Undergrad Are there signs that any Quantum Interpretation can be proved or disproved?

[WernerQH]

In QFT 'particles' are created and annihilated at a particular location.

Exactly. Only the locations are real. What "travels" between them (particles or waves) are figments of our classical imagination. The field quanta are identical, which means the locations can be connected in different, but indistinguishable ways. All Feynman diagrams contribute and have to be summed over.

 

[gentzen]

It’s not clear to me that Bose-Einstein statistics are particularly “quantum”.

That is a bit unfair, I already went from Planck's less "quantum" derivation in 1900 to Bose's in 1924, for this tiny bit of additional legitimacy. And what about the thermal state? In a sense, the possibility to define what is meant by "constant" (in time) gives significance to the energy eigenstates here. (In general relativity, it gets hard to define what is mean by "constant".) So you get an operational meaning from a symmetry. I find this very quantum.

Many energy eigenstate computations that students will do in their first course on quantum mechanics won't need more for being interpreted in the sense of providing predictions about the real world. (In a subsequent answer, I already stated that this does not cover all practically relevant preparation and measurement procedures.)

 

[stevendaryl]

It’s not clear to me that Bose-Einstein statistics are particularly “quantum”. Their derivation is the same as Maxwell-Boltzmann statistics except the assumption of indistinguishability (in counting the number of states).

I probably should amend that, The most convenient way to "count states" is to start with discrete energy levels, and count the number of ways those states can fill up with particles. So I guess quantum mechanics is implied by starting with energy levels.

 

[vanhees71]

The way to "count states" is what's particularly quantum for both fermions and bosons. One of the great puzzles solved by QT is the resolution of Gibbs's paradox. Before the discovery of quantum statistics by Bose and Einstein or Pauli, Jordan, and Dirac it was solved by Boltzmann with one of the many ad-hoc adjustments of the classical theory.

 

[atyy]

@Demystifier - is Bohmian Mechanics consistent with the standard lore of quantum statistical mechanics and identical particles? In classical mechanics, there are no identical particles since particles have distinct trajectories at all times, so the resolution of the Gibbs paradox is a fudge. It is often said that quantum mechanics gives the true resolution of the Gibbs paradox, since quantum particles don't have trajectories and can truly be swapped. But in BM, particles have trajectories, so does it mean that the proper derivation of the Gibbs factor is also a fudge in QM?

 

[Demystifier]

@Demystifier - is Bohmian Mechanics consistent with the standard lore of quantum statistical mechanics and identical particles? In classical mechanics, there are no identical particles since particles have distinct trajectories at all times, so the resolution of the Gibbs paradox is a fudge. It is often said that quantum mechanics gives the true resolution of the Gibbs paradox, since quantum particles don't have trajectories and can truly be swapped. But in BM, particles have trajectories, so does it mean that the proper derivation of the Gibbs factor is also a fudge in QM?

The answer to the last question is - no. To understand it, one must first fix the language. In the Bohmian language, the particle is, by definition, an object with well defined position $x$. So a wave function $\psi(x)$ is not a particle, it is a wave function that guides the particle. So when in quantum statistical mechanics we say that "particles cannot be distinguished", what it really means is that the wave function has certain symmetry (or anti-symmetry). In other words, quantum statistical mechanics is not a statistical mechanics of particles; it is a statistical mechanics or wave functions. This means that all standard quantum statistical mechanics is correct in Bohmian mechanics too, with the only caveat that one has to be careful with the language: standard quantum statistical mechanics is not a statistics of particles, but a statistics of wave functions. In particular, the Gibbs factor in standard quantum statistical mechanics is perfectly correct and well justified, provided that you have in mind that this factor counts wave functions, not particles.

 

[physicsworks]

Also I didn't claim that the macroscopic behavior is not described by the underlying microscopic dynamics. To the contrary it is derivable from it by quantum statistics.

Then you need to derive from quantum statistics that, upon interacting with a particle to be detected, the detector is not - as the Schrödinger equation predicts - in a superposition of macroscopic states with pointer positions distributed according to Born's rule, but that it is in a macroscopic state where one of the pointer positions is actually realized, so that we can see it with our senses.

Since you claim that this is derivable, please show me a derivation! If valid, it would solve the measurement problem!

