Is QM Inherently Non-local in EPR and Bell Discussions?

[Careful]

You still seem to see an observer as something absolute. But it is not. A stone could be an observer - a conscious one. You'll never find out (that's a well-known philosophical problem). There is not more a fundamental problem in considering "observer + rest" this way, than to consider a world line of an observer in GR, and the way this observer sees the universe. In exactly the same way, a "quantum observer" will see what happens along its "quantum world line", this time including its entanglement with whatever it is interacting locally with and making his "Born rule choices" in tracing out its world line.
This is not so very much stranger than an observer falling into a black hole observing (just before getting crushed) the entire universe's future (and hence being fried by all the radiation he gets at once).

Come on: conscious stones, we will come to highly intelligent electrons later on ! (that is one way to get realist theories which give quantum outcomes) Let me give some further objections to your already highly unrealistic point of view. I understand very well what you mean by your local observation operators, what you don't seem to understand is that you will need to create another bunch of superselection rules in order to figure out what the *localized* ``ground state´´ it is, your conscious mind is into, as well as the dynamical rules of the mind field operators (you are nowhere near doing this as far as I know) *** however for the localized vacuum consciousness state you might construct an adapted coordinate system in a tube around the classical worline and use the exponential map on the orthogonal space of the worldline; this could allow you to play the same Fourier analysis trick for functions vanishing outside this tube. However, I do not see how you could avoid the localized mind state from diffusing (which is one particular aspect of the cat problem) outside the tube so my guess is that you end up with a global state after all. Moreover, it is (a) a notoriously difficult problem to select the vacuum state for the universe and in any semiclassical approach (it is done wrt a preferred global congruence of observers in the classical solution) (b) your conscious mind state has to be localized, so it will be very difficult for you to couple it to the traditional QFT particle vacuum states since these are after all globally defined (that is one reason why I said the notion of particle in QFT is worth nothing) as well as to divise dynamics which keeps it local (the cat you do not want to tame). Now in quantum gravity, this becomes even more hopeless... moreover in quantum gravity, one of the motivations is that we figure out how a singularity smears out inside a black hole (your observers cannot even come there).

Short about the rest: I think the point SED is trying to make is that there is a background field which is in *equilibrium* with the environment, moreover, I am sure they introduce cutoffs in the modes too (no infinite energies). They do not explain the equilibrium from microphysics (which is for now still a weak point in my view), it is put as a constraint on the stochastic dynamics. I admit what I try to point out are HOPES. As we both know, the self field approach does not deviate much (the examples you gave showed a deviation of about two percent) from ``real´´ QM and that should be seen as hopeful. So, I have a clear guideline (indeed quantum chemistry) and a small percentage to bridge, and no, there has been no real attempt based in gravitation and classical EM to do this as far as I am aware of. I have surprised you a few times already, hope to do it in a more decisive way later on
It was nice talking to you.

Cheers,

Careful

PS: concering your computational efficiency, I disagree again. I will have to work with quite complicated matter models and highly non linear dynamics so that spoils it a bit.

 

[vanesch]

your conscious mind is into, as well as the dynamical rules of the mind field operators

That's the error often made: the "mind" is not a physical degree of freedom. There is no such thing as a "mind operator". Minds are simply associated with whatever physical structure we consider to be an observer ; or better, with the possible states these physical structures can be in. They are, if you want, an "asterix" on ONE term in the state of the universe in which one writes the state of the universe in a Schmidt decomposition (or a coarse-grained such decomposition) into "this physical structure" x "all the rest". In order to do so, you might need a foliation of spacetime ; why not take the one that corresponds to an observer frame that corresponds to the state of motion of the "previous" state of that physical structure, with an asterix ? (of course different states of the same physical structure can be in different motion states, and hence correspond to different world lines, but let's say that we only care about the one with the asterix). If a new interaction (unitary) entangles this "asterix state" with another state of something else, then the "asterix" goes now, following the Born rule, to one of these terms. This is then experienced by that mind as a "measurement" and is only aware of the state with the asterix.

I fail to see where the fundamental difficulty comes from (as long as we do not do quantum gravity).

PS: concering your computational efficiency, I disagree again. I will have to work with quite complicated matter models and highly non linear dynamics so that spoils it a bit.

I don't know if you have looked into computational quantum chemistry, but the "full" problem is almost intractable, hence the many smart selections of those few states that "ought to contribute". On something like a molecule that interests me, CF_4, you have 6 + 4 x 9 = 42 electrons, which means that (naively, ok, there are symmetries to be exploited) you have to find a set of solution functions of 126 real variables to find, as a result of a partial differential equation of second order in these 126 variables. True, the differential equation is linear, so what ? If I'd take, say, as an approximation, 50 hydrogen orbitals as a set of basis functions, then this gives me a priori a linear system of 50^42 variables to solve (again, modulo symmetries).
If I take a non-linear classical problem with an "electron field", I don't care how many of them are around; if I cut space up into, say, 100.000 cells in each dimension, I "only" have to solve a system of 10^15 variables to solve (iteratively, true, because the system is non-linear). That's difficult, but still easier.

cheers,
Patrick.

 

[Hurkyl]

The only way, in my opinion to solve schroedingers cat, is to make quantum theory non linear (another reason why I am keen on the self field approach) just as all realistic processes in nature are.

Out of curiousity, what do you find wrong with the following "solution"?

