I 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"?