If you need to write that the state HERE is directly a function of the state (or its rate of change) THERE, in the equations, then this thing is not considered local, even if what you crank out of it doesn't see the difference. Sometimes this can be an artefact. For instance, the principle of minimum action is certainly not something local: you need to integrate over vastly remote pieces of space just to find out what you will do here. So that theory is a priori non-local. If you can rewrite it as a differential equation (Euler-Lagrange) then it has become local. But the result is the same.

I still don't understand what you think this proves. Is it: that a deterministic theory automatically respects "outcome independence"? I suppose that's true, especially if you *define* determinism in terms of

P(A|a,b,L)

and

P(B|a,b,L)

equalling either 0 or 1. But then, what's actually relevant is not that those probabilities equal {0,1}, but simply that you've written them without any "outcome dependence"! And obviously a theory with no outcome dependence will respect OI. But that has nothing to do with whether it's deterministic.

Again, I don't care about "outcome independence". I didn't need conditional probabilities at all. I needed to SHOW that P(A,B) factorizes into P(A) x P(B). This can be rewritten into something that uses outcome independence if you like, but I don't care.
What I wanted to show was that from determinism (all probabilities are 1 or 0), and from information locality (P(A;a,b,L) = P(A ; a,L) and P(B ; a,b,L) = P(B;b,L) ) follows the factorization statement that is Bell locality:
P(A,B ; a,b,L) = P(A ; a,L) x P(B ; b,L).

In all this, I never used a conditional probability (and hence didn't need to say "outcome independence"). I used a property of the parametrisation of the family of distributions (namely, that all distributions with same b and L give the same probabilities for events B, no matter what a is ; this comes down to saying that my free choice of a has no influence on the probabilities of events at Bob's) ; and I used a property of each individual distribution (namely determinism, so that all results of mappings P is 1 or 0).
From that, I derived P(A,B ; a,b,L) = P(A ; a,L) x P(B ; b,L).

That's sufficient. I can now of course bring one right hand side member to the left, and write:
P(A,B ; a,b,L) / P(B ; b,L) = P(A ; a,L)

and use the definition of conditional probability on the left:

P(A|B ; a,b,L) = P(A ; a,L)

and you will be happy because I now derived some "outcome independence" ; but first of all this makes no mathematical sense in the case of deterministic distributions because I can divide by 0 (P(B ; b,L) is often 0), and second, it is only the use of a definition. Mind you, I didn't ASSUME this: I demonstrated it (although by dividing by 0).

As far as I can tell, this is true by fiat only. You define "determinism" in a way that precludes outcome dependence from the very beginning. But this is misleading and unnecessary, since we know that Bell Locality = OI and PI *regardless* of whether or not we have also determinism.

I would really like to know where I USED "outcome independence" and how this is defined. I used only a parametrized set of distributions, which are parametrized by a,b and L (meaning that all my probabilities are fixed when these parameters are fixed) ; then I used different events (subsets of omega), namely A, B and (A sect B), on which I applied my now well defined distribution. I showed that under the conditions I posed, P(A,B) = P(A) x P(B). That's all. Never I needed to use a conditional probability so I don't see where I made such an assumption.

cheers,
Patrick.

 

[ttn]

ttn, excuse me for breaking in, but I read this post pretty carefully, and I see you making a distinction between "signal locality" [...]
and "what relativity requires". But Einstein developed special relativity by considering observers (who might as well be called Alice and Bob) comparing their measurements in different inertial frames via signals limited to the speed c. So if QM obeys signal locality, why doesn't it satisfy what relativity requires?

Oh, yes, that's a good question. Certainly worth clarifying. I certainly don't mean to imply that relativity doesn't require signal locality. It does. Any theory which permits transmission of superluminal signals, contradicts relativity. Period.

The question is: is signal locality *all* that relativity requires? I think it's pretty clear that it's not, or at least it's extremely debatable. Maybe the clearest way to make this point is by example. Take Bohmian Mechanics. This theory is blatantly nonlocal. You have two particles following definite trajectories, trajectories that are "choreographed" by the wave function (according to a deterministic guidance formula). (Hopefully Bohm's theory is familiar enough that that one-liner summary is sufficient.) But the guidance formula is blatantly non-local: the trajectory of one particle depends on the instantaneous position of the distant particle (and hence indirectly on the fields encountered by that distant particle). So for example in the EPR type situation, the two particles fly off toward their respective detectors; one of them enters the detector and veers off in a certain way in response to the magnetic fields inside the detector (you know, veers off toward one or the other of the SG-device's output ports); and this veering causes the distant particle also to veer in a certain way that ensures that if it later encounters magnetic fields oriented the same way, it will emerge from the opposite output port. Or something like that. The point is, Bohm's theory is only able to reproduce the QM correlations because of this non-local mechanism.

And yet Bohmian Mechanics is perfectly consistent with signal locality! So there is this blatantly nonlocal mechanism happening (which probably requires some notion of absolute simultaneity to even be *defined* clearly) and yet it turns out to be impossible to build a superluminal-telephone according to the theory. Surely this suggests that "what relativity requires" is something stronger than merely the condition that you can't build a superluminal-telephone. Someone who believed in relativity and wasn't bothered by the nonlocality in Bohmian Mechanics would, I think we'd have to say, not have too deep an understanding of what relativity actually means.

Does that make sense?

Of course, one can make the same point with orthodox QM, which has two separate dynamical laws: Schroedinger's equation and the collapse postulate. And if you take Bohr's completeness doctrine seriously, the collapse postulate is a blatantly nonlocal mechanism by which something you do in one place can affect the state of the system somewhere else, instantaneously. And yet this theory too is consistent with signal locality. You can't transmit information superluminally using orthodox QM. So this too suggests that signal locality is a necessary, but not a sufficient, condition for consistency with relativity. (BTW, the reason it's harder to convince people of the point using OQM as an example is that there is a pervasive muddle-headedness about the collapse postulate. People seem to want to waffle back and forth on whether the collapse is epistemological or physical depending on whether they're presently defending the locality claim or the completeness claim. See the final section of quant-ph/0404016 for some further discussion and references on that point.)

So then, if signal locality is necessary but not sufficient for "genuine consistency with relativity" what other conditions are needed? Bell proposed "Bell Locality" as a candidate for this. He argues for it very eloquently in a number of his papers. See, for example, "La Nouvelle Cuisine", which is reprinted in the (new, 2nd edition of) "Speakable and Unspeakable". (I think it's the very last chapter in the book, written after the first edition of "Speakable..." came out.) It's a very good read. Highly recommended.

What role does "Bell Locality" play in this whole debate? Well, the obvious thing to say is that Bell Locality is the locality assumption that Bell imposes in the derivation of Bell's inequalities. He assumes you've got a hidden variable theory which satisfies Bell Locality, and then shows that such a theory (regardless of any of the details about what the hidden variables *are*, which is what makes this powerful) must satisfy the inequality. And since QM and experiment both say the inequality is not satisfied, this means that no Bell Local hidden variable theory can be the correct theory. Right?

But that's not the end of the story. If it were, then it would be right to take Bell's Theorem as tolling for the hidden variable program: if hv theories have to violate Bell Locality, that means they conflict with relativity, which just shows we should have believed Bohr all along that hidden variables were wrong, that OQM is already complete. But not so fast, because OQM also violates Bell Locality. (That is essentially the EPR argument.) And that means whether you have hidden variables or not, you're stuck with a violation of Bell Locality. No Bell Local theory can match experiment. So nature violates Bell Locality.

That much is (or at least ought to be) uncontroversial. The question is simply: is Bell's candidate for a stronger locality principle (i.e., his identification of "Bell Locality" with "what relativity really requires") correct? Or is there some intermediate between the obviously-too-weak "signal locality" and the allegedly-too-strong Bell Locality? That's an interesting question. But as far as I know, nobody has proposed any such plausible intermediate.

 

[ttn]

As I said, in all considerations of "causality" and "locality" and "determinism" and so on, one has to ASSUME FREE CHOICE somehow, and depending on this free choice, we CHANGE THE PROBABILITY DISTRIBUTION. So all what depends on our free choice goes into parameters that tell us which probability distribution we are going to use. The free choice is the setting of Bob and Alice's analysers: they can decide that freely, and as a function of the choice they make, we have different probability distributions of how things will happen. ALL things that will happen. There is also an extra parameter included, which is the COMMON cause, L, and which can be seen as a free choice of some unknown individual (a little devil, if you want). It fixes the entire probability distribution.

OK, I'm basically with you here, although I would point out that you can't define "L" (which is supposed to be Bell's "Lambda") twice. Bell defines it as a complete specification of the state of the particles. (It's of course hard if not impossible for us to know precisely what that consists of in general. But the point is: some particular *theory* whose locality you're assessing will *tell* you what a complete state specification consists of. For example, Orthodox QM tells us that the wave function alone provides this complete description.)

But then here you say that L can also be thought of as a freely chosen parameter. Well, maybe, maybe not. Again, this is something we can't just stipulate a priori but, rather, have to find out from a given theory. The theory we're judging will tell us whether it is or isn't possible to *prepare* a system with a specific, desired state. According to OQM, for example, this is possible. But according to Bohmian Mechanics it isn't. So you can't just assume that "L" is one of the freely chosen parameters the way "a" and "b" are.

This is an elementary point, but I'm worried that this is going to mean that (for some theories at least) "L" is an "uncontrollable" that is therefore in the same category as "A" and "B". I mean, isn't that the distinction you're making above? Controllable (ie freely choosable) variables constitute the "parameter set", and the uncontrollables are to be thought of as the "outcomes" -- the things we talk about the probability *of* given the parameter set. But then for a theory in which the state of the particle pair isn't freely choosable, we don't get to put "L" in the parameter set and ... welll... all hell breaks loose.

Ok, I formulated this badly, sorry. OI is not something that is "build into the axioms of probability theory", it is rather something that is well-defined within probability theory, but which I don't NEED. What I meant was, that P(A) and P(A|B) are two well defined quantities, meaning we can talk about P(A) without having to say that "it depends also on B or not".

I don't see that. In fact, you can't just talk about "P(A)" without specifying (using your terminology) the parameter set. Otherwise it's just vague. Do you mean P(A) with this setting or that setting or this state preparation or that state preparation or what?

But then, who are you to say a priori what the probability of A depends on *really*? For all we know going in, it might depend on a, b, L, B, the price of tea in china, and the color of my socks. In principle, physically speaking, we have to have some kind of argument that we've captured all the possibly-relevant variables. I can't put my finger on it yet, but you are somehow sneaking in a physical assumption -- outcome independence -- under the guise of the Kolmogorov formalism. Let's see if it emerges below...

In fact, P(A|B) is nothing else but P(A sect B) / P(B) ; so it is a derived concept. Saying that P(A|B) = P(A) just comes down to saying that
P(A sect B) = P(A) x P(B). We usually write P(A sect B) as P(A,B).
It makes perfectly sense to talk about P(A) and about P(A,B). These are numbers which are well defined if the probability distribution is well defined (meaning, the parameters which select the distribution from its family are fixed, in our case a, b and L).

OK, this is all fine.

As I said, the parameters select ONE of different probability distributions out of a family. Once we have our distribution, we can apply it to M. A conditional probability within this distribution is then nothing else but a shorthand for a fraction of two measures of this distribution.
You cannot write P(A ; a) = P(A and a) / P(a) if a is a parameter.

Yes, OK, because P(a) is meaningless if we're treating "a" as a freely-choosable variable. This all makes sense. Of course, I'm still worried that you're going to have to treat "L" exactly the way you say you can't treat "a" here, since (at least in some theories) "L" might not be freely-choosable. But let's see below if this actually comes up in any important way...

You can however, write very well P(A |B ) = P(A sect B) / P(B) ; it is its very definition.

Yes, sure.

[Bell locality] is to be re-written:
P(A|B ; a,b,L) = P(A ; a,L)

Yes, sure, mod my worry about "L".


OK, here's the real meat of your last post finally:

By definition, we have: P(A|B ; a,b,L) = P(A,B ; a,b,L) /P(B ; a,b,L)

Now, if we rewrite my "Bell condition" which is:
P(A,B ; a,b,L) = P(A ; a,L) x P(B ; b,L), together with the fact that P(B ; a,b,L) = P(B ; b,L) (does not depend on parameter a - that's information locality to me), and we fill it into the definition of P(A|B ; a,b,L) above,
we have:

P(A|B ; a,b,L) = P(A ; a,L) x P(B ; b,L) / P(B ; b,L) = P(A ; a,L) and we're home:

both statements are equivalent.

OK, this is fine. So "Bell Locality" and the def'n of conditional probability together yeild that

P(A|B ; a,b,L) = P(A ; a,L)

Right? But is this new? I mean, this is just exactly what I would have said before (not making any distinction between "parameter sets" and "variables we conditionalize on") by writing:

P(A|B,a,b,L) = P(A|a,L)

Right? So I don't think there's really anything new here, neither a new point nor something new and important that follows from your different math notation. But I'm sure you'll correct me if I'm missing something here.


Re: my worry that what you were saying was violated by OQM, you said:

I'm sorry that I misformulated this: I didn't mean to imply that in just any Kolmogorov system you have to have this factorisation of course ! What I meant to say (and I badly expressed myself) was:
P(A ; a,b,L) is perfectly well defined. You do not have to say that the expression is somehow "incomplete" because I didn't include B in the list to the right. I could have been talking about ANOTHER quantity P(A|B ; a,b,L) ; only, I didn't talk about it, I didn't need it, because I only wanted to demonstrate P(A,B | a,b,L) = P(A ; a,L) x P(B ; b,L).
That's a perfectly sensible statement, and the three quantities are well defined in just any Kolmogorov system (the equality, of course, is not always true and has to be demonstrated for the case at hand).
I could also talk about things like P(A|B ; a,b,L) and so on, but I simply didn't need to. It is not an ERROR to talk about P(A | a,b,L) and in doing so I do not make any assumption. That's what I put badly as "it is build into the axioms of probability theory".

OK, I don't see any problem with this. I mean, it's certainly true that in OQM it is possible to talk about P(A;a,b,L). It is, for example, 50% (indpendent of "a" and "b" if L is the singlet state and we're talking about the usual EPR/Bell situation).

That is correct. There could be of course a conspiracy that L compensates for every change in a that I make. I assume of course same L.

OK, but then keep in mind that your identification of parameter independence with signal locality is conditioned (ha ha ha) on this assumption. In fact, a violation of PI is not sufficient to establish violation of signal locality. You also need controllability of the state L. (How to formulate exactly how much controllability is needed, I'm not sure...??) That is,

NOT(Signal Locality) ==> NOT(Parameter Indpendence) + L-Controllability

Or: Inadequate L-controllability ~OR~ Parameter Independence is needed to have Signal Locality. Bohm gets it the first way, OQM the second.

Ok, we've had this discussion already a few times. Because the statistical predictions of both theories are identical, there's no discrimination between both on those "black box" outcomes of course. It is a matter of esthetics of the inner workings. If you need to write that the state HERE is directly a function of the state (or its rate of change) THERE, in the equations, then this thing is not considered local, even if what you crank out of it doesn't see the difference.

Of course. And my point is just that both OQM and Bohm violate this -- both theories require (in some form) the state HERE to depend on the state THERE, in the equations. In Bohm, the offending equation is the guidance formula; in OQM it's the collapse postulate.

You don't disagree with that, do you? Partly I keep saying the same thing over and over again because you and the others keep finding new ways to subtly reject what I thought had earlier been agreed upon!

OK, here's the other meaty part of your post:

Again, I don't care about "outcome independence". I didn't need conditional probabilities at all. I needed to SHOW that P(A,B) factorizes into P(A) x P(B). This can be rewritten into something that uses outcome independence if you like, but I don't care.
What I wanted to show was that from determinism (all probabilities are 1 or 0), and from information locality (P(A;a,b,L) = P(A ; a,L) and P(B ; a,b,L) = P(B;b,L) ) follows the factorization statement that is Bell locality:
P(A,B ; a,b,L) = P(A ; a,L) x P(B ; b,L).

OK, this all clarifies for me what you were doing in that previous post. So you're just saying that deteminism permits us to write

P(A,B ; a,b,L) = P(A ; a,b,L) x P(B ; a,b,L)

and then we can impose Parameter Independence and get that

P(A,B ; a,b,L) = P(A ; a,L) x P(B ; b,L)

Unfortunately, I can't see any way to object to that. (At least, not right now.)

So where does this leave us? If Bell Locality is equivalent to the conjunction of OI and PI -- and also to the conjunction of PI and Determinism -- does that mean that Outcome Independence is equivalent to Determinism? That's a surprising and kind of interesting conclusion I guess.

But I'm still not sure what this means in terms of interpreting Bell's Theorem. It seems only to show that for a deterministic theory, violation of PI is sufficient for violation of Bell Locality. So if you know that a given theory is deterministic, you don't have to check for Bell Locality to see if it's going to obey Bell's Inequality -- you can simply check for Parameter Dependence.

But you want to say something like this means what Bell was really adding to relativity's "no signalling" condition is an unwarranted desire for determinism? I don't see that, especially considering Signal Locality and PI aren't the same thing. Well, now that we're on the same page about what you actually showed here, I'm sure you can help me understand how you want to interpret it...