Suppose you had an experiment to detect whether the cat is "both" dead and alive. (according to whatever meaning you wanted to ascribe to this)

Then, since any state can be decomposed into two states, the first of which is internally consistent with the cat being 100% alive (and thus your experiment gives you a "no" answer, and the other internally consistent with the cat being 100% dead (and thus your experiment gives you a "no" answer), we must conclude that your experiment must always give a "no" answer.

In other words, there can be no observable oddities from the Schrödinger cat scenario.

 

[member 11137]

This discussion appears to be “semantic” dependant. If you accept a non professional in your discussion, first nobody seems to have the same definition for what the word “local” means. Secondly, and if you consider that physical phenomenon at quantum scale are concerning waves and correlated functions extended through space time (a little bit like at the surface of the see) I would intuitively say that: 1°) a wave alone is everywhere in space and in time. Such that two different observers placed at two different points in the universe could “see” the same and unique wave at the same time (“same time” being dependant on the practical tools that these two observers own to exchange and correlate informations concerning the wave). But we neglect here the fact that they need at least one other wave to transfer these informations concerning the first one; 2°) the concept of locality certainly is depending on the scale to which phenomenon are observed. This is for a part explaining why it is difficult to adopt a common point of view on what is local or not. For a phenomenon with the Planck’s length occurring inside a proton (e.g.), or between the proton and an electron, adopting a kind of classical point of view it is not sure that the proton or that the electron appears to be local… On the other side, the waves (functions) associated with this proton and this electron certainly extend until the region where this quantum phenomenon exists. 3°) For me and because of this, the concept of waves makes that nothing can be totally local as long as it stays inside the light- or the information-cone of something else. 4°) This vision explains the next one: space time itself is a fluctuating phenomenon. 5°) Concerning my vision: if a subset of these fluctuations is corresponding to what we call an identified particle, nothing is theoretically forbidding that a part of the particles are dual one or able to become dual, like two twin sisters, like two correlated balls of billiard. Can this vision help to understand the EPR experiment?

 

[member 11137]

To complete the above post I could recommand a recent article by Aharonov where (if I understand correctly) he is defending the idea that any event stays at the boarder between the past and the future; based on this idea he gives a re-definition of the probabilities, a.s.a...

 

[Sherlock]

Out of curiousity, what do you find wrong with the following "solution"?
Suppose you had an experiment to detect whether the cat is "both" dead and alive. (according to whatever meaning you wanted to ascribe to this)
Then, since any state can be decomposed into two states, the first of which is internally consistent with the cat being 100% alive (and thus your experiment gives you a "no" answer, and the other internally consistent with the cat being 100% dead (and thus your experiment gives you a "no" answer), we must conclude that your experiment must always give a "no" answer.
In other words, there can be no observable oddities from the Schrödinger cat scenario.

It makes sense to me. I've learned to think of the S-cat thing, and associated qm interpretational issues, as a non-problem. Sort of like the ancient Greek argument that arrows can't reach their targets. (A lot of Greeks died believing that.) :-)

Anyway, I've reached a conclusion about the question of this thread that I think is ok. Quantum theory is not inherently non-local -- and interpreting the theory to be local or non-local is a matter of how one chooses to understand the *bases* for the formalism (not what sort of non-physical stuff one can generate from its use, or abuse).

 

[Careful]

I don't know if you have looked into computational quantum chemistry, but the "full" problem is almost intractable, hence the many smart selections of those few states that "ought to contribute". On something like a molecule that interests me, CF_4, you have 6 + 4 x 9 = 42 electrons, which means that (naively, ok, there are symmetries to be exploited) you have to find a set of solution functions of 126 real variables to find, as a result of a partial differential equation of second order in these 126 variables. True, the differential equation is linear, so what ? If I'd take, say, as an approximation, 50 hydrogen orbitals as a set of basis functions, then this gives me a priori a linear system of 50^42 variables to solve (again, modulo symmetries).
If I take a non-linear classical problem with an "electron field", I don't care how many of them are around; if I cut space up into, say, 100.000 cells in each dimension, I "only" have to solve a system of 10^15 variables to solve (iteratively, true, because the system is non-linear). That's difficult, but still easier.
cheers,
Patrick.

EVERYTHING is PHYSICAL ! Concerning your computability argument: I said I would have to consider realistic electron models and perhaps another local interaction field (a spin field such as in einstein cartan theory perhaps, but I would not like to do that). So I will have to be a lot more creative than what you are hinting to and I do not a priori know what number of degrees of freedom I will end up with. And indeed, hopefully less than the number you hint at; but non linearities always bring subtle difficulties :-)

Cheers,

careful

 

[Careful]

Out of curiousity, what do you find wrong with the following "solution"?
Suppose you had an experiment to detect whether the cat is "both" dead and alive. (according to whatever meaning you wanted to ascribe to this)
Then, since any state can be decomposed into two states, the first of which is internally consistent with the cat being 100% alive (and thus your experiment gives you a "no" answer, and the other internally consistent with the cat being 100% dead (and thus your experiment gives you a "no" answer), we must conclude that your experiment must always give a "no" answer.
In other words, there can be no observable oddities from the Schrödinger cat scenario.

Huh ?? If you allow for a macroscopic state in which the cat is both alive and dead (an experiment which could decide upon that) then the alive and dead states do not form a complete basis.

