Undergrad What is the current perspective on quantum interpretation?

[vanhees71]

The articulation of the mystery: "What is the nature of reality/causal mechanism such that the formalism maps so well to the experimental outcomes?"

Your response: "The formalism maps so well to the outcomes because the formalism maps so well to the outcomes."

Do you understand that your response provides absolutely nothing for resolving the mystery? I can't make it any clearer than that.

The point is that there is no mystery. It's just an outcome of our investigations in physics that nature is not deterministic but has to be described by a probabilistic theory named QT. That the formalism maps so well to the observations is not trivial, as you seem to suggest. It's just amazing, in how simple a way we can describe almost everything with a mathematical theory, but to find such a description is only possible through observations and finding (with some luck ;-)) the right mathematical model to describe them with a quite sparse set of fundamental "postulates". If there is any mystery, it's the question, why these mathematical descriptions work so well, as was famously asked by Wigner.

 

[Morbert]

The articulation of the mystery: "What is the nature of reality/causal mechanism such that the formalism maps so well to the experimental outcomes?"

Your response: "The formalism maps so well to the outcomes because the formalism maps so well to the outcomes."

Do you understand that your response provides absolutely nothing for resolving the mystery? I can't make it any clearer than that.

Physical theories will always have a nomological character. Even in classical physics, we can e.g. ask why one Hamiltonian is more successful than another Hamiltonian.

 

[Fra]

If there is any mystery, it's the question, why these mathematical descriptions work so well, as was famously asked by Wigner.

I can share this statement and but probably unlike Wigner, I think the question is sensible. I suspect Wigner puts it as a rethorical question.

The response to the unreasonable effectiveness of mathematics is something Smolin treated in books. Its a foundational questions for science and physics. Effectively asking, why are the laws what they are? Also this is related to

In the context of evolving law, Lee Smolin pulls another favourite quotation from 1891 of Charles Sanders Pierce, which is the.

"To suppose universal laws of nature capable of being apprehended by the mind and yet having no reason for their special forms, but standing inexplicable and irrational, is hardly a justifiable position. Uniformities are precisely the sort of facts that need to be accounted for … Law is par excellence the thing that wants a reason.
...
Now the only possible way of accounting for the laws of nature and for uniformity in general is to suppose them results of evolution.”
-- https://www.jstor.org/stable/pdf/27896847.pdf

Smolin also suggests the unreasonable effectiveness of mathematics is because its limited, rather than universal.

/Fredrik

 

[PeterDonis]

The equation is, of course, for a homogeneous medium in its rest frame.

If it's only valid in one frame, it obviously is not Lorentz invariant, or indeed any kind of invariant.

this is not in contradiction with Lorentz invariance of the equation

This is nonsense. You are contradicting yourself.

it is not my point that the theory is well-tested. The point is that there is an interpretation of modern physics compatible with common sense

Schmelzer's theory is not just an interpretation; it makes different predictions from standard "modern physics", so it is a different theory, and must be judged as a different theory, not as "just an interpretation".

If you have in mind violations of the Bell inequalities, they can be easily obtained in a classical scenario if the measurement on one side causally influences the state of the other side.

Which is obviously impossible if the two measurements are spacelike separated. Which is the whole point of discussing the Bell inequalities in the first place.

 

[PeterDonis]

First, I would recommend you to learn how to behave in a scientific discussion.

This attitude has just earned you a warning and a thread ban.

 

[PeterDonis]

This, and the paper are stupid.

Statements like this should be avoided as they add nothing useful to the discussion.

 

[Tendex]

The test I have described, as I have already said, does not require having or adopting any theory at all. It is a purely empirical measurement of a very limited result, the order in which two signals arrive.

I'm not sure if I misinterpreted your meaning here. Performing such experiment is obviously possible without any previous commitment to this or that theory or theoretical assumption. However, interpreting it's result will be very different if you assume a simultaneity convention or if you reject constancy of light speed or any other assumption, IOW interpretation of an empirical test requires commitment to some assumption or to its rejection. Even interpreting if the difference of arrival of the signals is significant requires certain assumptions about the statistical error of the apparatus employed in detection, etc.

