Help me understand indeterminism in standard quantum mechanics

[ojitojuntos]

TL;DR

Hello. I’m having a hard time understanding indeterminism and the notion of collapse. Does indeterminism suggest that the future of the universe is not fully “set”?

Hello guys. Im having some trouble understanding the role of randomness in quantum mechanics, and what does that mean for the notion of an “open future”.
For example, let’s say I take a quantum event, like some atom decaying. Does indeterminism mean that, besides predictability, if it were possible to rewind time before that decay, the moment of decay would vary?
Thanks in advance!

 

[PeterDonis]

Moderator's note: Thread moved to the QM interpretations subforum.

 

[PeterDonis]

Im having some trouble understanding the role of randomness in quantum mechanics

That role is interpretation dependent. In some interpretations, such as the MWI, there is no actual randomness anywhere; everything is entirely deterministic. The apparent randomness comes from the fact that the different branches of the wave function don't interfere, so in each individual branch, it appears as though one randomly chosen result happened. But actually, all possible results happen, each in its own branch.

Whereas, in interpretations where collapse is an actual physical process, the randomness is (or at least is claimed to be) inherent in whatever underlying dynamics produces collapses.

let’s say I take a quantum event, like some atom decaying. Does indeterminism mean that, besides predictability, if it were possible to rewind time before that decay, the moment of decay would vary?

Again, the answer is interpretation dependent.

In the MWI, there are multiple branches of the wave function at which the atom decays at different times. If you "rewound" the wave function to the start and "re-ran" it again, exactly the same branches would arise, because everything is deterministic.

Whereas in interpretations where collapse is an actual physical process, yes, whatever underlying dynamics is producing collapses might produce one (i.e., might produce a detection of the atom decaying) at a different time if things were "re-run" again with exactly the same initial conditions.

Note that in practice it's never possible to re-run things again with exactly the same initial conditions, so there's no way of actually testing claims along these lines.

 

[pines-demon]

Just trying to contribute to the answer of PD here. In some interpretations, like Bohmian mechanics you get the same result every time because it is deterministic. It is deterministic without the need of parallel branches, but with the addition of hidden (nonlocal) variables.

 

[PeterDonis]

In some interpretations, like Bohmian mechanics you get the same result every time because it is deterministic.

But only if you force the exact same input state each time--which has to include the unobservable particle positions as well as the wave function. Whereas in the MWI, for example, all you have to "rewind" to get the exact same input state is the wave function.

 

[ojitojuntos]

That role is interpretation dependent. In some interpretations, such as the MWI, there is no actual randomness anywhere; everything is entirely deterministic. The apparent randomness comes from the fact that the different branches of the wave function don't interfere, so in each individual branch, it appears as though one randomly chosen result happened. But actually, all possible results happen, each in its own branch.

Whereas, in interpretations where collapse is an actual physical process, the randomness is (or at least is claimed to be) inherent in whatever underlying dynamics produces collapses.


Again, the answer is interpretation dependent.

In the MWI, there are multiple branches of the wave function at which the atom decays at different times. If you "rewound" the wave function to the start and "re-ran" it again, exactly the same branches would arise, because everything is deterministic.

Whereas in interpretations where collapse is an actual physical process, yes, whatever underlying dynamics is producing collapses might produce one (i.e., might produce a detection of the atom decaying) at a different time if things were "re-run" again with exactly the same initial conditions.

Note that in practice it's never possible to re-run things again with exactly the same initial conditions, so there's no way of actually testing claims along these lines.

Than you! If we assume the standard Copenhagen-like interpretations, does this mean that the evolution of the universe is fundamentally probabilistic? I know we can’t perfectly rewind or replicate all variables in an experiment, but I just find fascinating the idea that a fundamentally probabilistic outcome can derive from a given state.

I read that the 2022 Nobel was awarded to researchers who have basically constrained possible quantum interpretations, and that we have ti choose between non-locality and superdeterminism to keep a fully deterministic o outlook of reality.
Why I know that we’re talking about interpretations- can it be said that modern physics favors some type over others?

