Would this experiment disprove Bohmian mechanics?

[Demystifier]

one can't just steal equations ... this is how one spots plagiarism

It's not plagiarism if you don't say (as Bohm didn't) that you invented those equations.

that were derived on the assumption of no paths,

The Schrodinger equation is not derived from the assumption of no paths. It is guessed from the analogy with Hamilton-Jacobi equation, which does involve paths. Moreover, the first wave equation for quantum mechanics was proposed by de Broglie, who explicitly introduced trajectories. For that reason, Bohmian theory is also called de Broglie-Bohm theory.

call them axioms and then use them to claim paths exist (in any sense) and expect to be taken seriously.

As you can see, many have taken Bohm seriously. That proves that he was right in expecting to be taken seriously.

the claims (no paths) on which the entire theory rests.

As I already said, the theory does not rest on the claim of no paths. Read about history of quantum mechanics.

 

[bolbteppa]

The Schrodinger equation is not derived from the assumption of no paths. It is guessed from the analogy with Hamilton-Jacobi equation, which does involve paths. Moreover, the first wave equation for quantum mechanics was proposed by de Broglie, who explicitly introduced trajectories. For that reason, Bohmian theory is also called de Broglie-Bohm theory... As I already said, the theory does not rest on the claim of no paths. Read about history of quantum mechanics.

This is such a fundamental misunderstanding of the most basic claims of quantum mechanics - the Schrodinger equation is absolutely derived on the assumption of no paths, please carefully (it's a hard but cool book) read secton 1 (this alone for the basic claim of no paths, but to then get the general Schrodinger equation read), 2, 3, 6, 7, 8 and then 17 (to see how specialized the non-relativistic form of the Schrodinger equation is) of Landau vol. 3 and be ready to compare to ch. 1 of vol. 1.

I should not even need to point out the flaws with going by historical derivations or the first/early attempts at making sense of QM.

This is unfortunately very typical of all of the proponents of BM I have seen so far, for example the earlier paper quoted, or discussions of spin - start from a misunderstanding of QM and then end up contradicting literally the most basic claims of the theory without realizing it, even worse when it leads to questioning special, special!, relativity - again, how is this taken seriously.

 

[bolbteppa]

For a long time I couldn't accept BM for the very reasons you state, but that's just that I've read not the best expositions of the theory. The point is that BM does not give the usual probabilistic meaning to the wave function but takes it as a "pilot wave", and the theory is a non-local deterministic theory of particle trajectories in configuration space.

I would be very open to it if you could actually explain how it makes even a hint of theoretical sense to use things like wave functions let alone insanely complicated and specialized things like the non-relativistic (my god) Schrodinger equation without fundamentally contradicting either the most basic principles of either mathematics or classical mechanics, or without fundamentally contradicting the most basic claim of QM that paths don't exist.

I was really disappointed with the leaps Bohm made after his initial setup in his paper (which also has it's issues, but we could go with it for arguments sake), it's amazing that even recent books on BM take these things as postulates...

 

[Demystifier]

and then end up contradicting literally the most basic claims of the theory without realizing it

It's OK as long as one doesn't contradict any existing experiments. And Bohm's theory doesn't.

 

[vanhees71]

Well, for a very good reason one uses non-relativistic quantum theory where it is applicable. It's just simpler to solve certain problems, e.g., the bound-state problem. Also there is indeed tension between BM and relativistic QFT. I've not yet seen a convincing concept to extend the pilot-wave ideas to relativistic QFT, but I've also not read about a clear proof that such a formulation is not possible. With Bohm's original papers I've also never been happy, but with the exposition of the theory by Dürr et al in their papers and textbooks I got convinced that de Broglie and Bohm have had a point, but weren't able to explain it clearly enough to convince the Copenhagen believers, which formed the strongest group for decades concerning the interpretation of QT (and they are the main culprits to make QM as weird as some people think it is; even without BM there's nothing weird as soon as you accept the minimal interpretation, which is FAPP all you ever need to describe real-world observations).

