Problems with Many Worlds Interpretation

[Ken G]

This is just silly. It's like telling me that anyone who reads a real analysis textbook doesn't care about computing derivatives, that anyone reading The Lord of the Rings can't be interested in the geography of Middle Earth, or that anyone who makes use of a coordinate chart in classical mechanics cannot possibly care about what people see.

Then you miss my point, which is this: frogs see eigenvalues. The formalism of quantum mechanics accounts for this via the Born rule, and no other way. The Born rule is completely ad hoc, it's just a "rule for using wave functions." That is completely true in either CI or MWI, we haven't even gotten to an interpretation yet. We don't get to the intepretations until we ask what does the Born rule mean, once we have recognized that our theory has this completely ad hoc character to it. (It shouldn't bother us, all theories are ad hoc, they just have different degrees of it.) CI says "the Born rule means this is what we will perceive, statistically for individual outcomes or more deterministically for an entire ensemble", MWI says "the Born rule means how the splitting outcomes get weighted, so is deterministic in either the individual case or the entire ensemble, it just connects better to our experience in the ensemble case." That is not any less ad hoc, the sole difference there is how strongly we value our perception in individual cases.

I actually see very little scientific difference between CI and MWI, though a huge philosophical difference, and what's more, if and when quantum mechanics is found to be just another effective theory like all the rest were, we should ask: will CI need to change its stance, that the Born rule predicts statistical outcomes? No it won't, CI won't care at all if a new theory comes along, for the same reason that we continue to do Newtonian mechanics. Can MWI say the same, when it is founded on an ontology that completely falls apart if nonunitary evolution of a wave function can occur?

Using a coordinate chart when working with classical mechanics isn't an act of radical rationalism, is it?

A coordinate chart is nothing but a set of observers and their perceptions about rulers and clocks, with some arbitrarily chosen rule to define that set. Thus it is already an inherently empiricist concept, with no rationalism involved at all. However, the rule that connects the observers is causal-- they can actually compare notes, they are interested in things they can affect and that can affect them. Other branches of decohered mixed states, interpreted ontologically, simply don't fall under that category.

This is where the importance of relative state comes into play. Even if a whole system is in a pure^* state, its subsystems can be in mixed states -- in fact, they can transition from pure to mixed and back again. Overlooking that fact is the fatal flaw in the old argument that unitary evolution by itself is incapable of matching our experiences.

That's just pure quantum mechanics, it has positively zero to do with any of the interpretations. Give me an example of what you are calling a mixed state of a subsystem that evolved back into a pure state, and I will explain how CI handles that situation using an empiricist-constructed ontology.

*: The term "superposition state" has no inherent meaning -- the notion of superposition only makes sense when viewing states as kets, and even then only after having chosen a basis.

I'd say that can be said much clearer in empiricist language. A "superposition state" has a perfectly fine meaning, it is simply a pure state that is not an eigenstate of some observation that we have in mind to make that designation. It is a pure state in a context that is relevant to this discussion, so is an appropriate term here.

I find your view of my arguments completely baffling. As of yet, I have failed to discern any rhyme or reason to them, except by considering the hypothesis that you are either attacking a straw-man or have fallen victim to what you say I am doing -- that you have equated the very idea of experience with a particular philosophy and can't entertain the thought that they aren't literally as they are described classically.

Once again you seem to feel the need to "describe" your experiences. Don't you realize that most people just experience things? I realize that we always pass our experiences through some kind of mental processing, but all the same, most people really are pretty comfortable with the idea that putting your hand on a stove is a painful experience, and don't have to conceptualize that experience as some kind of mixed state of hand on / hand off the stove. If quantum mechanics gets replaced by nonunitary evolution that appears unitary in certain conditions, you claim that what you feel when you put your hand on a stove is going to be radically different? Your rationalism runs so deep that you don't seem to even be able to conceptualize empiricism. I don't criticize that, actually I think it's fascinating, I'm just trying to get you to see how different that is from the general definition of the term "experience."

 

[Dmitry67]

Observers can be outside each others' light cones without event horizons. They are just bearing witness to real events that cannot be shared, so each will form an incomplete picture of the whole. That is how empiricism works, we all get an incomplete picture, but we get the perceptions we get, and we build a reality from it. Some of us will never build a reality that has black hole singularities in it, that's empricism-- there's no problem there, it's just a pill we must swallow. Empiricism starts with the expectation that the reason we invoked physics in the first place was to predict the things that affect us, and use that to inform decisions about things that we can affect. The rest is angels on the pin.

The question here is what is the knowledge that physics gives us, not mathematics (mathematics knowledge is always purely tautological to the axioms, so it is an exercise in "knowing thy axioms." Physics for the empiricist is knowing , and gaining power over, thy experiences.). What is the purpose of quantum mechanics? I gave the answer that I think would be pretty standard for empiricism, what would you say is the purpose of quantum mechanics?

I asked 2 yes/no questions and I did not expect to get a ... poetry instead of Y/N reply.
It does not answer my questions at all.

 

[Dmitry67]

The Born rule is completely ad hoc, it's just a "rule for using wave functions."

No, it is derived by Max Tegmark from QM in 2010 (even not all people agree)

 

[Ken G]

It does not answer my questions at all.

One question you asked was "what version of CI was I using." I'm not using any particular version of CI, rather I've been quite clear about what the salient features are about what I'm calling CI-- the interpretation that the reality we need to explain is the reality of our measurements and nothing else. Thus if we do a measurement, and get an eigenvalue, we do not contort our view of reality to accommodate other eigenvalues that we did not get, but instead, we regard QM as a system for understanding why we got that eigenvalue. When we do that, we find that QM is incomplete-- it cannot say why we got that eigenvalue, but it can say how often we'll get that eigenvalue if we repeat the same experiment. That's CI, pure and simple-- it is a choice about what QM is for. People have all kinds of crazy ideas about CI attributing magical properties to wave function collapse, but what they don't realize is that CI never saw the wave function collapse as anything but a step in a mathematical process, designed to reach statistical predictions around the observed fact that what we see are eigenvalues. It's not a bizarre ontology, it's simply the rejection of unnecessary ontologies in the first place. This seems to me to be the central spirit of virtually everything that Bohr said about interpreting QM.

 

[Dmitry67]

I don't understand how you can't care about the version of CI, for example, Neumann vs Bohr. Even they appear to be similar, they are absolutely not compatible, they are opposite, for example, in one wavefunction is "real" while in the others it is NOT REAL! How you can talk about the reality ignoring these key facts?