 

[PeterDonis]

If we assume the standard Copenhagen-like interpretations, does this mean that the evolution of the universe is fundamentally probabilistic?

A standard Copenhagen-like interpretation doesn't take any position about what is really happening with "the evolution of the universe". All it says is that, when we make a measurement on a quantum system, we can only make probabilistic predictions about the results.

I read that the 2022 Nobel was awarded to researchers who have basically constrained possible quantum interpretations, and that we have ti choose between non-locality and superdeterminism to keep a fully deterministic o outlook of reality.

Such claims are debatable, because nothing about them can be tested by experiment--all QM interpretations make the same predictions for all experiments (because they all are interpretations of the same theory, QM, using the same or equivalent math). All they are really telling you about is the preferences of the people who make the claims about which interpretation they prefer.

can it be said that modern physics favors some type over others?

No. See above about all interpretations making the same predictions.

 

[ojitojuntos]

Oh, I see, that’s super helpful. I thought that Copenhagen did posit that the ontology was probabilistic. What type of experiment could discriminate between interpretations?

 

[PeterDonis]

I thought that Copenhagen did posit that the ontology was probabilistic.

No, Copenhagen basically says that we can't even know any "ontology" over and above the probabilistic predictions QM makes for measurement results.

What type of experiment could discriminate between interpretations?

Evidently you didn't read my post #7 carefully enough. Go read it again.

 

[ojitojuntos]

No, Copenhagen basically says that we can't even know any "ontology" over and above the probabilistic predictions QM makes for measurement results.


Evidently you didn't read my post #7 carefully enough. Go read it again.

Apologies, I understand now, I think. What do you think is the most important part of how an interpretation is built?

 

[PeterDonis]

What do you think is the most important part of how an interpretation is built?

I'm not sure what you mean. But I might be the wrong person to ask, since my own take on QM interpretations is that, while they can be useful as a crutch to help us in visualizing or intuiting what we expect to happen in a quantum experiment, none of the ones we have really work as a description of "what is really going on"--except for the "shut up and calculate" interpretation, which basically says not to bother worrying about "what is really going on" and just focus on making predictions and testing them.

 

[RUTA]

TL;DR: Hello. I’m having a hard time understanding indeterminism and the notion of collapse. Does indeterminism suggest that the future of the universe is not fully “set”?

Hello guys. Im having some trouble understanding the role of randomness in quantum mechanics, and what does that mean for the notion of an “open future”.
For example, let’s say I take a quantum event, like some atom decaying. Does indeterminism mean that, besides predictability, if it were possible to rewind time before that decay, the moment of decay would vary?
Thanks in advance!

Turns out the probabilistic (indeterministic) nature of quantum mechanics (QM) follows from the discrete outcomes. I can't explain all the details in a short post here, but you can see more starting at about the 6-min mark in my video:



Just ignore the context. I'm going to refer to work by Darrigol from this paper:

title = {``Shut up and contemplate!'': Lucien Hardy's reasonable axioms
for quantum theory},
author = {Darrigol, O.},
journal = {Studies in History and Philosophy of Modern Physics},
volume = {52},
pages = {328-342},
year = {2015}

I'm going to outline how he derives the spin-1/2 qubit probabilities using slides from my video. Here is your spin-1/2 qubit:

Now make this measurement:

Here is how Darrigol explains the outcome:

And here is how he derives the spin-1/2 qubit probabilities:

So, you see that if we would just obtain that cos(theta) outcome in the first place, we wouldn't need 'average-only' projection whence a probabilistic outcome (qubit superposition). It's the discrete outcomes that force us into implementing the "correspondence requirement" whence indeterminism. And, the discreteness requirement is itself a real mystery, as Darrigol admits:

From a physical point of view, [discreteness] is a non-trivial assumption. … In the present state of this approach, we should probably content ourselves with the insight that quantum discontinuity, if it is admitted as a fundamental feature of the microworld and if it is complemented with natural axioms concerning the relation between micro- and macro-world, necessarily leads to quantum mechanics as we know it.

In other words, if we assume discreteness and correspondence, then QM follows, but we don't have any a priori justification for the discreteness assumption.

