The reality of "Many Worlds"

  • #26
PeterDonis
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The first part - that in EPR-realistic SR one can prove Bell's theorem - is simply Bell's theorem.
Ok, so you're just using highly idiosyncratic terminology.

The quote I have given describes the preferred frame as one of the ways to solve the problem.
Which of the premises of Bell's Theorem is violated if there is a preferred frame that is unobservable, so Lorentz invariance still holds?
 
  • #27
PeterDonis
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I have to specify the Lagrangian of the matter fields to get an expression for the energy-momentum tensor of matter in the Einstein equations and to get equations for the matter fields. After this, we have already a well-defined theory with well-defined equations, and no longer a framework. But we have no particular solution yet.
If the stress-energy tensor is specified, you do have a particular solution.

Nobody defines an interpretation for some particular solution, say, a particular FLRW universe, once this can be done in a quite general way, for interpreting the fields of the theory and its equations.
We have already established that such general rules--for example, "the metric tensor describes spacetime geometry" vs. "the metric tensor describes a spin-2 field on a fixed background"--are interpretation frameworks, not interpretations, on the view we have been discussing, which you had said you agree with. If you are changing your mind and now disagree with that view, just say so and we can close out this whole subthread, which is getting pretty far off the topic of this thread anyway.

particular theories become frameworks too
Not if "particular theories" means "particular solutions of the EFE", which is what it means on the view we have been discussing. Again, if you have changed your mind and now disagree with that view, just say so. There's no point in continuing to talk past each other.

once the configuration space and the Hamilton operator is defined, we have no longer a framework, but already a particular quantum theory. Its equation is the Schrödinger equation for this particular Hamilton operator. Particular wave functions have not been chosen.
Sure they have, because only particular wave functions will solve the Schrodinger Equation for that particular Hilbert space and Hamiltonian.
 
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  • #28
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Which of the premises of Bell's Theorem is violated if there is a preferred frame that is unobservable, so Lorentz invariance still holds?
Lorentz invariance is does not hold for causality, because causality forbids only influencing the past, and only in the preferred frame. The EPR criterion of reality is no longer sufficient to prove that from the 100% correlation follows the existence of an element of reality. Either Alice's measurement of A can influence the state on Bob's side before he measures B, or Bob's measurement of B can influence the state on Alice's side before the measurement of A.

If the stress-energy tensor is specified, you do have a particular solution.
No, you have an expression for the stress-energy tensor in terms of the material fields, say, in terms of density and velocity ##\rho, v^i## of some dust.

A particular solution would require also a particular choice of the functions ##\rho(x,t), v^i(x,t)##
If you are changing your mind and now disagree with that view, just say so and we can close out this whole subthread, which is getting pretty far off the topic of this thread anyway.
Rereading my agreement, all I have agreed with remains valid, I have agreed with what I write here, GR as a general framework and GR for dust described by functions ##\rho, v^i## with a well-defined Lagrangian for the dust as a particular theory. There is nothing in this text about a specification of a particular solution
##\rho(x,t), v^i(x,t)##.

In the part about QT, you mention the particular configuration space and the Hamilton operator, but not a particular wave function.

So, my position is the framework defines a theory by defining a matter Lagrangian for GR, a configuration space and a Hamilton operator for QT, but neither a particular solution of the EFE nor a particular wave function. Your position sounds completely absurd to me.
 
  • #29
PeterDonis
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Lorentz invariance is does not hold for causality
This "causality" is unobservable in the theory you describe.

The EPR criterion of reality
I didn't ask about any "EPR criterion", I asked about Bell's Theorem. Bell's proof of his theorem doesn't use any vague ordinary language terms like "reality"; every one of his premises is stated in math. Which one is violated in a preferred frame theory of the type you're describing?

A particular solution would require also a particular choice of the functions
I thought that's what you meant by "the stress-energy tensor is specified". If you haven't specified a particular choice of the functions, then you haven't specified a stress-energy tensor, because you can't make predictions without specifying those functions; you've only given a stress-energy tensor framework.

In the part about QT, you mention the particular configuration space and the Hamilton operator, but not a particular wave function.
That's because once you have specified a Hilbert space and a Hamiltonian, solving the Schrodinger Equation tells you the wave function. Strictly speaking, I should also have included initial conditions.

Your position sounds completely absurd to me.
My position is simple: if you can't make actual predictions from it, it isn't a theory, it's just a framework. You have called a number of things "theories" that you can't make actual predictions from.
 