 

[Eqblaauw]

I just received a mail from Gerard 't Hooft, he says he thinks MWI is absolutely false: There is one World. QT gives us many-worlds, only because it's not capable of choosing one right world. Tough there is one world.
He also says he would have expected another outcome of the David Raub poll, because most of the physicists he knows are much more skeptical (tough he doesn't know what they would do when they get a poll).

 

[Eqblaauw]

I do know that of the few prominent dutch scientists I have contacted (Ewine van Dishoeck, Vincent Icke, Leo Kouwenhoven and Gerard t Hooft), none of them subscribe to the MWI. (And I didn't knew that in advence).
I also know that David Deutsch explicitly mailed to me he doesn't believe in the splitting of many-worlds, but in the differentiation of many worlds.

 

[Ken G]

I don't understand how you can't care about the version of CI, for example, Neumann vs Bohr. Even they appear to be similar, they are absolutely not compatible, they are opposite, for example, in one wavefunction is "real" while in the others it is NOT REAL! How you can talk about the reality ignoring these key facts?

Well, any interpretation that says the wave function is real is simply something I would not call CI. To me, the defining character of CI is empiricism.

 

[Ken G]

I'm not very familiar with MWI, but is it correct, that it postulates the density operator ϱ to be the fundamental state which describes reality?

Yes, I would say that the density operator is the fundamental way that quantum mechanics describes a state, and MWI takes that and translates it into the fundamental truth about the reality. In short, MWI takes the quantum mechanical state as being literally real, so in essence paints a reality that is beholden to the formal axiomatic structure of quantum mechanics, rather than the other way around. That's why MWI is so rationalistic.

This suggests that MWI is nothing quantum mechanical, but also present in classical mechanics (points in phase space vs. probability distributions). As far as I can see, this removes all information-theoretic content from statistical mechanics, which seems very odd to me.

Yes, since quantum mechanical principles continue to apply in classical physics, if one goes the MWI road, then purely classical physics is also subject to the MWI interpretation. In fact, any classical physicist could have made that same claim, without any inconsistency in their position. They just wouldn't have been taken seriously without the axiomatic structure of QM to support their viewpoint. There probably is some classical philosopher somewhere who maintained that it is impossible for a coin to come up either heads or tails, and so it must come up both-- philosophers are pretty clever that way.

I don't think this removes all information theoretic content, I think it simply forces one to reinterpret them, often by invoking the anthropic principle. In effect, instead of imagining the statistical distribution is over potential actualizations of some system that is doing only one of them, it is envisaged as being over the potential perceptions by a statistical distribution of observers who are experiencing a system that is doing all those things at once. What MWI proponents seem to ignore is that the Born rule is invoked, ad hoc, to characterize that distribution, no matter whether you interpret it as a distribution over potential outcomes, or a distribution over potential perceptions of a single unified outcome. Tomato, tomahto.

To me, the main difference is flexibility if the axiomatic structure is found wanting. In CI, the axiomatic structure was always taken as a handy device, so CI has no trouble with any cracks in it. MWI is essentially a radical world view that hangs entirely on the infallibility of the axiomatic structure, and since when has physics ever devised an infallible axiomatic structure?

 

[Hurkyl]

Then you miss my point, which is this: frogs see eigenvalues. The formalism of quantum mechanics accounts for this via the Born rule, and no other way. The Born rule is completely ad hoc, it's just a "rule for using wave functions."

I'm not entirely sure I would agree with the claim that "the weights on the components of a mixed state correspond to the probabilities observed in experiment" is ad-hoc, but I can sort of see it.

Hypothetically^* speaking, would your opinion change (or, at least, weaken) if one could theoretically derive that the weights on the components of a mixed stateBut I don't see your point -- what does this have to do with your assertion that anyone who talks about something that isn't an eigenvalue cannot care what frogs see? Are you claiming that measurements involve spontaneous decoherence which cannot be the product of a system interacting with its environment through unitary evolution?*: I don't think it's hypothetical at all.

(It shouldn't bother us, all theories are ad hoc, they just have different degrees of it.)

Yes it should -- a theory with greater degrees of it has less ability to make precise predictions, and correspondingly experimental evidence for the theory becomes less meaningful.

CI says "the Born rule means this is what we will perceive, statistically for individual outcomes or more deterministically for an entire ensemble"

The CI is more specific than that -- depending on the version, it further asserts that a mixed state is a matter of ignorance or non-determinism, that one should specifically not interpret it as corresponding to the physical system.

(I refer to the individual case, since I haven't thought through ensemble variations beyond the initial impression that they represent "giving up" in some sense)

, MWI says "the Born rule means how the splitting outcomes get weighted, so is deterministic in either the individual case or the entire ensemble, it just connects better to our experience in the ensemble case."

On the statistics, MWI says that one should think of the mixed state as corresponding to the physical system.On the origin of the weights, they come from decoherence, which MWI posits is the effect unitary evolution, rather than being spontaneous.

Does your variety of CI posit that measurement involves spontaneous decoherence? Or causal decoherence followed by spontaneous collapse?

But, I expect the above is a diversion, and doesn't actually address the point we disagree upon.

I actually see very little scientific difference between CI and MWI

CI is extremely antagonistic to the idea that a measuring device or an observer obeys the laws of quantum mechanics.

I honestly cannot see how a collapse-as-reality interpretation can survive if quantum mechanical theories start expanding their domain to scales which include measuring devices and observers.

A collapse-as-being-just-as-good-of-a-description-of-reality-as-a-mixed-state interpretation would likely survive, but that's not CI.

Can MWI say the same, when it is founded on an ontology that completely falls apart if nonunitary evolution of a wave function can occur?

Yes, for the same reason we still do Netwonian mechanics. MWI can only fall apart if quantum thermodynamics doesn't work out.

A coordinate chart is nothing but a set of observers and their perceptions about rulers and clocks, with some arbitrarily chosen rule to define that set.

Empiricism now is about the experiences of imaginary people?

Once again you seem to feel the need to "describe" your experiences.

Er, yes. So do you, it seems:

• people just experience things
• putting your hand on a stove is a painful

 

[Hurkyl]

As an aside, I've been reminded of a fact about General Relativity (assuming I recall correctly).