 

[Careful]

It makes sense to me. I've learned to think of the S-cat thing, and associated qm interpretational issues, as a non-problem. Sort of like the ancient Greek argument that arrows can't reach their targets. (A lot of Greeks died believing that.) :-)
Anyway, I've reached a conclusion about the question of this thread that I think is ok. Quantum theory is not inherently non-local -- and interpreting the theory to be local or non-local is a matter of how one chooses to understand the *bases* for the formalism (not what sort of non-physical stuff one can generate from its use, or abuse).

How how, the S cat problem attracks still a lot of research (at eminent research centres) and it is not philosophy at all. The rest of your conclusion might be true but (a) we do not know wether realistic interacting QFT's satisfy the Wightman axioms (b) you have to really solve the cat in my opinion.

 

[Hurkyl]

Huh ?? If you allow for a macroscopic state in which the cat is both alive and dead (an experiment which could decide upon that) then the alive and dead states do not form a complete basis.

Let's start with this: why do you think the Schrödinger cat scenario is a problem?

 

[Careful]

Let's start with this: why do you think the Schrödinger cat scenario is a problem?

Very simple: you have to show a couple of things (a) how come do we only observe dead or alive cats (while QM allows for both at the same time), how can we dynamically derive from QM what macroscopic states are allowed in nature (b) why, and from what scale on, do objects satisfy the classical laws of nature and behave as classical non fuzzy objects (take care here: the argument that the mass simply gets large is not sufficient here) (c) why is Bell locality such a good principle from a scale of 10^{-8} meters in our universe while QM would predict entanglement as the generic rule. These topics are the centre of very active research and are not solved by any means if you wish to stick to unitary mechanics. Usually people try to dispose of them by using handwaving (often incorrect (!)) quantum statistical arguments. You undoubtedly saw that Vanesh had to cook up a non dynamical parallel mental world (which he cannot explain) coupled to the physical word in order escape from this. Moreover, most MWI's think differently about this and really want to pursue the points I mentioned.

 

[Hurkyl]

(a) how come do we only observe dead or alive cats (while QM allows for both at the same time)

This is exactly what my post was addressing.

QM allows both at the same time only in the sense that it allows a superposition of states in some of which the cat is unambiguously alive, and the rest in which the cat is unambiguously dead.

Therefore, it is impossible for any experiment to distinguish between a state in which the cat is unambiguously dead or alive, and a state in which we have both "at the same time". In other words, we only observe dead or alive cats.

 

[Careful]

This is exactly what my post was addressing.
QM allows both at the same time only in the sense that it allows a superposition of states in some of which the cat is unambiguously alive, and the rest in which the cat is unambiguously dead.
Therefore, it is impossible for any experiment to distinguish between a state in which the cat is unambiguously dead or alive, and a state in which we have both "at the same time". In other words, we only observe dead or alive cats.

Oh yeh, what in QM tells me that I do not have projection operators on such superpositions (which are clearly non commuting with the pure dead and alive projection state operators). By the way all these states can clearly be distinghuised from a statistical point of view (for example vanesh would be able to do this, since his consciousness does not intervene and has to produce the correct statistical results). First, perhaps tell me what measurement procedure you use, reduction/consciousness or environmental decoherence). You should also comment on the other issues which were subject of many papers of Zurek and others...

 

[Hurkyl]

Careful: none of this is answering my question to you. You have made the claim:

The only way, in my opinion to solve schroedingers cat, is to make quantum theory non linear (another reason why I am keen on the self field approach) just as all realistic processes in nature are.

which, of course, begs the question "In your opinion, why must other approaches fail?"

My inability to prove that an alternate approach completely addresses the question is not a proof that other approaches fail. It is not even evidence that the approach is lacking, since the fact I am not a quantum physicist is more than sufficient to explain my inability!

Oh yeh, what in QM tells me that I do not have projection operators on such superpositions (which are clearly non commuting with the pure dead and alive projection state operators).

I never said you didn't. But, I don't see how such projection operators would allow one to experimentally distinguish between a cat that's alive or dead and a cat that's alive and dead.

Maybe I should explain why I mean more formally? If M is an operator that satisfies:

M(any-living-cat-state) = 0
M(any-dead-cat-state) = 0

Then we must have that M is the zero operator.

In particular, this means there cannot be an experiment that gives one result when applied to a cat that's dead or alive, and some different result when applied to a cat that's both dead and alive.


This answers the question of why we don't perceive some chimeric dead-and-alive hybrid cat: any perception we make must be consistent with a cat that's either dead or alive.


Being able to tell statistically is something entirely different: sure, if we had many different copies of a dead-and-alive superposition, we could observe them and see that some turn into living cats and some turn into dead cats, and thus we know the underling state was a superposition, but AFAIK, that's not the paraodx -- the paradox is why we don't see a chimeric dead-and-alive hybrid cat.

First, perhaps tell me what measurement procedure you use, reduction/consciousness or environmental decoherence).

I'm not entirely sure I understand this question properly.

At the moment, I internalize the notion of measurement as being essentially synonymous with computing a function in a quantum computer: I take as input the state

phi x |unmeasured>

and produce as output:

phi1 x |1> + phi2 x |2> + ...

where phi = phi1 + phi2 + ...

and have thus performed a measurement.

 

[Sherlock]

How how, the S cat problem attracts still a lot of research (at eminent research centres) and it is not philosophy at all.