 

[vanesch]

But then here you say that L can also be thought of as a freely chosen parameter. Well, maybe, maybe not. Again, this is something we can't just stipulate a priori but, rather, have to find out from a given theory.

L is the "complete description of the state according to the theory at hand". In quantum theory, L is just the wave function, indeed. In another theory, it is whatever describes the state completely.

The theory we're judging will tell us whether it is or isn't possible to *prepare* a system with a specific, desired state. According to OQM, for example, this is possible. But according to Bohmian Mechanics it isn't.

I would say that that is a theory that has a serious problem. In fact, if that is the case, then the L is not the "state of the system" ; the state should then be less well specified, but "preparable" and the stochastic effects of what is fundamentally uncontrollable should be part of the probability distribution, and not of the state L. At least if it is IN PRINCIPLE impossible to prepare the system that way, and not highly unpractical (such as, say, the phase space point of a classical gas).

So you can't just assume that "L" is one of the freely chosen parameters the way "a" and "b" are.

I think it is somehow a problem if IN PRINCIPLE you cannot prepare freely the "state" of the system L. Because what is a "state" then ? Isn't it just part of the stochastic description then ? But ok, we can do away with this objection by giving ourselves a god status who is not bothered by this, and who CAN decide upon L.

This is an elementary point, but I'm worried that this is going to mean that (for some theories at least) "L" is an "uncontrollable" that is therefore in the same category as "A" and "B". I mean, isn't that the distinction you're making above?

It shouldn't. Of course, you can give a DISTRIBUTION to L, and redefine all your probability distributions by integrating over the uncontrollable parts of L. That just took out part of L and put it into the distribution P.

Controllable (ie freely choosable) variables constitute the "parameter set", and the uncontrollables are to be thought of as the "outcomes" -- the things we talk about the probability *of* given the parameter set.

Right, but they aren't even part of the "outcomes", they are part of the function P(). Of the distribution.

I don't see that. In fact, you can't just talk about "P(A)" without specifying (using your terminology) the parameter set.

It was tacitly assumed that we fixed a,b and L.

But then, who are you to say a priori what the probability of A depends on *really*? For all we know going in, it might depend on a, b, L, B, the price of tea in china, and the color of my socks. In principle, physically speaking, we have to have some kind of argument that we've captured all the possibly-relevant variables. I can't put my finger on it yet, but you are somehow sneaking in a physical assumption -- outcome independence -- under the guise of the Kolmogorov formalism.

No, if we have a theory that gives us the probability of A, then it is just that. We can now try to find out if there are CONDITIONAL probabilities the way you suggest (the price of the tea in china and so on - as long as they are part of the set of events M), but we're not interested in that. If this bothers you, think of P(A) as the probability of A, weighted with all its possible "dependencies" according to the probabilities of the dependencies.

After all, there's a theorem in probability theory that says:

if {B1,B2,...Bn} are mutually exclusive and complete (their union is Omega), then:

P(A) = P(A|B1) P(B1) + P(A|B2) P(B2) + ... P(A|Bn) P(Bn)

Think of B1 = 1 kg of tea in china costs $1.0 ; B2 = 1kg of tea in china costs $2.0 etc... :-)

Yes, OK, because P(a) is meaningless if we're treating "a" as a freely-choosable variable. This all makes sense. Of course, I'm still worried that you're going to have to treat "L" exactly the way you say you can't treat "a" here, since (at least in some theories) "L" might not be freely-choosable.

Again, two ways out. 1) I'm god and I can choose L freely. 2) Include in L only the parts I can choose freely, consider the uncontrollable parts simply as part of the probability distribution.

Right? But is this new? I mean, this is just exactly what I would have said before (not making any distinction between "parameter sets" and "variables we conditionalize on") by writing:

P(A|B,a,b,L) = P(A|a,L)

Right? So I don't think there's really anything new here, neither a new point nor something new and important that follows from your different math notation. But I'm sure you'll correct me if I'm missing something here.

What is new (or maybe not), is that if you only assume:
P(A ; a,b,L) is not a function of b
P(B ; a,b,L) is not a function of a

(this is information locality, right?)

and you assume determinism:
P maps only onto {0,1}

that you can DERIVE P(A,B ; a,b,L) = P(A ; a,L) x P(B ; b,L)

(Bell locality).

If you do not assume determinism, you cannot do so.
If you do not assume information locality, you can still write the product, but P(A;a,b,L) will be there and you still don't have Bell Locality, because P(A) depends still on a,b and L.

Now, this, together with the other theorems (namely that from Bell locality you can have information locality (trivial) and that from Bell locality you can always find a deterministic underlying theory (in the god assumption, eventually) that is equivalent to it, and deterministic, I arrived at my final conclusion that Bell locality is equivalent to information locality AND underlying determinism.

Maybe all this is known already since ages. I would think so !

OK, I don't see any problem with this. I mean, it's certainly true that in OQM it is possible to talk about P(A;a,b,L). It is, for example, 50% (indpendent of "a" and "b" if L is the singlet state and we're talking about the usual EPR/Bell situation).

You got it. In fact, this independence already means information locality in this particular case. And even if L is any state (depending on 4 complex numbers u,v,w,x: u|+>|+> + v |+>|-> + w|->|+> + x|->|->), P(A) will be a number depending on a (the orientation of analyser a) and L but will not depend on b.

OK, but then keep in mind that your identification of parameter independence with signal locality is conditioned (ha ha ha) on this assumption. In fact, a violation of PI is not sufficient to establish violation of signal locality. You also need controllability of the state L. (How to formulate exactly how much controllability is needed, I'm not sure...??) That is,

NOT(Signal Locality) ==> NOT(Parameter Indpendence) + L-Controllability

Or: Inadequate L-controllability ~OR~ Parameter Independence is needed to have Signal Locality. Bohm gets it the first way, OQM the second.

Again, one should think hard what it means, if a "state" L is *in principle* uncontrollable. In what way can we then say that it is a *different* state ? Shouldn't we just extract what is in principle (even if not in practice) controllable, and only use that as a state ; saying that the fundamentally random part, is, well, fundamentally random, and not "part of an uncontrollable part of the state" but just part of the probability distribution ?
Isn't this similar to trying to distinguish fundamentally identical particles ?

So where does this leave us? If Bell Locality is equivalent to the conjunction of OI and PI -- and also to the conjunction of PI and Determinism -- does that mean that Outcome Independence is equivalent to Determinism? That's a surprising and kind of interesting conclusion I guess.

That doesn't follow logically ; it isn't because

A AND B <==> A AND C that B <==> C !

It seems only to show that for a deterministic theory, violation of PI is sufficient for violation of Bell Locality. So if you know that a given theory is deterministic, you don't have to check for Bell Locality to see if it's going to obey Bell's Inequality -- you can simply check for Parameter Dependence.

Right.

But you want to say something like this means what Bell was really adding to relativity's "no signalling" condition is an unwarranted desire for determinism?

I think that that was the idea. Or an unwanted consequence :-)

I don't see that, especially considering Signal Locality and PI aren't the same thing.

Well... I'd say they are. I don't see the use of postulating a fundamental impossibility of fixing L in principle. And then they are equivalent, no ?

 

[DrChinese]

...because any non-deterministic theory can be made into a deterministic one by adding more hv's...

Assuming that you are defining one theory as relatively "more" deterministic than another - this requires a couple of extra points to be added.

1. When comparing two theories, I believe it is fair to define a theory (Y) as being objectively BETTER than another (X) IF its predictive results are more accurate/descriptive. So I am mapping your concept of MORE DETERMINISTIC with my concept of BETTER. Is this the sense you intended?

2. Assuming you agree with this mapping, I would then agree that for any such Y, it must always have more input variables (previously hidden variables) than X.

3. Adding input variables to X will not necessarily lead to a BETTER theory Y. If it doesn't, then Y is an AD HOC theory.

On the other hand, if you are saying that adding hidden variables to a non-deterministic theory such as QM will yield a deterministic theory... I would challenge that sense of your statement. You would first need to find such hidden variables to be convincing.

 

[ttn]

Assuming that you are defining one theory as relatively "more" deterministic than another - this requires a couple of extra points to be added.

Huh?? A theory is deterministic if future states are predicted precisely by current states -- if there is no randomness in the dynamics. Determinism is like being pregnant: either you are or you aren't.

1. When comparing two theories, I believe it is fair to define a theory (Y) as being objectively BETTER than another (X) IF its predictive results are more accurate/descriptive. So I am mapping your concept of MORE DETERMINISTIC with my concept of BETTER. Is this the sense you intended?

Not at all, no.

Note also the explicit positivism of this definition of "better." Get with the times, man.

For whatever it's worth, I agree completely with Einstein that the main reason for wanting to add hidden variables to QM is to solve various *problems* (real or apparent) such as the measurement problem and the apparent non-locality (this latter would have been advocated by Einstein). I really couldn't care less if a theory is or isn't deterministic. If the only negative point about OQM were that the collapse rule was stochastic, I would rest easy at night and be completely happy with the theory.

 

[ttn]

I would say that that is a theory that has a serious problem. In fact, if that is the case, then the L is not the "state of the system" ; the state should then be less well specified, but "preparable" and the stochastic effects of what is fundamentally uncontrollable should be part of the probability distribution, and not of the state L. At least if it is IN PRINCIPLE impossible to prepare the system that way, and not highly unpractical (such as, say, the phase space point of a classical gas).

I agree with you about how to deal with this. If a given theory says you can only prepare a state with some non-trivial probability distribution rho(L), you just go through everything the same way and average over L with the weighting rho(L). No problem. But I don't agree that if a theory says you can't completely control the state, that means the theory has no business calling that the state. Where would such a requirement come from? If X exists, it must be possible to put X in any state you choose? This assumes (roughly) that humans are omnipotent. Maybe they are; who knows. But that's for the laws of physics to decide.

I think it is somehow a problem if IN PRINCIPLE you cannot prepare freely the "state" of the system L. Because what is a "state" then ? Isn't it just part of the stochastic description then ? But ok, we can do away with this objection by giving ourselves a god status who is not bothered by this, and who CAN decide upon L.

But this will lead you to perpetually and incorrectly identify "Parameter Independence" with "Signal Locality." But such an identification is only valid for your god. This god might be able to signal with a theory that only violates PI, but that doesn't mean we can. So does that count as consistent with relativity? The question is a reductio of itself!

And the worse problem is: if there really is a theory according to which it's in principle impossible to prepare a system in a complete controllable way, what kind of god is it that is able to elude this? Evidently it's a god that can violate the laws of physics. But then, you might as well say that all theories are nonlocal because god could choose to violate the (normally local) laws of that theory and signal superluminally with them. This whole line of reasoning gets you into theological questions like how many angels can dance on the head of a pin... which can only mean we took a wrong turn somewhere!

I think we have to accept theories on their own terms. If a given theory says that in principle signalling FTL is forbidden according to the laws of that theory, then the theory is signal local. Any talk of what god could do should be dismissed as irrelevant, arbitrary, meaningless, speculative non-science.

It shouldn't. Of course, you can give a DISTRIBUTION to L, and redefine all your probability distributions by integrating over the uncontrollable parts of L.

Agreed, that's the right way to deal with it.

What is new (or maybe not), is that if you only assume:
P(A ; a,b,L) is not a function of b
P(B ; a,b,L) is not a function of a

(this is information locality, right?)

I don't know what you mean by that term. It is not the same as "signal locality" as I'm defining that since, in addition to parameter dependence you'd need "sufficient preparability", e.g., rho(L) = delta(L-L0).

and you assume determinism:
P maps only onto {0,1}

that you can DERIVE P(A,B ; a,b,L) = P(A ; a,L) x P(B ; b,L)

(Bell locality).

If you do not assume determinism, you cannot do so.

Well, you can assume something like OI (which is not determinism) instead, and still get Bell Locality.

If you do not assume information locality, you can still write the product, but P(A;a,b,L) will be there and you still don't have Bell Locality, because P(A) depends still on a,b and L.

Now, this, together with the other theorems (namely that from Bell locality you can have information locality (trivial) and that from Bell locality you can always find a deterministic underlying theory (in the god assumption, eventually) that is equivalent to it, and deterministic,

That last part is misleading. That you can always supplement a non-deterministic theory with more variables to make it deterministic doesn't in *any* sense follow from Bell Locality. You can do that with any theory, Bell Local or not. The only interesting question is whether a *particular* stochastic non-Bell-Local theory (namely orthodox QM) could maybe be morphed into a deterministic Bell Local theory by adding HV's. (That's what Einstein was hoping for, right?) But now we know it can't be done.

I arrived at my final conclusion that Bell locality is equivalent to information locality AND underlying determinism.

Maybe all this is known already since ages. I would think so !

I'm not sure, but I remember a colleague who knows the literature on this stuff quite well once mentioning determinism as one of the things that it's possible to analyze Bell Locality into. I don't remember the context or the specific claim, but now that you've convinced me that PI and determinism are equivalent to Bell Locality, I bet that's probably what he mentioned. I'm planning to read through some of the classic articles on all this from the 80's and 90's in the next month or so, so I'll let you know if I find something along the lines of your proof.

Again, one should think hard what it means, if a "state" L is *in principle* uncontrollable. In what way can we then say that it is a *different* state ?

Well, for example, the wave function is the same but the particle's in a different place (in Bohm's theory).

That doesn't follow logically ; it isn't because

A AND B <==> A AND C that B <==> C !

Yes, what I meant was that that would be an interesting conclusion if it were true. Maybe it is, but you'd have to prove it, I agree.

 

[DrChinese]

Huh?? A theory is deterministic if future states are predicted precisely by current states -- if there is no randomness in the dynamics. Determinism is like being pregnant: either you are or you aren't.

Then I wonder why you said that any non-deterministic theory can be converted into a deterministic one by adding hidden variables? If you can do that with QM, I believe a Nobel is yours for the taking... but you will have to prove it first.

So where or what are these HVs? Or were you guessing? Get with it, "man".

 

[ttn]

Then I wonder why you said that any non-deterministic theory can be converted into a deterministic one by adding hidden variables? If you can do that with QM, I believe a Nobel is yours for the taking... but you will have to prove it first.

Unfortunately it's impossible to get a Nobel prize for discovering a deterministic hidden variable theory that reproduces all the predictions of OQM, since it's already been done -- 50 years ago (or 80 depending on who you ask) by Bohm (and/or de Broglie), both of whom are dead. The theory is called Bohmian Mechanics (or sometimes dBB for de Broglie - Bohm theory, or sometimes the "pilot wave theory", etc.).

But this is actually a much more serious theory than what I had in mind. My point was along the lines of what Patrick showed in some detail, quite some time ago in this thread. Namely, a totally un-physically-motivated ad hoc type theory where you just arbitrarily make up variables whose probability distributions are chosen in a totally ad hoc way simply to determine the outcomes that the stochastic theory says aren't determined. Writing down such a theory is indeed trivial.

So Bohm's achievement in writing down a physically motivated, physically intuitive deterministic hv theory that reproduces all the QM predictions is indeed remarkable.

I agree with you that he probably should have won a Nobel prize for it.

 

[DrChinese]

Unfortunately it's impossible to get a Nobel prize for discovering a deterministic hidden variable theory that reproduces all the predictions of OQM, since it's already been done -- 50 years ago (or 80 depending on who you ask) by Bohm (and/or de Broglie), both of whom are dead. The theory is called Bohmian Mechanics (or sometimes dBB for de Broglie - Bohm theory, or sometimes the "pilot wave theory", etc.).

Well, where are the hidden variables? Oops. BM is not a theory in the normal sense of the word. It is completely AD HOC as is MANY WORLDS (sorry Vanesch if you don't agree). There are actually no additional variables provided by these theories which were previously hidden, as they produce no different predictions than OQM. There are no additional input variables, no additional output precsision. What these theories offer is the PROSPECT of future benefit, as does string theory. I.E. They do not turn a non-deterministic theory into a deterministic theory. They are completely alternative theories intended to reproduce the results of QM. Not the same by a long shot. Why?

QM => Prediction set A
QM + new ideas of BM => Prediction set A
QM + Santa Claus => Prediction set A
...

I think you see the point. There is nothing to falsify, nothing to test, no benefit, etc. All you have done is simply assert that which you are trying to prove, which is that (QM + anything) is a DETERMINISTIC theory just because it wants to be. Well, it's not.

I think Bohm was an genius (I really like his book "Causality and Chance in Modern Physics"), but BM is not Nobel material by a long shot. New theories must give something to us that we didn't already have. That is basic.

 

[vanesch]

But I don't agree that if a theory says you can't completely control the state, that means the theory has no business calling that the state. Where would such a requirement come from?