 

[Sunil]

If it's only valid in one frame, it obviously is not Lorentz invariant, or indeed any kind of invariant. ... You are contradicting yourself.

It's not the only one. You can take the sound-Lorentz-transformed coordinates of the rest frame and get other frames where the same equation holds. The only problem is that nobody will use such artificial coordinates. The context gives us a lot of other things, like light rays, to study sound waves in condensed matter theory, and these many other things don't follow that sound-Lorentz invariance. So, the sound together with the other environment has a preferred frame.

This does not contradict that the equation for the sound waves taken alone has that sound-Lorentz invariance.

The point is that there is an interpretation of modern physics compatible with common sense

Schmelzer's theory is not just an interpretation; it makes different predictions from standard "modern physics", so it is a different theory, and must be judged as a different theory, not as "just an interpretation".

In the limit $\Xi, \Upsilon\to 0$ it gives the Einstein equations in harmonic coordinates on $\mathbb{R}^4$, thus, the field-theoretic version of GR. Which is a standard version, and, for example, used by Donoghue et al for the quantization of GR as an effective field theory.

And it gives an ether interpretation of it.

Which is obviously impossible if the two measurements are spacelike separated. Which is the whole point of discussing the Bell inequalities in the first place.

No, it is not obviously impossible, it is impossible only if one accepts Einstein causality in its strong version (that means, not microcausality of QFT or signal causality) and rejects classical causality connected to a preferred frame.

 

[PeterDonis]

I'm not sure if I misinterpreted your meaning here.

I'm not either since you keep talking about things that have nothing to do with the experiment I proposed. See below.

interpreting it's result will be very different if you assume a simultaneity convention or if you reject constancy of light speed or any other assumption

No, it won't. As I have already said, the only "result" of the experiment I proposed is which signal arrives first. There is no measurement of speed or indeed any numerical value involved; it's just a simple choice between three discrete possibilities: A arrived before B, B arrived before A, or A and B arrived at the same instant. The time ordering is all along a single timelike worldline. No "interpretation" is required. No assumption about simultaneity or the speed of light or anything else is required.

Even interpreting if the difference of arrival of the signals is significant requires certain assumptions about the statistical error of the apparatus employed in detection, etc.

No, it doesn't. The three possible results are discrete alternatives--see above. There is of course a finite resolution to our comparison of arrival times of the two signals, but that just means the third discrete alternative, "A and B arrived at the same instant", has a finite "width", so to speak--if the two signals arrive within some small enough time interval of each other, our apparatus will tell us they arrived at the same instant even though that's not literally true. But this is not a matter of statistical error; it's just a matter of finite resolution, which will be true for any detector.

 

[PeterDonis]

the sound together with the other environment has a preferred frame.

Exactly.

This does not contradict that the equation for the sound waves taken alone has that sound-Lorentz invariance.

There is no such thing as "the sound waves taken alone". The sound waves don't exist without what you are calling the "environment". This makes it fundamentally different from light, which can travel through a vacuum. You can't just handwave away that fundamental physical difference.

In the limit

By this criterion, General Relativity is the same theory as Newtonian mechanics, since "in the limit" it makes the same predictions.

classical causality connected to a preferred frame.

If your theory has a preferred frame, what's the point of even talking about Lorentz invariance--or any other kind of invariance, for that matter?

 

[Tendex]

No, it won't. As I have already said, the only "result" of the experiment I proposed is which signal arrives first. There is no measurement of speed or indeed any numerical value involved; it's just a simple choice between three discrete possibilities: A arrived before B, B arrived before A, or A and B arrived at the same instant. The time ordering is all along a single timelike worldline. No "interpretation" is required. No assumption about simultaneity or the speed of light or anything else is required.

I'm sure you can make the distinction between "result" (the 3 possibilities) and "conclusions that can be obtained from a certain result depending on the theoretical assumptions applied" just as well as I can. The latter are what give different interpretations of a "result".