 

[ojitojuntos]

Thank you!
Now, I was reading about the PBR theorem. As I understand it, it states that the wave function must be a real physical thing. Is this an implicit support of deterministic interpretations? Specially since I’ve read that collapse models are increasingly constrained.

 

[PeterDonis]

As I understand it, it states that the wave function must be a real physical thing.

That's not quite what it says, although many of its proponents claim that it is. Their claim is based on the particulare interpretation (or class of interpretations) of QM that they are implicitly assuming.

What the PBR theorem actually says, strictly speaking, is that the wave function cannot be a probability distribution over some set of underlying states. But that already makes implicit assumptions about what kind of interpretation of QM you are using.

See these previous PF threads for more:

Graduate Thread 'Is the Ensemble Interpretation Inconsistent with the PBR Theorem?'

Jan 17, 2021

[Moderator's note: Spun off from another thread due to topic and subforum change.]

I think Ballentine's interpretation is ruled out by the PBR theorem. Maybe we could discuss that?

• Demystifier
• Ensemble Interpretation Theorem
• Replies: 85
• Forum: Quantum Interpretations and Foundations

Graduate Thread 'Is there an additional assumption in the PBR theorem?'

Nov 17, 2018

I have been reading up on the PBR theorem, and it seems to me that there might be an additional assumption that is not discussed in the treatments I have read. The most comprehensive treatment of the general subject of theorems of which PBR is an example (theorems which attempt to show that the quantum state $\psi$ must be ontic) is this paper by Leifer:

https://arxiv.org/pdf/1409.1570.pdf

I'll briefly sketch my understanding of the theorem in order to point out the additional assumption that seems to me to be made, but which I don't see discussed. In Example 7.9 in Leifer's...

• PeterDonis
• Theorem
• Replies: 120
• Forum: Quantum Physics

Undergrad Thread 'Understanding PBR's Additional Assumption'

Nov 27, 2018

This thread is inspired by PeterDonis' thread about "hidden" assumptions in the PBR Theorem. He referenced Matt Leifer's in depth article on PBR (original referenced). And Demystifier has provided an excellent summary of PBR as a PDF file, which I have attached.

Leifer's "Is The Quantum State Real?" (comprehensive discussion of the subject)
https://arxiv.org/pdf/1409.1570.pdf

PBR Original (a bit more technical)
https://arxiv.org/abs/1111.3328

I am trying to follow PeterDonis' thread, but I realize I have several things I am not sure I fully understand. So I want to ask a...

• DrChinese
• Theorem
• Replies: 46
• Forum: Quantum Physics

• 

I think a fair quick summary of all this is that there is not general agreement in the QM physics community about exactly what the PBR theorem does or does not show about the "reality" of the wave function.

 

[PeterDonis]

I'll probably get yelled at for branching off into philosophy

Not yelled at, but your post has been deleted. Please stick to the thread topic. Your branching off, in addition to being philosophy, makes the discussion much too broad--the actual thread topic is much narrower.

 

[RUTA]

Thank you!
Now, I was reading about the PBR theorem. As I understand it, it states that the wave function must be a real physical thing. Is this an implicit support of deterministic interpretations? Specially since I’ve read that collapse models are increasingly constrained.

Here is a nice explanation of the PBR theorem by Maudlin:



He only acknowledges the assumption of statistical independence, so you need to read the PF threads in post #14 above.

 

[bhobba]

I’m having a hard time understanding indeterminism and the notion of collapse. Does indeterminism suggest that the future of the universe is not fully “set”?