You say that the S-cat problem is:
a) How come we only observe dead or alive cats, while QM allows for both at the same time.

Hurkyl has provided one way to understand this. The way I think about it is that the cat is a measuring instrument, like a PMT in optical Bell tests. A dead cat means that a particle was emitted from the radioactive substance during a certain time interval initiated by opening the radioactive substance's enclosure. Until the cat dies, it's alive. We know this by continually monitoring it. Just like a PMT either registers a detection, or it doesn't during a certain interval. Of course there's an interval during which the cat is in the process of dying and the PMT is in the process of registering.

QM does not allow for cats to be both alive and dead, or PMTs to both register and not register during a certain instant of time, in any physical sense. Alive, dead, not register, register -- are simply the possible results of the experiment (ie., the macroscopically allowed states -- which QM does specify). Dead cats and PMT-generated data streams are unambiguous and irreversible.

So, this doesn't seem to be a problem.

You continue with:
b) why, and from what scale on, do objects satisfy the classical laws of nature and behave as classical non fuzzy objects?

This is a harder question. The correspondence line is fuzzy and changes as technological capabilities progress. I suppose that distinguishing the quantum and classical 'realities' will always be somewhat fuzzy. (eg., they can quantum entangle systems consisting of thousands of atoms now). But whether a beaker of cyanide gas is broken or not, or a cat dead or alive, is not fuzzy. Whether a piece of radioactive material has emitted a particle or not is somewhat fuzzy. The macroscopic behavior (measurement result) of the barrier that is used to intercept and detect the particle isn't at all fuzzy.

Why is the particle-emission behavior of the radioactive substance fuzzy (ie., random)? Because the only information that we have about these materials pertaining to particle emissions comes from putting detectors next to them and noting when they register. Of course it's more complicated than that, but nonetheless the info is still pretty spotty.

I see this as essentially an instrumentation and detection problem.

And you conclude with:
c) why is Bell locality such a good principle from a scale of 10^{-8} meters in our universe while QM would predict entanglement as the generic rule?


Bell locality isn't at odds with quantum entanglement.

Bell locality, P(A|a) = P(A|a,B,b), isn't really an arbiter of locality. Bell locality is about the independence, or dependence, of observations and their associated statistics. (Assuming that dependence of spacelike separated measurements implies non-locality is, imo, wrong.) QM says that entangled measurements, A and B, and associated observational parameters, aren't independent. Why? Because the disturbances that eventually produced A and B originally came from the same emitter, or had interacted with each other, or were altered in some way common to both, and are being analyzed and detected by the same sorts of devices.

I can't really critique your program, but I wonder why the people who developed quantum theory didn't go that route?

 

[vanesch]

Out of curiousity, what do you find wrong with the following "solution"?
Suppose you had an experiment to detect whether the cat is "both" dead and alive. (according to whatever meaning you wanted to ascribe to this)
Then, since any state can be decomposed into two states, the first of which is internally consistent with the cat being 100% alive (and thus your experiment gives you a "no" answer, and the other internally consistent with the cat being 100% dead (and thus your experiment gives you a "no" answer), we must conclude that your experiment must always give a "no" answer.
In other words, there can be no observable oddities from the Schrödinger cat scenario.

That doesn't work this way. Imagine that |D> is the "dead cat state" and |L> is the "live cat state" (or a representative of the orthogonal spaces that correspond to that property).
If the cat is in a |L>+|D> state, then the operator that is diagonal in the basis {|L>+|D>,|L>-|D>} (the observable corresponding to your proposed experiment) with eigenvalues "yes" and "no", would give "yes" 100% to |L>+|D> state; while it would give "yes" only in 50% for a |L> or for a |D> state. In other words, this is an interference experiment with cats, notoriously difficult to do in the lab.
The reason why it is difficult is that a live, or a dead cat state quickly entangles with the environment, so that you get:
|envL>|L> + |envD>|D> as an overall state. Applying your operator NOW to this entangled state, will result in 50% yes only, as if we only had a |L> or a |D> state ; this is due to the essential orthogonality of |envL> and |envD>.
So once your cat gets entangled with its environment (the air, the radiation field...) you cannot get this interference out anymore. The reason why it is essentially the |envL> and |envD> states that couple respectively, in this basis, to |L> and |D> is due to the specific form of the interaction between a cat and its environment, which is heavily position-dominated (for instance, coulomb interaction is in 1/r)
This is the essence of the environmental decoherence program, explaining why we don't often see "macroscopic quantum interference effects".

 

[vanesch]

You undoubtedly saw that Vanesh had to cook up a non dynamical parallel mental world (which he cannot explain) coupled to the physical word in order escape from this. Moreover, most MWI's think differently about this and really want to pursue the points I mentioned.