This last quote misses the point. Because the detector entangled with the microscopic system in question is a macroscopic object consisting of typically more than $N=10^{20}$ atoms and because our observations are based on its collective coordinates, i.e. quantities averaged over macroscopic numbers of order $10^{20}$, it turns out that quantum interference effects between two (approximately) classical states of these collective coordinates are suppressed by the double exponential factor of $e^{-10^{20}}$, and are, even in principle, unobservable. This double exponent is so astonishingly small, that its inverse, viewed as a time interval, doesn't even need a unit of time to be attached to it, because it is basically the same HUMONGOUS number, no matter if one measures it in Planck units or in ages of the Universe. In addition, since macroscopic detectors are almost impossible to completely isolate from the environment, especially on such gigantic time scales, the usual environmental decoherence makes the above overlap between states even tinier.

Thus, in dealing with such collective coordinates, we may employ the usual rules of classical probability, if we are willing to make an error of order less than $e^{-10^{20}}$. In particular, we may employ the rules of conditional probability and, after monitoring individual histories of collective coordinates (corresponding to specific positions of a needle on the dial of our macroscopic detector), apply Bayes’ rule to throw out the window the portion of the probability distribution that was not consistent with our observation of the collective coordinate, and to rescale the rest of the distribution. This is essentially what "collapse" is all about.

All of the above is nicely and pedagogically explained in the new QM book by Tom Banks (a great addendum to Ballentine's book, in my opinion).

 

[Jarvis323]

In terms of interpretation being a misnomer for interpretations which make new predictions, is there a formal definition of what a prediction in this sense is? Do they need to be analytical predictions? Or could they be predictions which are only derivable through simulation, and how about recursively enumerable but not co-recursively enumerable predictions (sets of predictions which cannot be analytically determined to be predictions, and are only determinable to be predictions if they are predictions)?

In other words, in some cases, maybe it is not knowable whether an interpretation is an interpretation, and whether it is provable testable, until/unless it is successfully proven tested. If that were the case, then we could be in store for a never ending quest to determine if an interpretation adds predictions on top of QM, or if it is supported by observation is correct, and in the meantime, nobody could ever rule the question in hand to be a matter of philosophy rather than science.

 

[A. Neumaier]

in dealing with such collective coordinates, we may employ the usual rules of classical probability

This is common practice, but not a derivation from first principle. Nobody doubts that quantum mechanics works in practice, the question is whether this working can be derived from a purely microscopic description of the detectors (plus measured system and environment) and unitary quantum mechanics.

I'd be very surprised if such a derivation is in the book by Banks. Can you point to the relevant pages?

 

[WernerQH]

This is common practice, but not a derivation from first principle.

It may be helpful to step back and have a closer look at what those "first" principles are. Otherwise you may be setting yourself an unattainable goal.

 

[A. Neumaier]

you may be setting yourself an unattainable goal.

It is a cheap way out to declare a goal that is not yet achieved to be unattainable.

Progress is made by making the unreachable reachable.

 

[Fra]

This last quote misses the point. Because the detector entangled with the microscopic system in question is a macroscopic object consisting of typically more than $N=10^{20}$ atoms and because our observations are based on its collective coordinates, i.e. quantities averaged over macroscopic numbers of order $10^{20}$, it turns out that quantum interference effects between two (approximately) classical states of these collective coordinates are suppressed by the double exponential factor of $e^{-10^{20}}$, and are, even in principle, unobservable.

By a similar argument one could argue that the detailed hamiltonian for such system + macroscopic detector is in principle not inferrable by an observer?

If it is not inferrable, does it have to exist? We have high standards for the observable status of certain contexual things, but not on the hamiltonian, why? Isn't this deeply disturbing?

/Fredrik

 

[physicsworks]

This is common practice, but not a derivation from first principle.

a derivation of what? The above estimation by Banks is just a way to show that the quoted statement

you need to derive from quantum statistics that, upon interacting with a particle to be detected, the detector is not - as the Schrödinger equation predicts - in a superposition of macroscopic states with pointer positions distributed according to Born's rule, but that it is in a macroscopic state where one of the pointer positions is actually realized, so that we can see it with our senses.

is a common mistaken belief and, more importantly, to demonstrate in what sense classical mechanics emerges as an approximation of QM. It uses simple counting of states, it is very general (i.e. not relying on a particular model of the macroscopic detector) and is based on first principles, such as the principle of superposition, locality of measurements, etc. It is not a derivation per se because we are dealing with the dynamics of a macroscopic number of particles constituting the detector, for which humans have not yet developed exact solutions of EOMs and probably never will. However, this is OK, and we don't need to wait for them to make such an amazing accomplishment, because we know from the above estimation (rather, underestimation) that the discussed interference effects are not observable even in principle. Not for all practical purposes, but in principle, since any experiment that is set to distinguish between classical and quantum-mechanical predictions of these effects would have to ensure the system is isolated over times that are unimaginably longer than the age of the Universe.