The answer is interpretation-dependent. In many worlds, for example, it is fully deterministic. Copenhagen - no. Decoherent histories (favoured by Gell-Mann and, in his final days, Feynman) sort of has a bet each way (depending on your view of 'real' and 'potentially real'):


First, I think you need to become acquainted with the modern version of Gleason's Theorem:
https://arxiv.org/abs/quant-ph/9909073

Also, it must be remembered that we know ordinary, non-relativistic QM (abbreviated here to QM) is wrong, and that our current best theory is relativistic quantum field theory (abbreviated to QFT). Surprisingly, the non-relativistic limit of QFT is not QM. This is an undergrad-level discussion, and the explanation is advanced, so those reading this are not expected to understand why, but here is the paper explaining it anyway:
https://arxiv.org/abs/1712.06605

So interpretations of QM, while interesting, are not relevant if you want to understand what QM means - basically, it is simply an approximation to QFT. We need an interpretation of QFT. The best book I know on that is unfortunately a bit pricey, but it does have the advantage of actually addressing the correct issue:
https://www.amazon.com.au/Fields-Their-Quanta-Quantum-Foundations-ebook/dp/B0DLNLLG7Y

At first, QM is mysterious, even though it is, strictly speaking, wrong (which most textbooks do not point out), and this, understandably, leaves students (thinking ones, that is, most accept it) puzzled.

As an attempt to make that puzzle more reasonable, I like to consider the following, which I call a mathematical modelling view. Think of an observation as two things interacting (at present, we think they are quantum fields) and the result of that interaction, which gives a number (assumed real), is conceptually displayed as a digital readout for simplicity. Arrange the possible numbers as vectors. The first possible number is the first entry in a vector; the second is the second entry, and so on. Arrange the vectors in a diagonal matrix, and you have a Hermitian operator (in a specific basis, but of course, we know from linear algebra that bases are really irrelevant - it is actually a linear operator in some vector space). These, we think of as observables. Now apply Gleason and, lo and behold, you have the generalised form of the Born rule. In fact, one can reasonably develop QM from these two rules alone (see Ballentine - QM: A Modern Development). Chapter 19 applies QM to the EM field (hence explaining photons), which is a good stepping stone to QFT (it evades the limiting-case issue because the photon is its own antiparticle, which, of course, is not true generally). It also contains a detailed discussion in Chapter 8 of the indeterminacy relations, which even Heisenberg got wrong (and Bohr corrected).

Bottom line here is, at the undergraduate level, I would not worry too much about these issues - they really need more advanced treatments at the graduate level. You can read Art Hobson's book as an undergraduate with a first course in QM under your belt (or simply read Lenny Susskind's book on QM - a popular book that appeared on the best seller list that includes the math - a marvel), but for now, I would leave it at that. Why is QM statistical? The interpretation-independent answer is Gleason's Theorem, and that observables are modelled as Hermitian operators. Beyond that, I would leave it until you have studied Many Worlds, Decoherent Histories and other interpretations.

Thanks
Bill

 

[bhobba]

What do you think is the most important part of how an interpretation is built?

That you must interpret QFT - not QM. Art Hobson did that in his book I referenced. While I currently advocate that interpretation, it does have issues, e.g., exactly why it is probabilistic, and even why we get single outcomes from observations.

Personally, while I believe what Art wrote is an advance over the usual literature on interpretations, further research is needed. For some speculative stuff at the lay level, see:


Thanks
Bill

 

[bhobba]

I thought that Copenhagen did posit that the ontology was probabilistic.

Not when looked at carefully. What Bohr and some other adherents did say (unecessaryily IMHO) was it was complete. That Einsten, correctly IMHO took exception to. It is a myth that Einstein thought QM incorrect - he thought it correct (as far as it went) but incomplete.

This led to the EPR paper that even today is still being reserched.

If you would like to read more on this, get 'Speakable and Unspeakable in Quantum Mechanics' by John Bell. It's been so long since I read it, I can't say if it's approachable at the undergrad level. Others may like to comment.

Thanks
Bill

 

[PeterDonis]

What Bohr and some other adherents did say (unecessaryily IMHO) was it was complete.

Only with a very...nuanced...meaning to the word "complete".

I think a better way to describe it would be that Bohr and other Copenhagen adherents said that what standard QM gives us is all we're ever going to get: that there is no deeper description of reality that standard QM is an approximation to.

Einstein took exception to that because he believed there had to be such a deeper description of reality. But so far nobody has found one.

 

[bhobba]

Thank you!
Now, I was reading about the PBR theorem.

It does not imply the reality of the quantum state (nor can it, since QM is wrong).