Einstein has been convinced for a short time after Bohm's theory came out, but very quickly he realized the "non-locality" which he (and many other physicists) couldn't accept at the time. This non-locality, however is inherent in standard QT without BM. The point of course is that (a) there was the work by Bell who made this metaphysical quibbles of Einstein's a physically testable issue, and as has been proven by zillions of experiments since the 1980ies when Aspect pioneered the field, the "non-locality" of QT is precisely what's realized in Nature.

However, and even this is denied by some proponents of Copenhagen who follow the collapse hypothesis, there's no tension with Einstein causality, because relativistic QFT is by construction microcausal and thus the S-matrix obeys the linked-cluster principle. In other words, the interactions in realtivistic QFT are strictly local by construction, while the "non-local" correlations (I prefer to say "long-range correlations" between far-distantly observed parts of a single quantum system) described by entanglement are of course still there as it must be for any QT and in accordance with all the very precise Bell experiments.

The merit of BM is that, at least for non-relativistic QT, shows that there is a consistent non-local deterministic theory which let's you derive the probabilistic interpretation (Born's rule) for microscopic systems as measured by macroscopic systems (measurement devices). On top there's no quantum-classical cut to be assumed within BM. In my opinion, however, that's also not the case in conventionally minimally interpreted QT as soon as one uses the appropriate coarse-graining procedures of many-body quantum statistics to describe the macroscopic measurement devices necessary to make observations on the microscopic systems.

 

[bolbteppa]

It's OK as long as one doesn't contradict any existing experiments. And Bohm's theory doesn't.

This is why it is absolutely shocking BM is taken seriously - just ignore all the egregious issues and inherent contradictions (coupled with basic misunderstandings of QM in actual published literature for good measure) and claim it's all OK, we are a step away from justifying intelligent design by this logic...

 

[bolbteppa]

but with the exposition of the theory by Dürr et al in their papers and textbooks I got convinced that de Broglie and Bohm have had a point, but weren't able to explain it clearly enough to convince the Copenhagen believers,

https://arxiv.org/pdf/quant-ph/9503013.pdf

https://arxiv.org/pdf/quant-ph/9504010.pdf

https://arxiv.org/pdf/quant-ph/9512031.pdf

https://arxiv.org/pdf/0903.2601.pdfThere's a bunch of papers by Duerr that all blindly use wave functions and Schrodinger equations out of thin air, just as the Quantum Physics Without Philosophy book also does - how is this convincing in the slightest?

It's basically no different to Bohm's paper starting from wave functions and the Schrodinger equation (and the craziness of using concepts derived/needed explicitly on the assumption of no paths, otherwise it'd be crazy to even use these concepts, to end up with paths existing, [again Landau vol. 3 sec 1]).

 

[Demystifier]

This is why it is absolutely shocking BM is taken seriously - just ignore all the egregious issues and inherent contradictions (coupled with basic misunderstandings of QM in actual published literature for good measure) and claim it's all OK, we are a step away from justifying intelligent design by this logic...

It's actually good for BM to have opponents like you, because then the other former opponents of BM tend to turn into supporters.

 

[bolbteppa]

It's actually good for BM to have opponents like you, because then the other former opponents of BM tend to turn into supporters.

Thank you

I'm open to being convinced, indeed that's obviously why I read into this stuff, it really is just very very unlikely given how confused the basic claims are and how they have to hide behind stealing equations and calling them axioms, I was expecting better than this - I similarly encourage you to read the references I have mentioned and to think about how seriously BM conflicts with the most basic claims of QM.

 

[Demystifier]

This non-locality, however is inherent in standard QT without BM.

Are you now fine with calling it non-locality? Recently, before you turned into a BM sympathizer, you insisted that it should be called non-separability.

 

[Demystifier]

It's basically no different to Bohm's paper starting from wave functions and the Schrodinger equation (and the craziness of using concepts derived/needed explicitly on the assumption of no paths, otherwise it'd be crazy to even use these concepts, to end up with paths existing, [again Landau vol. 3 sec 1]).