Proper time is not an observable in GR (for the same reasons that relative coordinate time is not observable in SR and coordinate velocity is not observable in Galilean Relativity). This is part of a larger measurement problem GR once experienced.

People eventually discovered things that could be observed in GR, which includes things like the classic 'light clock' of Einstein's original batch of thought experiments.

I'm curious to see how Ken G would react to such information.

 

[PAllen]

As an aside, I've been reminded of a fact about General Relativity (assuming I recall correctly).

Proper time is not an observable in GR (for the same reasons that relative coordinate time is not observable in SR and coordinate velocity is not observable in Galilean Relativity). This is part of a larger measurement problem GR once experienced.

People eventually discovered things that could be observed in GR, which includes things like the classic 'light clock' of Einstein's original batch of thought experiments.

I'm curious to see how Ken G would react to such information.

A little off topic, but since you raised it, this is new to me. I've always considered proper time along a timelike world line as an invariant observable. Can you clarify what you mean?

 

[Ken G]

Proper time is not an observable in GR (for the same reasons that relative coordinate time is not observable in SR and coordinate velocity is not observable in Galilean Relativity). This is part of a larger measurement problem GR once experienced.

I would find that quite a problem yes, but like PAllen, I would like clarification. It sounds to me like the basic problem that "rigidity" is impossible in GR, but that always seems like a standard problem in physics, that the concept of measurement is always idealized. In effect, physics is structured to be an approximate science. So I would have thought that GR could treat proper time as an observer, simply by taking an idealized limit that instruments like clocks and rulers were small enough and rigid enough to avoid having to worry about tidal effects.

 

[Fredrik]

I'm not very familiar with MWI, but is it correct, that it postulates the density operator ϱ to be the fundamental state which describes reality?

Yes, I would say that the density operator is the fundamental way that quantum mechanics describes a state, and MWI takes that and translates it into the fundamental truth about the reality. In short, MWI takes the quantum mechanical state as being literally real, so in essence paints a reality that is beholden to the formal axiomatic structure of quantum mechanics, rather than the other way around. That's why MWI is so rationalistic.

I think "no" is a more accurate short response then "yes". I would say that the main assumption is that it makes sense to talk about the wavefunction of the universe, and that this wavefunction describes reality. Density operators are still needed, in particular to describe the correlations between subsystems after decoherence (and therefore to describe the frog's view), but the wavefunction of the universe is what "describes reality" (the bird's view anyway).

Proper time is not an observable in GR (for the same reasons that relative coordinate time is not observable in SR and coordinate velocity is not observable in Galilean Relativity). This is part of a larger measurement problem GR once experienced.

Can you elaborate? If this is accurate, I would like to know more about it. I like to think of the statement "a clock measures the proper time of the world line that represents its motion" as a part of the definition of GR.

 

[Fra]

CI is extremely antagonistic to the idea that a measuring device or an observer obeys the laws of quantum mechanics.

I agree it's a problem that the formalism only makese sense for "classical obervers". But as I see it this is a problem of QM itself, not of interpretations.

Note that it is no solution to consider bigger and bigger observers (so the big observer can describe the original observer) quantum mechanically. I think instead the challange is to reconstruct measurement theory so that it does make sense from the point of view of a general observer. The non-classicaliy is just one problem here, the other problem is that a general observer typically must have limited information capacity to encode the theory.

Some as I understand MWI thinking, you consider the inside observer as described as a quantum system, but described from the bird's view. Which makes one of the problems worse: namely that you need even more information capacity - you espace this issue but somehow considering this information in some mathematial realm. (this is something I can't accept)

I see this related to the problem of constructing local observables as well.

Te point is however that FAPP; the classical context of a laboratory looking into say an atom, DOES provide the classical context the original theory needs. So the "classical observer" is justified as a limit ca, so the history of QM is understandable. The problem starts when we try to understa unification and cosmologial theories, then we can't keep referring to classical observers anymore. but these problems was not things taken into considerations when QM was constructed. The MAIN "problem" way back was the failure of classical probability to explain experiment... hte other subtle issue we know of today was not known then.

So to me this is a deeper issue, it has little to do with interpretations but I agree with your issue.

I honestly cannot see how a collapse-as-reality interpretation can survive if quantum mechanical theories start expanding their domain to scales which include measuring devices and observers.

I wonder what definition of real we use here?

The way I see it the collapse isa matter of perspective, and thus obsever independent. What comes as a collapsing surprise to one observer, might well be expect by anotther one. In this sense the collapse is not real as in "objective". It is however real in the sense of phenomena since the objective implication of this, is that one can imagine a mechanism (whe nreconstructing measurement theory) where the ACTION of a system, depends on that it experiencs a collapse, because at each collapse the action changes in a non-trivial way, and if you consider a sequence of collapses resulting in rational information updates - this looks just like a dynamical evoluion to a different observer.

But it would I think be a deep misake to think that this answers the original question which is to find the inside picture, which genereally always contains collapses.

/Fredrik

 

[Hurkyl]

A little off topic, but since you raised it, this is new to me. I've always considered proper time along a timelike world line as an invariant observable. Can you clarify what you mean?

I've heard it a couple times, but I didn't think to keep a reference, and I couldn't find one with a brief search -- IIRC it's either something akin either to the hole argument or something to the effect of the stress-energy tensor (including time evolution) isn't enough to determine the metric (and thus isn't enough to determine the proper time of a time-like path)


But even if I'm flat out wrong, it still makes a good mental exercise for the topic under discussion.

 

[Ken G]

I'm not entirely sure I would agree with the claim that "the weights on the components of a mixed state correspond to the probabilities observed in experiment" is ad-hoc, but I can sort of see it.

Well I'm glad we can kind of agree that this is an ad hoc element of both MWI and CI! I really don't see any difference in the two interpretations in this regard, frankly-- to me, CI imagines a statistical distribution of single outcomes witnessed by a single observer (which certainly feels like what is happening), and MWI imagines a statistical distribution of single observers witnessing a single event that embodies all the possible outcomes. Which end you put your statistical distribution on, and whether or not you imagine an ontological unity behind the distribution, is pretty irrelevant to the physics. It all comes down to one's own philosophical preferences, largely rationalist vs. empiricist.

Hypothetically^* speaking, would your opinion change (or, at least, weaken) if one could theoretically derive that the weights on the components of a mixed state

Yes, if the Born rule had a derivation in one interpretation, that wasn't "rigged" like using anthropic thinking, then I would indeed see that as a huge advantage for said interpretation.