See the original paper:
https://arxiv.org/abs/1111.3328

'Here we present a no-go theorem: if the quantum state merely represents information about the real physical state of a system, then experimental predictions are obtained which contradict those of quantum theory. The argument depends on a few assumptions. One is that a system has a "real physical state" – not necessarily completely described by quantum theory, but objective and independent of the observer. This assumption only needs to hold for systems that are isolated and not entangled with other systems. Nonetheless, this assumption, or some part of it, would be denied by instrumentalist approaches to quantum theory, in which the quantum state is merely a calculational tool for predicting macroscopic measurement outcomes. The other main assumption is that systems that are prepared independently have independent physical states.'

Knowing that QM is not the limiting case of QFT means it can't be real; it is just a calculational tool (implied by Gleason's Theorem).

The real question is, are quantum fields real? Art Hobson's view is yes: their excitations have energy, momentum, etc. If fields are the final answer, then yes, they are real. But are they the final answer, or simply a computational tool that is an approximation to a deeper theory? As of now, we do not know (but something called effective field theory has an interesting take the reader can look into).

Most physicists agree with Art Hobson. In many ways, physicists are 'simple souls' not tying themselves up in philosophical sophistry. That said, some like David Wallace and Sean Carroll (these days anyway - he is a professor in both the physics and philosophy department at Johns Hopkins). Interestingly, both are proponents of Many Worlds.

Wienberg's view on such things makes for interesting reading:
https://web.physics.utah.edu/~detar/phys4910/readings/fundamentals/weinberg.html

Thanks
Bill

 

[gentzen]

Also, it must be remembered that we know ordinary, non-relativistic QM (abbreviated here to QM) is wrong, and that our current best theory is relativistic quantum field theory (abbreviated to QFT).

At first, QM is mysterious, even though it is, strictly speaking, wrong (which most textbooks do not point out), and this, understandably, leaves students (thinking ones, that is, most accept it) puzzled.

I think we should be more critical towards people like Niels Bohr (and also John Bell) who insist on never saying or writing anything wrong. Maybe Werner Heisenberg was a bit too cavalier, but I still like the following passage from "Physics and Philosophy" (1958):

This shows that we can never know beforehand which limitations will be put on the applicability of certain concepts by the extension of our knowledge into the remote parts of nature, into which we can only penetrate with the most elaborate tools. Therefore, in the process of penetration we are bound sometimes to use our concepts in a way which is not justified and which carries no meaning. Insistence on the postulate of complete logical clarification would make science impossible. We are reminded here by modern physics of the old wisdom that the one who insists on never uttering an error must remain silent.

 

[pines-demon]

I think we should be more critical towards people like Niels Bohr (and also John Bell) who insist on never saying or writing anything wrong.

One challenge in modern interpretations of physics is to not contradict anything Bell said. Not because it is hard, but because he is taken as the ultimate grain of truth (regarding his wording on interpretation of entanglement, not his theorem).

I was reminded today of this passage of Sidney Coleman lectures on QM:

The other day I was looking at a British videotape of Feynman explaining elementary concepts in science to an interrogator, whom I think was the producer Christopher Sykes. He asked Feynman to explain the force between
magnets. Feynman hemmed and hawed for a while, and then he got on the right track, and he said something that’s dead on the nail. He said:

You’ve got it all backwards, because you’re not asking me to explain the force between your pants and the seat of your chair. You want me, when you say the force between magnets, to explain the force between magnets in terms of the kinds of forces you think of as being fundamental—those between bodies in contact.

Obviously, I’m not phrasing it as wonderfully as Feynman. But, well, as Picasso said in other circumstances, it doesn’t have to be a masterpiece for you to get the idea. We physicists all know it’s the other way around: the fundamental force between atoms is the electromagnetic force which does fall off as one over R squared. Christopher Sykes was confused because he was asking something impossible. He should have asked to explain the pants-chair force in terms of the force between magnets. Instead he asked to derive the fundamental quantity in terms of the derived one.

Likewise, a similar error is being made here. The problem is not the interpretation of quantum mechanics. That’s getting things just backwards. The problem is the interpretation of classical mechanics.