Even from a strictly logical point of view, if there was a theorem saying

no paths $\Rightarrow$ Schrodinger equation

it would not logically follow that

Schrodinger equation $\Rightarrow$ no paths

 

[bolbteppa]

Even from a strictly logical point, if there was a theorem saying

no paths $\Rightarrow$ Schrodinger equation

it would not logically follow that

Schrodinger equation $\Rightarrow$ no paths

Indeed, I said the same thing a few posts ago:

Yes, Bohm derived everything from the Schrodinger equation, of course one can take PDE's like the Schrodinger equation and end up calling things velocity fields or paths or whatever you want, one needs to justify why one can even do this.

that's why it's so insane to take the Schrodinger equation as an axiom, and hilarious to take the special case of the non-relativistic one...

 

[Demystifier]

Indeed, I said the same thing a few posts ago:

So do you agree that Schrodinger equation is compatible with the possibility that paths might exist?

 

[bolbteppa]

So do you agree that Schrodinger equation is compatible with the possibility that paths might exist?

Just so we're clear - you're asking me if one can take a PDE and then end up calling some curve/characteristic on the surface satisfying this PDE a path? Absolutely, and this is exactly why one would expect the Hamilton-Jacobi formalism to be the most likely to end up approximately similar to QM in some cases...

 

[Demystifier]

Just so we're clear - you're asking me if one can take a PDE and then end up calling some curve/characteristic on the surface satisfying this PDE a path? Absolutely, and this is exactly why one would expect the Hamilton-Jacobi formalism to be the most likely to end up approximately similar to QM in some cases...

So let me try to explain your objection against BM in my own words. You like the idea that the theory is based on paths. You just don't like the idea that a theory that is based on paths takes the Schrodinger equation as one its postulates. You would be more happy if Schrodinger equation was somehow derived, perhaps as some kind of approximation resulting from a more fundamental theory based on paths. Would that be right?

If that's your objection, then I can agree with you that such theory would be much better than BM. And some people are trying to do something like that. Nevertheless, such attempts have not been very successful, so BM seems to be the best we can do at the moment. Perhaps we should not take BM too seriously as the final theory, but I believe that at least it can serve as an inspiration in a search for a better theory.

 

[vanhees71]

https://arxiv.org/pdf/quant-ph/9503013.pdf

https://arxiv.org/pdf/quant-ph/9504010.pdf

https://arxiv.org/pdf/quant-ph/9512031.pdf

https://arxiv.org/pdf/0903.2601.pdfThere's a bunch of papers by Duerr that all blindly use wave functions and Schrodinger equations out of thin air, just as the Quantum Physics Without Philosophy book also does - how is this convincing in the slightest?

It's basically no different to Bohm's paper starting from wave functions and the Schrodinger equation (and the craziness of using concepts derived/needed explicitly on the assumption of no paths, otherwise it'd be crazy to even use these concepts, to end up with paths existing, [again Landau vol. 3 sec 1]).

Why out of thin air? The Schrödinger equation is 92 years old. You cannot say it comes out of thin air at all. There is no "assumption of no path" anywhere. You cannot derive QT logically from anything else since it's the most fundamental theory we have today. It's always a creative act to get it somehow by intuition. In Schrödinger's case it was based on de Broglie's assumption of "wave-particle duality" also for particles from the idea of "wave-particle duality" for light. Then he used the analogy to go from wave optics to ray optics by using the eikonal approximation (singular perturbation theory) backwards to derive his equation as the wave equation whose eikonal approximation leads to the Hamilton-Jacobi partial differential equation. For Heisenberg it were transition probabilities as the "observable quantities" which he derived on the island Helgoland on the example of the harmonic oscillator, and for Dirac it was the idea of "q-numbers" obeying commutation relations as given through the Poisson brackets in classical Hamiltonian mechanics.