Most MWIers are making in any case an implicit assumption of "what is perceived" although many of them forget to say so! As you correctly point out, unitary QM just ends up entangling your body with different classical views. MWIers then tacitly assume that we only perceive ONE of them, but that, in itself, is A FUNDAMENTAL ASSUMPTION that they sometimes forget to specify. There is a priori nothing wrong with a world in which we are aware of BOTH our body states (the body seeing a live cat, and the body seeing a dead cat).
Most efforts MWIers concentrate on is to do 2 things:
1) solve the "preferred basis problem"
2) derive somehow the Born rule from some "more natural" statistics such as state counting, or "rational decision theory" or whatever.
But my point (my heresy in MWI !) is that, even if you had very plausible mathematical arguments for 1) or 2), YOU STILL HAVE TO POSTULATE that you don't observe the "entire state", and YOU STILL HAVE TO POSTULATE the "more natural statistical rule", which applies in your "more naturally derived preferred basis".
In other words, you CANNOT *derive* classical observations from a strictly unitary QM ; you STILL need to add some extra postulate that links the total wavefunction to the "perceived" one. The only discussion is about HOW NATURAL this can be done.
So my viewpoint is that *if you have anyhow to add a postulate* why not make life easy, and simply postulate that an observer will observe consciously this state according to the preferred basis that corresponds to observation (classical world) and using the Born rule.
This is "deus ex machina" of course, and now all derivations of MWI proponents just make these postulates "sound a bit more natural".
But there's no reason WHY I cannot postulate this directly. I could try to go to more "fundamental" postulates, and derive the preferred (position) basis and the Born rule from there, but I can just as well posit it directly in the mean time.
The point to see is that *in any case* a postulate will have to be added in order to find agreement between unitary QM and observation. This is nothing else but a postulate that DETERMINES WHAT IS CONSCIOUS OBSERVATION. No matter how you turn it. Because my *body* IS in a superposition. My brain *IS* in a superposition. If it only depended upon my body, I would see the cat BOTH alive and dead. I wouldn't perceive a classical world. I would see myself both in the grocery store and posting on PF. And, as I want to point out, there's nothing wrong with that - only that's not what we perceive. So any "derivation" of classical perception from unitary QM MUST postulate something about perception. Many MWIers seem to do this implicitly by using "world counting rules" and trying to establish "naturally-looking" preferred bases for this "world counting". But, even if this succeeds, they forget that the STILL need to postulate that this "world counting" must be done in the first place !
cheers,
Patrick.

 

[vanesch]

I wrote:

Because my *body* IS in a superposition. My brain *IS* in a superposition. If it only depended upon my body, I would see the cat BOTH alive and dead. I wouldn't perceive a classical world. I would see myself both in the grocery store and posting on PF.

but I should make something probably clearer. When I say: I would see the cat BOTH alive and dead, then I just mean that: I would be aware of TWO classically-like worlds. I WOULDN'T see the cat in a SUPERPOSITION of live and dead. That problem is solved already by environmental decoherence. There are 3 levels in this problem:

1) "the cat is in a strange state, a superposition of live and dead"

2) "the cat is dead in one "world" and the cat is alive in the other"

3) "with probability 50%, I see a dead cat, with probability 50%, I see a live cat"

1) was Schroedinger's objection (that's a state that doesn't seem to exist). However, environmental decoherence shows us that 1) decays extremely rapidly into 2). Indeed, (|L> + |D>)|env> quickly goes into (|envL>|L> + |envD>|D>), where we can consider these two terms as "worlds".

What is unsolvable without an extra postulate, IMO, is the 2) -> 3) transition. I should see BOTH the world with the live cat and the world with a dead cat, as in 2). Why I only perceive ONE of them, with a certain PROBABILITY, can never be deduced (IMO) from the unitary formalism.

The measurement Careful was talking about, about testing the (|L> + |D>) state, is difficult to perform, because we would need to UNDO the 1) -> 2) evolution.

 

[Sherlock]

That doesn't work this way. Imagine that |D> is the "dead cat state" and |L> is the "live cat state" (or a representative of the orthogonal spaces that correspond to that property).
If the cat is in a |L>+|D> state, then the operator that is diagonal in the basis {|L>+|D>,|L>-|D>} (the observable corresponding to your proposed experiment) with eigenvalues "yes" and "no", would give "yes" 100% to |L>+|D> state; while it would give "yes" only in 50% for a |L> or for a |D> state. In other words, this is an interference experiment with cats, notoriously difficult to do in the lab.
The reason why it is difficult is that a live, or a dead cat state quickly entangles with the environment, so that you get:
|envL>|L> + |envD>|D> as an overall state. Applying your operator NOW to this entangled state, will result in 50% yes only, as if we only had a |L> or a |D> state ; this is due to the essential orthogonality of |envL> and |envD>.
So once your cat gets entangled with its environment (the air, the radiation field...) you cannot get this interference out anymore. The reason why it is essentially the |envL> and |envD> states that couple respectively, in this basis, to |L> and |D> is due to the specific form of the interaction between a cat and its environment, which is heavily position-dominated (for instance, coulomb interaction is in 1/r)
This is the essence of the environmental decoherence program, explaining why we don't often see "macroscopic quantum interference effects".

I thought Hurkyl's point was that QM doesn't allow the observation of an alive-and-dead state composed of separate alive and dead states. Anyway, there's no need to jump through all these hoops about this. We're talking about one 'detector', and it can't be in both, mutually exclusive, possible detection states at the same time.

QM says that, Cat = 1/(sqrt 2) {psi_alive + psi_dead}, means that we will *not* observe a Cat that is both alive and dead. So, what QM says about this isn't really the problem. It's consistent with experimental results. The cat is always observed to be either alive or dead.

The problem is sometimes stated as -- why don't we ever observe anything corresponding to interference between alive and dead cats? (Why don't don't we ever observe cats which are both alive and dead at the same time? A silly question?)

As you note, every macroscopic object (including cats, alive *or* dead) can be considered as a manifestation of interfering wave systems on an environmental scale.