  • #30
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This "causality" is unobservable in the theory you describe.
So what? What matters is if it has some observable consequences. It has, namely the possibility of violations of the Bell inequality.
I didn't ask about any "EPR criterion", I asked about Bell's Theorem. Bell's proof of his theorem doesn't use any vague ordinary language terms like "reality"; every one of his premises is stated in math.
No. Bell has later emphasized that formula (2) of his paper was not postulated but derived, and here is the derivation from the original paper (emph. mine):
Now we make the hypothesis [2], and it seems one at least worth considering, that if the two measurements are made at places remote from one another the orientation of one magnet does not influence the
result obtained with the other
. Since we can predict in advance the result of measuring any chosen component of ##\vec{\sigma}_2##, by previously measuring the same component of ##\vec{\sigma}_1##, it follows that the result of any such measurement must actually be predetermined.
This is nothing but applying the EPR criterion of reality in combination with Einstein causality and formulated in sloppy physics language. [2] refers to a verbal quote of Einstein.
Which one is violated in a preferred frame theory of the type you're describing?
The emphasized part.
That's because once you have specified a Hilbert space and a Hamiltonian, solving the Schrodinger Equation tells you the wave function. Strictly speaking, I should also have included initial conditions.
Ok, so this was clearly a misunderstanding. I think my use of the word "theory" as defining the equations, but not specifying particular initial conditions (beyond the specification of the initial value problem, namely that the initial value has to be some arbitrary function ##\psi(q)\in\mathcal{L}^2(Q)## for the (also specified) configuration space Q, is the standard one.
My position is simple: if you can't make actual predictions from it, it isn't a theory, it's just a framework. You have called a number of things "theories" that you can't make actual predictions from.
That you also, additionally to the theory, have to make assumptions about the initial conditions, and, moreover, have to use even other theories (namely theories about all the involved measurement devices) is standard too. Quine has taken this position to the extreme, claiming that it is always only the whole of physics which is falsified and that to identify the part of that whole is always speculative.

I can understand your position, but it would require renaming of established terms, naming theories "framework" and naming particular solutions of a theory "theory". It would be in conflict even with established grammatic, people talk all the time, say, about "Newtonian theory", instead of "Newtonian theories" as they would have if every solution of the Newtonian equations defines a different theory.
 
  • #31
PeterDonis
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Bell has later emphasized that formula (2) of his paper was not postulated but derived, and here is the derivation from the original paper (emph. mine)
That's not a "derivation". A "derivation" would be a mathematical derivation of the mathematical statement that Bell uses in his paper from some other mathematical premise.

The emphasized part.
That's not what I asked for. What I asked for was which mathematical statement in Bell's paper is violated. It appears that your answer to that would be formula (2) of his paper.

I can understand your position, but it would require renaming of established terms
Yes, I know that (I assume that by "renaming" you actually mean "redefining"). But your position also requires redefining a term: "interpretation". This whole subthread started because you objected to my statement that all interpretations of QM use the same math. As far as I know that statement is just as "standard" as the usage of "theory" that you are saying is standard.
 
  • #32
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That's not a "derivation". A "derivation" would be a mathematical derivation of the mathematical statement that Bell uses in his paper from some other mathematical premise.
That's not what I asked for. What I asked for was which mathematical statement in Bell's paper is violated. It appears that your answer to that would be formula (2) of his paper.
If you want to restrict Bell's theorem to the part of the article beginning with formula (2), your choice. If I refer to Bell's theorem, I refer to the full paper.

The derivation is of the necessary level for a physics paper and is certainly sufficient to classify (2) as derived, and to identify the EPR criterion of reality and Einstein causality as the assumptions necessary to derive it. One should not forget that there is the EPR paper as the background which is presupposed to be known, and the derivation is rather trivial given the EPR criterion and Einstein causality. Both are formulated in a verbal way, thus, to insist on some formula written down for it makes no sense.
This whole subthread started because you objected to my statement that all interpretations of QM use the same math. As far as I know that statement is just as "standard" as the usage of "theory" that you are saying is standard.
The standard use is AFAIK that all interpretations make the same empirical predictions.

But this does not mean the same math, dBB theory in quantum equilibrium makes the same empirical predictions, but it also uses math which is not part of standard QM math, namely the guiding equation. Of course, I do not object against naming it a different theory too, given that it is a well-defined theory even outside the quantum equilibrium, and makes completely different predictions outside this equilibrium. But naming it an interpretation is also sufficiently standard.
 
  • #33
PeterDonis
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If you want to restrict Bell's theorem to the part of the article beginning with formula (2)
I have said no such thing. I simply asked which mathematical statement the theory you were referring to violated. You never answered that question, so I had to make my best guess.
 
  • #34
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I have said no such thing. I simply asked which mathematical statement the theory you were referring to violated. You never answered that question, so I had to make my best guess.
If Einstein causality is sufficiently mathematical for you, then it is Einstein causality. In a theory with preferred frame, classical causality, as defined by absolute time, is what defines causality.
 
  • #35
PeterDonis
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If Einstein causality is sufficiently mathematical for you, then it is Einstein causality. In a theory with preferred frame, classical causality, as defined by absolute time, is what defines causality.
Oh, for goodness' sake. Bell's paper has mathematical statements in it. Each one has a number. Which number points to a false statement? I fail to see why you can't just answer that question without going off into the vagaries of ordinary language terms like "Einstein causality".
 
  • #36
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Oh, for goodness' sake. Bell's paper has mathematical statements in it. Each one has a number. Which number points to a false statement? I fail to see why you can't just answer that question without going off into the vagaries of ordinary language terms like "Einstein causality".
(2) points already to a statement that cannot be proven in SR with a preferred frame. I refer to Einstein causality because I thought a precise answer has to identify the principle which holds in spacetime SR but not in preferred frame SR and to explain why (2) cannot be derived in preferred frame SR. Such an explanation has to compare how (2) is derived for spacetime SR, and to show why it fails in preferred frame SR. This derivation is given in informal, verbal form, so my explanation has an informal, verbal form.

But once you insist, no problem, (2) cannot be proven in preferred frame SR.
 

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