It's debatable of course, but I would take that easily as part of what we mean by "state". Of course, "state" by itself has only a meaning when we look at the set of all possible states ; the state by itself doesn't mean much. The real mathematical object we're looking for is the "set of all different dynamical states" such as is phase space in classical physics, or the projective Hilbert space (rays up to a complex factor) in QM.
I subtly introduced "DIFFERENT" dynamical states, in that it is of course tacitly assumed that two different elements of the set of states must correspond to two different physical situations. Now, for two situations to be physically different, this means that somehow I must be able, at least in principle, to make systems in these states. It can be practically impossible, that's no big deal. Then I can still ontologically consider these states, and use a phenomenological theory that tries to avoid these differences of states and averages over their distributions. That's what we do in thermodynamics: the microstate is the point in phase space of my gas, but it is not possible in practice to put my system in such a state (although it is not forbidden in principle). So I work with a phenomenological model, where I just have pressure and temperature as my state (2 real variables). I have no problem with the underlying micro model as an explanation, because it is not in principle forbidden to work with such a single phase space point even though no experimenter in his right mind will ever try to do so.
However, I have more difficulties considering two different states which are IN PRINCIPLE not preparable. My conclusion would then simply be that these are not two different states of the system. Take as an analogy that we have two different states: one with electron number 1 in atom 1 and electron 2 in atom 2 ; and ANOTHER state with electron number 1 in atom 2 and electron number 2 in atom 1, but it is IN PRINCIPLE impossible to make the difference between both. I think that the right answer is then that these are not two different states of the system, but only 1: AN electron in atom 1 and AN electron in atom 2. This is not exactly identical of course, you will object, because the two states here make same predictions (and wrong predictions because the true state is a symmetrised or antisymmetrised combination of them!). But with a bit of effort you get the message.
If the "state" of a system is IN PRINCIPLE always drawn out of one of 7 different distributions we can in principle prepare, I'd say that the TRUE state space of the system consists of 7 elements, which are the 7 distributions, and not the 500 states that can be drawn but which are in principle "unpreparable". You do not win anything by blowing up the state space from 7 distributions to 500 points. In fact, by limiting yourself to the 7 distributions, you've incorporated, in your theory, the principle that forbids to prepare the 500 points individually, and hence you have a theory that exhibits more explicitly a symmetry of nature (the impossibility of preparing one of the 500 points). The 500 points are an unneeded construction which destroy an explicit symmetry, just like the ether destroys an explicit symmetry in SR. And as such, the ether forbids you to see the true underlying mathematical object (4-dim geometry) - I think in the same way the "overspecification" of state space forbids you to see the true structure behind it.

In fact, something similar occurs in quantum theory. When we are no longer looking at pure states, but at statistical mixtures, we have such an in principle forbidden differentiation. It is the "probability distribution of pure states". We could naively think that the statistical state of a QM system is given by a weighting function, which gives a certain weight to each possible pure state. But it turns out that we have an overspecification, and that the only object that is objectively different is the density matrix. Two different weighting functions over pure states that give rise to the same density matrix are not distinguishable. It turns out that we have to consider these states as in fact, one and the same state.

So I think that one should include in the definition of state space the fact that it is in principle possible to prepare a system in each of those states individually, because otherwise we can miss an essential symmetry of the theory. But - as I said - this is debatable, and you can hold onto another definition of state space.

 

[vanesch]

Well, where are the hidden variables? Oops. BM is not a theory in the normal sense of the word. It is completely AD HOC as is MANY WORLDS (sorry Vanesch if you don't agree). There are actually no additional variables provided by these theories which were previously hidden, as they produce no different predictions than OQM.

I think that BM and MWI are two attempts at giving an ontological sense to standard QM + some dearly kept other principles.
I think it is obvious to anyone that standard QM only makes an epistemological sense: a way of organizing relationships between observations. Some people are happy with that, but others (ttn and I for instance) cannot accept that. Well, we can, of course, to do calculations, but it is hard to accept that a fundamental theory of nature doesn't tell you anything about nature, but only about what you measure about it. It doesn't tell you what state nature is in, but just that if you first measure property A (preparation) and then property B (measurement), then you will find this and that probability for B. This is perfect as a falsifiable theory, but misses the ontological part completely, and as such, I don't see what "principles" it should obey: it is just a black box out of which come numbers which we can compare to readings on the dial. It is then strange that we should write down some of these calculational procedures AS IF they were describing something on a 4-manifold, or so, because we have to take it that they don't, in the end - the whole thing being merely an epistemological calculation scheme.

If you stick to "realism" - if you want to build a theory that looks like classical mechanics in some way, then you can do what Bohm did. But you need to sacrifice something dear: the relativity principle. The ontology in Bohm's theory is not described by geometrical objects in 4-dim spacetime. And there are other problems.

If you stick to the relativity principle, then the only part you can save in QM is the unitary evolution, and you end up in an MWI variant. Moreover, as QM has never specified anything else, for physical interactions, than unitary evolution, this makes QM "universally valid" and then you cannot avoid bodies to end up in entangled states. And there are other problems.

What's the use of all this ? I think that trying to make sense of what we know is useful. I hate to think that we just have to accept that the "world out there" is not describable, and that we have to satisfy ourselves with simple calculational rules which relate preparations and measurements, without it containing any representation of what "really happens".
But I think there is another use to it too. It is the fight between different fundamental principles which ought to gouvern the laws of physics (like the relativity principle, the superposition principle, locality, causality...). These gedanken exercises (it is nothing more than that) give - I think - great insight of what are the consequences of sticking to one principle ; and what principles are incompatible.

 

[ttn]

It's debatable of course, but I would take that easily as part of what we mean by "state". [...] I have more difficulties considering two different states which are IN PRINCIPLE not preparable. My conclusion would then simply be that these are not two different states of the system.

I still don't see any real argument for this. Like you said, it's debatable, so maybe we'll just have to agree to disagree. But a few points.

It seems like what bothers you is not specifically the notion that you can't prepare systems in a desired micro-state (to use the classical stat mech terminology), but something more general: the notion that you can't empirically distinguish the different microstates in principle. I have a little bit of sympathy for the latter formulation (none really for the former). Take again the example of Bohmian Mechanics. If you prepare a particle to have a certain wave function, you lose control over the position -- the position will be |psi|^2 distributed in the wave, just according to how that theory works.
So there is this whole slew of distinct microstates, each corresponding to one possible position of the particle in the wave.

But now suppose you let the system evolve for a while (like, maybe you send the particle through a 2 slit apparatus with this known initial wf). Well, now you can measure the particle's position and, using the known dynamical laws, evolve backward in time to find out where the particle was initially. (In particular, you can infer which slit it went through... yet still the interference pattern builds up... oooooh, spooky!) So the micro-states aren't empirically indistinguishable in principle. You can tell one from the other by (say) seeing what happens later. What you're prevented from knowing is the exact microstate of a system *now*. But you can find out later what it *was*, no problem.

Another general point on this. I'm reminded of something important Einstein once said, that I only recently came to appreciate fully. Something like: "It's the theory that tells us what can be measured." I always read this as some sort of vague expression of "theory ladenness of observation", but that's not quite right. I think he is pointing out that when you do an experiment in the lab, you get some definite result (that part is not influenced in any way by theory) but whether you think the measurement was a genuine *measurement* in the strict sense -- whether or not it revealed the value of some pre-existing property -- there is no way to know just from the fact of having gotten a certain outcome. You need a theory to tell you. For example, in OQM you cannot genuinely measure the position of a particle. What is called a "position measurement" is really a complicated interaction that *causes* the particle to assume a definite position; prior to that it didn't have one. On the other hand, in Bohmian Mechanics, position measurements *are* genuine measurements, and some other things (like momentum and spin) probably aren't. In those cases, the "momentum measurement" or whatever actually influences the system so that the "outcome of the momentum measurement" isn't (necessarily) the same as the momentum the particle had before you "measured" it.

My point is just that you have to be in some sense willing to take a theory seriously on its own terms. There are some strange and surprising things in QM (like the uncertainty principle) and you have to allow in principle for different possible ways of dealing with these. You can't just say by fiat that any theory in which x and p aren't simultaneously measureable (but which has x and p as part of the microstate) is ruled out. And it's the same point for preparation as for measurement.

The more general point behind this is that you can't pick some aspect out of one theory and then force others to accept it. There's a long history of this kind of thing in regard to QM, because the orthodox theory (which is so silly and thus contains so many weird aspects) "got in first" -- so then you have, e.g., von Neumann "proving" that no hidden variables type theory is possible, by assuming that some curious and surprising feature of QM would have to apply the same way to a hvt, etc. But this rules something like Bohm out of court. And I say it is prima facie obvious that any methodology which does that is obviously flawed. It is a tremendously valuable thing to know that Bohmian Mechanics is possible, that it exists. Even if you don't think it's true, it clarifies so much by showing how *radically different* a theory can be (from OQM) and yet still be empirically viable.

If the "state" of a system is IN PRINCIPLE always drawn out of one of 7 different distributions we can in principle prepare, I'd say that the TRUE state space of the system consists of 7 elements, which are the 7 distributions, and not the 500 states that can be drawn but which are in principle "unpreparable". You do not win anything by blowing up the state space from 7 distributions to 500 points.

How can you possibly make such a claim? Who is to say what you might "win"? For example, look at all the goodies you win by doing this in Bohm's theory!

In fact, something similar occurs in quantum theory. When we are no longer looking at pure states, but at statistical mixtures, we have such an in principle forbidden differentiation. It is the "probability distribution of pure states". We could naively think that the statistical state of a QM system is given by a weighting function, which gives a certain weight to each possible pure state. But it turns out that we have an overspecification, and that the only object that is objectively different is the density matrix. Two different weighting functions over pure states that give rise to the same density matrix are not distinguishable. It turns out that we have to consider these states as in fact, one and the same state.

This doesn't really make your case, because, well, there's no theory I know of that takes density matrices as complete state specifications. Everybody knows the real micro-states according to OQM are wave functions. And if you're unsure (in some quantifiable way) which microstate the system is in, you use a density matrix.

It is indeed a curious and interesting fact that different weightings of the microstates can give rise to the same overall empirical predictions. Different kinds of ignorance can yield the same outcome probabilities. But this is no argument that the density matrices should be taken as microstates.

 

[ttn]

Well, where are the hidden variables? Oops. BM is not a theory in the normal sense of the word. It is completely AD HOC as is MANY WORLDS (sorry Vanesch if you don't agree). There are actually no additional variables provided by these theories which were previously hidden, as they produce no different predictions than OQM.

This makes it sound like you just don't know what "hidden variables" means.

I.E. They do not turn a non-deterministic theory into a deterministic theory.

No, they show that a non-deterministic theory could be in principle replaced by a deterministic one. Which is precisely what you seemed to think was impossible yesterday.

They are completely alternative theories intended to reproduce the results of QM.

What in the world were you hoping for? Orthodox QM all over again? That wouldn't be worth a Nobel prize. Or a theory that was deterministic but made a bunch of predictions that are known already to be false? Also not worth much. But an alternative theory which reproduces the correct predictions of the orthodox theory, and yet suffers from no measurement problem, no "unprofessionally vague and ambiguous" blather about measurement vs non-measurement, and generally provides a clear ontology for the micro-world? Oh, you think that's the equivalent of Santa Claus.

I think Bohm was an genius (I really like his book "Causality and Chance in Modern Physics"), but BM is not Nobel material by a long shot. New theories must give something to us that we didn't already have. That is basic.

All this positivistic philosophy is really quite anti-science. For example, by these standards you would have rejected Copernicus as not just wrong but *meaningless* since his alternative theory didn't provide any immediately superior predictions to the geocentric theory.

 

[DrChinese]

This makes it sound like you just don't know what "hidden variables" means.

Pot calling kettle black?

I think we both know this discussion is going nowhere, so I am going to propose we wind this down.



-DrC

 

[vanesch]

It is a tremendously valuable thing to know that Bohmian Mechanics is possible, that it exists. Even if you don't think it's true, it clarifies so much by showing how *radically different* a theory can be (from OQM) and yet still be empirically viable.

I fully agree with that. But the trick plays just as well on you: I think it is tremendously valuable that an MWI view which respects relativity exists also. Even if you don't think it's true it clarifies also much how radically different a theory can be and yet be empirically viable.

I prefer the MWI view over BM (although I respect the BM view too) because that great principle of relativity can be saved, in the sense that all objects to which we assign ontological existence are geometrical objects over the 4-manifold.

 

[ttn]

I fully agree with that. But the trick plays just as well on you: I think it is tremendously valuable that an MWI view which respects relativity exists also. Even if you don't think it's true it clarifies also much how radically different a theory can be and yet be empirically viable.

I prefer the MWI view over BM (although I respect the BM view too) because that great principle of relativity can be saved, in the sense that all objects to which we assign ontological existence are geometrical objects over the 4-manifold.

Oh I agree with you, no doubt. It's tremendously clarifying and satisfying to know that the next best alternative after giving up the *fundamentality* of relativity is... solipsism.

 

[vanesch]

Oh I agree with you, no doubt. It's tremendously clarifying and satisfying to know that the next best alternative after giving up the *fundamentality* of relativity is... solipsism.

Well, solipsism with a grain of salt. I once made the error of tagging this word to it, but it is not truly solipsism in fact ; after all, there is postulated to be an ontological reality which GENERATES the observations one's mind makes, so in that sense it is not solipsist. It is solipsist only in the way that each individual consciousness experiences its own world (which is an aspect of the ontologically postulated world), and that these experiences don't have to be "tuned together" so that we have a "common experience". Maybe "individualist" is better suited as a word than solipsist.

I have a question regarding BM. It is not an attack (yet :-), but a question. Why do we observe the POSITIONS of particles when we do a measurement in BM ? And why don't we observe something like the wave function ? After all, the state is a pair {positions, wavefunction}, and we seem to observe only the positions. Nevertheless, the interaction that is used by the measurement device is entirely given by a hamiltonian, working on the wavefunction, but we seem to finally "observe" only the positions. How come ? Is it because consciousness is only sensitive to the positions and not to the wavefunction?

cheers,
Patrick.

EDIT: I'd like to add a comment, why it is more important to prefer relativity, and accept this consciousness nonsense than the other way around, and that's the following: relativity works with differential geometry and that's just COOOOL . It would be a pity to learn all this cool stuff just not to use it, wouldn't it. On the other hand, about consciousness, as not much can be said affirmatively about it, I prefer it to do the garbage collection You're not destroying anything cool by doing so.

 

[ttn]

Well, solipsism with a grain of salt. I once made the error of tagging this word to it, but it is not truly solipsism in fact ; after all, there is postulated to be an ontological reality which GENERATES the observations one's mind makes, so in that sense it is not solipsist. It is solipsist only in the way that each individual consciousness experiences its own world (which is an aspect of the ontologically postulated world), and that these experiences don't have to be "tuned together" so that we have a "common experience". Maybe "individualist" is better suited as a word than solipsist.

But aren't all those "other consciousnesses" not really there? Or at least there can be, in principle, no evidence that they're really there, any more than (on this view) there can be evidence that the table in front of me right now is really there. Sure, that's what my consciousness happens to be experiencing right now, but I can't be sure the experience is correct. In fact, just the opposite: I can be certain it *isn't* correct. The odds are astronomically against the real universal wf being an eigenstate of the "is there a table there right now?" operator.

Anyway, I really don't have the stomach to spend time arguing about all this. Our views are clear to each other and to other readers, and it's nice that we agree that it's nice to know about both possibilities. Shall we just leave it there?

I have a question regarding BM. It is not an attack (yet :-), but a question. Why do we observe the POSITIONS of particles when we do a measurement in BM ? And why don't we observe something like the wave function ? After all, the state is a pair {positions, wavefunction}, and we seem to observe only the positions. Nevertheless, the interaction that is used by the measurement device is entirely given by a hamiltonian, working on the wavefunction, but we seem to finally "observe" only the positions. How come ? Is it because consciousness is only sensitive to the positions and not to the wavefunction?

I'm not sure what kind of answer you want. If you mean: why is Bohm's theory constructed in such a way that position measurements actually reveal the positions of particles, you could give a historical/experimental/motivational answer. With, say, the 2-slit experiment with single electrons (that Tonomura et al did in the 80's), we see pointlike scintillations on the screen that just seem to cry out: "a particle landed here"! So take that as your paradigm simple example of a position measurement. You send a particle through the apparatus (prepared in some way) and then you see where it lands. You detect its position. And the obvious thing to try (if you're on the premise that "particle means particle", i.e., that the particle that you just saw hit the screen followed some definite path through the apparatus) is that the place where it makes the mark on the screen is the place where it was just before it hit the screen, i.e., you detect it in a certain place because that's where it *is*. So if you can have a theory like that, it's ideal. And it turns out you can. So that's why position measurements are thought of as actually revealing the position.

Now, I suspect you were looking for something slightly different here, along the lines of: how come position measurements are genuine measurements, while, say, momentum or spin measurements aren't? This is a really good question because it helps bring out what I said earlier about the need to take a theory on its own terms and not impose external requirements from other theories (or from what you think god should be able to do or whatever).

