Undergrad One does not “prove” the basic principles of Quantum Mechanics

[bhobba]

I am slowly going through the book 'What Is a Quantum Field Theory?' by Michel Talagrand.

I came across the following quote:
One does not" prove” the basic principles of Quantum Mechanics. The ultimate test for a model is the agreement of its predictions with experiments.

Although it may seem trite, it does fit in with my modelling view of QM.

The more I think about it, the more I believe it could be saying something quite profound. For example, precisely what is the justification of the usual procedure to quantise a system from the Hamiltonian? Sure, as shown in Chapter 3 of QM - A Modern Development, the Schrodinger equation is derived. This suggests the usual quantisation procedure - it does not prove it.

What do others think?

Thanks
Bill

 

[PeterDonis]

What do others think?

I think it's true of any physical theory.

 

[Hornbein]

Many models lead to the same math. So a wrong model can lead to correct mathematics. This happens all the time.

 

[Herman Trivilino]

One does not" prove” the basic principles of Quantum Mechanics. The ultimate test for a model is the agreement of its predictions with experiments.

That's true for the basic principles of every physical theory.

Look at it this way. A proof starts with assumptions and uses deductive reasoning to reach conclusions. As long as the assumptions are valid the conclusion is too. But there is nothing in the conclusion that's not already in the assumptions.

Inductive reasoning reaches conclusions that are not necessarily valid, but those conclusions contain new information. The test is Nature. Do the results match what we observe in Nature? That's the value, not some proof.

 

[DEvens]

There is a lot going on here. I think the quoted text is talking about the ideas of a Popper-like approach to science. But let me sneak up on it.

There is the subject of english meanings of words like "prove." This is quite a bit laxer than a scientific meaning of it. It could be "make plausible" for example, which is not usually what science wants.

There is the somewhat stronger but still pretty lax meaning of experimental efforts. One might design an experiment that explores the predicted consequences of a particular model of a physical system. If the experiment is then performed and agrees with the model, then some might say (with quite a bit of inaccuracy) that they had proved the model. Of course we know this is not correct. Several of our most familiar models stood up to extensive tests with quite impressive accuracy and precision. And yet, they were shown to not agree with later experiments. Newton's gravity followed by Einstein's relativity is but one example.

Experiments can validate a model in a range. The statement of that is kind of dry. "This model works for this range of parameters with this degree of accuracy." It's not proof. It's demonstration the model is sufficient for a purpose to a given level of accuracy.

Very roughly speaking, this is the standpoint of Karl Popper. You don't prove theories through experiment. You test them. They either pass the test or fail. If they pass, you extend the range of validity. If a model has never failed an experimental test it is said to be viable. Meaning it could be the actual description of how the universe works. If it fails a test then it is not viable. Though it could still be adequate for calculation purposes. For many situations using Newtonian physics is perfectly adequate. And it's usually easier to do the calculations that way than using relativity. It's probably not necessary nor helpful to worry about metrics and geodesics when working out the path of a baseball in a game.

Usually scientists will have some version of this process that isn't far from this. There will undoubtably be minor ttweaks and caveats and such.

Note that it places a lot more skepticism on the process than we might in every day life. Compare an idea about, say, your neighbors and their dog and the brown material that keeps showing up on your lawn. If you saw the brown material 8 or 9 times right after doggy's walkies, then you would not keep any doubt about the accuracy of the idea. But we keep trying to test quantum mechanics after it has passed a huge number of really careful and clever tests.

So when the textbook says we don't prove the basic principles it is saying that we don't prove theory. We test it. If it passes the test then we keep the theory as a candidate for being the real way reality is. If it fails we move it over to the "use in this range of parameters for ease of calculation" shelf.

Which is a comfort to many since it tends to produce job security for scientists. A theory is never proved. So we always need to be hunting down places to test it. Can't fire me. General Relativity has not been proved. Quantum Field Theory has not been proved. There is still a huge amount of work to do.

 

[WernerQH]

One does not" prove” the basic principles of Quantum Mechanics. [quoting Michel Talagrand]

What are the "basic principles" of Quantum Mechanics? In mathematics proofs start from axioms, which were once thought to be self-evident and didn't need further proof. But Euclid's fifth axiom turned out not to be "self-evident". Most physical theories have not been axiomatized, because of the huge number of assumptions that would need to be made explicit. Also experiments and observations (for example of the heavens!) need interpretation.