But I don't see your point -- what does this have to do with your assertion that anyone who talks about something that isn't an eigenvalue cannot care what frogs see? Are you claiming that measurements involve spontaneous decoherence which cannot be the product of a system interacting with its environment through unitary evolution?

No, it is quite apparent that measurements involve spontaneous (in the thermodynamic sense, not some magical sense) decoherence that is describable through unitary evolution of the closed system. Projections onto open subsets produce the mixed states. That's just quantum mechanics, it has nothing to do with any interpretation of quantum mechanics. The interpretation doesn't even enter until you specify what you think is the ontological message of the mixed state. In CI, the message is, "one of the outcomes actually occurred, and you just don't know which, but you will when you look." In MWI, the message is, "all the outcomes occurred, so there is no need to know which, even when you look, because then you are just entering into some kind of illusion." Decoherence has exactly nothing to do with that difference, it merely clarifies why we get to the place where we need to address the difference, which we already knew we'd get to.

Yes it should -- a theory with greater degrees of it has less ability to make precise predictions, and correspondingly experimental evidence for the theory becomes less meaningful.

I agree-- I meant that the existence of ad hoc elements shouldn't bother us, what should bother us is if there are too many such elements. I claim that CI involves no more ad hoc elements than does MWI, the "collapse" is not ad hoc, it is what we see. It is no more "ad hoc" to try to create a theory that connects to mystifying aspects of our experience than it is ad hoc to pretend our experiences fit the axioms of the theory and we just don't know that they do, which is more or less what you are saying.

The CI is more specific than that -- depending on the version, it further asserts that a mixed state is a matter of ignorance or non-determinism, that one should specifically not interpret it as corresponding to the physical system.

A mixed state in CI is an absence of information about the state, I agree. It is completely dual to the way MWI treats a mixed state as an absence of information about the observer's perception. I really don't see any difference there, except in one's priorities about what one thinks physics is for.

(I refer to the individual case, since I haven't thought through ensemble variations beyond the initial impression that they represent "giving up" in some sense)

I agree, the ensemble approach is the place where CI and MWI are really indistinguishable even in principle, because an ensemble is already a kind of "many worlds." So in going to an ensemble, one is dodging the need for an interpretation.

On the statistics, MWI says that one should think of the mixed state as corresponding to the physical system.

Yes, but in effect the distribution is then over the observers interacting with the mixed state. It's no more different than the Schroedinger vs. Heisenberg difference in whether the wave functions evolve or the operators. Dynamics in the dual space of states vs. observations is equivalent, and so are statistical distributions in that same dual space. It's nothing but philosophical priorities, and the advantage of CI is that it isn't motivated by a need for the theory to be ontologically exact because it adopts the empiricist attitude that theories are tools. This makes it much more flexible, unless QM axioms happen to be exactly correct.

On the origin of the weights, they come from decoherence, which MWI posits is the effect unitary evolution, rather than being spontaneous.

There's still no difference there, it is not the least bit important to CI what causes those weights to appear. Spontaneous doesn't mean magical, it just means that some very high-dimensional phase space is maximizing its entropy. That's just exactly what decoherence says too.

Does your variety of CI posit that measurement involves spontaneous decoherence? Or causal decoherence followed by spontaneous collapse?

The former. Remember, in CI collapse isn't a "happening", the observation is the happening. The collapse is what explains the observation, and quantum mechanics explains the collapse. All we need the interpretation for is to say what the collapse means. Your objections to CI sound like ones I often hear from people that I don't think really understand CI-- if I thought of it the way you do, I wouldn't like it either.

But, I expect the above is a diversion, and doesn't actually address the point we disagree upon.

I'm not sure what point we disagree on, so let me clarify what I'm saying:
1) CI and MWI are scientifically equivalent, in that they use all the same mathematics, make all the same predictions, and suggest the same observations to test these predictions. They only differ in their philosophical priorities, and in how they might guide us toward new theories that are not QM. Thus, it behooves us to recognize these different philosophical priorities, to help us understand the guidance these interpretations are giving us.
2) The main philosophical priorities that differ is that CI takes the perception of the observer as the crux of the purpose of doing physics, and MWI takes the axiomatic structure of the theory as the crux of the purpose of doing physics. This leads CI to treat the axiomatic structure as a kind of tool or effective theory, designed only to make predictions about outcomes. It also leads MWI to regard the perceptions of observers as illusory, even though they will find that the theory does predict what they do see on a statistical basis, because the actual reality must fit the axioms not the perceptions. In a nutshell, this means CI is motivated by the empiricist fondness of the relative concreteness of experience and measurement, and MWI is motivated by the rationalistic fondness of the aesthetic beauty of unified postulates.

Now, what aspect of the above are we not agreeing on? I realize that some of what I said was critical of MWI, but mostly it was not a logical inconsistency kind of criticism, it was a failure to recognize the philosophical and extra-scientific elements of the interpretation. So about the only way you could really disagree with me is if you think that MWI is "just good science", and does not represent the rather one-sided philosophical priorities that I suggested it does.

CI is extremely antagonistic to the idea that a measuring device or an observer obeys the laws of quantum mechanics.

Yes, that is true. Indeed, like any empiricist interpretation of any physical theory, it is antagonistic to the very idea that there is any such thing as "obeying laws" in the first place. To the empiricist, the very words "obeying laws" have a much weaker meaning-- it just means "allows us to interpret the outcome of observations by mathematically manipulating the measurables according to some highly unifying yet idealized principles that are presumed to be only approximate." Since the role of "laws" is as approximation tools for the observer, it does not even make sense to imagine that the observer obeys laws-- the observer is the master of the laws, not their slave. All the same, observers can observe each other, so a law is not useful if it cannot also be used to explain observations made on other observers. That does not require that the observers "obey" laws in any way but the weak sense already described.

I honestly cannot see how a collapse-as-reality interpretation can survive if quantum mechanical theories start expanding their domain to scales which include measuring devices and observers.

I have no doubt that quantum mechanics works fine on that domain, yet collapse-as-reality has no difficulty with any of that. It would all fit just fine with the statements I just made that characterize the crux of empiricism, and often summarized as "the map is not the territory."

A collapse-as-being-just-as-good-of-a-description-of-reality-as-a-mixed-state interpretation would likely survive, but that's not CI.