Nobody doubts that quantum mechanics works in practice, the question is whether this working can be derived from a purely microscopic description of the detectors (plus measured system and environment) and unitary quantum mechanics.

I am sorry, this sounds like circular logic to me. Are you really talking about deriving quantum mechanics from quantum mechanics here? The above estimation is quantum mechanical. We are trying to interpret classical mechanics, not quantum mechanics. Otherwise we would look like Dr. Diehard from the celebrated lecture by Sidney Coleman titled "Quantum mechanics in your face", who thought that deep down, it's classical.

Progress is made by making the unreachable reachable.

To this regard and in the context of the above discussion, I can quote Banks:

the phrase “With enough effort, one can in principle measure the quantum correlations in a superposition of macroscopically different states”, has the same status as the phrase “If wishes were horses then beggars would ride”.

By a similar argument one could argue that the detailed hamiltonian for such system + macroscopic detector is in principle not inferrable by an observer?

Why? An observer records particular values of collective coordinates associated with the macroscopic detector. As long as this detector, or any other macroscopic object like a piece of paper on which we wrote these values, continues to exist in a sense that it doesn't explode into elementary particles, we can, with fantastic accuracy, use Bayes' rule of conditioning (on those particular values recorded) to predict probabilities of future observations. If those macroscopic objects which recorded our observations by means of collective coordinates cease to exist in the above mentioned sense, then we must go back and use the previous probability distribution before such conditioning was done.

 

[A. Neumaier]

a common mistaken belief

Your beliefs and standards are so different from mine that a meaningful discussion is impossible.

 

[stevendaryl]

However, this is OK, and we don't need to wait for them to make such an amazing accomplishment, because we know from the above estimation (rather, underestimation) that the discussed interference effects are not observable even in principle.

This line of argumentation is not at all convincing to me. We agree on this fact:

• If probabilities are classical (that is, they represent lack of information; a coin is either heads or tails, but we just don't know which, and we are using probabilities to reason about the uncertainty), then there are no interference effects.

But you seem to be arguing the converse, that if there are no interference effects, then the probabilities must be classical. That's just invalid reasoning, it seems to me.

 

[physicsworks]

@stevendaryl, the argument is quite different from that. Quantum systems do not obey classical rules of probability, but a special class of compatible observables associated with macroscopic objects, the so-called collective coordinates by means of which we record our observations of the microscopic system in question, do approximately obey these rules with an unprecedented accuracy. Classical probability theory with its sum over histories rule and with probabilities representing the lack of information about initial conditions or our ignorance about it, is only an approximation of the probability theory in QM. As with any approximation, it eventually fails; in this case, when we talk about unavoidable quantum uncertainties in the initial position and velocity of a collective coordinate like the center of mass of a detector, the approximation fails if you wait long enough.

 

[stevendaryl]

@stevendaryl, the argument is quite different from that. Quantum systems do not obey classical rules of probability, but a special class of compatible observables associated with macroscopic objects, the so-called collective coordinates by means of which we record our observations of the microscopic system in question, do approximately obey these rules with an unprecedented accuracy. Classical probability theory with its sum over histories rule and with probabilities representing the lack of information about initial conditions or our ignorance about it, is only an approximation of the probability theory in QM.

Even if you want to say it is only an approximation, it seems invalid to me. In the quantum case, we know that the probabilities are NOT due to ignorance.

 

[EPR]

Quantum systems cannot obey classical probabilities, much less approximate classical probabilities for some obscure reason.
Assuming that they do is circular reasoning. Nothing in the theory says that quantum systems tend to or must approximate anything classical. Including classical probabilities.

 

[physicsworks]

Even if you want to say it is only an approximation, it’s bogus. In the quantum case, we know that the probabilities are NOT due to ignorance.

What is bogus, exactly? And, of course in QM they are not, the question is to explain in what sense classical world is an approximation to quantum, not the other way around.

Quantum systems cannot obey classical probabilities, much less approximate classical probabilities for some obscure reason.

I am not sure if this is addressed to me, but I will reply with almost an exact quote from the previous message which you probably missed or misunderstood:

Quantum systems do not obey classical rules of probability, but a special class of compatible observables associated with macroscopic objects ---- do

approximately, of course.

Assuming that they do is circular reasoning.

No one is assuming that.

I suggest reading Banks, he explains this in much more detail than I do (and much better).

 

[stevendaryl]

What is bogus, exactly? And, of course in QM they are not, the question is to explain in what sense classical world is an approximation to quantum, not the other way around.