So maybe the problem can be stated as -- why don't we ever observe anthing corresponding to interference between cats (alive or dead) and the environment.

Well, an *interference effect* is what *any* macroscopic object *is*, isn't it?

We can actually see interference, as it's happening, wrt many wave phenomena in macroscopic media. But, the structure of more fundamental media and direct apprehension of disturbances in those media are not currently part of our knowledge.

There is a problem, to be sure. But it's not essentially a problem with quantum theory itself. Maybe it's not even essentially a theoretical problem any more. The media scale, wave-reality of quantum level phenomena is, except for intermittent probes, invisible to us -- and this is the problem, quantum-level phenomena can't be tracked.

Quantum theory is part of the solution to this problem. Interpretations, or reformulations of QM (or entirely different theoretical approaches) are not addressing the real, physical problem.

 

[Careful]

Careful: none of this is answering my question to you. You have made the claim:
which, of course, begs the question "In your opinion, why must other approaches fail?"
.

Ok, I see vanesh answered that already in his first reply. Although, as I mentioned this coupling to the environment is not quite satisfactory (Vanesh doubted that also a while ago), since you are relying in fact on a kind of quantum statistical argument here (exact computations with very small model environments have been done recently) and the Born rule comes out rather well, but not quite all the time (due to recurrency times as far as I understand) (you should search it up in the book of Bernard d'Espagnat or Ghirardi Rimini and Weber also comment on this in their overview paper, you can find on quant-ph). Let me say already this: if you want to stick to copenhagen or want to buy your way out ``kinematically´´ as Vanesh does, and you are pleased with that. Then, for you there is no problem. But this is FAPP as Bell calls it, I am interested in an explanation of the measurement, not in some trick like R (when does it take place, by what act which apparatus should be seen as classical and so on) or a mental world like in MWI.

Ok Vanesh nicely explained what measurement is about in his third message: it is indeed the AND -> OR transition. For sherlock: yes I abused Bell causality here: it should have been local realism (if you want an exact definition, you may ask me one).
The reason why I am interested in a true explanantion is to be found in quantum gravity. I shall come back to that in another post.

 

[vanesch]

Anyway, there's no need to jump through all these hoops about this. We're talking about one 'detector', and it can't be in both, mutually exclusive, possible detection states at the same time.

Well, the problem is that if you take quantum theory seriously, that's exactly what happens: your detector IS in two "mutually exclusive states" at the same time. That's what unitary evolution dictates, and it is the very founding principle of quantum mechanics.
This is called the superposition principle, and it is exactly the same principle that says that an electron in a hydrogen atom is both above and below the nucleus, and to the left and to the right of it, which are also "classically mutually exclusive states". This is exactly what the wavefunction is supposed to mean: the electron is in the state ABOVE the nucleus, is ALSO to the left of it, is ALSO to the right of it, and is ALSO below it, with the amplitudes given by the value of the wavefunction.
A quantum particle that impinges on a screen with several holes goes through the first hole, and ALSO goes through the second hole, and ALSO goes through the third hole.
And if you take this principle seriously all the way (that's what MWI does) then your particle detector SAW the particle, and DIDN'T see the particle. So on the display of the detector it is written "CLICK" AND it is written also "NO CLICK". And if you look at it, your eyes will BOTH see "click" and "no click". And your brain will BOTH register the information of the fact that your eyes saw "click" and that your eyes DIDN'T see click.
Only... you are only consciously aware of ONE of these possibilities.
*IF* quantum theory as we know it applies to all the particles and interactions in this scheme (the atoms of the detector, of your eyes, of your brain etc...) then there is no escaping this conclusion. This is due to the fact that *ALL* interactions we know (electroweak, strong, except for gravity), are, as far as we know in current quantum theory, described by a UNITARY EVOLUTION OPERATOR.
So what are the ways out of this riddle ?
1) this is indeed what happens, and for some strange (?) reason, we are only aware of one of the states. This is the picture I'm advocating - unless we've good indications of the other possibilities.
2) this unitary evolution is a very good approximation which is in fact, slightly non-linear. this can be a minor modification to QM, or this can be just an indication that QM is a good effective theory for something totally different.
3) we've not yet included gravity. Maybe gravity will NOT be described by a unitary evolution operator.
4) there's maybe another interaction that spoils the strictly unitary evolution
5) somehow the act of observation (what's that ?) is a physical process that acts upon the wavefunction (that's the von Neumann view: but WHAT PHYSICS is this act of observation then ?) and reduces the state of whatever you're "observing".

 

[vanesch]

Let me say already this: if you want to stick to copenhagen or want to buy your way out ``kinematically´´ as Vanesh does, and you are pleased with that. Then, for you there is no problem. But this is FAPP as Bell calls it, I am interested in an explanation of the measurement, not in some trick like R (when does it take place, by what act which apparatus should be seen as classical and so on) or a mental world like in MWI.