I don't understand, if collapse is just as good as mixed state, then one can adopt either. That means one can still use either CI or MWI, which would certainly be my expectation. If your basis for accepting MWI is that you don't think CI is workable, and that motivates you to tolerate the more bizarre ontological constructs of MWI, then I suggest the problem is with your understanding of CI. I have no doubt that you understand the MWI profoundly, and it probably helps you do QM, which is reason enough for it to be a good interpretation for you. But even an interpretation has two meanings-- the harmless one, which is a picture that one uses while one is applying a theory, and a more insidious one, which is a picture that generates a devoutness to a world view. Devoutness to world views is probably not supposed to be a goal of science, though we certainly all have our own personal reasons for doing it.

Yes, for the same reason we still do Netwonian mechanics. MWI can only fall apart if quantum thermodynamics doesn't work out.

If any aspect of QM doesn't work out, then both CI and MWI are wrong, but they only "fall apart" if one uses them for more than they should be used for in the first place. I learned Newtonian mechanics, then I learned it wasn't right, but it never "fell apart" for me because I was never devout about it and I knew I could still use it in all the same situations.

Empiricism now is about the experiences of imaginary people?

The word "imaginary" is problematic, I prefer "hypothetical." But yes, empiricism would be a completely powerless perspective on science if it did not support the concept of a hypothetical observer. The point of empiricism is not that we have to interpret reality based on what actually observers really saw (the tree in the woods business), it is that we have to interpret reality based on what actual observers are capable of observing and communicating to others-- whether they were there or not. However, whether they are there or not is part of the reality, so we recognize that a reality that contains a hypothetical observer might be quite a bit different from one that contains no observer. This rarely comes up in relativity though, hence the concept of a coordinate chart based on the concept of a reality with hypothetical observers being the same as one without. But yes, the whole issue of hypothetical observers in empiricism is just as misunderstood as the CI, and there may be "hard core" empiricists who reject the concept, just as there are "hard core" CI proponents who think the wave function is real and it really collapses. I am not speaking for the hard-liners, rather the garden variety empiricists.

Er, yes. So do you, it seems:

• people just experience things
• putting your hand on a stove is a painful

This is the point you keep returning to, and it is the reason you do not understand empiricism. I have already agreed with you that there is no such thing as "pure" empiricism, because rocks don't make measurements, thinking beings do. Similarly, there are no "raw" experiences, and your experience of the pain of a stove might not be the same as mine. But they don't need to be, all that is required for empiricism is the ability to establish consistencies of experience. Measurable outcomes like "heads" when a coin is flipped, that's all that is required, because it allows us to do science on those experiences without bothering to characterize them any more than saying "the distance is X" or the "coin was heads." So as long as you cannot understand experiencing "heads" or "tails" when you look at a flipped coin, you will never understand empiricism.

 

[Ken G]

I've heard it a couple times, but I didn't think to keep a reference, and I couldn't find one with a brief search -- IIRC it's either something akin either to the hole argument or something to the effect of the stress-energy tensor (including time evolution) isn't enough to determine the metric (and thus isn't enough to determine the proper time of a time-like path)


But even if I'm flat out wrong, it still makes a good mental exercise for the topic under discussion.

And notice how rationalistic are all those answers! You are not really saying the proper time isn't the fundamental observable in GR (it is, along with local distances), you are saying the concept isn't bulletproof in GR. Empiricists are never surprised to find any theory is not bulletproof! But we still find it telling that the beating heart of GR is the observable proper time, that's the most important scalar to know about any world line.

You see, empiricists don't much care when a theory says that an observation cannot be made, we care about making the observation. If the theory was wrong, then the observation is still the reality, and if the theory was right, then the theory is describing a fundamental limit about reality. Neither is a problem for the empiricist, we would still just say that the mathematical structure of GR is constructed around the concept of proper time, which dovetails with an observable, and empiricists find that quite telling. If that concept doesn't always work, we say, welcome to the world of the limitations of either physics theories, or reality itself, depending on whether or not the observation is actually possible. (What's more, an empiricist of my own brand doesn't think observations are actually reality, I just think that they are what we have to do science with. So I would call the observations the scientific reality, and what actual reality is is essentially mysterious. I don't object to MWI on the grounds that its ontology is mysterious, just that it is not supported by empiricism.)

 

[Ken G]

I think "no" is a more accurate short response then "yes". I would say that the main assumption is that it makes sense to talk about the wavefunction of the universe, and that this wavefunction describes reality. Density operators are still needed, in particular to describe the correlations between subsystems after decoherence (and therefore to describe the frog's view), but the wavefunction of the universe is what "describes reality" (the bird's view anyway).

But doesn't the density operator preserve all the useful information in the wave function, both before and after decoherence? I realize that the mapping from the wave function to the density operator is not invertible, but is any relevant information lost? For example, surely even MWI can't believe that the global phase of the wave function is physically part of the state of the system, as that would really be angels on a pin, even for MWI!

 

[Hurkyl]

Note that it is no solution to consider bigger and bigger observers (so the big observer can describe the original observer) quantum mechanically.

You're referring to the argument that considering a quantum system presupposes an observer that observes the system?

I've heard the argument, but I've never heard a convincing argument for the presupposition. I don't need to posit Wigner's existence in order to consider the evolution of a quantum system that includes Wigner's friend. The point of also having Wigner in the thought experiment is so that you can have two observers disagreeing on their description of reality. For example, one reason would be to refute of the paired hypotheses

• All observers are equal
• Collapse is something that happens at the interface between our experience and the external world

I think instead the challange is to reconstruct measurement theory so that it does make sense from the point of view of a general observer.

The general approach I'm familiar with is:

• Construct a theory that is easy to understand and work with
• Extract what a general observer sees

For example, in Newtonian mechanics, it's rather effective to:

• suppose the universe is described by three-dimensional Euclidean geometry
• work out the theory in that context using ordinary methods of Euclidean geometry (rather than, e.g., trying to always work in observer-centered coordinate charts)
• work out what general observers can observe -- e.g. he can't observe position, but can observe the distance between two positions

You could try to build that last point in right into the beginning -- but interestingly, this is a case of less is more. The only good mathematical structure I know for doing such a thing boils down to adding structure -- to equip everything in the mathematical universe with an action by the Euclidean group (rotations, translations, and reflections), and then insist everything must respect symmetry.