The question is what, if anything the lack of macroscopic interference terms tells us. I thought you were suggesting that if there aren’t any interference effects, then we might as well assume the ignorance interpretation of probabilities. If you weren’t suggesting that, then what is relevance of the lack of interference effects?

 

[physicsworks]

The question is what, if anything the lack of macroscopic interference terms tells us. I thought you were suggesting that if there aren’t any interference effects, then we might as well assume the ignorance interpretation of probabilities.

I think I see now what you are asking. First, not to be too pedantic, but just to be super clear, it's not that there aren't any interference effects, it's that they are unobservable on humongous time scales compared to the age of the universe. Second, we don't assume, based on the above, the ignorance interpretation of probabilities. We merely note that (in this particular setting, when we talk about collective coordinates of macroscopic objects used to record our observations of a microscopic system entangled with them) predictions based on two calculations, one done in classical probability theory and the other done in full quantum theory, cannot be distinguished by any experiment, even in principle. In his book (and his papers) Banks uses this to explain an apparent classicality of the macroscopic world.

 

[stevendaryl]

I think I see now what you are asking. First, not to be too pedantic, but just to be super clear, it's not that there aren't any interference effects, it's that they are unobservable on humongous time scales compared to the age of the universe.

Understood, except I would say there are no observable interference effects involving macroscopically distinguishable alternatives, such as a dead versus live cat.

Second, we don't assume, based on the above, the ignorance interpretation of probabilities. We merely note that (in this particular setting, when we talk about collective coordinates of macroscopic objects used to record our observations of a microscopic system entangled with them) predictions based on two calculations, one done in classical probability theory and the other done in full quantum theory, cannot be distinguished by any experiment, even in principle. In his book (and his papers) Banks uses this to explain an apparent classicality of the macroscopic world.

Sure, I don’t disagree with that.

 

[EPR]

We merely note that (in this particular setting, when we talk about collective coordinates of macroscopic objects used to record our observations of a microscopic system entangled with them) predictions based on two calculations, one done in classical probability theory and the other done in full quantum theory, cannot be distinguished by any experiment, even in principle. In his book (and his papers) Banks uses this to explain an apparent classicality of the macroscopic world.

The above is circular reasoning.

Of course in the classical limit both QM and classical mechanics make approximately the same predictions. If

"Banks uses this to explain an apparent classicality of the macroscopic world."

then Banks doesn't know what he is talking about. You can't assume what you are trying to explain in much the same you don't assume that the reason you have a flat tire is because... you looked and saw that you have a flat tire.

 

[physicsworks]

except I would say there are no observable interference effects involving macroscopically distinguishable alternatives, such as a dead versus live cat.

Yes, it all needs to be taken in the above context of dealing with macroscopic objects and the recorded values of corresponding collective coordinates.

Sure, I don’t disagree with that.

I'm glad we understood each other.

The above is circular reasoning.

An example of circular reasoning is the 2nd sentence in #129.

Of course in the classical limit both QM and classical mechanics make approximately the same predictions.

The usual discussion of the "classical limit" of QM is incomplete at best, because it doesn't address neither the decoherence of collective coordinates, nor the locality of interactions.

then Banks doesn't know what he is talking about.

Clearly, you haven't read Banks, so you cannot tell what he is talking about.

 

[A. Neumaier]

Because the detector entangled with the microscopic system in question is a macroscopic object consisting of typically more than $N=10^{20}$ atoms and because our observations are based on its collective coordinates, i.e. quantities averaged over macroscopic numbers of order $10^{20}$, it turns out that quantum interference effects between two (approximately) classical states of these collective coordinates are suppressed by the double exponential factor of $e^{-10^{20}}$, and are, even in principle, unobservable. [...] Thus, in dealing with such collective coordinates, we may employ the usual rules of classical probability,

Unfortunately, this claim does not solve the measurement problem. Let $\psi$ be the wave function of a macroscopic system where a macroscopic pointer has, as Banks asserts, the nonzero position $x$ with tiny relative uncertainty. Let $T$ be an operator than moves the pointer from $x$ to $-x$, and consider the same system in the superposition proportional to $\psi+T\psi$. (This state can be generated by coupling to a source that moves the pointer if the measured spin turns out to be up, while it does not move it when the spin turns out to be down.) In this nonclassical macroscopic state of the device, the pointer has the very uncertain position $0\pm O(x)$. Thus Banks statement about classical states is irrelevant for the measurement problem since the collective coordinates do not behave classically on nonclassical states.

All of the above is nicely and pedagogically explained in the new QM book by Tom Banks (a great addendum to Ballentine's book, in my opinion).