So, (if you like) on the basis of the historical/experimental/motivational story sketched above, you just have to accept the Bohmian ontology. There's a wave function obey sch's eq, and in addition there are *particles*, and "particle" really means "particles". So the universe's evolution consists of all the particles following definite trajectories which are orchestrated in some way by the wave function. That's just given, that's what the theory *says*, and you have to accept it "all the way down" if you want to ask further questions about the theory. So now suppose you ask: what happens if I make a measurement of the momentum of a particle? Well, there's no way to answer that question until you define what you mean by *measurement*. And on the premise of Bohm's theory, here's what that turns out to (be required to) mean: a "measurement" is an interaction of one thing (the apparatus) with another thing (the object being "measured") which results in some part of the apparatus (the "needle") having some macroscopically unique final configuration (i.e., the needle points in a certain direction). I probably haven't worded that as clearly as possible, but here's the crucial thing: since Bohm's theory is fundamentally a theory about the positions of particles, you have to define "measurement" in terms of the position of particles. There's nothing else to define it in terms of.

So now you can just see what happens, *according to the theory*. Set up an apparatus with a needle that points in a certain direction that correlates with the wave number (k = p/hbar) of a particle which has been prepared to be following a plane-wave wf with a definite k. That is, we calibrate the device (or design it or whatever) so that the needle points to the value of "p" that the particle has when we know it has a definite value p. Now just ask what happens in general, when the particle we're measuring is in some general state, e.g., its initial wf is a standing wave (not a p eigenfunction). Well, the interaction causes the system particle to accelerate from rest up to some stable final momentum, and the needle points to a certain direction which corresponds (according to the calibration) to that same final momentum. (Which final value of course depends on the initial position of the particle.) That's just what happens according to the theory, and if you want to call it a "momentum measurement" I won't object. I'll only ask that you put scare-quotes around the word "measurement" since, really, it isn't one (in the strict sense of revealing a pre-existing property -- the final position of the needle doesn't tell us how fast the particle was moving just before the interaction happened, rather only how fast it's moving after the interaction). For this very reason, Bell urged people to stop using the word "measurement" entirely, though I don't think he meant this seriously. There's also a very very nice paper by Sheldon Goldstein et al -- something about "naive realism about operators" -- which shows some of the extreme confusions people have gotten themselves into, essentially by abuse of the term "measurement".

Well, maybe that was all kind of a tangent. You asked specifically about consciousness. But I like to avoid talking about consciousness if at all possible, at least when one is trying to formulate a theory of micro physics. What can I actually say about consciousness though? I think at least I have to say that all the consciousnesses I know of become conscious of things by observing the positions of things in the macroscopic world. So the only "theory of consciousness" I need to attach to Bohmian Mechanics is that it is possible to become conscious of configurations which are macroscopically distinct. So if 10^25 particles are all sitting in front of me in the shape of a table, it is (somehow.. I don't know how, nor do I need to know how) possible for me to look out and perceive this, i.e., become aware of it. As far as consciousness being sensitive only to positions and not to the wave function, I suppose you could say that. But then by the time you're at a sufficiently macroscopic scale, the wave function is rather irrelevant. This is all related to the decoherence effect, which, in the context of Bohm's theory and only there, does solve the measruement problem completely.

EDIT: I'd like to add a comment, why it is more important to prefer relativity, and accept this consciousness nonsense than the other way around, and that's the following: relativity works with differential geometry and that's just COOOOL . It would be a pity to learn all this cool stuff just not to use it, wouldn't it. On the other hand, about consciousness, as not much can be said affirmatively about it, I prefer it to do the garbage collection You're not destroying anything cool by doing so.

I can't tell if you're serious. I doubt it. But if you are, do you really think that holding on to some particular bit of cool math is worth the price of jettisoning everything you ever rationally believed was true about the physical world (e.g., that there's a table in front of you, that there are other people in the world who are also conscious, that there are stars and galaxies and planets, etc...)??

 

[vanesch]

But aren't all those "other consciousnesses" not really there? Or at least there can be, in principle, no evidence that they're really there, any more than (on this view) there can be evidence that the table in front of me right now is really there. Sure, that's what my consciousness happens to be experiencing right now, but I can't be sure the experience is correct. In fact, just the opposite: I can be certain it *isn't* correct. The odds are astronomically against the real universal wf being an eigenstate of the "is there a table there right now?" operator.

I think you misunderstood the MWI view (and my flavor of it). At least that's the impression I get when you think that it says: "my consciousness is experiencing this, but it isn't there". Of course it IS really there... in the branch your consciousness has been assigned to. I mean, let us write naively that the objective, ontological, state is:

|psi> = |happymebody>|tablewithabeer> + |sadmebody>|tablewithwater>

This is what is really there: there is a branch where my body is happy and sees a table with a beer, and there is a branch where my body is sad, and sees a table with a glass of water. This is the true bare reality of what is really out there.
But now comes the "consciousness assignment" of my consciousness to my body, and okus pokus: it is assigned to the branch with "happymebody". I tag it with a *:

|psi> = |happymebody*>|tablewithabeer> + |sadmebody>|tablewithwater>

So I (= the conscious me) will now experience a body which is happy and which sees a table with a beer. That's real. It is not a dream or so. The vast majority of unteractions that are possible will not disentangle the two terms (will not allow us to factor out a body state). That's why for all practical purposes, the two terms will keep their own identity, and to know what will happen to the entire state, we can evolve each term individually. As I will only observe things that happen to "happymebody" I can just as well continue only with that term (effective projection) in the vast majority of cases. Note that this is EXTREMELY CLOSE TO WHAT BOHM DOES !
In my term, the "happymebody" will only interact with "tablewithbeer" and so on, so I only observe this aspect of reality. And this "tablewithbeer" state is really an eigenstate of the "tablebeer" observable :-)

The difference with Bohm is this, from the moment that there is another conscious observer:

|psi> = |happymebody*>|tablewithabeer> |laughinbob> + |sadmebody>|tablewithwater> |cryingbob>

In the same way as I only see a table with beer in my term, I also only see the body of bob laugh. But - and here we differ with Bohm - upon the split, it could be that Bob's consciousness has been assigned to "cryingbob". This means that the conscious bob sees my body sad (which I don't experience consciously), sees water on the table, and is crying. I indicate his consciousness with a %:

|psi> = |happymebody*>|tablewithabeer> |laughinbob> + |sadmebody>|tablewithwater> |cryingbob%>

As I can never find out if another body is really consciously experienced by a consciousness or not, it will not bother me - I cannot tell - whether the body of bob who is laughing, is really consciously observed by bob. His body can physically act whether or not it is consciously observed.

In Bohm's story, all the tokens must be in the same term, because they are determined by the positions (hence my question...). It is this "taking together" of the different experiences which denies the 4-dim geometrical picture in Bohm.

But again, what is experienced is really there: my body is in two states of which I experience one, and that one state is there, in a product state with a table with a beer and a laughing bob. It is not a dream in my head.
In the same way, bob experiences really that he's crying (his body really is, at least the state he's aware of) and so on. It is not a dream in his head.

It is the separation of the different "tokens", which in BM are the particle positions, and in my version of MWI are the consciousnesses, that allow this version of MWI to respect relativity, because each branching only occurs locally (in the rest frame of the body to which the consciousness is associated).

BM is only different in one respect:

we have the wavefunction in the position basis, which I suppose can be summarized in the same terms:
|psi> = |happymebody>|tablewithabeer> |laughinbob> + |sadmebody>|tablewithwater> |cryingbob>

and the positions hit with the first term, which I mark by putting them between {}:
|psi> = {|happymebody>|tablewithabeer> |laughinbob>} + |sadmebody>|tablewithwater> |cryingbob>

which selects out the term in the wave function which all conscious observers observe.

The term that is consciously observed in BM is marked globally, for all bodies. It is this globalness which destroys this tagging as a geometrical object.

Now, you will object: hey, conscious observers don't observe the wavefunction, they observe the particle positions. My question to you is: why?

So take that as your paradigm simple example of a position measurement. You send a particle through the apparatus (prepared in some way) and then you see where it lands. You detect its position. And the obvious thing to try (if you're on the premise that "particle means particle", i.e., that the particle that you just saw hit the screen followed some definite path through the apparatus) is that the place where it makes the mark on the screen is the place where it was just before it hit the screen, i.e., you detect it in a certain place because that's where it *is*. So if you can have a theory like that, it's ideal. And it turns out you can. So that's why position measurements are thought of as actually revealing the position.

Ok, then what differentiates "position measurements" from "interactions" ? After all, interactions are in BM, as in QM, described by a hamiltonian, right ?
Or, to put it differently, their action is on the wavefunction. But a measurement apparatus has now 2 different states: it has its hilbert space state (the associated wavefunction), and it has its particles position state. What state does the apparatus, if it were conscious, 'know' ? Does it know (experience) its associated wavefunction, or does it know its particles position ? I guess in order to be correct, it can only experience its particles position, and not its wavefunction which will end up entangled all over the place. But that means it is only aware of ONE TERM of its wavefunction (and the wavefunction is nevertheless an entire part of the ontology of the conscious apparatus). As of this, I'd say that we are almost saying the same things: a conscious observer observes one term of its wavefunction, in such a way that the Born rule is respected. But now a problem appears for BM I would think: if a conscious measurement apparatus is aware of the positions of (some of) its particles, all the time, isn't that a violation, by itself, of the HUP ? Because the "being aware of" is of course not subjected to yet another measurement apparatus.

Now, I suspect you were looking for something slightly different here, along the lines of: how come position measurements are genuine measurements, while, say, momentum or spin measurements aren't?

No, I understood this: in the same way as Bohm is not 4-dim geometrical, it is not really unitary in its machinery in that the position basis is postulated to be special.

I can't tell if you're serious. I doubt it.

I was in a superposition of both. Still am

cheers,
Patrick.

 

[ttn]

I think you misunderstood the MWI view (and my flavor of it). At least that's the impression I get when you think that it says: "my consciousness is experiencing this, but it isn't there". Of course it IS really there... in the branch your consciousness has been assigned to.

Well, maybe this just turns into semantics. We both have a good point. Your point (if I understand correctly) is that the conscious experience isn't a total fantasy -- it's a "valid awareness" of something that is real, namely one branch of the universal wf. So it's a valid awareness of "part of reality" you might say. And I'm sure you'd want to add that validity of one experience doesn't presuppose omniscience. You don't have to know everything to know something. You don't have to know the price of tea in china to know that there's a beer on the table in front of you. An awareness of a "mere part" of reality is still a valid awareness, not a delusion. Right?

But I think there is an important distinction between different senses of "part" here. I would agree that you can know there's a beer there without also knowing the price of tea in china. But your case with MWI is really quite different. Because the different branches in the universal wf aren't like separate facts pertaining to different things. So to experience one to the exlusion of the others isn't to grasp one fact but not others -- it's to be deluded systematically about the whole. To experience one branch of the wave function (to use your example) is to believe that there is a beer on the table, that your friend bob is happy, etc. But literally speaking that is not true of the world. The world is not in fact in a "yup" eigenstate of the "beer on the table?" operator, and so forth. So if you think it is, you're just wrong.

I think the confusion here results from an equivocation on the word "branches". If you take that terminology too literally, you fool yourself into thinking of the branches spatially (like real branches on trees) -- one of them exists here, another exists over there, etc., and the whole thing *seems* rather like the case of there being some facts about the table here, some facts about the price of tea in china over there, and so forth. But really they are not parallel at all, I think.

At least, this is what I have in mind when I repeat ad nauseum that according to MWI everything we believe is completely false. *Everything.* And since that includes all the stuff about space and time and the speed of light and so forth, I just don't see how this can be considered seriously relativistic. It pulls the rug out from under relativity, then the floor, then the foundation, then the earth, ... =)

So I (= the conscious me) will now experience a body which is happy and which sees a table with a beer. That's real. It is not a dream or so.

I hate to sound like Bill Clinton, but it depends on what you mean by "real." If you mean that the real state of the world out there involves there definitely being a table with a beer, no, it isn't real. If this term has been redefined to mean "that's really the experience you're having right now", then, sure, it's real in that sense, but that sense if precisely the *opposite* of what we were originally talking about when we insisted on a realistic ontology.

In Bohm's story, all the tokens must be in the same term, because they are determined by the positions (hence my question...).

The way you phrase this makes it sound like you aren't really accepting Bohm's theory on its own terms. All the talk of particle positions in Bohm's theory isn't just some cheap trick to put an asterisk in one branch of the universal wave function. We talk of particle positions because we're doing physics, and physical stuff -- matter -- is *made* of particles, and we're interested in talking about the configuration of that stuff and how it evolves in time. So it's really the wrong emphasis to say "all the tokens must be in the same term, because they are determined by the positions." Much better to say something like: the particles that the matter in the universe is made of just *are* in some definite configuration, and that's why all of us conscious observers find ourselves agreeing about such things.

It is this "taking together" of the different experiences which denies the 4-dim geometrical picture in Bohm.

I don't think so, or at least that isn't the clearest thing to point to. The actual dynamical evolution law has the velocity of one particle depending (in principle) on the whole configuration of other particles at that time (even though the others are far away). And so you just can't really avoid having some notion of absolute simultaneity, just to give that law a precise meaning.

But again, what is experienced is really there: my body is in two states of which I experience one, and that one state is there, in a product state with a table with a beer and a laughing bob. It is not a dream in my head.

See, this is what I don't agree with. Your body isn't in two states. It's not like "over there my body is doing such and such, while over here my body is doing thus and so". No. Your body is in a certain entangled state with a bunch of other tables and beer and stuff. That's it. That's the real truth. And if you experience something else (like, it feels to you like your body isn't in some crazy macro entangled state, it's just doing one thing that you experience) then your experience is in fact delusional.

It is the separation of the different "tokens", which in BM are the particle positions, and in my version of MWI are the consciousnesses, that allow this version of MWI to respect relativity, because each branching only occurs locally (in the rest frame of the body to which the consciousness is associated).

I don't even know what that last part could possibly mean. There is no one "rest frame..." Probably the real state involves a superposition of your body sitting in front of the table looking a full glass of water, and your body running full speed to the bathroom leaving behind an empty glass of beer. So which one is the rest frame? I guess you want to say: the one for the body in whichever branch you're experiencing. But I think that's a delusion, which makes the rest frame delusional too and... blech.

BM is only different in one respect:

we have the wavefunction in the position basis, which I suppose can be summarized in the same terms:
|psi> = |happymebody>|tablewithabeer> |laughinbob> + |sadmebody>|tablewithwater> |cryingbob>

and the positions hit with the first term, which I mark by putting them between {}:
|psi> = {|happymebody>|tablewithabeer> |laughinbob>} + |sadmebody>|tablewithwater> |cryingbob>

which selects out the term in the wave function which all conscious observers observe.

Yes, that's true, but (to repeat) it's a very funny way of putting it from the point of view of Bohm's theory. It makes it sound like, really, what we observe is some branch of the wave function, and the role of the "tokens" is to lure everybody's attention to this one particular branch. But that totally leaves out what makes Bohm's theory really cool -- it allows you to actually believe in a common-sense physical world that is built out of the familiar kinds of particles having certain spatial arrangements. All conscious observers agree about whether the glass has water or beer, because *in fact*, out there in the real physical external world, either the glass-shaped configuration of silicon atoms are surrounding a big collection of H20 molecules, or, hopefully, a big collection of beer molecules. It really (really, out there, physically, in terms of the particles!) just is either one way or the other. There's just an objective physical fact about whether the glass is filled with beer or water. So *of course* all the human observers (who observe it) are going to agree.

Now, you will object: hey, conscious observers don't observe the wavefunction, they observe the particle positions. My question to you is: why?

Hell if I know. That just seems to be how consciousness in fact works. Maybe god or some martians can look out at the world and "see" something else, like little blobs of goo that correspond to branches of the universal wf where the actual configuration isn't. Who can say? All I know is that *I* can't do that and neither can anyone else I've ever talked to.

If classical Newtonian mechanics had turned out to be the true fundamenal theory, nobody would raise a question like this. Newton says f=ma and that such and such objects end up getting pushed over *here* and we actually see that happen (we see that object end up here), but WHY? WHY are we able to see what the theory says should happen? I don't know, Newton doesn't know, nobody knows. Maybe some day in a thousand years psychologists or biologists will learn enough about consciousness to have something useful to say on this. My point is just that it shouldn't be the kind of question that in any way undermines a physics theory. There's a world out there with things in it, and those things move around and we can see where they are if we're close enough to them. We've all known that since age 6 months. Why does it suddenly become a problem that needs answering just because you now have a more sophisticated physics theory that, at the end of the day, says the same thing?

Ok, then what differentiates "position measurements" from "interactions" ?

Nothing, it's just a special case. The electron hits some particular molecule of silver halide or whatever in the screen, and this starts some kind of chain reaction that eventually results in a macroscopically distinct configuration (so now we don't have to worry about interference between branches and we can see the spot on the film). Maybe you're asking: how come momentum "measurements" aren't genuine measurements but position measurements are? That's just what the theory says. It's not like some kind of additional assumption, that's just how the theory in fact works out.

Maybe you'll ask: could I make a theory that's like Bohm except that (say) momentum is special, so that momentum measurements are real measurements but position measurements are mere interactions (or "position is a contextual property", or however you want to say it)? Yes, you could. There's a whole class called "modal theories" that basically do this. But they're all unmotivated and uninteresting from a physics point of view. The fact is, position is special because we actually experience the spatial arrangement of stuff in the world. That's not to say that the modal theories aren't logically consistent (in the way that your MWI is) or that it's not a good thing that people have shown how to write them down, they are just much much harder to integrate into a common sense picture of the world (including explaining in a simple and clear way all the important experimental results like 2-slit etc).