Despite the appearance more machinery, the requirement of symmetry really does result in the effect we've removed structure -- for example, in this setup, Euclidean space doesn't have any points at all! (picking a point doesn't respect symmetry)

 

[PAllen]

I've heard it a couple times, but I didn't think to keep a reference, and I couldn't find one with a brief search -- IIRC it's either something akin either to the hole argument or something to the effect of the stress-energy tensor (including time evolution) isn't enough to determine the metric (and thus isn't enough to determine the proper time of a time-like path)


But even if I'm flat out wrong, it still makes a good mental exercise for the topic under discussion.

Well, the hole argument I recall was a famous mistake of Einstein's that delayed GR a couple of years.

The stress energy tensor is equal to the Einstein tensor, and determines the metric modulo diffeomorphism and boundary conditions.

If the metric is unknown GR has no observables or predictions at all. So either proper time on a world line is an observable, or GR has not content at all.

 

[Ken G]

I agree it's a problem that the formalism only makese sense for "classical obervers". But as I see it this is a problem of QM itself, not of interpretations.

The way I like to put what might be a similar idea is that if electrons could do physics, they wouldn't do quantum mechanics, because quantum mechanics is manifestly a theory for determining the outcomes of macroscopic couplings. So it's not that quantum mechanics doesn't work in the classical world, it's that quantum mechanics only works in the classical world. This idea might not be consistent with your ideas about generalized observers, or with Hurkyl's qubit observer, so it would be interesting to follow where that leads-- perhaps on its own thread!

I think instead the challange is to reconstruct measurement theory so that it does make sense from the point of view of a general observer.

What worries me about this program is that I see physics as fundamentally a language. It is a language that involves mathematical structures, and observational testing, but it's a language all the same. If so, then it suffers from the same limitations of all languages-- it can never do anything more than draw connections between experiences. That's all any dictionary can do, it cannot really explain what any words mean, it can only connect words to experiences by connecting words to other words that are already connected to experiences. So we might have a very complex language of particles and waves and mathematical postulates, but at the end of the day we are just connecting some experiences to other experiences, and finding patterns. How do we ever get the "classical" out of that situation, given that our experiences are the experiences of beings with a vast number of interacting subsystems? If Penrose is right that we do think "quantum thoughts", in effect, then perhaps I am wrong. But if we are fundamentally classical thinkers and perceivers, I think we're stuck with that, and no language involving a "general observer" will ever really mean anything that we can understand because we only understand what we can connect to our experiences.

The problem starts when we try to understa unification and cosmologial theories, then we can't keep referring to classical observers anymore. but these problems was not things taken into considerations when QM was constructed.

I believe that we are referencing classical observers when we construct models like unification and the early moments of the Big Bang. Certainly matter as we know it would not have existed then, so we cannot embed a Stern-Gerlach apparatus into the first femtosecond of the Big Bang, but I claim that this is essentially what we do all the same. It's because although the Stern-Gerlach and its brethren aren't there on the scene, they still provide us with all the elements of the language we will be using to talk about those early times. So the ghosts of those classical apparatuses are everywhere in the machine of the early universe, implicitly, just in ways that we can all too easily overlook if we take a highly rationalistic perspective on what is happening there. How could it be otherwise? If the language we learned from our own apparatus is no useful agent for analyzing the early universe, then it would be like saying physics changes with time, and if the language is useful, then it's still fundamentally classical.

The way I see it the collapse isa matter of perspective, and thus obsever independent. What comes as a collapsing surprise to one observer, might well be expect by anotther one. In this sense the collapse is not real as in "objective". It is however real in the sense of phenomena since the objective implication of this, is that one can imagine a mechanism (whe nreconstructing measurement theory) where the ACTION of a system, depends on that it experiencs a collapse, because at each collapse the action changes in a non-trivial way, and if you consider a sequence of collapses resulting in rational information updates - this looks just like a dynamical evoluion to a different observer.

That's an interesting insight. I guess I'd need to see an example.

 

[Fredrik]

But doesn't the density operator preserve all the useful information in the wave function, both before and after decoherence? I realize that the mapping from the wave function to the density operator is not invertible, but is any relevant information lost? For example, surely even MWI can't believe that the global phase of the wave function is physically part of the state of the system, as that would really be angels on a pin, even for MWI!

D'oh, for some reason I forgot to consider phase factors when I wrote that post. It's more accurate to say that a 1-dimensional subspace describes the universe than to say that a unit vector $|\psi\rangle$ in that subspace does. The 1-dimensional subspace can be represented by its projection operator $|\psi\rangle\langle\psi|$, which happens to satisfy the definition of a state operator. So I guess I have to take back what I said. The state of the universe is represented by $|\psi\rangle\langle\psi|$, not $|\psi\rangle$.

 

[Eqblaauw]

a serious question to people who believe in mwi,
do you feel less sad when a beloved one dies in an unlikely quantum chance event, for then he will live on in many worlds, then in a death less chance related?

 

[Fra]

it's that quantum mechanics only works in the classical world.

Good way of putting it. Makes good sense to me. Indeed QM (as it's currently formulated) ONLY works given a classical context. This is simply how it is. This is however not a statement of nature, it's more a statement of the current state of the theory.

My ambition is to improve of course, but reinterpretations doesn't solve anything as far as I can see.

That's an interesting insight. I guess I'd need to see an example.

Actually I won't deny that this is non-trivial. Like I said this isn't an pure interpretation, it's rather an interpretation that "understand QM" valid only for limiting cases. So in the extension taking this seriously really is a deep conjecture that may or many not bear fruit.

Until I am prepare to be explicit, I suppose I was hoping that the conceptual point would get across? The conceptual point is that if you consider a physical system as a player in a game, whose actions follow more or less "rationally" from what he infers from his experience in the game, then it should be clear the "description" of how this player acts, from the point of view of an outside observer will contain evolution rules suchs as hamiltonians that are in principled originating from the ignorance of the system of it's own environment.

So while no eternal observer sees the actual collapse, we can see that the system behaves just as if it did see a collapse, given the above conjecture.

Suppose you see a ghost. I see you and infer that "you look just like you've seen a ghost". It means I didn't see a ghost, but I did see someone that acts in consistency with having seen a ghost (ie. there I am connecting the presumed experience of the collapse with a rational REaction). So maybe the ghost isn't real to me, but your behaviour is. And that all that matters. This is why in the external "descrpition" the ghost is gone! Yet it's essential for understanding the action.