What de Broglie and later Bohm did was to use the Schrödinger equation and the resulting wave function but they reinterpreted the physical meaning of this wave function completely compared to the mainstream Copenhagen interpretation, which indeed has more problems than it pretends to solve, because it's merely philosophical with ad-hoc assumptions that are untenable like the naive collapse used in some flavors and the quantum-classical cut, which cannot be empirically verified at all (to the contrary the more refined our engineering gets the larger objects we can prepare in "non-classical" states), and then Bohr came around murmaring mystifyingly about "the principle of complementarity". Bohm just reinterpreted the wave function as pilot wave which guides the particles on their trajectories.

 

[vanhees71]

Are you now fine with calling it non-locality? Recently, before you turned into a BM sympathizer, you insisted that it should be called non-separability.

No, as I wrote, one should not use the same word for different things. E.g., relativistic local QFT is, as its name says, local in the sense that interactions are local, but as any QT it necessarily leads to entanglement of observables of far-distant parts of quantum systems (e.g., the polarization entangled state of photon pairs from parametric down-conversion). Also Einstein carefully called this inseparability rather than non-locality. Note that Einstein was not particularly happy with one of his most famous papers, i.e., the EPR paper, and he wrote a single-authored paper later in 1948 (however in German), where he makes this particular point very clear. I guess that's also the main reason for Einstein to dislike BM, because it didn't get rid with this unseparability. Nowadays we know of course that this is a feature rather than a bug for any theory, because as the empirical results concerning Bell's inequality and all that shows that this inseparability is as Nature really behaves, and thus it's a feature not a bug of QM or BM. I think Bell is a hero from bringing QM towards "physics without philosophy/Bohrian esoterics".

 

[vanhees71]

Just so we're clear - you're asking me if one can take a PDE and then end up calling some curve/characteristic on the surface satisfying this PDE a path? Absolutely, and this is exactly why one would expect the Hamilton-Jacobi formalism to be the most likely to end up approximately similar to QM in some cases...

Obviously you haven't read the very few pages needed to understand what BM is all about. So please check, e.g., the first few pages of the 2nd paper you quoted above yourself.

 

[Demystifier]

No, as I wrote, one should not use the same word for different things.

My question is this. If we accept the terminology according to which Bell theorem shows that QM is non-separable, and if we accept the QFT-textbook terminology according to which relativistic QFT interactions are local, then what is the correct word to describe BM? Is BM non-local, or is it just non-separable?

Another important point. To understand locality of interactions in quantum theory, you don't need to deal with QFT. Ordinary non-relativistic QM has local interactions if the potential in the $n$-body Schrodinger equation has the form
$$V({\bf x}_1,\ldots, {\bf x}_n)=V_1({\bf x}_1)+\cdots +V_n({\bf x}_n)$$
BM works perfectly for such local interactions in non-relativistic QM and again leads to characteristic Bohmian "non-locality" in entangled states. Again, would you call it non-locality of BM or non-separability of BM?

Or perhaps we need a third word to charactrize BM?

 

[Boing3000]

This is such a fundamental misunderstanding of the most basic claims of quantum mechanics - the Schrodinger equation is absolutely derived on the assumption of no paths, please carefully (it's a hard but cool book) read secton 1

Indeed you have a very fundamental misunderstanding of what Landau writes.

In quantum mechanics there is no such concept as the path of a particle. This forms the content of what is called the uncertainty principle, one of the fundamental principles of quantum mechanics, discovered by W. HEISENBERG in 1927.t In that it rejects the ordinary ideas of classical mechanics, the uncertainty principle might be said to be negative in content. Of course, this principle in itself does not suffice as a basis on which to construct a new mechanics of particles. Such a theory must naturally be founded on some positive assertions, which we shall discuss below (§2).

The emphasis is mine. I am under the impression that you cannot make the difference between those two propositions:
-QM is not based on path
-QM is based on no path.

It must also be said that the uncertainty principle is not something special within QM, and that it also apply to classical mechanics (which if I understood Landau correctly, is not refuted, contains path, and is a special case of QM.

I should not even need to point out the flaws with going by historical derivations or the first/early attempts at making sense of QM.