After all, interactions are in BM, as in QM, described by a hamiltonian, right ?
Or, to put it differently, their action is on the wavefunction. But a measurement apparatus has now 2 different states: it has its hilbert space state (the associated wavefunction), and it has its particles position state. What state does the apparatus, if it were conscious, 'know' ? Does it know (experience) its associated wavefunction, or does it know its particles position ? I guess in order to be correct, it can only experience its particles position, and not its wavefunction which will end up entangled all over the place. But that means it is only aware of ONE TERM of its wavefunction (and the wavefunction is nevertheless an entire part of the ontology of the conscious apparatus). As of this, I'd say that we are almost saying the same things: a conscious observer observes one term of its wavefunction, in such a way that the Born rule is respected. But now a problem appears for BM I would think: if a conscious measurement apparatus is aware of the positions of (some of) its particles, all the time, isn't that a violation, by itself, of the HUP ? Because the "being aware of" is of course not subjected to yet another measurement apparatus.

I don't get your point here. Why should an apparatus be able to observe itself? What does that even mean? You're obviously using "observe" in some generalized way (unless you think particle detectors all just became conscious... that might make a good physics horror movie, btw... like the matrix, only it's just the physics equipment that goes crazy and tries to measure us all to death..). But I don't see the point.

No, I understood this: in the same way as Bohm is not 4-dim geometrical, it is not really unitary in its machinery in that the position basis is postulated to be special.

I"m not sure what you mean by "unitary" here. The wf is going to obey the same sch eq your MWI theory has it obeying, and that is certainly unitary. As far as the other dynamical equation in BM being unitary, I don't know what that even means. There's no "norm" for the configuration that has to be preserved by the evolution. There's just the evolving configuration. And I don't think it's the right emphasis to say that it's because "the position basis is postulated to be special" that "Bohm is not 4-dim geometrical". It's because (as explained above) the theory requires a foliation of 4 into 3+1. But that doesn't really have anything to do with the position basis. I'm sure there's the same issue in the "modal theories" I mentioned which take some other "observable" as special.

 

[vanesch]

Because the different branches in the universal wf aren't like separate facts pertaining to different things. So to experience one to the exlusion of the others isn't to grasp one fact but not others -- it's to be deluded systematically about the whole. To experience one branch of the wave function (to use your example) is to believe that there is a beer on the table, that your friend bob is happy, etc. But literally speaking that is not true of the world. The world is not in fact in a "yup" eigenstate of the "beer on the table?" operator, and so forth. So if you think it is, you're just wrong.

But exactly the same thing happens in BM! Remember that the wavefunction is just as well part of the ontology of the world as is the point in configuration space giving us the particle positions. This means that the wavefunction in BM has exactly these superposed terms as does MWI: there is a term where there is beer in the glass, and at exactly the same spot in space, there is a term where there is water in the glass, and that's really part of the world according to BM just as well as in MWI. But BM has something extra: the beer in the glass state corresponds to the point in configuration space that is "active" while the water in the glass term corresponds to a point in configuration space that is not active. These are "ghost" branches in the wf, but they are nevertheless part of the world.

I hate to sound like Bill Clinton, but it depends on what you mean by "real." If you mean that the real state of the world out there involves there definitely being a table with a beer, no, it isn't real.

If this term has been redefined to mean "that's really the experience you're having right now", then, sure, it's real in that sense, but that sense if precisely the *opposite* of what we were originally talking about when we insisted on a realistic ontology.

It is in between both: what's really real is that there is both a beer on the table, and water on the table. I happen to observe only part of it. Yes, this is less real than that there is "really beer on the table and I see that", but it is more real than "I just have an illusion of seeing beer on the table".
Probably the best description is that the state is real (both beer and water), and the consciousness worldline is real (in the branch of the beer) ; the result of this being that the consciousness at hand observes (has the illusion) of only seeing the beer as a result of its world line.
I wanted to emphasize that BM has a very similar problem:
the REAL wavefunction also describes beer and water on the table, but the world line in the configuration space makes us only observe the beer.

The way you phrase this makes it sound like you aren't really accepting Bohm's theory on its own terms. All the talk of particle positions in Bohm's theory isn't just some cheap trick to put an asterisk in one branch of the universal wave function. We talk of particle positions because we're doing physics, and physical stuff -- matter -- is *made* of particles, and we're interested in talking about the configuration of that stuff and how it evolves in time.

Yes, I know that that is how Bohmians want to make it sound, and of course I pulled the Bohmian representation a little bit to the MWI side to emphasize certain similarities that you attack in MWI but that are in a certain way also present in BM.

So it's really the wrong emphasis to say "all the tokens must be in the same term, because they are determined by the positions." Much better to say something like: the particles that the matter in the universe is made of just *are* in some definite configuration, and that's why all of us conscious observers find ourselves agreeing about such things.

Bohmians systematically forget that the wavefunction is just as much part of the ontological description of the world as is the configuration in configuration space. They use the configuration in configuration space to give you that good old classical feeling, and they use the wavefunction to get the dynamics right ; but when interpreting the theory they pretend that the wavefunction isn't there anymore. But you can't do that. The wavefunction is just as well part of the "real world" as is the configuration, but we only seem to consciously observe the configuration.
Of course, MWIers cannot play that trick because all they have is the wavefunction ! But the problems MWIers have of having "too much stuff happening that is not observed" is identical in BM !

See, this is what I don't agree with. Your body isn't in two states. It's not like "over there my body is doing such and such, while over here my body is doing thus and so". No. Your body is in a certain entangled state with a bunch of other tables and beer and stuff. That's it. That's the real truth.

Yup, just as well in BM as in MWI, btw...

And if you experience something else (like, it feels to you like your body isn't in some crazy macro entangled state, it's just doing one thing that you experience) then your experience is in fact delusional.

That's too strong a statement. Your experience is only partial would be better... Just as in BM, where you only experience your configuration space part of the body state, and not the wf part.

I don't even know what that last part could possibly mean. There is no one "rest frame..." Probably the real state involves a superposition of your body sitting in front of the table looking a full glass of water, and your body running full speed to the bathroom leaving behind an empty glass of beer. So which one is the rest frame?

The one which had my consciousness token.

I guess you want to say: the one for the body in whichever branch you're experiencing. But I think that's a delusion, which makes the rest frame delusional too and... blech.

No, it is not a delusion. Because this version of MWI does not have as only world description the wavefunction. It also has the "world lines" of consciousnesses (tracing their world line throught the branches). The observed state is the state given by the world line of the consciousness (in the same way as in BM, the observed state is the state given by the point in configuration space), except that my world line is a world line in wf branches, not directly in 4-dim. But of course it INDUCES a world line in minkowski space, because the consciousness is not only associated to a term, but also to a system (a body). As this body, in the associated term, follows a world line in Minkowski space, we have our associated world line which defines our local rest frame. I don't see why this is more delusional than the configuration space in BM...

Yes, that's true, but (to repeat) it's a very funny way of putting it from the point of view of Bohm's theory. It makes it sound like, really, what we observe is some branch of the wave function, and the role of the "tokens" is to lure everybody's attention to this one particular branch. But that totally leaves out what makes Bohm's theory really cool -- it allows you to actually believe in a common-sense physical world that is built out of the familiar kinds of particles having certain spatial arrangements. All conscious observers agree about whether the glass has water or beer, because *in fact*, out there in the real physical external world, either the glass-shaped configuration of silicon atoms are surrounding a big collection of H20 molecules, or, hopefully, a big collection of beer molecules. It really (really, out there, physically, in terms of the particles!) just is either one way or the other.

Yes, yes, ... in part of the state, namely the configuration state part. But the wf part doesn't say so ! But as a good Bohmian you do not mention the wf in the interpretation - but use it only to get the dynamics right :-)

Hell if I know. That just seems to be how consciousness in fact works. Maybe god or some martians can look out at the world and "see" something else, like little blobs of goo that correspond to branches of the universal wf where the actual configuration isn't. Who can say? All I know is that *I* can't do that and neither can anyone else I've ever talked to.

Your _almost_ sounding like an MWIer :-))

If classical Newtonian mechanics had turned out to be the true fundamenal theory, nobody would raise a question like this. Newton says f=ma and that such and such objects end up getting pushed over *here* and we actually see that happen (we see that object end up here), but WHY? WHY are we able to see what the theory says should happen? I don't know, Newton doesn't know, nobody knows.

No, the big difference with true classical physics is that the configuration space is all there is to the ontological state of the world. And Bohmians like to think that their theory does the same thing. But that's not true. The wf IS just as much part of the ontological state of the world as is the configuration space world line. And then - that was the point of my discussion - you run in similar "consciousness" problems as do MWI-ers.

There's a world out there with things in it, and those things move around and we can see where they are if we're close enough to them. We've all known that since age 6 months. Why does it suddenly become a problem that needs answering just because you now have a more sophisticated physics theory that, at the end of the day, says the same thing?

Maybe you're asking: how come momentum "measurements" aren't genuine measurements but position measurements are? That's just what the theory says. It's not like some kind of additional assumption, that's just how the theory in fact works out.

I know you would like me to ask that, but I won't. I can accept that BM prefers the position basis in Hilbert space.

I don't get your point here. Why should an apparatus be able to observe itself? What does that even mean?

Well, you insist upon the "reality" of the configuration space point, because that's what we (consciously) observe. If the apparatus is your brain, you will experience consciously some aspect of the state of your brain. Now, the state of your brain consists of two parts: the point in configuration space corresponding to its particles, and the wf of the hilbert space representing its state. If you'd experience the wf, which is entangled with a lot of stuff, you'd be in trouble. So I take it that you experience only the configuration space part. AND IT IS THIS FACT, namely that you only observe the configuration space part of the state of your brain, which makes you also only observe the configuration space part of all other things around you, such as the state of teh dial on the instrument and so on. If you would have been sensitive to the wf of your brain, you'd be also sensitive to the wf of the apparatus and so on, and you'd have the same difficulties as MWI people.
So it is the fact that you are only consciously aware of the configuration space part of your brain that makes this classical picture work in BM.

It's all I wanted to point out. From the moment that an ontology is given to the WF, and it evolves unitarily (common to both MWI and BM), this consciousness stuff shows up.

 

[ttn]

But exactly the same thing happens in BM! Remember that the wavefunction is just as well part of the ontology of the world as is the point in configuration space giving us the particle positions. This means that the wavefunction in BM has exactly these superposed terms as does MWI: there is a term where there is beer in the glass, and at exactly the same spot in space, there is a term where there is water in the glass, and that's really part of the world according to BM just as well as in MWI. But BM has something extra: the beer in the glass state corresponds to the point in configuration space that is "active" while the water in the glass term corresponds to a point in configuration space that is not active. These are "ghost" branches in the wf, but they are nevertheless part of the world.

Yes, absolutely. I make no attempt to "hide" this, as you seem to suggest. But you really do have to get over the dogma that we were all given in kindergarten that the wave function is what's really real. I know you understand Bohm OK, but still, the way you phrase certain things makes it sound as if, at the end of the day, the particle positions are some kind of dispensible "hidden variable" that doesn't really do anybody any good, and then you run home to mommy wave function. =) I think the unfortunate historical description of Bohmian positions as hidden variables maybe contributes to this sense. That terminology is just stupid when it comes to BM. The particle positions are the one thing that is in no sense whatever hidden! It's the wave function which is sort of lurking in the shadows in the background, orchestrating the motion of the particles but never really *appearing* directly on the stage itself. I totally agree with you that, in terms of fundamental ontology, the wf has to be regarded as real -- as real, in fact, as the particles and their positions. But then you just have to remember that *in Bohm's theory* we're going to basically redefine a number of concepts that people have been used, for some time, to thinking about as reducible to wavefunctions. For example, the number density of particles in a certain region of space. In OQM, there are no particles, just the wf -- so you have to parse talk of "particle number density" in terms of what would be observed if you went there and collapsed the wave function, etc etc. But that and a zillion other things all have a perfectly ordinary direct meaning in Bohm's theory. Number density of particles? That just refers to the number density of the particles! Which is a real part of the ontology -- not the whole thing, as you stress correctly, and if you want to know where the particles are going to be 10 minutes from now you definitely better not forget about the lurker in the shadows. But if you just want to talk about ordinary things like glasses of beer and where the planets are and so forth -- that is, if you want to talk about where the particles that matter is made of are located and how they move -- then you can do this *completely* in terms of the particle ontology. It's not an attempt at deception to sometimes not mention the wf. It's just that for a lot of ordinary talk about physics things, the wf isn't directly relevant.

It is in between both: what's really real is that there is both a beer on the table, and water on the table. I happen to observe only part of it. Yes, this is less real than that there is "really beer on the table and I see that", but it is more real than "I just have an illusion of seeing beer on the table".
Probably the best description is that the state is real (both beer and water), and the consciousness worldline is real (in the branch of the beer) ; the result of this being that the consciousness at hand observes (has the illusion) of only seeing the beer as a result of its world line.
I wanted to emphasize that BM has a very similar problem:
the REAL wavefunction also describes beer and water on the table, but the world line in the configuration space makes us only observe the beer.

NO, no, no. =) "The REAL wavefunction also describes beer and water on the table..." No, it doesn't! Beer and water are physical substances made of certain kinds of particles in certain arrangements. They are literally not made of wavefunctions. OK? So BM simply does not suffer from this same problem. It's not that the accident that the "token" happens to be in a certain branch "makes us only observe the beer." We only observe the beer because only the beer is actually, physically, particle-fully *there*.

Bohmians systematically forget that the wavefunction is just as much part of the ontological description of the world as is the configuration in configuration space. They use the configuration in configuration space to give you that good old classical feeling, and they use the wavefunction to get the dynamics right ; but when interpreting the theory they pretend that the wavefunction isn't there anymore. But you can't do that. The wavefunction is just as well part of the "real world" as is the configuration, but we only seem to consciously observe the configuration.
Of course, MWIers cannot play that trick because all they have is the wavefunction ! But the problems MWIers have of having "too much stuff happening that is not observed" is identical in BM !

No, it's not. At least, not if what you mean by "happening" is parsed out in terms of particles. (And this isn't just making it true by definition, either. Virtually 100% of the time that an ordinary non-physicist talks about something happening, as long as he isn't talking about consciousness, he's talking about something happening that can be completely reduced to the motion of particles.) It's true that there is more happening than this, there's this other lurking real-but-hidden object which is evolving in a certain way. But that just isn't on the stage, in a very real and very meaningful sense. It's causally affecting what's on the stage, so it's extremely important, no doubt. But it's not usually what we are directly talking about when we point to some guy on the stage and say: look at what he's doing!

No, it is not a delusion. Because this version of MWI does not have as only world description the wavefunction. It also has the "world lines" of consciousnesses (tracing their world line throught the branches). The observed state is the state given by the world line of the consciousness (in the same way as in BM, the observed state is the state given by the point in configuration space), except that my world line is a world line in wf branches, not directly in 4-dim. But of course it INDUCES a world line in minkowski space, because the consciousness is not only associated to a term, but also to a system (a body). As this body, in the associated term, follows a world line in Minkowski space, we have our associated world line which defines our local rest frame. I don't see why this is more delusional than the configuration space in BM...

This is taking us in a slightly different direction, but a question just occurred to me. How exactly does the Born rule work in this scheme? I know you say you just postulate it (since it seems impossible to derive). But what exactly does it *say*? I know you want it to govern the probability that at any given moment the consciousness-token is "in" this or that branch. But still, how exactly does this work? How often do you apply the Born rule? (In OQM, you apply it only when you make a "measurement". Is there something like that for you? You only apply it... when??) And then, however you answer, doesn't this lead to a really frightening sort of "hopping" from branch to branch, so that, in the next moment not only might the water switch to beer (though of course I wouldn't notice this since my brain would also switch to a state that makes me remember that there was always beer!), but the sun might have gone supernova so my body doesn't even exist, and... you see how crazy it gets. Or is the idea closer to the deterministic Bohm theory, where you have an *initial* Born-rule placement of the "token" and then you have some kind of equivariance type theorem so that the consciousness token just evolves in a deterministic way down the branching structure?

Anyway, enough questions... you can see I really have no idea how this is supposed to work (now that I think about it carefully).

No, the big difference with true classical physics is that the configuration space is all there is to the ontological state of the world. And Bohmians like to think that their theory does the same thing. But that's not true. The wf IS just as much part of the ontological state of the world as is the configuration space world line. And then - that was the point of my discussion - you run in similar "consciousness" problems as do MWI-ers.

But you don't, not if you just say that consciousness is (by some mechanism that maybe we'll understand in a thousand years) a faculty for becoming aware of particle configurations. Then that's that, it's no different from classical physics *on that point*, which was my point. I'm not saying it is classical physics, and I"m not denying that this means there is (at least for now!) a really important and really real "thing" (the wf) that we aren't able to be conscious of in any direct way. (We have to infer its existence from the fact that particles follow really weird trajectories!) But in principle there is no "problem of consciousness" any more than there was in classical physics. There's just something we aren't conscious of.