Just to make this clear: I'm certainly not "happy" with the mental MWI explanation. I only stick to it because, IMO, it is what fits closest to the *current formalism* of quantum theory - in fact I don't worry, because there's probably still a lot to discover in physics, and this won't be our "last theory".
I think the fundamental difference between Careful's view and mine is that I consider that, no matter how FAPP our current QM is, I think its entanglement predictions are (even FAPP) correct, because so many experiments confirm it indirectly. As such *I know that there is a serious problem* and I don't know how to solve it.
Careful's view seems to deny this prediction of entanglement, so that he can rely on some hopes that a more classical field theory including GR will do the trick (and which can of course never produce ideal entanglement predictions because it will be an LR theory). The argument being that you then don't have to face the serious problems, and that everything is much cleaner and nicer.
I think that no matter how nice a scheme one has, the final judge is the experiment, and I wouldn't bet my money on hoping that the entanglement predictions of QM are wrong (even only FAPP), them having had so many indirect successes ; nevertheless if he thinks there's some hope for his approach, why not.
In the mean time (until one has a better WORKING theory), I still think it is interesting to have a story that fits with the currently WORKING theory, which is QM - and that's all I want to do here.

 

[Careful]

I think that no matter how nice a scheme one has, the final judge is the experiment, and I wouldn't bet my money on hoping that the entanglement predictions of QM are wrong (even only FAPP), them having had so many indirect successes ; nevertheless if he thinks there's some hope for his approach, why not.
In the mean time (until one has a better WORKING theory), I still think it is interesting to have a story that fits with the currently WORKING theory, which is QM - and that's all I want to do here.

Indeed, that is the only point where we disagree and that is why EPR experiments are so damn important. My filosofy is that GR and QM are both equally working theories but that GR is by far the superior THEORY. We have to look for a unifying framework and the misery of QM is, if you want to include GR, the superpostion principle. It is notoriously difficult (an in my view even meaningless) to add up different spacetimes. That is why I would argue that one should try to push the GR scheme as far as possible and this is not by any means easier in the sense that you will have to answer questions about ``how do elementary particles look from the inside´´. Moreover, even if this would turn out not to be possible, and if there really turns out to be a non locality scale in nature, then any local realist attempt will clearly bring insight into the more precise nature of this non locality. This would allow one to introduce non locality in a *controlled* way and study the corrections. This is in a sense what Penrose proposes: his OR scheme is a controlled way to exclude macroscopically too different alternatives (only he does not know how to do it in a covariant way). The point I want to make is that the *pure* quantum strategy is too wild for these purposes. Therefore, it makes sense to start with the purest local strategy and see how far one gets. This will certainly provide insightful results, also for QM. My hope is of course that there is no non locality scale at all.

Cheers,

Careful

 

[Hurkyl]

If the cat is in a |L>+|D> state, then the operator that is diagonal in the basis {|L>+|D>,|L>-|D>} (the observable corresponding to your proposed experiment) with eigenvalues "yes" and "no", would give "yes" 100% to |L>+|D> state; while it would give "yes" only in 50% for a |L> or for a |D> state. In other words, this is an interference experiment with cats, notoriously difficult to do in the lab.

Maybe I'm misunderstanding the point of Schrödinger's cat...

I thought the question is "Why don't we ever see a cat that looks like it's a superposition of states?"

and my answer is

"No single experiment can detect a superposition -- they're only detectable by looking at the statistics of repeating an experiment on identical copies of the state"

(At the moment, I claim that the same is true for microscopic states)

Or to put it differently, a superposition of states looks normal, until you do experiments with repeated copies of it and look at the statistics.

 

[Careful]

Maybe I'm misunderstanding the point of Schrödinger's cat...
I thought the question is "Why don't we ever see a cat that looks like it's a superposition of states?"
and my answer is
"No single experiment can detect a superposition -- they're only detectable by looking at the statistics of repeating an experiment on identical copies of the state"
(At the moment, I claim that the same is true for microscopic states)
Or to put it differently, a superposition of states looks normal, until you do experiments with repeated copies of it and look at the statistics.

That is a FAPP argument, which boils down to the statement : ``QM is good as long as we ask the correct questions (correct = good common sense borrowed from everyday life experience)´´. In the Copenhagen framework, this leads to the introduction of a different (and conflicting) dynamics R from U. Nobody knows what R means physically (but is is damn necessary to make predictions since unitary dynamics by itself is not enough as Vanesh points out). People find this unsatisfying since we would like to have ONE unified dynamics which also tells us why we only observe one world. You say: no single experiment can distinguish between both pure eigenstates and a linear combination of eigenstates. That is true (by definition in the copenhagen framework) but the issue is what an experiment IS PHYSICALLY (this is the measurement problem which is usually explained using Schroedingers cat picture). Let me recall you a thought experiment from Penrose about the weather on a planet. It is well known that weather is very chaotic and therefore quantum effects will in general make sure that after suffiently long time the weather state of the planet is a sum of many different macroscopic distinghuishable weather states (for example storm or no storm in america). At this moment in time, you have to wonder why we only percieve one weather state. This what reduction does for you, or Vanesh consciousness does. You might also hope that the classical instability argument is miraculously solved by quantum theory (but this seems not the case, and you might want to percieve this as some specific form of the cat problem). I think that you simply say that BY definition R does the trick and we have commented already that (a) this is not satisfying (b) what about non local observables (c) usually you implement R by use of a global foliation (which brings along causality problems unless you only wonder about local observables, moreover foliations are troublesome in quantum gravity).