But this is also why I think this suggestion is non-trivial. It's not just something that makes no difference, it's rather an "interpretation" suggest a research direction that I personally see as rooted in the Bohrs view. Just that maybe we try to do what Bohr "should have done" if he knows what we knows today at that time. That's how I see it.

/Fredrik

 

[Ken G]

The conceptual point is that if you consider a physical system as a player in a game, whose actions follow more or less "rationally" from what he infers from his experience in the game, then it should be clear the "description" of how this player acts, from the point of view of an outside observer will contain evolution rules suchs as hamiltonians that are in principled originating from the ignorance of the system of it's own environment.

I do think that is an interesting perspective to take, it sort of reverses the old "god made man in his own image" into "intelligence makes perception into its own image." So perhaps we would not say the systems are themselves intelligent negotiators with their environments, but we are, so we must cast our perceptions of nature into a similar form if we are to gain understanding. So understanding is not entering into "the way nature thinks", as we often picture the process, but instead it is finding a workable way to "get nature to think like we do." It's still science because it must pass tests, but we recognize from the outset that the tests are rigged-- they have to make sense to us.

So while no eternal observer sees the actual collapse, we can see that the system behaves just as if it did see a collapse, given the above conjecture.

That sounds similar to what I would call the role of the "hypothetical" observer in science. It's a form of counterfactuality.

Suppose you see a ghost. I see you and infer that "you look just like you've seen a ghost". It means I didn't see a ghost, but I did see someone that acts in consistency with having seen a ghost (ie. there I am connecting the presumed experience of the collapse with a rational REaction). So maybe the ghost isn't real to me, but your behaviour is. And that all that matters. This is why in the external "descrpition" the ghost is gone! Yet it's essential for understanding the action.

Yes, I think that is a fitting metaphor for more or less everything that physics does. May I use it in informal settings? (On another thread, we are discussing just how "real" are or are not "virtual" particles-- your metaphor would be quite apt there.)

But this is also why I think this suggestion is non-trivial. It's not just something that makes no difference, it's rather an "interpretation" suggest a research direction that I personally see as rooted in the Bohrs view.

I agree that the real value of a good interpretation is not how it helps you understand the current theory (that's subjective), but rather how it guides you to the next one.

 

[Eqblaauw]

i'm posting it again

a serious question to people who believe in mwi,
do you feel less sad when a beloved one dies in an unlikely quantum chance event, for then he will live on in many worlds, then in a death less chance related?

 

[Hurkyl]

I don't understand, if collapse is just as good as mixed state, then one can adopt either. That means one can still use either CI or MWI, which would certainly be my expectation. If your basis for accepting MWI is that you don't think CI is workable, and that motivates you to tolerate the more bizarre ontological constructs of MWI, then I suggest the problem is with your understanding of CI.

Be aware that you are the first person I've ever encountered who says they prefer CI but could also admit that retaining the mixed state is just as good as collapsing it. (even if you prefer not to think in the former way)

I mentioned it earlier, but I think it warrants bringing it up again -- my actual take on the matter is that when an observer collapses a wave-function after measurement, it's nothing more significant than a change of "reference frame".

So when we want to understand how systems evolve, we probably consider the process of unitary evolution, without the notion of collapse entering our minds. Later, when we want to condition on past observations, we might invoke collapse to simplify the both the physical questions we ask and (possibly) calculations needed to answer them.

 

[Eqblaauw]

why don't you answer the question hurkyl? Maybe you don't explain why, maybe you do explain why, I'm curious

 

[Hurkyl]

why don't you answer the question hurkyl? Maybe you don't explain why, maybe you do explain why, I'm curious

I haven't responded to what you've written because I've been busy conversing with Ken G, and when skimming your posts, I didn't see anything that made me feel like jumping into another thread of conversation.

And to be honest, fairly or not, I felt you had been somewhat pushy and was mildly irritated. I had actually planned to make a brief response to your question, but I was put off by your insistence and it was about time to leave for work so I didn't bother.

I hadn't planned to make a big deal out of it, but since you asked directly...

And the question is pretty much purely psychology anyways. (My response would have been basically this sentence, possibly with a little more elaboration)

 

[Eqblaauw]

ok sorry for being pushy, but I think it's a relevant question, though purely psychology since when you believe a theory, it's interesting how much it affects your life,
and since we're human, it's interesting to know the human consequences of a theory

 

[Fra]

I mentioned it earlier, but I think it warrants bringing it up again -- my actual take on the matter is that when an observer collapses a wave-function after measurement, it's nothing more significant than a change of "reference frame".

I think I see your point, but there is another thing that only makes this view a partial answer IMO.

I certainly agree that collapse or not is observer dependent. This is what I said in some previous post too.

The difference that makes this still different from the usual picture of references frames of say SR is that the set of all most general observers and it's "transformations" are not konwn. I'd even say that it's impossible for an observer to defined any observer invariants, because any attempt to do so still contains another level of observer dependence and thus in principle the equivalents of higher level collapses. This is because the bird is just a big frog.

So if the big frog is the primary observers (from his picture) then all the small frogs he is watching are secondary observers. What this big frog can do, is to define invariants with respect to the secondary observers, since from the perspecive of the big frog these are like gauge choices.

This is clear, but once you acknowledge that no real observer is infinite or omnipresent, there is still an evolution of the picture the big frog has. This has implications for when you consider two big frogs interacting.

So I think I agree with that the collapse is a matter of "observer choice", but this does not mean that it's possible to fundamentally get rid of it (like we get rid of the references frames in SR). This situation is much more complex, because the covariance of the secondary pictures needs to be inferred withing the primary picture (which again is a choice).

So I'd say my picture is this: there is an hierarchy of coupled gauges (like micro and macro gauges):

In conventaional models, there is usually a "classical domain" where things are wrapped up and you get rid of all gauges and establish the invariants. In my view this is an idealisation that ignores the cosmological interactons and it's selection on the laws. /Fredrik

 

[kith]

I would say that the main assumption is that it makes sense to talk about the wavefunction of the universe, and that this wavefunction describes reality.

[...] if one goes the MWI road, then purely classical physics is also subject to the MWI interpretation.

Thanks KenG and Frederik! I'm not sure, if my issues are already solved. ;-)

First of all, it now seems clear to me that the fundamental state is a pure state also in MWI, while I was assuming that it could be mixed when I wrote my last post.