Today, most physicists take it as evident that photons exist. Don't the experiments of Zeilinger and others "prove" their existence every day? Even effects like "entanglement" have been claimed as established fact. But when Bell-type experiments are explained with photons, they present us with a conundrum:
(1) Photons have polarization.
(2) The polarization of photons is preserved while they travel from the source to the detectors.
(3) The detected anti-correlation of the photons is due to them being produced at the source in opposite states of polarization.
(4) Bell's theorem shows that it is impossible to assign definite polarization states to those photons.
This explanation doesn't seem to be consistent. [edit: Isn't this proof by contradiction that photons, i.e. objects travelling from the source to the detectors, cannot exist?]

QED describes the photons in Bell-type experiments as completely unpolarized (considering their reduced density matrix). Based on the field concept, QED is considered a local and causal theory. But locality and causality are puzzling features of this "explanation". The "quantum field" is local only if you consider it as a single object that exists everywhere at once. I think it is more natural to view QED as a non-local theory describing correlations between short-lived microscopic currents. (There is a parallelism between the current fluctuations in the emitting atoms and in the absorbing atoms of the detectors.)

 

[Hornbein]

I often read that an experiment is testing relativity or quantum mechanics. I think the experiment is really testing some new machine. They choose relativity or quantum mechanics because they are fairly certain there will be no confounding surprises.

 

[Herman Trivilino]

I think the quoted text is talking about the ideas of a Popper-like approach to science

Yes, but the author's claim seems to imply that it's something that applies only to quantum mechanics:

One does not" prove” the basic principles of Quantum Mechanics.

When in fact it's not unique to quantum mechanics.

 

[bhobba]

When in fact it's not unique to quantum mechanics.

That's why I did the post.

I now think it was just an offhand remark, applicable to all science, really.

Thanks
Bill

 

[bhobba]

What are the "basic principles" of Quantum Mechanics?

If you read Ballentine, he uses two axioms - the operator eigenvalue axiom and the Born Rule. Gleason links the two, leaving just one axiom that can be heuristically justified (I have posted how elsewhere).

The basic principles are clear enough and can even be heuristically reasonable.

What is not reasonable is some of its deductions, like EPR, which seem to challenge basic principles like locality. It is often not mentioned (Peter Donis is a notable exception) that locality is nuanced depending on context. It has got me into trouble several times. That's why I prefer factorisability rather than locality when discussing Bell. Note that ordinary QM, as explained by Ballantine, is explicitly based on the Galilean transformations, not the Lorentz transformations. With the Galilean transformation, locality is not an issue; to be a problem, QFT is needed, which is the unique result of replacing the Galilean transformations with the Lorentz transformations. In modern times, QFT is seen only as an Effective Field Theory - so what nature actually is is somewhat murky. If asked, I would say everything is a Quantum Field - but it is much more nuanced than that.

While the basic principles can be presented reasonably, the 'weirdness' of its logical consequences makes 'The ultimate test for a model is the agreement of its predictions with experiments' important. As well as clarity of language, of course - otherwise (and yes, I have fallen for the trap) things can get confused. I am also reading a book by Alyssa Ney, 'The World In The Wavefunction', in which she presents the view that wavefunctions are real but make more sense when viewed in a higher dimension. I will not make my final judgement until I finish the book, but I am not sure how to reconcile the reality of both wavefunctions and quantum fields. I am suspicious there may be some 'misconception' involved - they are just so easy to creep in with discussing QM.

Thanks
Bill

 

[javisot]

I am also reading a book by Alyssa Ney 'The World In The Wavefunction' where she presents the view wavefunctions are real, but make more sence when viewed in a higer dimension. I will not make my final judgement until I finish the book, but I am not sure how to reconcile the reality of wavefunctions and quantum fields. I am suspicious there may be some confusion involved.

Thanks
Bill

I don't understand that point. A function is a mathematical object (a very interesting one). The wave function is also a mathematical object.

What do they mean by saying that the wave function is "real"?

 

[bhobba]

What do they mean by saying that the wave function is "real"?

What we mean is like what we see around us every day - tables, chairs, computers, etc. That said, for a more nuanced view, read the first few chapters of Feynman's Lectures on Physics, where he discusses the example of a flat surface.

For example, when Gell-Mann proposed his quark model, he thought they were merely theoretical constructs to aid understanding of subatomic physics. Deep-inelastic scattering experiments at the Stanford Linear Accelerator Centre in 1968 provided evidence for the reality of all flavours by the scattering of particles from something inside other particles. It was like when Rutherford showed that the atom was not fundamental but had a nucleus. He fired alpha particles at a target, and now and then they scattered as if they had hit something inside the atom. Physicists are simple folk, and with that sort of evidence, they concluded that atoms were not indivisible but had structure, with something dense and complex at the centre, i.e., the nucleus. The Quark experiments similarly showed that the protons and neutrons of the nucleus had a real internal structure.