The above estimation by Banks is just a way to show that the quoted statement is a common mistaken belief and, more importantly, to demonstrate in what sense classical mechanics emerges as an approximation of QM. It uses simple counting of states, it is very general (i.e. not relying on a particular model of the macroscopic detector) and is based on first principles

To this regard and in the context of the above discussion, I can quote Banks

I suggest reading Banks, he explains this in much more detail than I do (and much better).

Did it ever occur to you that Thomas Banks, your source of quantum revelations, might be mistaken in his arguments? You learned from Banks the sophist's art of ''proving'' controversial statements by repeated assertion, but not the science of self-critical logical thinking.

Banks was more self-critical than you (though not enough to see his own errors): While your language tells everyone that you know the truth and the others are mistaken, he explicitly qualifies his controversial statements on p.1 of his book as his personal beliefs:

Comparing it to one of the older texts, you will find some differences in emphasis and some differences in the actual explanations of the physics. The latter were inserted to correct what this author believes are errors, either conceptual or pedagogical, in traditional presentations of the subject.

In the piece quoted by you, Banks makes a very surprising probabilistic statement (that collective variables behave classically in arbitrary states) that I never saw anyone else make. Since you didn't want to give references to where he justified his claim I obtained his book and looked for myself. The only ''proof'' of his statement, made first on p.4 and repeated with variations numerous times throughout the book, is by manifold repeated assertion, not by a logical argument. My counterexample shows that there cannot be a valid proof of his assertion.

 

[physicsworks]

Let ψ be the wave function of a macroscopic system where a macroscopic pointer has, as Banks asserts, the nonzero position x with tiny relative uncertainty. Let T be an operator than moves the pointer from x to −x, and consider the same system in the superposition proportional to ψ+Tψ. (This state can be generated by coupling to a source that moves the pointer if the measured spin turns out to be up, while it does not move it when the spin turns out to be down.) In this nonclassical macroscopic state of the device, the pointer has the very uncertain position 0±O(x). Thus Banks statement about classical states is irrelevant for the measurement problem since the collective coordinates do not behave classically on nonclassical states.

What above and similar types of reasoning miss completely is that pointer states are ensembles with huge numbers of states that are exponential in $N=10^{20}$. This is the source of exponentially small overlap of classical histories of collective coordinates. Now, Banks's book (Chapter 10) has not one but three different arguments to show the exponentially small overlap.

[Moderator's note: Off topic content deleted.]

 

[PeterDonis]

To this regard and in the context of the above discussion, I can quote Banks:

the phrase “With enough effort, one can in principle measure the quantum correlations in a superposition of macroscopically different states”, has the same status as the phrase “If wishes were horses then beggars would ride”.

The same would apply to the claim of Banks that you are pressing in this thread, about the exponentially small interference terms that take much longer than the lifetime of the universe to observe. If it is wrong to attribute any "reality" to theoretical entities that are in principle unobservable, then it's wrong; but the position you (and Banks) are taking is that it's wrong for other people to do it, but not wrong for you.

 

[physicsworks]

If it is wrong to attribute any "reality" to theoretical entities that are in principle unobservable

these are your words, not Banks's and not mine, so the conclusion you draw from your own words in the next sentence has zero relevance to what Banks is writing.

 

[PeterDonis]

these are your words

If you want to suggest better words to describe what Banks is asserting in the quote you gave, which I referenced, feel free; I gave the quote to make sure it was clear what I was referring to, so there is no excuse for fixating on the words I used instead of the substantive point. The point I am making is based on the substance of what Banks is asserting in that quote: I am saying that that same substance also applies to Banks' own claims about the exponentially small interference terms. If you have a substantive response to that substantive point, by all means make it.

the conclusion you draw from your own words in the next sentence has zero releavance to what Banks is writing

Incorrect, since the conclusion I drew was based on the substance of what Banks said, not on the words I used to describe it.

 

[physicsworks]

If you want to suggest better words to describe what Banks is asserting in the quote you gave, which I referenced, feel free.

I suggest you read Banks's paper itself first, so you know in what context that quote was given and what are actual conclusions that he draws from the smallness of the above discussed overlap: arXiv:0809.3764. Also, you used the word "reality" which is a heavy loaded term. Given that we are in the "quantum interpretation" branch of the forum, you may want to define what you mean by that, before making conclusions about other people's positions.

Incorrect, since the conclusion I drew was based on the substance of what Banks said, not on the words I used to describe it.

I may not be the best "medium" between you and Banks. If you have not read the above paper, you can't make sensible conclusions based on one quote from it.