But we can't choose whether we represent this fundamental state as a ray in Hilbert space or as a density operator in MWI, because the density operator is required for assigning reality to the subsystems.

So my current understanding is this: in CI, a density operator describes the state of an ensemble of single systems. In MWI, a density operator describes the state of the single system itself (even if it's mixed). However, we cannot obtain the fundamental state by combining the states of all subsystems, due to entanglement. This gives rise to probability distributions in classical mechanics. Does this sound correct?

 

[Fredrik]

But we can't choose whether we represent this fundamental state as a ray in Hilbert space or as a density operator in MWI, because the density operator is required for assigning reality to the subsystems.

A ray is a 1-dimensional vector subspace. (Some prefer to define it differently, but this definition is good enough for this discussion). 1-dimensional subspaces are closed sets. Closed vector subspaces corrrespond bijectively to projection operators. The projection operator for a 1-dimensional subspace that contains the unit vector $|\psi\rangle$, is $|\psi\rangle\langle\psi|$. This projection operator is a state (i.e. density) operator for a pure state, and every pure state operator can be expressed in the form $|\psi\rangle\langle\psi|$ for some unit vector $|\psi\rangle$. So there's a bijective correspondence between rays and pure state operators.

So my current understanding is this: in CI, a density operator describes the state of an ensemble of single systems.

Right, and the members of the ensemble don't have to exist at the same time. It could be the systems that participate in the measurements you do when you run the same experiment over and over.

In MWI, a density operator describes the state of the single system itself (even if it's mixed). However, we cannot obtain the fundamental state by combining the states of all subsystems, due to entanglement. This gives rise to probability distributions in classical mechanics. Does this sound correct?

I don't understand what you're saying here. This is my (possibly flawed) understanding of MWI and decoherence: The state of the universe is always pure. If we decompose the universe into subsystems, say "specimen+everything else", and choose to express the state of the universe in a basis that's consists of eigenvectors of an operator that commutes with the part of the Hamiltonian of the universe that describes the interaction between the specimen and the rest of the universe, then the state operator will be approximately diagonal (after the interaction). So even though it's still pure, it will be practically indistinguishable from a mixed state.

 

[Ken G]

Be aware that you are the first person I've ever encountered who says they prefer CI but could also admit that retaining the mixed state is just as good as collapsing it. (even if you prefer not to think in the former way)

What I mean is, to an empiricist, the "state of a system" means identically this: "the way a physicist with certain information characterizes their expectations about the behavior of that system." The point being, the "state" depends on the physicist, and their information. Now, we might assert the presence of a physicist (hypothetical or real) who has access to "all the information possible in the actual reality", and give special weight to the "state" as they would describe it, but all the same, some other physicist at that same time will not mean that as the "state" of the system-- they will mean their own version, because that is what they can use. Good thing too-- generally, there is no physicist who ever has the complete information.

Given this, I can't possibly see how any CI-user, or indeed any empiricist, would see any difficulty in having a state that is "mixed" for one physicist be "just as good" for their needs, and "collapsed" for another, being "just as good" for theirs. We know what we know, and that's what we want physics for, not some imaginary situation where we know more than we know. The first physicist has seen the coin flip, but not the coin, the second has seen the coin. Neither is a "better way" to talk about that coin, one just involves having more knowledge about the coin. It is only the rationalist who demands that "the state of the coin" be something absolute, and that priority forces them to choose the mixed state over the collapsed state simply because the mixed state fits into a unitary representation of the closed system. That also forces the rationalist to discount the extra information that the physicist who has seen the coin has, as some kind of illusion. Ironic that-- the extra information they have, from having seen the coin, is treated by the rationalist as a loss of true knowledge of the coin-- before they looked, they could treat the coin in its "correct" mixed state, but now that they have looked, they must enter into their own illusion in order to function in their world! Are you starting to see the radical character of rationalism, and what empiricism is?

I mentioned it earlier, but I think it warrants bringing it up again -- my actual take on the matter is that when an observer collapses a wave-function after measurement, it's nothing more significant than a change of "reference frame".

Actually, that analogy really doesn't hold if you dig into it. An observer in a reference frame is not treated as having incomplete information about a system-- because they can transform their information into any other frame. In your analogy, the person who has looked at the coin is entering into an illusion that the coin is "heads", they cannot transform their information into any frame where the coin is "tails". In relativity, observer A can say "tell me my relationship to observer B, and I will tell you what they see". This means that A and B are seeing essentially the same thing, just in a different lexicon, they are not seeing incomplete elements of something larger than either. But if I see "heads" on a coin, there is no observer that I can say will see "tails", except exactly the observers that I imagine see tails. No other information makes that transformation for me, no communication, nothing-- it's completely tautological, those who see tails are defined by those I imagine as seeing tails. Zero empirical content, not at all like relativity. The analogy does not hold.

Indeed, I claim you have the analogy to LET exactly backward. In relativity, the "equivalence class" is all the sets of ways of talking about an event that are really saying the same thing (the invariant), so we don't need an aether because the aether embodies something different that never shows up-- the speed through the aether is not an invariant, it's not even an observable-- it is irrelevant. That's exactly the relationship we have to the "tails" result the instant we perceive "heads"-- the class of observers who see "heads" have no way of communicating or taking information of any kind from other observers to determine if they saw tails-- other than asking them what they saw (which is impossible because there's no communication across worlds). No matter what experiment the "heads" camp does to try to make contact with the existence of a "tails" camp, reality thwarts them-- no way they can detect the presence of the "tails" camp. That sounds an awful lot like an aether to me. Note that LET, just as with MWI, is not falsifiable by experiment-- but it is rejected on the grounds that if nature foils your every attempt to detect something, like the aether or anyone seeing "tails", then the empiricist takes it as a law of nature that what nature renders invisible, does not exist. That's what happened in relativity, the rationalist-motivated expectation that there should be an aether lost to the empiricist recognition that what cannot be detected should not be said to exist.

So when we want to understand how systems evolve, we probably consider the process of unitary evolution, without the notion of collapse entering our minds. Later, when we want to condition on past observations, we might invoke collapse to simplify the both the physical questions we ask and (possibly) calculations needed to answer them.

Absolutely. Said just like a CI user, except that in CI, "how systems evolve" means "how our expectations of the system change with time". Then the "notion of collapse" only enters our minds in the sense that collapse defines the very nature of what we mean by unitary evolution in the first place.