No, it doesn't. The three possible results are discrete alternatives--see above. There is of course a finite resolution to our comparison of arrival times of the two signals, but that just means the third discrete alternative, "A and B arrived at the same instant", has a finite "width", so to speak--if the two signals arrive within some small enough time interval of each other, our apparatus will tell us they arrived at the same instant even though that's not literally true. But this is not a matter of statistical error; it's just a matter of finite resolution, which will be true for any detector

We agree here, I just called error what you called resolution.

 

[PeterDonis]

The latter are what give different interpretations of a "result".

And my whole point was that you do not need to do any of this in order to test whether "FTL influences" are present. The results of such a test might have different implications for different interpretations of theories, yes. But that is not what originally started out this subthread. Here is the original statement of yours that I responded to, and my response:

I would ask you how you are determining that light travels at its characteristic speed, using a one-way or a round-trip measure of lightspeed to campare it with the FTL influences

You don't have to know what speed light is traveling to test for FTL influences. You just have to emit a light signal at the same time you emit whatever supposed FTL influence you are testing, and see which one arrives first at the destination.

 

[Tendex]

And my whole point was that you do not need to do any of this in order to test whether "FTL influences" are present. The results of such a test might have different implications for different interpretations of theories, yes. But that is not what originally started out this subthread. Here is the original statement of yours that I responded to, and my response:

Ok, I have no problem with that response. I might have mixed it up with a second instance where you responded talking about your experiment being "one way" but that was when we hadn't cleared up yet about the issue with tachyons. Sorry about my insistence.

 

[Sunil]

In classical theory with just Galilean relativity FTL influences are no big deal and don't affect causality in any way since the speed of light is not a maximum,so they shouldn't require a theory that constructs probabilities in a different way than the classical real probabilities, however quantum theory does require it to obtain better predictions.

There is no reason and no base to construct probabilities in some different way. $\rho(q)=|\psi(q)|^2$ is a quite normal probability, it follows a continuity equation.

There is no such thing as "the sound waves taken alone". The sound waves don't exist without what you are calling the "environment". This makes it fundamentally different from light, which can travel through a vacuum. You can't just handwave away that fundamental physical difference.

We don't know the theory below Planck length, so we don't know if the waves we observe travel through a "vacuum" or some sort of ether which does not have Lorentz invariance on the fundamental level. If there is a fundamental difference between them is your metaphysical hypothesis.

By this criterion, General Relativity is the same theory as Newtonian mechanics, since "in the limit" it makes the same predictions.

No. I have not said that the limit is the same theory. What I claim is that an ether interpretation of field theoretic GR exists. It is the limit of Schmelzer's ether theory.

If your theory has a preferred frame, what's the point of even talking about Lorentz invariance--or any other kind of invariance, for that matter?

It allows to construct for every solution of the equations various Doppler-shifted solutions. So it is a quite useful mathematical tool. Symmetries of the equations are always useful tools, even if they are only approximate symmetries.

 

[Tendex]

There is no reason and no base to construct probabilities in some different way. $\rho(q)=|\psi(q)|^2$ is a quite normal probability, it follows a continuity equation.

That's the quantum one which is different to the classical.

 

[Sunil]

That's the quantum one which is different to the classical.

It follows a slightly different equation, but it is also a standard probability distribution, which is non-negative everywhere and has an integral of 1 over the whole configuration space. Qualitatively the same. It only changes differently. If you simply put $\hbar=0$ you get the classical equation.

This holds for the Schrödinger equation rewritten in "hydrodynamic" variables. With $\hbar=0$ the equations become classical, without the quantum potential.

 

[Tendex]

It follows a slightly different equation, but it is also a standard probability distribution, which is non-negative everywhere and has an integral of 1 over the whole configuration space. Qualitatively the same. It only changes differently. If you simply put $\hbar=0$ you get the classical equation.