I suppose philosophers could 'finesse' the situation and maintain that the nucleus, quarks, etc., were merely mathematical constructs. Still, as I said, physicists are simple souls - it was much easier for them to be real.

Wavefunctions are not like that. There is no compelling evidence that they are real - they could be just a calculational tool. Quantum Fields could be the same as well - it's just that in QFT, things we think of as real, like Quarks, are 'excitations' in the quantum field. Again, physicists are simple souls - it is easier to think of quantum fields as also real. But these days we think of quantum fields as a low-energy approximation to something at much higher energies (Effective Field Theory), which muddies the waters somewhat.

 

[PeterDonis]

That's why I prefer factorisability rather than locality when discussing Bell. Note that ordinary QM, as explained by Ballantine, is explicitly based on the Galilean transformations, not the Lorentz transformations. With the Galilean transformation, locality is not an issue; to be a problem, QFT is needed

This might be a bit misleading. Bell did not make any specifically relativistic assumptions when deriving his inequalities, so Bell inequality violations are just as much of a conceptual issue for non-relativistic QM as for relativistic QM (QFT). Bell used the word "locality" to describe what is really the factorizability assumption, so his version of "locality" is also just as much of a conceptual issue for non-relativistic QM as for QFT.

 

[bhobba]

This might be a bit misleading. Bell did not make any specifically relativistic assumptions when deriving his inequalities, so Bell inequality violations are just as much of a conceptual issue for non-relativistic QM as for relativistic QM (QFT). Bell used the word "locality" to describe what is really the factorizability assumption, so his version of "locality" is also just as much of a conceptual issue for non-relativistic QM as for QFT.

As always, Peter, thanks for the clarification. If QFT were actually, in the Einstein SR sense, non-local, then it would be in big trouble - but of course it isn't. It's just being 'loose' with language.

Thanks
Bill

 

[PeterDonis]

If QFT were actually, in the Einstein SR sense, non-local, then it would be in big trouble - but of course it isn't.

Yes, that's true, although the way it isn't is somewhat counterintuitive. Spacelike separated measurements can still be correlated, sufficiently to violate the Bell inequalities--they just have to commute, i.e., the results can't depend on the order in which they're made. Some people seem to be fine with calling that "local"; others, not so much.

 

[A. Neumaier]

I am also reading a book by Alyssa Ney, 'The World In The Wavefunction', in which she presents the view that wavefunctions are real

More interesting (and applicable to QFT) is the book
A. Hobson, Fields and Their Quanta, 2024.
It also gives a realist account, but in 4 dimensions!

 

[bhobba]

More interesting (and applicable to QFT) is the book
A. Hobson, Fields and Their Quanta, 2024.
It also gives a realist account, but in 4 dimensions!

Art has written some popular accounts with Rodney Brooks. It's not cheap, but it's Christmas time, and I am 70 now - you can't take it to the grave. So I got a copy - thanks for the recommendation.

I think Alesa may be a professional philosopher, and so far, it does have that flavour.

Thanks
Bill

 

[WernerQH]

The basic principles are clear enough and can even be heuristically reasonable.

Do you think that the "basic principles" of quantum theory have reached their final form? I don't. Ballentine's two postulates depend on two notions that I find problematic: "state" and "observable". Ballentine emphasizes that they are not mathematical, but physical concepts and firmly related to the real world. But "state of a system" implicitly assumes (pseudo-)markovian evolution, the convenient idea that the evolution of a system does not depend on its entire previous history, but merely on its "state" at a particular instant of time. Of course it is possible to introduce fields as book-keeping devices tracking a system's history. With the additional "advantage" of giving the appearance of locality to a theory that is clearly non-local. Art Hobson, in his article There are no particles, there are only fields wrote:

Localization occurs at the time of this click. Each region i responds by interacting or not interacting, with just one region registering an interaction because a quantum must give up all, or none, of it's energy.

How can one insist on "locality", when conservation of total energy, a clearly non-local concept, plays such a critical role? For me, locality is not a fundamental physical principle, but more a technical detail of some theories. But I don't want to enter another endless debate on the proper meaning of "locality".

My main point was about the term "quantum object". Objects are thought to have properties, but we can't always attribute definite polarization states to photons. With uncertainty coming in, the focus was wisely shifted from "measuring" pre-existing properties to what is accidentally "observed". John Bell was obviously unhappy with the term "observable" and created the word "beable" to emphasize that it is tied to the real world and not just a mathematical operator. In another thread here on PF another neologism was used: "emergeable". Unfortunately, these words just don't clarify what quantum (field) theory is about. I can't believe that it is about wavefunctions, or quantum objects and measurements performed on them.