Well, you insist upon the "reality" of the configuration space point, because that's what we (consciously) observe. If the apparatus is your brain,...

Ah, now I see where you're going!

... you will experience consciously some aspect of the state of your brain.

Neither I nor anyone else is really going to be able to satisfy you here. I just don't know the relationship between mind and brain. But as a purely philosophical point, I would say that what you experience consciously is something in the external world, not a state of the brain. You see the glass of beer out there by means of reflected light and lenses in your eye and electrical impulses and all sorts of craziness in the brain... who the hell knows how it works. But what you actually *see* is the glass of beer, not a kaleidoscope of neuron firings.

Now, the state of your brain consists of two parts: the point in configuration space corresponding to its particles, and the wf of the hilbert space representing its state. If you'd experience the wf, which is entangled with a lot of stuff, you'd be in trouble. So I take it that you experience only the configuration space part.

Yes, or as I'd rather phrase the same thing, your experience of the glass of beer uses or depends on the configuration of electrons and other goop in your brain, and not (directly) on the wf.

AND IT IS THIS FACT, namely that you only observe the configuration space part of the state of your brain, which makes you also only observe the configuration space part of all other things around you, such as the state of teh dial on the instrument and so on. If you would have been sensitive to the wf of your brain, you'd be also sensitive to the wf of the apparatus and so on, and you'd have the same difficulties as MWI people.

OK, sure.

So it is the fact that you are only consciously aware of the configuration space part of your brain that makes this classical picture work in BM.

It's all I wanted to point out. From the moment that an ontology is given to the WF, and it evolves unitarily (common to both MWI and BM), this consciousness stuff shows up.

I still don't see what the problem is. In MWI there's a problem because what we all think we're conscious just doesn't match up with the actual state of the world out there. In Bohm, what we think we're conscious of *does* match up with the actual state of the world out there -- or at least a really important part of it. So it's not parallel at all in terms of being the same problem. In MWI if you think there's really a glass of beer, that the real state of the world includes there definitely being a glass of beer, you're just *wrong*. In Bohm, if you think there's really a glass of beer -- and what you mean by that is what people normally *do* mean by that, namely, that there are a bunch of silicon atoms and beer molecules arranged in a certain way in front of them -- you are *right*. Now, I think you're probably right to point out that, in Bohm's theory, you can push the "knowledge is knowledge of configurations only" all the way back into the brain until it buts up against consciousness. And then who knows. But, for Bohm, this just means there's going to be interesting science left to do in a thousand years. There's no real pressing *problem*.

(And I should maybe add: I don't think there's really a *problem* for MWI on this point either -- you just have to be willing to accept that everything you believe in is a delusion -- that, in fact, the world is *nothing* like what you think it's like. So there's not really a fatal logical flaw or anything... just a very high price to pay, merely to save some formal principle that no longer even means what you thought it meant when you set out on the quest to save it!)

I should also confess that I smile to myself every time I get to mention "beer molecules". I guess it would be even better if beer were an actual element so it would appear right there on the periodic table.

So, have I converted you into a Bohmian yet? Or do you need a few more glasses?

 

[vanesch]

I know you understand Bohm OK, but still, the way you phrase certain things makes it sound as if, at the end of the day, the particle positions are some kind of dispensible "hidden variable" that doesn't really do anybody any good, and then you run home to mommy wave function.

Well, apart from emotional qualifiers like "mommy" and "silly" and so on, I haven't seen much of a logical argument against my statements ; guess that means you run out of those

And of course I'm sketching a view of the formalism of BM that is orthogonal to the view that Bohmians want to convey. I do this on purpose in order to show that several "silly" problems in MWI also occur in BM.

I don't deny the particle positions (it's of course the aspect that has an advantage and a disadvantage: the advantage is that it helps us not needing the projection postulate - in that sense it is superior over OQM. The disadvantage is that it is must obey a dynamics which cannot be described geometrically, so relativity goes over board). But I'm pointing you to the following:

The particle positions are the one thing that is in no sense whatever hidden! It's the wave function which is sort of lurking in the shadows in the background, orchestrating the motion of the particles but never really *appearing* directly on the stage itself. I totally agree with you that, in terms of fundamental ontology, the wf has to be regarded as real -- as real, in fact, as the particles and their positions. But then you just have to remember that *in Bohm's theory* we're going to basically redefine a number of concepts that people have been used, for some time, to thinking about as reducible to wavefunctions.

I understand that: all *observable* stuff relates only to the particle positions. But what I wanted to make clear was: this very definition of what is observable, is simply a statement about what is consciously experienced, that's all. Because the dynamics of BM plays just as well on the wavefunction as on the particle positions, so two things "happen". But only one is observed. That gives some special status to "observation" of course. But the situation is not as bad as in OQM, because in OQM, this observation comes in and changes the ontological state of the universe (projection), while in BM it is only passively observed.
However, I wanted to stress this, that your conscious observation in BM ALSO DOESN'T OBSERVE WHAT IS REALLY THERE. (what is really there is the couple: {particle positions + wave function}). It is exactly the same thing that you find silly in MWI: that one doesn't observe "reality", because reality is the whole wavefunction, and one consciously observes only one part of it (a term, or branch). All your insistance that the particle positions are what is "really real" and the wavefunction is only what is "ghostly real" is not so much different from my statement that the branch the consciousness is in is really real and the other terms are "ghostly real".

But if you just want to talk about ordinary things like glasses of beer and where the planets are and so forth -- that is, if you want to talk about where the particles that matter is made of are located and how they move -- then you can do this *completely* in terms of the particle ontology. It's not an attempt at deception to sometimes not mention the wf. It's just that for a lot of ordinary talk about physics things, the wf isn't directly relevant.

Yes, but we're now doing CLASSICAL physics !

NO, no, no. =) "The REAL wavefunction also describes beer and water on the table..." No, it doesn't! Beer and water are physical substances made of certain kinds of particles in certain arrangements. They are literally not made of wavefunctions. OK?

I think we have to disagree on this. Beer and water, in BM are made up of the pair {particle positions, wavefunction}, period. We seem to only observe consciously the particle positions ; I even tried to show that we don't even observe the particle positions of the beer, but only the particle positions of our brain. And that this awareness leads us only to "know about" the particle positions in the beer, and not the wavefunction of the beer+water. However, the wf of our brain IS entangled with the wf of beer+water. So if we'd be aware of the wf of our brain, and not to the particle positions of our brain, we'd only be aware of the wf of "beer+water" and we wouldn't even see where the particles are !

Your only argument for this is that in classical physics, the ontology is completely given by particles (that's what you do with your examples). But in BM, this is not true anymore: the ontology is given by the pair {particles,wf}. Nevertheless, as you point out, the wf seems to live a ghostlike existence which is never consciously observed (although we observe the effects of its dynamics!). I showed you that this is because of a property of conscious observation, which relates only to the particle positions. This is not a critique of BM of course. But it shows you that you have to postulate that you only observe consciously part of the entire world ontology (namely the particle part). This is exactly what you find "silly" in MWI.
The argument that, in classical physics, you also observe consciously the particle positions is not very strong, because in classical physics, the particle positions ARE the entire world ontology ! So here you DO observe the entire world ontology consciously, in which case you don't have to talk about it.

So BM simply does not suffer from this same problem. It's not that the accident that the "token" happens to be in a certain branch "makes us only observe the beer." We only observe the beer because only the beer is actually, physically, particle-fully *there*.

That's indeed the case in classical physics, where the entire world ontology is given by the particle positions ; from which BM inherited the sentiment that particle positions are really real, but the situation changed drastically: the world ontology is not given anymore by the particle positions !

Virtually 100% of the time that an ordinary non-physicist talks about something happening, as long as he isn't talking about consciousness, he's talking about something happening that can be completely reduced to the motion of particles.)

Yes, most of the time an ordinary non-physicist talks about something, he works in classical physics (or Aristotelian physics :-)

It's true that there is more happening than this, there's this other lurking real-but-hidden object which is evolving in a certain way. But that just isn't on the stage, in a very real and very meaningful sense. It's causally affecting what's on the stage, so it's extremely important, no doubt. But it's not usually what we are directly talking about when we point to some guy on the stage and say: look at what he's doing!

Right, we only observe a classical world, like with Copenhagen :-)

This is taking us in a slightly different direction, but a question just occurred to me. How exactly does the Born rule work in this scheme? I know you say you just postulate it (since it seems impossible to derive). But what exactly does it *say*?

Ok, a consciousness (token) is attached to a state of a system (a state of my brain, say). My physical brain has a Hilbert space associated to it, which is of course a subspace of the Hilbert space of the universal wavefunction.

So it is associated to the state vector of my brain that occurs in one of the terms in the wf:

|psi> = a|brain1*>|moon>|sun> + b|brain2>|moon>|sun>

Now, it cannot be associated with an entangled state. So as long as the sun and the moon interact amongst themselves, but not with the brain1 state, I remain in that state. Imagine that a quantum experiment projects the moon in the sun with amplitude 0.3:

|psi> = a |brain1*> (0.3 |mooninsun> + 0.99 |moon>|sun>) + b |brain2>|moon>|sun>

This is still ok, because brain1 didn't get entangled. But now I open my eyes and look through a telescope ; I will hence see whether the moon is in the sun or not. Through a long chain of unitary interactions, this entangles my brain state:

|psi> = a (0.3 |brain1A*> |mooninsun> + 0.99 |brain1B*> |moon>|sun>) + b |brain2>|moon>|sun>

However, that's not allowed: the consciousness cannot be associated to an entangled state of the brain, so now a choice must be made:
according to the Born rule, the token is now associated randomly to "brain1A" or to "brain1B" according to a 10% - 90% chance (the Hilbert norm squared). As this is something that happens locally to an interaction between the brain states and the token, it is really local. So say that the 90% option is stochastically taken, then the state is now:

|psi> = a 0.3 |brain1A> |mooninsun> + 0.99 a |brain1B*> |moon>|sun> + b |brain2>|moon>|sun>

and I observed that the moon didn't fall into the sun after all, with 90% chance.

How often do you apply the Born rule?

Each time the state the token is associated with, entangles with something else through a (local) interaction.

And then, however you answer, doesn't this lead to a really frightening sort of "hopping" from branch to branch, so that, in the next moment not only might the water switch to beer

No, because you start from the previous "tokenized" state, and jump only to one of its daughter states.

In fact, I think about it: you could associate such a token to EVERY system, not only to brains. In that case you don't call it consciousnesses, but you call it "particle positions". Looks like BM, doesn't it :-)
However, there are two differences:
1) the dynamics is not deterministic and global, but it is stochastic and local
2) the tokens are not in the same branch of the wf of course

In the same way as in BM, what you consciously are aware of of the state of your brain is the token, not its wave function. That makes you observe the branch of the wf the token of your brain is in, and of the other objects you observe the state in that branch, NOT their token of course (because your brain memory state is determined by interactions with the state in the branch, and not by the token of the other object - which has no dynamical implications).

Hey, how do you call this ? Bohmian many worlds ? :-)

Ok, I pulled BM a bit to the MWI side, and I changed MWI a bit to the Bohm side by introducing tokens (particle positions) for everything out there. We share the postulate that we only consciously are aware of the particle positions of our brain.
But: this MWI version is relativistically ok :-)

Or is the idea closer to the deterministic Bohm theory, where you have an *initial* Born-rule placement of the "token" and then you have some kind of equivariance type theorem so that the consciousness token just evolves in a deterministic way down the branching structure?

Almost. The evolution is not deterministic but stochastic. But that's indeed the idea.

cheers,
Patrick.

 

[ttn]

I understand that: all *observable* stuff relates only to the particle positions. But what I wanted to make clear was: this very definition of what is observable, is simply a statement about what is consciously experienced, that's all.

But you miss an incredibly important point by putting it this way. In BM, that is what is consciously experienced *because* that is (part of) the actual physical state of the objects being observed. And this is what's crucial, what you try to hide below: "part" here means literally *part*. The particle positions are *real*. Yes, there's also the wave function and when we wake up in the morning and open our eyes, we see only particles, not wf. So we see *part* of what exists. In MWI, this is not the case. Our experience is not an experience of *part* of what exists, not in the literal sense of *part*. And this is crucial. In classical physics (which BM is not, but in which we don't have some allegedly pressing consciousness problem for physicists) we also only see part of what exists. I see the stuff in this room right now, but not distant galaxies and not individual atoms. Those things exist, to be sure, but I can't experience them directly. I have to infer their existence by doing physics, right? Just exactly in the same way that in BM one has to infer the existence of the wf because one doesn't perceive it directly. My point is: just because I can't perceive those distant galaxies directly doesn't make my perception of my coffee invalid. To perceive "only a part of reality" is all that anyone could ever rationally have insisted on as a standard of perception. To demand omniscience is to posit an indefensible standard. The question is not: do you become aware of everything, but rather: is what you're aware of actually there, actually real? In BM, it is.

However, I wanted to stress this, that your conscious observation in BM ALSO DOESN'T OBSERVE WHAT IS REALLY THERE. (what is really there is the couple: {particle positions + wave function}).

Your + sign here is a clever attempt, but you won't fool me. The ontology is not a *superposition* of particle positions and wave function. Both, separately, exist. Just like coffee exists in my mug here, and a galaxy exists over there somewhere. They are two separate things -- not two distinct "branches" in a wave function. But that latter is what you mean when you claim there is a parallel to MWI, that also in MWI what we observe is "part" of reality. No, it isn't "part". It's one term in a superposition. That's more analogous to watching the waves on a beach and saying "I see only the lambda = 1.273 m Fourier component", so I see a part of what's really happening. No, if that's what you see (and don't ask me how that would actually happen!) then you are just *wrong* -- wrong, for example, about the height of the water at various positions and other relevant features of the actual waves.

This is the whole issue. Is what you perceive a real part of reality? In BM I think we can answer yes (though it is admittedly only a part, yes). In MWI, I don't think we can say yes. That's why I say that according to MWI we are deluded about everything, while in BM what we have is valid knowledge.

It is exactly the same thing that you find silly in MWI: that one doesn't observe "reality", because reality is the whole wavefunction, and one consciously observes only one part of it (a term, or branch).

Reality is *not* the whole wf (according to Bohm), it's the wave function plus all the particle positions. What one observes is *not* one term/branch of the wf, but the particle positions. You want to say: oh, but really it's just like MWI because those particle positions are just like a circle god draws around one term in the universal wf to indicate that that's the "real" one, the one that people should have experiences of or whatever, such that really when push comes to shove what us humans experience is just this one branch of the wave function. But that is not fair at all. The particle positions are real, as real as the wf, and it's those particles (not a branch of the wf) that we observe. End of story.

I think we have to disagree on this. Beer and water, in BM are made up of the pair {particle positions, wavefunction}, period.

I admit, different levels of description are possible. You can legitimately say: Beer is made up of beer molecules. Or you can go deeper: beer is made of such and such atoms all combined up in a certain way into beer molecules. Or: beer is made of electrons and protons and neutrons and electromagnetic and weak and strong nuclear fields. Or:...

Same in Bohmian Mechanics. It's legitimate to say the beer is just made of the beer particles. This isn't a complete account, true. But it's legitimate foreshortening, just like "beer molecules" above.

We seem to only observe consciously the particle positions ; I even tried to show that we don't even observe the particle positions of the beer, but only the particle positions of our brain. And that this awareness leads us only to "know about" the particle positions in the beer, and not the wavefunction of the beer+water. However, the wf of our brain IS entangled with the wf of beer+water. So if we'd be aware of the wf of our brain, and not to the particle positions of our brain, we'd only be aware of the wf of "beer+water" and we wouldn't even see where the particles are !

Yes, I think that's right. So that just puts some kind of constraint on how consciousness relates to the brain (which we know diddly squat about anyway). So let the people in 1000 years worry about it.

Your only argument for this is that in classical physics, the ontology is completely given by particles (that's what you do with your examples). But in BM, this is not true anymore: the ontology is given by the pair {particles,wf}. Nevertheless, as you point out, the wf seems to live a ghostlike existence which is never consciously observed (although we observe the effects of its dynamics!). I showed you that this is because of a property of conscious observation, which relates only to the particle positions. This is not a critique of BM of course. But it shows you that you have to postulate that you only observe consciously part of the entire world ontology (namely the particle part). This is exactly what you find "silly" in MWI.

No, I don't think so. As I tried to say above, I don't think the crucial word here -- "part" - -has the same meaning in the two theories. In Bohm you observe a real part of the world, the way one of its pieces of furniture really is. In MWI, there is no "really is" about different branches of the wf, anymore than in QM 101 you can say: the wf is a superposition of |slit 1> and |slit 2> but is it *really* slit 1 or slit 2? As long as the wf is the whole ontology, there is no answer, it's not even a legitimate question. What exists is the superposition of slit 1 and slit2, period. Neither branch is real.

You want to say: ah, but there's a consciousness token which makes you experience only one branch. Well so much the worse for this alleged "consciousness" then. What it claims to be conscious of doesn't actually exist (which, by the way, means it isn't conscious after all, but that's a different point...).