This is an issue with a long history; Bohr and Heisenberg were very quickly aware that one had to introduce classical concepts into quantum mechanics in order to make contact with the real world. People nowadays try to dispose of this undesirable feature since QM, if it were to serve as a fundamental theory, should explain classicality and not use it. Vanesh already agreed with me, that if you want to do this in a satisfying and dynamical way, you will have to give up unitarity (and in my view also linearity). You might want to read in the book of de Broglie ``non linear wave mechanics´´ in order to get a deeper understanding of this issue which was around since 1919 as far as I know. My personal opinion about this, is that QM is an effective devise to give statistical results and that the Schroedinger equation therefore is NOT a one particle equation but a devise to describe outcomes of many experiments. Therefore, one should look for a true (classical in my mind) chaotic dynamics whose statistical mechanics exactly coincides with the Schroedinger predictions. Barut has once put this in a nice way: it is not because that 50% of the population is male and 50% female that any person is half man and half woman. :-)

 

[vanesch]

Vanesh already agreed with me, that if you want to do this in a satisfying and dynamical way, you will have to give up unitarity (and in my view also linearity).

are you a lawyer ?

 

[Careful]

are you a lawyer ?

You can prosecute me if I abused your authority

 

[Sherlock]

... it should have been local realism (if you want an exact definition, you may ask me one).

Isn't Bell's general formulation for local realistic theories an exact definition?
P(a,b) = integral d lambda rho(lambda) A(a,lambda) B(b,lambda)

 

[vanesch]

You can prosecute me if I abused your authority

What I meant was:
I *still* consider strict unitarity a possibility, but I only pointed out that we'll then have to posit some postulates about conscious perception. The last thing is uncomfortable, I agree, and if we could avoid it it would be probably better. But maybe we can't. So somehow it is correct that this is not a "dynamical way" ; so that your statement is correct that there is no "dynamical way" to obtain classicity *without* some statement about conscious perception, which can indeed be considered somehow unsatisfactory.

And the way you put all these elements together make it sound as if I said that considering that unitary evolution were strict is quite a silly idea

 

[Careful]

Isn't Bell's general formulation for local realistic theories an exact definition?
P(a,b) = integral d lambda rho(lambda) A(a,lambda) B(b,lambda)

Oh, you can also see it like that: the question then is (a) why Bell locality has to be statisfied for ``big´´ objects (starting from a size of 10^{-8} meters) and (b) why the probability function becomes deterministic (ie.
P(\lambda) = 1 or 0). It is (b) which is also necessary.

Cheers,

Careful

 

[Careful]

What I meant was:
I *still* consider strict unitarity a possibility, but I only pointed out that we'll then have to posit some postulates about conscious perception. The last thing is uncomfortable, I agree, and if we could avoid it it would be probably better. But maybe we can't. So somehow it is correct that this is not a "dynamical way" ; so that your statement is correct that there is no "dynamical way" to obtain classicity *without* some statement about conscious perception, which can indeed be considered somehow unsatisfactory.

And the way you put all these elements together make it sound as if I said that considering that unitary evolution were strict is quite a silly idea

Aha, the noble art of stating exactly what others said while twisting the emotional output Perhaps, I should become a lawyer indeed ...

 

[DrChinese]

Isn't Bell's general formulation for local realistic theories an exact definition?
P(a,b) = integral d lambda rho(lambda) A(a,lambda) B(b,lambda)

That is the separability requirement, also often referred to as "Bell Locality". It is also sometimes called "factorizability" which may or may not be the same thing, depending on your exact definition. Separability is sometimes defined as the following, where A and B are the two systems:

1) Each [system] possesses its own, distinct physical state.
2) The joint state of the two systems is wholly determined by these separate states.

But that does not include the "realistic" requirement which I call "Bell Reality". It is the requirement that there are values for observables which could have been measured alternately. "It follows that c is another unit vector..." from Bell, just after his (14). If you don't insert this assumption into the mix, there is no Bell Theorem.

 

[NateTG]

It is the requirement that there are values for observables which could have been measured alternately. "It follows that c is another unit vector..." from Bell, just after his (14). If you don't insert this assumption into the mix, there is no Bell Theorem.

Actually, it is the requirement that there are well-defined probability distributions for the values for observables which could have been measured alternately. Which is actually a strictly stronger condition than that that the values exist.

It is (mathematcally) quite feasible to construct a deterministic model which matches the QM predictions for EPR experiments -- in this model, for every run of the experiment, a definite result is assigned to every possible measurement, but the probability for impossible combinations of measurement results are undefined.

 

[DrChinese]

1. Actually, it is the requirement that there are well-defined probability distributions for the values for observables which could have been measured alternately. Which is actually a strictly stronger condition than that that the values exist.

2. It is (mathematcally) quite feasible to construct a deterministic model which matches the QM predictions for EPR experiments -- in this model, for every run of the experiment, a definite result is assigned to every possible measurement, but the probability for impossible combinations of measurement results are undefined.

1. I want to think about this, but I may agree with your assessment.

2. I wonder if you might have anything up your sleeve in the way of an example or reference I could take a peek at? Or perhaps you can elaborate on your position? You had mentioned this in an earlier post too in which you were talking about the undefined results.

 

[RandallB]

You might want to read in the book of de Broglie ``non linear wave mechanics´´ ...

Also, find some interesting insights from Louis de Broglie’s Preface in his “New Perspectives in Physics”. He comments on the 'hostility' he encountered until he aligned himself with the uncertainty view in 1928, and reconsiders that over 20 year alignment.
To be fair this is dated 1955, not long after Einstein’s passing and before the Bell 60’s, but I think he really liked / wanted to go back to a realist view.