This holds for the Schrödinger equation rewritten in "hydrodynamic" variables. With $\hbar=0$ the equations become classical, without the quantum potential.

But $\hbar\neq0$, and I don't want to put $\hbar=0$, also "slightly different" is highly subjective, so I don't see the relevance of your answer besides pushing once more the dBB agenda. My point was that going back to a classical explanation(like using classical trajectories or ether preferred frame) doesn't fit very well with the change in procedure to obtain probabilities from just adding up to 1 absolute values of possible outcomes to adding up squares of numbers. It doesn't matter that we get nice good old probability distributions, it doesn't fit well either that the only answers are these irreversible probabilities unlike in the classical case, so I'd say that besides what Bell's theorem discards, it also hints that interpretations that just take the math of QM and varnish it with classical trajectories go nowhere.

 

[vanhees71]

It's a bit sloppy to say $\hbar=0$. What's really meant is to do an expansion in powers of $\hbar$. Usually it's in the sense of "singular perturbation theory". It leads to the WKB approximation when applying "wave mechanics". Within the path-integral formalism the saddle-point approximation of the path integral for the propagator (or the corresponding generating functional or quantum action) is used to get equivalent results.

 

[Tendex]

It's a bit sloppy to say $\hbar=0$. What's really meant is to do an expansion in powers of $\hbar$. Usually it's in the sense of "singular perturbation theory". It leads to the WKB approximation when applying "wave mechanics". Within the path-integral formalism the saddle-point approximation of the path integral for the propagator (or the corresponding generating functional or quantum action) is used to get equivalent results.

Sure, I didn't mean there is no classical limit(in fact QM has a weird unexplained dependence on it), I was just highlighting the departure of that limit that's characteristic for QM.

 

[Sunil]

It's a bit sloppy to say $\hbar=0$. What's really meant is to do an expansion in powers of $\hbar$. Usually it's in the sense of "singular perturbation theory". It leads to the WKB approximation when applying "wave mechanics". Within the path-integral formalism the saddle-point approximation of the path integral for the propagator (or the corresponding generating functional or quantum action) is used to get equivalent results.

No, I simply meant that if you have written down the equations appropriately (continuity equation for ρ with the velocity defined by the gradient of the phase, and the phase following the quantum variant of the Hamilton-Jakobi equation) you can simply put ℏ=0 and obtain the unchanged continuity equation together with the classical Hamilton-Jacobi equation.

Without doubt, the equations are mathematically even better in the quantum variant, the classical equation usually runs quite fast into caustics. So $\hbar\neq0$ can be seen as a sort of regularization of those caustics. And you can, of course, do your expansion in powers of $\hbar$ if you like. But to get the classical equations in the hydrodynamic variables you can simply put $\hbar=0$.

But $\hbar\neq0$, and I don't want to put $\hbar=0$, also "slightly different" is highly subjective, so I don't see the relevance of your answer besides pushing once more the dBB agenda. My point was that going back to a classical explanation(like using classical trajectories or ether preferred frame) doesn't fit very well with the change in procedure to obtain probabilities from just adding up to 1 absolute values of possible outcomes to adding up squares of numbers. It doesn't matter that we get nice good old probability distributions, it doesn't fit well either that the only answers are these irreversible probabilities unlike in the classical case, so I'd say that besides what Bell's theorem discards, it also hints that interpretations that just take the math of QM and varnish it with classical trajectories go nowhere.

As usual if somebody makes claims about my "agenda", the guess is wrong, I think there are better interpretations than dBB. If you don't see the relevance of my reply, then you may have a point, given that I also have not seen the relevance of your argument.

Of course, the complex function $\psi$ does not define a probability, the probability is defined by $|\psi|^2$. So, if you want to get some probability from $\psi$ you have to do something nontrivial. Why this would be relevant or give some hints about whatever I don't understand.

 

[jambaugh]

Orthodox Copenhagen Interpretation
(Consciousness causes collapse because wave functions represent what we know about a quantum system. They are not analogues of the system's physical reality. Wave function collapse = "when we suddenly change what we know, we suddenly change what we know.")