The argument that, in classical physics, you also observe consciously the particle positions is not very strong, because in classical physics, the particle positions ARE the entire world ontology !

What about fields and other such things? What about other people's consciousnesses? There are all sorts of things which aren't directly observable in classical physics, yet this doesn't raise any problems. That I can't experience your consciousness directly doesn't mean my perception of this coffee cup is invalid.

Ok, a consciousness (token) is attached to a state of a system (a state of my brain, say). My physical brain has a Hilbert space associated to it, which is of course a subspace of the Hilbert space of the universal wavefunction.

So it is associated to the state vector of my brain that occurs in one of the terms in the wf:

|psi> = a|brain1*>|moon>|sun> + b|brain2>|moon>|sun>

Now, it cannot be associated with an entangled state. So as long as the sun and the moon interact amongst themselves, but not with the brain1 state, I remain in that state. Imagine that a quantum experiment projects the moon in the sun with amplitude 0.3:

|psi> = a |brain1*> (0.3 |mooninsun> + 0.99 |moon>|sun>) + b |brain2>|moon>|sun>

This is still ok, because brain1 didn't get entangled. But now I open my eyes and look through a telescope ; I will hence see whether the moon is in the sun or not. Through a long chain of unitary interactions, this entangles my brain state:

|psi> = a (0.3 |brain1A*> |mooninsun> + 0.99 |brain1B*> |moon>|sun>) + b |brain2>|moon>|sun>

However, that's not allowed: the consciousness cannot be associated to an entangled state of the brain, so now a choice must be made:
according to the Born rule, the token is now associated randomly to "brain1A" or to "brain1B" according to a 10% - 90% chance (the Hilbert norm squared). As this is something that happens locally to an interaction between the brain states and the token, it is really local. So say that the 90% option is stochastically taken, then the state is now:

|psi> = a 0.3 |brain1A> |mooninsun> + 0.99 a |brain1B*> |moon>|sun> + b |brain2>|moon>|sun>

and I observed that the moon didn't fall into the sun after all, with 90% chance.

OK, that's clarifying. I'm still worried that in order to have a real dynamics for all of this, you need some very clean rule for when the wf branches. Clearly this happens somewhere between your first and last expressions for psi. But when *exactly*? Wouldn't the moon crashing into the sun be such a massive macroscopic change that, after 8 minutes or whatever, your brain would get tangled in the superposition, whether you had looked through a telescope yet or not?

No, because you start from the previous "tokenized" state, and jump only to one of its daughter states.

Yes I see how you want this to work. A different question (that I think you answered before, but just to be clear): is there just *my* consciousness token, or does everybody have one? If everybody has one, there's near 100% probability that the other people's tokens are no longer in the same branch as mine, right? So all the people I see around me and talk to and (say) argue about physics with on the internet, are actually mindless hulks? (Not that I think that applies here... )

1) the dynamics is not deterministic and global, but it is stochastic and local

I still don't understand clearly in what sense the dynamics is local in 4-d spacetime.


BTW, where do consciousness tokens go when people die? (That's not a joke, I really want to know how that's supposed to work in this theory.)

 

[vanesch]

But you miss an incredibly important point by putting it this way. In BM, that is what is consciously experienced *because* that is (part of) the actual physical state of the objects being observed.

Ok, let us put it differently: "part of" is the intuitive notion of an unfaithful mathematical representation. By that, I mean: if (A,B,C) is the state, then "part of" the state is a function of (A,B,C), f(A,B,C). If it is unfaithful, it simply means that it is not 1-1, so that it is not because I know f(A,B,C) that I know (A,B,C).
Now, in BM, we have the couple {pos,wf}. And I can define "part of" as f(pos,wf) = pos.

In a similar way, in (my version of) MWI, I have the state {wf, mytoken}. Now of course my "part of" is not as simple, but I can unambiguously define f(wf, mytoken) = mybranch, namely the term in wf that contains mytoken.

And this is what's crucial, what you try to hide below: "part" here means literally *part*. The particle positions are *real*. Yes, there's also the wave function and when we wake up in the morning and open our eyes, we see only particles, not wf.

I see what you mean, but it is very easily mathematically turned around. After all, my state {wf, mytoken} can just as well be transformed in a 1-1 relation into {wf, mybranch}. And then "mybranch" is literally "part of" my state. A state is always defined up to a 1-1 function of course ; after all, our mathematical representation is only that: a representation.

The particle positions are real, as real as the wf, and it's those particles (not a branch of the wf) that we observe. End of story.

Well, as I showed above, I can very easily find a mathematical transformation of my state that obeys exactly the same thing. You mean that it is allowed to take "the first element of a pair" as real, but not the "term that is indicated by the other part". Well, I then transform my state as not just {wf, token} but into {termwithtoken,wf} and we're in exactly the same situation. The first element of the pair is what is "real".

What about fields and other such things? What about other people's consciousnesses?

I think you should re-read my previous post. I only need one token for myself, but I can introduce as many tokens as I wish. I can even introduce a token for each individual system (say, each individual particle) and call it the "particle position", exactly as in BM. It indicates the branch the particle would observe consciously if ever it were conscious. If it isn't conscious, then the token of the particle doesn't play any role: it doesn't enter in any dynamics.

There are all sorts of things which aren't directly observable in classical physics, yet this doesn't raise any problems. That I can't experience your consciousness directly doesn't mean my perception of this coffee cup is invalid.

Yes, but now we're not dealing with classical physics.

OK, that's clarifying. I'm still worried that in order to have a real dynamics for all of this, you need some very clean rule for when the wf branches. Clearly this happens somewhere between your first and last expressions for psi. But when *exactly*? Wouldn't the moon crashing into the sun be such a massive macroscopic change that, after 8 minutes or whatever, your brain would get tangled in the superposition, whether you had looked through a telescope yet or not?

Of course. Every little interaction that "carries the message" is sufficient for my brain state to split, of course. In fact, it is sufficient that the event is in the past light cone of my brain and for sure SOMETHING (a cosmic proton, whatever) will probably interact and make my brain state split.
When exactly ?
Doesn't really matter: during the unitary transformation, you would have 3 terms:
a |brain1> |stuff> + b |brain1A> |stufff> + c |brain1B> |stufff>
You can already apply the Born rule here: if I remain in brain1, I haven't yet noticed anything, if I am put to brain1A I already have state brain1A. If after that, there is still interference, and brain1A splits partly back into |brain1> and |brain1A> then you simply apply the Born rule again...

Yes I see how you want this to work. A different question (that I think you answered before, but just to be clear): is there just *my* consciousness token, or does everybody have one? If everybody has one, there's near 100% probability that the other people's tokens are no longer in the same branch as mine, right? So all the people I see around me and talk to and (say) argue about physics with on the internet, are actually mindless hulks? (Not that I think that applies here... )

Yes, you got it. It is indeed the fundamental difference with BM (and in fact the only way to save relativity). But "mindless hulks" are behaviourally not distinguishable from conscious bodies. *this* is the "solipsist" part.
You could think up of many solutions to this apparent riddle (which, I repeat, is not observable). For instance, you could "start" new consciousnesses. Or you could say (I'm in fact philosophically really favorable for that one) that there is in fact only one true consciousness, which is my own. Or you can give a consciousness to every particle in the universe.
But all this doesn't make any observational difference, so you fill in whatever suits you. I only need one consciousness in the whole business to explain my observations and that's good enough.

I still don't understand clearly in what sense the dynamics is local in 4-d spacetime.

Well, the unitarily evolving wf has local dynamics (can be made a geometrical object). The token "worldline" is a mapping from an "eigentime" tau into a pair of objects: one is a point in 4d (an event) and the other is a state in the Hilbert space of "mybrain". As long as no split occurs, the unitary evolution of "mybrain" determines the following point in 4d and so on ; decoherence makes that this unitary evolution remains "lumped in space", so this 4d world line segment makes sense.
When an interaction occurs with another system, then (because of the locality of the Hamiltonian), this can only happen at the same event in 4d. This interaction is then responsible for the split (entanglement) of the state in the brain Hilbert space with the state of this other system we're interacting with, but which must be localized in 4-d at the same event. As a result of this interaction we apply the Born rule (which can of course be completely determined at the same 4-d event), to jump to another brain state (one of the two entangled states, say), also associated with the same 4-d event. So all of this happens on a fibre associated with one single spacetime event, where the local interaction of my brain with another system took place.
In this, I tacitly assumed that decoherence will make us work in the position basis in the relevant Hilbert spaces, but that's probably the case.
As I said, I never worked this out in rigorous detail, but this intuitive sketch should be sufficient to at least make it plausible that this dynamics is local in spacetime.

BTW, where do consciousness tokens go when people die? (That's not a joke, I really want to know how that's supposed to work in this theory.)

Be my guest. Some even say that this is the secret of eternal life. Look after "quantum suicide" in the quant-phys archive, there's a very funny article about it. In that there is a modification to the Born rule in that your consciousness will always pick only one of the "live" states. Or just terminate the token worldline at the event where the "bad" choice is made into a dead brain state :-)

Admit that such a view is much more spicy than this boring particle position stuff in BM

No, seriously, to me, the point is that we CAN save relativity.

 

[ttn]

Ok, let us put it differently: ...

I had no doubts that you could suitably redefine "part" to make Bohm and MWI parallel. And given the way you did that, you're absolutely right. But I still stand by my earlier claim, that there is a real and prima facie difference between the two on this point. So let's just leave it at that, yes?

Yes, but now we're not dealing with classical physics.

I realize that. My point was just that there is no essential difference b/w Bohm and Classical physics in regard to consciousness.

Of course. Every little interaction that "carries the message" is sufficient for my brain state to split, of course. In fact, it is sufficient that the event is in the past light cone of my brain and for sure SOMETHING (a cosmic proton, whatever) will probably interact and make my brain state split.
When exactly ?
Doesn't really matter: during the unitary transformation, you would have 3 terms:
a |brain1> |stuff> + b |brain1A> |stufff> + c |brain1B> |stufff>
You can already apply the Born rule here: if I remain in brain1, I haven't yet noticed anything, if I am put to brain1A I already have state brain1A. If after that, there is still interference, and brain1A splits partly back into |brain1> and |brain1A> then you simply apply the Born rule again...

It's the "doesn't really matter" that bothers me. It's true, FAPP, it doesn't really matter. But in terms of being able to write down a clean theory. As you know, Bell criticized OQM as being "unprofessionally vague and ambiguous." This wasn't because it violated Bell Locality (though it does) and it wasn't because Bohr was a dumbass (though he was) -- it was because the dynamics of OQM hinges on the meaning of a certain human concept ("measurement") which has no precise meaning *in the theory*. So it's vague. Yes, yes, it makes no difference FAPP. But it's still ugly. And it seems like your version of MWI shares that bit of ugliness... which maybe isn't too surprising, given that it comes in in precisely the same way: when do you apply the Born rule? Well, when {vaguely waving arms}... and it doesn't make any difference in practice when *exactly* you do it.

Yes, you got it. It is indeed the fundamental difference with BM (and in fact the only way to save relativity). But "mindless hulks" are behaviourally not distinguishable from conscious bodies. *this* is the "solipsist" part.

Yes, I see. By the way, both for you and anyone else still reading this zombie of a thread, David Albert has some really nice articles on MWI. The classic one is I believe called "Interpreting the Many Worlds Interpretation", where he (and maybe a co-author??) introduce all the stuff about consciousness, talk about the "many minds" version of the theory, worry about mindless hulks and such. It's a good read for anyone that takes MWI seriously. I think there is also some good material along these lines in his book, "Quantum Mechanics and Experience", which I would also highly recommend. But I can't remember for sure what's in there since I haven't read it in a while. I also find it interesting that, for Prof. Albert, all of this stuff is essentially a reductio of MWI. If you have to go to these lengths, worrying about mindless hulks and all that silliness, you've clearly gone off the track somewhere. I agree with that sentiment completely, though I recognize the reasons that others (like vanesch here) don't.

You could think up of many solutions to this apparent riddle (which, I repeat, is not observable). For instance, you could "start" new consciousnesses. Or you could say (I'm in fact philosophically really favorable for that one) that there is in fact only one true consciousness, which is my own. Or you can give a consciousness to every particle in the universe.
But all this doesn't make any observational difference, so you fill in whatever suits you. I only need one consciousness in the whole business to explain my observations and that's good enough.

Good enough for you anyway.

Well, the unitarily evolving wf has local dynamics (can be made a geometrical object). The token "worldline" is a mapping from an "eigentime" tau into a pair of objects: one is a point in 4d (an event) and the other is a state in the Hilbert space of "mybrain".

That's the piece I'm missing. What is this "event" in 4-D? A moment of awareness of the consciousness? But where does that happen? In the brain? But where in the brain? etc... It's just very funny for consciousness (and nothing else!) to be having a worldline through spacetime. Or maybe I'm totally misunderstanding something.

Be my guest. Some even say that this is the secret of eternal life. Look after "quantum suicide" in the quant-phys archive, there's a very funny article about it. In that there is a modification to the Born rule in that your consciousness will always pick only one of the "live" states. Or just terminate the token worldline at the event where the "bad" choice is made into a dead brain state :-)

I'll check it out. But not until I've drained the beer molecules out of my next glass-shaped configuration of silicon particles.

Admit that such a view is much more spicy than this boring particle position stuff in BM

It is, it's great fun. A nice way to spend a semi-intoxicated weekend, before getting back to serious clear-headed Bohmian physics Monday morning.

No, seriously, to me, the point is that we CAN save relativity.

I know. For what it's worth, I think we can save it too -- in the same way we can save the laws of thermo or "p=mv" when we discover microphysics or relativity -- as a limiting case or approximation that applies just fine in some domain. Believing that relativity isn't the last word in spacetime structure isn't the same as tossing it and everything it's influenced in the garbage-can-shaped configuration of...

 

[vanesch]

Believing that relativity isn't the last word in spacetime structure isn't the same as tossing it and everything it's influenced in the garbage-can-shaped configuration of...

But I'm with you, here, in keeping open the possiblitiy that relativity is not the last word. Not for the same reasons, though. I think that "stuff will happen" on the GR / QM unification front and this might change the entire vision on it. At that moment, we can then tell another story. But for the moment all this is wishful thinking and relativity is still strictly part of our formal toolset and it is THAT formal toolset that has to be made sense out of. As long as we don't have another principle that replaces it (if ever), I think it is not a good idea to toss it. My point is that you cannot "toss it a bit". Relativity stands or falls, completely. ALL objects are 4-dim geometrical objects, or the 4-dim geometry doesn't make sense.
See, my main complaint I have about BM is that it is a theory that is not relativistic at all, but "plays one on TV". All the elements in the theory absolutely don't have to be 4-dim geometrical objects (because that 4-dim geometry clearly has no meaning, given that *part* of the theory is not geometrical), but for some unexplained reason, everything that pertains to the wavefunction has to look like it is a 4-dim geometrical object. It is as if you'd say that most of the laws of physics have to obey a form which is translation invariant, but the dielectric constant of the vacuum is depending on the distance from the left big too of my grandmother ; nevertheless it is somehow in principle forbidden to find out, from measurements, where exactly that big too is, so "translation invariance" gives somehow the impression to be respected. Clearly, as is, translation invariance is NOT a principle of nature. Ok, the big too of my grandma has maybe some profound influence on nature. But then, why did the laws of nature have to mimick such a non-existing translation invariance ??
The answer "well, it will probably turn out later that translation invariance is some approximate symmetry of nature induced by another principle" doesn't satisfy me as long as we don't have the slightest hint as what that other principle is ; in any case that other principle will then totally alter the entire formalism and hence the entire interpretation, so this renders useless the current exercise anyway.

 

[ttn]

See, my main complaint I have about BM is that it is a theory that is not relativistic at all, but "plays one on TV". All the elements in the theory absolutely don't have to be 4-dim geometrical objects (because that 4-dim geometry clearly has no meaning, given that *part* of the theory is not geometrical), but for some unexplained reason, everything that pertains to the wavefunction has to look like it is a 4-dim geometrical object. It is as if you'd say that most of the laws of physics have to obey a form which is translation invariant, but the dielectric constant of the vacuum is depending on the distance from the left big too of my grandmother ; nevertheless it is somehow in principle forbidden to find out, from measurements, where exactly that big too is, so "translation invariance" gives somehow the impression to be respected. Clearly, as is, translation invariance is NOT a principle of nature. Ok, the big too of my grandma has maybe some profound influence on nature. But then, why did the laws of nature have to mimick such a non-existing translation invariance ??
The answer "well, it will probably turn out later that translation invariance is some approximate symmetry of nature induced by another principle" doesn't satisfy me as long as we don't have the slightest hint as what that other principle is ; in any case that other principle will then totally alter the entire formalism and hence the entire interpretation, so this renders useless the current exercise anyway.

I understand your point of view, but, not surprisingly, I don't agree with it.