That's true, historian's fallacy will not help at all. That's why it is fine that "silly" QFT was kept alive in the 30th even though it was not mathematically sound, plaged with infinities, and I am quite sure many people name-call it "shameful laughable unjustifiable plagiarism".
Anyway, all those theories are confirmed by experiments (in their regime) and that's why they are called "scientific".

even worse when it leads to questioning special, special!, relativity - again, how is this taken seriously.

How can QFT can be taken seriously then ? It leads to question general, general!, relativity. It is unjustifiable shameful laughable to take seriously a theory that refute that apples fall

 

[bolbteppa]

There is no "assumption of no path" anywhere.

Even proponents of BM, such as slide 4 of http://www.tcm.phy.cam.ac.uk/~mdt26/PWT/lectures/bohm7.pdf , are very clearly aware that all of standard QM can be based on the claim that there are no paths (after which you need to set up things to replace CM and this is the 'positive content' of QM as Landau calls it), it literally quotes the Landau reference I keep bringing up:

..an attitude which propagated into more or less every modern textbook:
“It is clear that [the results of the double slit experiment] can in no way be reconciled with the idea that electrons move in paths.
In quantum mechanics there is no such concept as the path of a particle.” [Landau and Lifshitz]
slide 4 - http://www.tcm.phy.cam.ac.uk/~mdt26/PWT/lectures/bohm7.pdf

In BM the Schrodinger equation comes out of thin air, it's completely unjustified... In normal QM it absolutely does not come out of thin air, it is derived, either as e.g. Dirac does it, or as e.g. Landau does based on the HUP claiming no paths exist, Born, and the necessary existence of a quasi-classical limit, it's all in the Landau reference from first principles that even BM proponents reference...

The Schrodinger equation in BM is clearly just stolen from QM and at best (this is very common) hand-wavingly justified by the existence of these historical derivations as if that makes any theoretical sense or with ludicrous things like the de Broglie relation or probability conservation out of thin air - one can even understand why people would go along with BM: 'if you take X as axioms then Y happens', fine, but it's just a game unless one can face up to the immediate issues that normal QM answers so concisely in starting from 'no paths exist'... The Durr references are no basically different to all the other BM references in this respect.

Clearly if you steal an equation derived on the assumption of no paths and then end up with paths you've made such a gigantic error your 'theory' is immediately nonsense, it's so basic...

What de Broglie and later Bohm did was to use the Schrödinger equation and the resulting wave function but they reinterpreted the physical meaning of this wave function completely compared to the mainstream Copenhagen interpretation, which indeed has more problems than it pretends to solve

I am not even going after the many contradictions other people claim arise even when you take BM at face value, that's another huge discussion, my issues with BM are way more basic, the very tools it uses are completely illegitimate to even use if they do not begin by declaring that paths don't exist and this by itself immediately invalidates the whole thing.

 

[bolbteppa]

So let me try to explain your objection against BM in my own words. You like the idea that the theory is based on paths. You just don't like the idea that a theory that is based on paths takes the Schrodinger equation as one it's postulates. You would be more happy if Schrodinger equation was somehow derived, perhaps as some kind of approximation resulting from a more fundamental theory based on paths. Would that be right?

If that's your objection, then I can agree with you that such theory would be much better than BM. And some people are trying to do something like that. Nevertheless, such attempts have not been very successful, so BM seems to be the best we can do at the moment. Perhaps we should not take BM too seriously as the final theory, but I believe that at least it can serve as an inspiration in a search for a better theory.

Roughly that's correct yeah, I even would happily justify/defend BM if I thought it made sense - it would be so shocking and so revolutionary if the claims of BM were true since they would so directly refute the most fundamental issues in QM that one simply has to examine how BM was set up, test it's logic, and see what's going on - unfortunately it just falls apart and it just isn't serious if you question it, it would be shocking if BM proponents could genuinely set up a coherent theory, the field is wide open

 

[Demystifier]

Roughly that's correct yeah, I even would happily justify/defend BM if I thought it made sense - it would be so shocking and so revolutionary if the claims of BM were true since they would so directly refute the most fundamental issues in QM that one simply has to examine how BM was set up, test it's logic, and see what's going on - unfortunately it just falls apart and it just isn't serious if you question it, it would be shocking if BM proponents could genuinely set up a coherent theory, the field is wide open

So, what's your favored view of QM? The standard Landau/Lifshitz one? Or perhaps you prefer something radically different from QM and object that BM is not radically different enough?