 

[stevendaryl]

Orthodox Copenhagen Interpretation
(Consciousness causes collapse because wave functions represent what we know about a quantum system. They are not analogues of the system's physical reality. Wave function collapse = "when we suddenly change what we know, we suddenly change what we know.")

I don't think that interpreting wave function collapse as simply a change in the knowledge of the observer is actually consistent. To say that only your knowledge changed is (it would seem to me) to say that whatever you learned was true before you learned it to be true. But that is not consistent with Bell's inequality (unless we give up locality, or exploit one of the other loopholes).

 

[jambaugh]

... But that is not consistent with Bell's inequality (unless we give up locality, or exploit one of the other loopholes).

How does Bell's inequality relate in any way to wave-function collapse? If you view wave functions as mathematical objects of the same nature as probability distributions over classical sets of states then note that they both collapse when we update our information due to observation.

The collapse in Copenhagen Int. is due to CI's interpretation of wave functions et al as being descriptions of knowledge, not descriptions of state.

 

[AlexCaledin]

Oh, just assume the whole physical reality to be somehow the outcome of Collapse - and then the Copenhagen FAPP-applicability follows.

 

[Fra]

How does Bell's inequality relate in any way to wave-function collapse?

I am gussing the link stevendaryl has in mind is if you consider the wave function collapse to "only" be a simple information update of the physicists ignorance, then that is exactly the line of thinking underlying Bells hidden variables. Ie. the information is out there, and preset, and its just the experimenet who is not informed.

But violation of Bells inequality suggests the systems interacts even with the measurement device "as if" there is more to this than just ignorance of the experimenter. Ie. it seems like not only the physicists, but the whole environment, including the measurement device, is ignorant about this, and then its something more to this than merely something in the head of the physicists.

/Fredrik

 

[vanhees71]

Well, this confusion just arises from not taking the probabilistic interpretation of the state seriously. Within QT an observer has the most complete knownledge about a system, if he has prepared it in a pure state. You cannot have "more information" about the system. That's quantified by the von Neumann entropy which is 0 for pure states, which means that you have "complete information".

What's different to classical physics is that having "complete information" about the system does not imply to know the outcome of measurements of all observables but only of any complete set of compatible observables for which the prepared pure state is $\hat{\rho}=|\psi \rangle \langle \psi|$ with $|\psi \rangle$ being a common normalized eigenstate of the self-adjoint operators representing these complete compatible set of observables. Note that the preparation of the system making a complete set of compatible observables simultaneously determined uniquely leads to the preparation in the state $\hat{\rho}$.

The difference between classical and quantum physics is the difference in what is considered a state: In classical physics complete knowledge means to know the point in phase space at some time (and thus knowing the point in phase space and thus the values of all observables on the system at any time through the time-evolution of the system). That's "determinism", i.e., complete knowledge about a classical system means to know the values of all possible observables of the system.

In quantum mechanics if you completely know the system at one time, this means it's prepared in a pure state at this time, and then you have complete knowledge about the system at any later time (causality), i.e., through the time evolution of the quantum system it stays in a pure state, but this doesn't imply that you know the values of all possible observables (indeterminism).

 

[Fra]

Within QT an observer has the most complete knownledge about a system, if he has prepared it in a pure state. You cannot have "more information" about the system.

I am sure we agree on all this.

My point was rather that, at least from my perspective QM suggests to me that there is MORE to this than "only" what information the observer has or can have: When you start thinking about possible causations that can explain Alice/Bob outcomes in entanglement, its not only the original observer (which in QM is not part of dynamical interactions, except in the preparation and final detection) that has constraints on the possible knowledege, it seems to be there are also constrations on relations of the internal parts of the systems (which are NOT observer in the Copenhagen view) - because how else can we understand how "quantum interference", even after the other remote particle is disclosed?

Ie. We do not yet understand the "logic" of the quantum inteactions. All we know is that the classical Bell logic does not work. And entanglement and collapses of alice and bob are somehow key elememets in this. I am sure there is more in this to be understood here.