In BM we do have a fair sense of at least one candidate for a new principle to replace Lorentz invariance: quantum equilibrium. Valentini had some very cool papers about this in the 90's. If you assume BM but *don't* assume that the initial particle positions are |psi|^2 distributed, you can do all sorts of crazy things: you can beat the Heisenberg uncertainty principle, you can signal faster than light, etc. In other words, a Bohmian universe in quantum equilibrium will forbid faster-than-light signalling *because of* quantum equilibrium -- it is quantum equilibrium that gives rise to the apparent Lorentz symmetry (and some other things like HUP). This is just a brief sketch, but it's the kind of point that can be elaborated more if you think following a Bohmian path is somehow "sterile" theoretically because you are left with no guiding principles (having junked fundamental relativity).

 

[vanesch]

I understand your point of view, but, not surprisingly, I don't agree with it.

In BM we do have a fair sense of at least one candidate for a new principle to replace Lorentz invariance: quantum equilibrium.

Ok, I don't know much about this (read some stuff when we had a previous discussion, but only sketchy). However, I think you don't see exactly what my criticism is. The point is not that you can add something (like quantum equilibrium) to restore Lorentz invariance. It is, by itself, not sufficient. The interactions, described by the unitary quantum evolution (the lagrangian, or the hamiltonian) need also to be Lorentz in variant, otherwise quantum equilibrium will not save it.
What I mean, for instance, is that in the Lagrangian of a quantum field theory, the lagrangian density needs to be a Lorentz scalar (a geometrical object over 4-dim spacetime). This is an enormously powerful principle, which, from gazillions of possible theories, only leaves out very few, and those that happen to work in the lab are exactly picked out of those few. It is this underlying 4-dim geometry, which is first destroyed in BM, and then restored with something like quantum equilibrium. But because of the destruction, it means that this 4-dim geometry is meaningless, so there's no reason, in the first place, to have this Lorentz-invariant Lagrangian density. And if you do not have that (you do not have a lorentz-invariant unitary evolution), then quantum equilibrium will not "restore" it for you. It can only restore it because it was already built into the unitary evolution. And THIS is incomprehensible to me: why would nature obey this 4-dim geometry, if the geometry is in fact meaningless ; in such a way that all *observable* stuff, again, seems to obey that 4-dim geometry. This seems to me to indicate that the intermediate step, which makes the 4-dim geometry meaningless, is misguided. And this intermediate step is exactly the non-geometric evolution equation for the particle positions.
Before you reiterate your (justified) critic of OQM, I agree that it suffers from exactly the same problem of course if you introduce an "ontological collapse" (and it suffers from a SECOND problem, which is unrelated to it, and which is the vagueness in what mechanism is responsible for the collapse - in a certain way, it is with this vagueness that I'm struggeling too ; everybody has his own problems :-).

It might be, of course, that a totally different underlying principle can tell us why nature DOES seem to obey this 4-dim geometry while it isn't there. It is something like that that I'm secretly hoping for, but it's not in sight, is it. And that's why I find it "dangerous" to toss out this 4-dim geometry before knowing what will force us to introduce it again.

 

[ttn]

Ok, I don't know much about this (read some stuff when we had a previous discussion, but only sketchy). However, I think you don't see exactly what my criticism is. The point is not that you can add something (like quantum equilibrium) to restore Lorentz invariance. It is, by itself, not sufficient. The interactions, described by the unitary quantum evolution (the lagrangian, or the hamiltonian) need also to be Lorentz in variant, otherwise quantum equilibrium will not save it.

Oh, I think you just misunderstood my point (perhaps because I misunderstood yours earlier?). I wasn't claiming that the concept of quantum equilibrium (in Bohm's theory) saves Lorentz invariance. It doesn't. If Bohm is right, then Lorentz invariance *as a fundamental principle* is dead, at least so far as I can tell. So my point wasn't to save it. I thought part of what you were saying before was that, without that basic theory-constraining principle, we'll be "lost at sea". Well, my point was that something like quantum equilibrium could provide a deeper, replacement principle that could perhaps guide future theory construction, guide people in making bold but not crazy predictions for worthwhile things to study empirically (eg, looking for plausible effects of quantum non-equilibrium), etc.

I wouldn't want to push this point too hard. Who knows if "quantum equilibrium" is the new "Lorentz invariance" for the 21st century. My point was more just the principle of the thing: just because you accept Bohm (and hence deny Lorentz invariance as a fundamental principle) doesn't mean you won't have any good ideas for how to move knowledge forward in the immediate future.

And THIS is incomprehensible to me: why would nature obey this 4-dim geometry, if the geometry is in fact meaningless ; in such a way that all *observable* stuff, again, seems to obey that 4-dim geometry.

Well the nice thing about the concept of quantum equilibrium is that it answers precisely this question. Hence, while on the one hand Bohm requires you to reject Lorentz invariance as a fundamental principle, it also provides a framework for actually making sense of the curious fact that Lorentz invariance seemed to serve so well as a guiding principle.

It might be, of course, that a totally different underlying principle can tell us why nature DOES seem to obey this 4-dim geometry while it isn't there. It is something like that that I'm secretly hoping for, but it's not in sight, is it. And that's why I find it "dangerous" to toss out this 4-dim geometry before knowing what will force us to introduce it again.

Your position is not unreasonable here, but it's also reminiscent of the view taken by, e.g., the "energeticists" in the late 19th century. They liked to remind each other that the continuous differential equations of classical thermodynamics had served us so well, that there seemed to be no good reason to reject that fundamental principle of continuity for some crazy idea like the atomic theory of matter. I'm sure they all thought that physics would be lost at sea without this fundamental principle of "smoothness" (as opposed to granularity, atom-ness) that had had so much success (all the differential equations of classical physics, etc). It's a valid point, but hardly strong evidence against the existence of atoms. In fact, I'd even admit that people were right to be somewhat suspicious until at least the atomists were able to show that their theories reduced to the continuous, macro, classical view in a certain limit.

All of this is rather parallel to the current debates over the interp of QM. The only difference is: now we know for sure there are atoms, but we don't yet know for sure that Bohm is right about QM.

 

[vanesch]

Hence, while on the one hand Bohm requires you to reject Lorentz invariance as a fundamental principle, it also provides a framework for actually making sense of the curious fact that Lorentz invariance seemed to serve so well as a guiding principle.

This is what I fail to see. If lorentz invariance is "dead", what stops me from writing terms in the Lagrangian which are not lorentz invariant, in which case I will see deviations from Lorentz invariance in the lab, no matter whether there is quantum equilibrium or not ? So how can quantum equilibrium "make sense" of the fact that Lorentz invariance IS actually observed (ie, that we need to write Lorentz invariant terms in the Lagrangian ?)
It seems that in doing so, we've LOST a lot of understanding, no ? You will argue that we've lost an illusion and are now ready to move on, but nothing *replaced* our previous illusion of an understanding.

Your position is not unreasonable here, but it's also reminiscent of the view taken by, e.g., the "energeticists" in the late 19th century. They liked to remind each other that the continuous differential equations of classical thermodynamics had served us so well, that there seemed to be no good reason to reject that fundamental principle of continuity for some crazy idea like the atomic theory of matter. I'm sure they all thought that physics would be lost at sea without this fundamental principle of "smoothness" (as opposed to granularity, atom-ness) that had had so much success (all the differential equations of classical physics, etc).

The analogy doesn't work completely, and the difference is my point: The proponents of an atomic theory REPLACED the continuity principle by another one FROM WHICH THEY COULD DERIVE the apparent continuity on macroscopic scales. I wanted to indicate that quantum equilibrium in BM DOES NOT allow you to derive apparent lorentz invariance if you do not put it in by hand in the unitary dynamics.

I can buy your argument in the following sense: the status of BM is that somehow they're convinced that smoothness is NOT, finally, a fundamental principle of nature, but they've not yet thought up the atomic theory.
My point is that such an argument is moot: I can then clearly state that whatever we know today are indeed NOT fundamental principles of nature, only, I haven't yet thought up any alternative :-) It is not going to get me very far unless I have a brilliant flash of inspiration in the coming days. In the mean time, I stick with what works today...

 

[ttn]

This is what I fail to see. If lorentz invariance is "dead", what stops me from writing terms in the Lagrangian which are not lorentz invariant, in which case I will see deviations from Lorentz invariance in the lab, no matter whether there is quantum equilibrium or not ? So how can quantum equilibrium "make sense" of the fact that Lorentz invariance IS actually observed (ie, that we need to write Lorentz invariant terms in the Lagrangian ?) It seems that in doing so, we've LOST a lot of understanding, no ? You will argue that we've lost an illusion and are now ready to move on, but nothing *replaced* our previous illusion of an understanding.

Ah, you're getting to know me well. If *fundamental Lorentz invariance* is an illusion, then it represents a step in the right direction to recognize this clearly. And by the way this is true whether anything replaces the illusion or not. It's better to stop believing one lie and have nothing to put in its place (right away) than to pretend one knows a lot by believing the lie.

The analogy doesn't work completely, and the difference is my point: The proponents of an atomic theory REPLACED the continuity principle by another one FROM WHICH THEY COULD DERIVE the apparent continuity on macroscopic scales. I wanted to indicate that quantum equilibrium in BM DOES NOT allow you to derive apparent lorentz invariance if you do not put it in by hand in the unitary dynamics.

Oh, I see your point. So you're saying if we take some N-particle dirac theory (just to give an example of a theory for which a Bohmian version is actually known to exist), we can prove that "superluminal signalling" is impossible only in quantum equilibrium, and thus (in a certain sense) explain the origin of observed Lorentz invariance. But you're saying: the Dirac equation is still Lorentz invariant, and we have no explanation for that.

That's true. I'm not sure what to say that I haven't said before, though. It's better to know that a certain feature is unexplained than to hold onto a false explanation of it. The first makes it possible that you'll eventually discover the true explanation; the second prevents this possible future progress.

I can buy your argument in the following sense: the status of BM is that somehow they're convinced that smoothness is NOT, finally, a fundamental principle of nature, but they've not yet thought up the atomic theory.
My point is that such an argument is moot: I can then clearly state that whatever we know today are indeed NOT fundamental principles of nature, only, I haven't yet thought up any alternative :-) It is not going to get me very far unless I have a brilliant flash of inspiration in the coming days. In the mean time, I stick with what works today...

This is a very strange attitude. Does anyone actually think that rapid progress in the "coming days" is going to be made by some first year grad student writing down only Lorentz scalar terms in the Lagrangian of some field theory? Nobody has made any serious progress on anything significant in that way for decades, as far as I know. In fact nowdays it's just the opposite: people postulate non-Lorentz-invariant terms to explain the observed violations of GZK cutoff for high energy cosmic rays, etc.

Real progress of the kind that interests me, at least, comes from understanding the correct ontology for microphysics. If Bohm is that correct ontology, then it is huge major step in the right direction even to recognize that for non-rel QM. I know it wasn't the mapping I intended originally, but maybe that's the fundamental parallel to the atomic theory. If theorists are more concerned these days with figuring out what terms they should permit students to write in Lagrangians than in figuring out what the real world is like at small scales, then something is seriously wrong.

 

[vanesch]

It's better to stop believing one lie and have nothing to put in its place (right away) than to pretend one knows a lot by believing the lie.

Then this is where we agree to disagree. I think at ANY moment in history (past or future) our understanding of nature will ALWAYS be "superficial", in that we will ALWAYS only know some "illusion". We can only hope for the fact that the illusion will be better and better, going from some paint on a cave wall over black and white photography to THX sound systems and 3-D goggles in a movie theatre.
I prefer watching the movie than somebody switching off the projector and yelling that it is just a movie :-) However, contrary to the epistemologists, I nevertheless think that in order for the illusion to be an acceptable illusion, it has to do the big game, and present an illusion of an ontology: a story (not correct of course) needs to come with the illusion of how things "really" are. But the story is only that: a story to complete the illusion. In more serious terms, what I call "illusion" is usually called "paradigm". And in THIS context, I think it should be clear (also to you, even if you don't agree), that it is not reasonable to do away with part of the illusion and not replace it with something else (which will, in any case, again be another illusion).
So, today, at the beginning of the 21st century, we have an "illusion" which explains quite a lot, and consists of 2 principles: relativity and (unitary) quantum theory. It is for this illusion that I want a story (and as you rightly point out several times, the USUAL story of OQM is not consistent of course).
Now, saying that the story is silly and that a much more "realistic" story, with particles, is the way to go, but doing away with part of the paradigm is, IMHO, not the thing to do, because you have now LESS explanatory power (relativity being gone and not replaced).
You are free of course to set up another illusion (paradigm), have a story that goes with it and so on, but in order for it to be an improvement, it need AT LEAST to explain everything which the previous illusion could explain. Saying that my illusion is fundamentally wrong is no news! I know that! And yours is just as wrong and the theories we'll have 500 years from now will be just as wrong.
I think the only REAL illusion, at any point, is to think we NOW know fundamentally what is ultimately right. It is the only statement which has been proven wrong systematically throughout all of history. THIS statement is probably fundamentally right :-) Eh...

Oh, I see your point. So you're saying if we take some N-particle dirac theory (just to give an example of a theory for which a Bohmian version is actually known to exist), we can prove that "superluminal signalling" is impossible only in quantum equilibrium, and thus (in a certain sense) explain the origin of observed Lorentz invariance. But you're saying: the Dirac equation is still Lorentz invariant, and we have no explanation for that.

Yes, exactly.

That's true. I'm not sure what to say that I haven't said before, though. It's better to know that a certain feature is unexplained than to hold onto a false explanation of it. The first makes it possible that you'll eventually discover the true explanation; the second prevents this possible future progress.

In a way I could return the argument and saying that you want to cling onto a configuration space of particles as in good old Newtonian physics prevents this possible future progress. As long as the future progress is not on the table, there's no way to tell !

This is a very strange attitude. Does anyone actually think that rapid progress in the "coming days" is going to be made by some first year grad student writing down only Lorentz scalar terms in the Lagrangian of some field theory? Nobody has made any serious progress on anything significant in that way for decades, as far as I know.

I'd say that theoretical physics hasn't done much ELSE the last 50 years ! From QED up to string theory.

In fact nowdays it's just the opposite: people postulate non-Lorentz-invariant terms to explain the observed violations of GZK cutoff for high energy cosmic rays, etc.

I don't know much about this but the point is of course that from the moment that you relax, for your specific application, some general principle, your "explanatory possibilities" become much larger. If it weren't already the case in this thread, as an example I'd cite Bohmian mechanics :-) The difficulty resides then in re-explaining, without the doomed general principle, everything which was already explained by it, the exercise I wanted you to do.

But I can understand your point too: if relativity is a wrong principle, then tossing it out is the first step in finding a better one ; nevertheless, the intermediate situation, where the "wrong" principle is tossed out, but the better one is not found yet, should remain confined to the studyroom of the genius that will find the better principle. This intermediate step is NOT a theory of course :-)
Otherwise I'll find an even better theory: relativity AND quantum theory are wrong. There. :-)

If theorists are more concerned these days with figuring out what terms they should permit students to write in Lagrangians than in figuring out what the real world is like at small scales, then something is seriously wrong.

I had the impression that was what people did in most of the 20th century. Something is rotten in this country :-)

 

[ttn]

...contrary to the epistemologists, I nevertheless think that in order for the illusion to be an acceptable illusion, it has to do the big game, and present an illusion of an ontology: a story (not correct of course) needs to come with the illusion of how things "really" are. But the story is only that: a story to complete the illusion. In more serious terms, what I call "illusion" is usually called "paradigm". And in THIS context, I think it should be clear (also to you, even if you don't agree), that it is not reasonable to do away with part of the illusion and not replace it with something else (which will, in any case, again be another illusion).

Well, we have a significant philosophical difference then. I think we actually know what we know (though of course we don't know everything). You think we know nothing, that everything we could believe is an illusion, and the only serious question is whether the illusion you posit is in some superficial sense consistent with your personal mental experience. I guess this explains why you advocate this strange solipsist version of MWI. Try as I might, I can't even bring myself to take that idea seriously. It just isn't a serious theory in the way meant by such scientific realists as Einstein and Bell.

So, today, at the beginning of the 21st century, we have an "illusion" which explains quite a lot, and consists of 2 principles: relativity and (unitary) quantum theory. It is for this illusion that I want a story (and as you rightly point out several times, the USUAL story of OQM is not consistent of course).
Now, saying that the story is silly and that a much more "realistic" story, with particles, is the way to go, but doing away with part of the paradigm is, IMHO, not the thing to do, because you have now LESS explanatory power (relativity being gone and not replaced).

"Explanatory power" is not a subjective game. It's about what is true, what corresponds to the way the real world actually is. Lies have zero explanatory power.

You are free of course to set up another illusion (paradigm), have a story that goes with it and so on, but in order for it to be an improvement, it need AT LEAST to explain everything which the previous illusion could explain. Saying that my illusion is fundamentally wrong is no news! I know that! And yours is just as wrong and the theories we'll have 500 years from now will be just as wrong.

And to think, all this time I wasted trying to convince you that your beliefs were a mere illusion. Now you say you knew it all the time. Sigh...

I absolutely do not believe that in 500 years we will all believe that the world is flat, that matter is not atomic, that DNA plays no role in inheritance, etc. We actually *know* some things, things about how the world acutally *is*, and science has as its goal finding out *more* things. All I can say is, if you disagree with that it's no wonder you don't see why Bohm is a serious and promising theory.