 

[Lord Jestocost]

If we accept the terminology according to which Bell theorem shows that QM is non-separable, and...

Bell’s theorem is about local classical theories that are a priori based on the concept of "physical realism", nothing more. It has nothing to do with what quantum mechanics is about.

 

[vanhees71]

My question is this. If we accept the terminology according to which Bell theorem shows that QM is non-separable, and if we accept the QFT-textbook terminology according to which relativistic QFT interactions are local, then what is the correct word to describe BM? Is BM non-local, or is it just non-separable?

Another important point. To understand locality of interactions in quantum theory, you don't need to deal with QFT. Ordinary non-relativistic QM has local interactions if the potential in the $n$-body Schrodinger equation has the form
$$V({\bf x}_1,\ldots, {\bf x}_n)=V_1({\bf x}_1)+\cdots +V_n({\bf x}_n)$$
BM works perfectly for such local interactions in non-relativistic QM and again leads to characteristic Bohmian "non-locality" in entangled states. Again, would you call it non-locality of BM or non-separability of BM?

Or perhaps we need a third word to charactrize BM?

Of course, you cannot discuss locality vs. non-locality in a Newtonian, i.e., non-relativistic context, since Newtonian mechanics is never non-loacal but a typical action-at-a-distance theory. What you call "non-local" in QM or BM should, however, be renamed somehow, but this will be impossible, because the unprecise language with this notion is too common.

"Locality" should be preserved for the notion in relativistic (Q)FTs, and then you should somehow name the "quantum correlations" described by entanglement differently. I think these correlations are what Einstein had in mind what he called it "inseparability" ("Inseperalität" in German). That's why my suggestion is to call it inseparability.

 

[vanhees71]

Bell’s theorem is about local classical theories that are a priori based on the concept of "physical realism", nothing more. It has nothing to do with what quantum mechanics is about.

The word "realism" I'd completely abandon from any serious physics discussion. I have never understood what the philosophers precisely mean. In most of the cases they mean "deterministic". Bell's theorem is about what he called "local deterministic theories", and that's how we should label this class of models which are all ruled out by all "Bell tests" done today.

 

[Demystifier]

Bell’s theorem is about local classical theories that are a priori based on the concept of "physical realism", nothing more. It has nothing to do with what quantum mechanics is about.

The first half of the Bell's theorem is indeed an inequality which only talks about local classical theories. But there is also the second half, which shows that quantum mechanics violates the inequality from the first half.

 

[Demystifier]

Of course, you cannot discuss locality vs. non-locality in a Newtonian, i.e., non-relativistic context, since Newtonian mechanics is never non-loacal but a typical action-at-a-distance theory.

That of course is wrong. Newtonian mechanics (which is more general concept than Newton gravity) can have both local and non-local forces. The Newton gravity is of course non-local, but potential of the form I have written in the post above is local, i.e. does not involve action at a distance.

 

[vanhees71]

Local forces are only if you have an external field, i.e., if $\vec{F}=\vec{F}(t,\vec{x}(t))$. Interactions must be instantaneous due to the Lex Tertia. That's the very point why the most simple way to realize causality in relativity is to use fields to describe interactions, i.e., you can obey momentum conservation without action at a distance since the fields are dynamical quantities carrying energy, momentum, etc.

 

[bolbteppa]

So, what's your favored view of QM? The standard Landau/Lifshitz one? Or perhaps you prefer something radically different from QM and object that BM is not radically different enough?