So I would like to put it so that I am taking the probabilistic interpretation more seriously than copenhagen interpretation, and suggests that its necessarily agent-relative, and that the "information updates" are not "only" revision of the physicists information, I think it is at the core of all physical interactions. Its not conceptually consistent imo to think of it as "only" applicable to the observer on the other side of the Heisenberg cut, exactly because the cut while important, is arbitrary.

/Fredrik

 

[jambaugh]

Jumping back in. We collapse the wave-function or rather "re-set" it with updated knowledge but to say that knowledge is resetting ignorance is presupposing the very hidden variables being denied.

In the specific EPR case. Our original knowledge is, say, that whatever we observe for A will be mirrored for B. At the same time, due to complementarity what will be measured for A (and likewise B) is something we are totally ignorant of and inherently indeterministic.

When we then measure X for component system A, we have effectively also measured system B in spite of never having interacted with it and our knowledge of them is now expressed as a distinct wave-function for each. A classically correlates product wave function for the two systems.

It hurts our ontologically habituated minds but we can see here that the measurement process is not a matter of measuring previously defined subsets of state variables at the same time as necessarily scrambling complementary state variables that were also predefined. Our measurement of A has no causal effect on B but our change in our knowledge of A changes our knowledge of B in how we are able to predict what future observations of B will be, hence both their wave-functions update. This is no different than say measuring a position of a particle after measuring its momentum. The local measurement of A is complementary to the joint measurement of A and B's "entangled" correlation.

What we have here is, according to CI, facts in that we observe specific outcomes and predictions of transition probabilities for future observed outcomes. This description of what happens is scraping the foundation of our fundamental understanding and there is no operationally meaningful way to dig deeper. It is as ill posed a question to speak about what goes on between or beneath this as it is to ask which twin is older in the classic relativistic paradox without defining a frame of reference.

Bell's theorem helps confirm this fact. But, other than this, it does not speak to the nature of the wave function/density matrix/hilbert space vector et al as representations of our knowledge of the systems potential behavior (past or future) relative to a fact of present observation. This is a distinct and intuitively unsatisfying variation from our usual, classical representation of systems as states within an ontological model.

 

[stevendaryl]

How does Bell's inequality relate in any way to wave-function collapse?

It seems that it has everything to do with wave function collapse. Einstein believed that the “collapse” was not physical, that there was some pre-existing fact of the matter about whether a measurement would give this answer or that answer, and measurement just revealed this pre-existing answer. Bell showed that interpretation can’t be correct (except for various loopholes such as superdeterminism, FTL influences, etc.)

 

[Fra]

This description of what happens is scraping the foundation of our fundamental understanding and there is no operationally meaningful way to dig deeper. It is as ill posed a question to speak about what goes on between or beneath this as it is to ask which twin is older in the classic relativistic paradox without defining a frame of reference

I think our main point of disagreement, is wether we think we can make scientitic progress by digging here or not.

We both agree we are on the edge of scientific development, therefore we necessarily stand with one foot in the air. But how else to make progress?

They KEY reason for why i think there is potential here, has do do with how one can understand the emergent behavior(hamiltonian) of a complex system, from simpler systems. This is something that the foundations of QM does not explain at all. It is simply a postulate that "there exists" a hamiltonian for example. The "knowledge" implicit in the hamiltonian, is not treated on the same beautiful footing as the state. This is why QM is not complete. But this incompleness has a totally different meaning that the Einstein meaning.

And in this line of reasoning, the "information update" seems a key concept. I object to saying it is only an information update of the observer. There is likely physics containt here. But it is not obvious until you raise the question about "interacting observers". Communicating wigners friends etc is a sort of pre-version of interaction observers. This is out of scope for current consensus of course. But I do not see how one can dismiss this as meaningless. The hypothesis generation part of the scientific process is possibly ill posed yes, but this is more a philosophical question of science.

/Fredrik