If I had to choose two books I would pick Landau and Dirac, of these two I would pick Landau - it's amazing that Bell translated it and becomes one of the main BM proponents

The whole Landau-Peierls Bohr-Rosenfeld relativistic quantum theory debacle is fascinating, c.f. volume 4 section 1 also, its this kind of craziness that made me look at BM properly, I can't imagine how BM could ever deal with these kinds of things (even if it made sense non-relativistically).

 

[Demystifier]

Local forces are only if you have an external field, i.e., if $\vec{F}=\vec{F}(t,\vec{x}(t))$.

That's in perfect agreement with what I said about local forces in non-relativistic Newtonian mechanics.

 

[vanhees71]

That's the big question. I'd be converted completely to BM as soon as it could be sensibly used for relativistic QFT. My feeling is, it won't be about particle trajectories but field equations with an "infinite tower" of equations a la the Schwinger-Dyson equations in standard QFT.

BTW I don't know, whether I ever have understood anything of Bohr's writings. I mean original papers by Bohr. I cannot make sense of his reply to the infamous EPR paper with the same title.

The Peierls argument concerning the non-localizability of relativistic particles, however has a heuristic point, clearly telling every beginner in relativistic QT not to waste time with socalled "relativistic QM", which is even more difficult and even less well-defined than relativistic QFT. In other words, start with relativistic QFT right away. In the "extreme relativistic" case, i.e., massless quanta (e.g., photons) you cannot even define a position observable to begin with. So any attempt to use first-quantization pictures for relativistic QT are a priori flawed, and indeed the best theory Dirac could come up with within a heuristical start with first quantization was his hole-theoretical formulation of QED, which is finally equivalent to the QFT formulation of QED, which is the only way QED should be taught in the 21st century. So forget Bjorken/Drell vol. I. Vol. II is better but also outdated (although some things are very well treated compared to some more sloppy treatments in more modern textbooks, e.g., the LSZ reduction formula).

 

[vanhees71]

That's in perfect agreement with what I said about local forces in non-relativistic Newtonian mechanics.

Yes, but they are always an approximation. The really fundamental systems in Newtonian mechanics are however closed systems of interacting particles obeying the Third Law, and thus are action-at-a-distance models.

 

[bolbteppa]

The Peierls argument concerning the non-localizability of relativistic particles, however has a heuristic point, clearly telling every beginner in relativistic QT not to waste time with socalled "relativistic QM", which is even more difficult and even less well-defined than relativistic QFT. In other words, start with relativistic QFT right away. In the "extreme relativistic" case, i.e., massless quanta (e.g., photons) you cannot even define a position observable to begin with. So any attempt to use first-quantization pictures for relativistic QT are a priori flawed, and indeed the best theory Dirac could come up with within a heuristical start with first quantization was his hole-theoretical formulation of QED, which is finally equivalent to the QFT formulation of QED, which is the only way QED should be taught in the 21st century. So forget Bjorken/Drell vol. I. Vol. II is better but also outdated (although some things are very well treated compared to some more sloppy treatments in more modern textbooks, e.g., the LSZ reduction formula).

There is a really interesting subtlety here, my understanding is that while a position-space single particle first-quantized wave function for a photon is impossible by their arguments, a momentum-space first-quantized wave function however is not only completely fine, even more insanely - only free particle momentum-space wave functions are inherently measurable in QFT in general and measuring interactions in RQT are just as meaningless as paths are in non-rel QM - as he says in the first 3 pages (previewable on amazon) here: https://www.amazon.com/dp/0750633719/?tag=pfamazon01-20

As to the first volume of B&D, the historic stuff at the beginning I still wonder about it, but once he gets to scatting he uses multi-particle wave functions so I think it's actually totally fine, and in fact a bit quicker to get things like Compton scattering, and the bits of volume 2 I've read so far are shockingly good.

 

[Lord Jestocost]

The word "realism" I'd completely abandon from any serious physics discussion.

Why? Simon Gröblacher et al. state it quite simply in "An experimental test of non-local realism" (https://arxiv.org/abs/0704.2529v2):

"Physical realism suggests that the results of observations are a consequence of properties carried by physical systems."