I Is Einstein Causality Proven in Preferred Frame SR?

[entropy1]

If MWI and collapse-theory are both possible interpretations of QM, then both of them are not a fact, right? If MWI is a fact then collapse isn't and vice versa, you could say the least. So, shut up and calculate, i.e. the minimal interpretation, makes no inference about the realness of these two interpretations. So could I then be allowed to suggest many world are not really 'many' worlds, but rather mathematical semantics?

 

[PeterDonis]

If MWI and collapse-theory are both possible interpretations of QM, then both of them are not a fact, right?

If by "fact" you mean "confirmed by experiment", then no, no interpretation of QM is confirmed by experiment. If one were confirmed by experiment, it wouldn't be an interpretation of QM any more, it would be a new theory that replaced the QM we have now.

shut up and calculate, i.e. the minimal interpretation, makes no inference about the realness of these two interpretations

Or of any other interpretation, yes.

could I then be allowed to suggest many world are not really 'many' worlds, but rather mathematical semantics?

Why would you want to suggest this? Saying "interpretation X isn't real" isn't any more justified by experiment than saying "interpretation X is real".

 

[entropy1]

Why would you want to suggest this? Saying "interpretation X isn't real" isn't any more justified by experiment than saying "interpretation X is real".

Interpretations of QM have to be compatible with the minimal math, but the minimal math is not the interpretation, for interpretations differ and thus have to contain at least one variable that distinguishes them. This extra assumption(s) are not accounted for by the minimal math. So the existence of countless universes may just be a consequence of unaccounted for assumptions. It seems that the definition of the interpretation-concept is that you are free to get one in your flavour.

 

[PeterDonis]

interpretations differ and thus have to contain at least one variable that distinguishes them

No, they don't. What distinguishes interpretations is not anything in the math; they all use the same math, what you are calling the "minimal math". If they used different math, they would make different predictions for the results of some experiments and would be different theories, not different interpretations.

 

[entropy1]

No, they don't. What distinguishes interpretations is not anything in the math; they all use the same math, what you are calling the "minimal math". If they used different math, they would make different predictions for the results of some experiments and would be different theories, not different interpretations.

Exactly! So the assumptions made are not mathematical. But then the minimal interpretation lacks some power of covering all the (non-mathematical) aspects of QM, since they are left open to interpretation and contradictory! And if that is the case, why should I take an interpretation like MWI literally?

And if I would adopt an interpretation, a different one would basicly be exactly as legitimate.

 

[PeterDonis]

So the assumptions made are not mathematical.

Whatever distinguishes the interpretations is not mathematical, yes.

 

[entropy1]

I guess I could say that "I am seeing only one world, so why should I believe in other worlds?", which is exactly the measurement problem.

 

[PeterDonis]

I guess I could say that "I am seeing only one world, so why should I believe in other worlds?"

Yes, that's a common objection to the MWI.

which is exactly the measurement problem

No, because the measurement problem exists for every interpretation of QM, not just the MWI.

 

[Elias1960]

No, they don't. What distinguishes interpretations is not anything in the math; they all use the same math, what you are calling the "minimal math".

Wrong. Interpretations can use additional math. An interpretation of relativistic gravity with preferred coordinates would use a particular coordinate condition (say, harmonic coordinates) which plays no role in the spacetime interpretation of GR. Bohmian mechanics and Nelsonian stochastics use the particular mathematics of the Schrödinger equation in the configuration space representation, mathematics which depend on the Hamilton operator having a quadratic dependence on the momentum variables. This gives, as a consequence of the Schrödinger equation, a continuity equation in configuration space, which allows to postulate the existence of continuous trajectories and defines an average velocity. From the point of the minimal interpretation, these are irrelevant properties of some particular quantum theories. Interpretations of gauge fields as physical fields defined by the gauge potential require a particular gauge condition to be interpreted as a physical equation defining the evolution of the gauge potential.

If they used different math, they would make different predictions for the results of some experiments and would be different theories, not different interpretations.

This is possible, but in no way obligatory. So, I'm not aware of anything which would make the interpretation of classical EM theory that interprets potentials as physical and the Lorenz gauge as a physical equation distinguishable from that which uses the fields as physical and the potentials as irrelevant mathematics.

Moreover, it may be that they are in principle different theories, but de facto there is no chance to distinguish them by observation. One can reasonably argue that many of those things named interpretations are in fact different theories. This would be, in fact, a natural way of theory development. One starts with inventing a new interpretation, being unaware that there exist empirical differences given that the equations are the same. Then it appears that there are, nonetheless, subtle differences that lead to some differences in empirical predictions too. But once it was named an interpretation initially, the name remains, and it is named an interpretation despite being, in a more accurate consideration, a different theory.

Nelsonian stochastics would be a classical example. It was thought to be an interpretation, but then came the Wallstrom objection, which claimed that it is, in fact, a different theory.

 

[Elias1960]

No, because the measurement problem exists for every interpretation of QM, not just the MWI.

In dBB theory as well as other realistic interpretations there exists no measurement problem.

Those interpretations have a configuration space trajectory $q(t)\in Q$ as part of the reality. This allows to define, together with a quantum description for the system as well as the measurement device, also an effective wave function of the system alone which depends on the trajectory of the measurement device, and this effective wave function collapses:
$$\psi_{eff}(q_{sys}) = \psi_{full}(q_{sys},q_{dev}(t))$$

 

[PeterDonis]

Interpretations can use additional math.

What you are describing is not "additional math". Choosing a coordinate chart is part of the standard math of GR. An analogous choice in QM would be a choice of basis in the Hilbert space of a quantum system, or a choice of representation (Schrodinger, Heisenberg, interaction, etc.).

From the point of the minimal interpretation, these are irrelevant properties of some particular quantum theories.

No, they aren't. They are part of the math that is used to make predictions. That's part of the math of the minimal interpretation. It is not "additional math".

I'm not aware of anything which would make the interpretation of classical EM theory that interprets potentials as physical and the Lorenz gauge as a physical equation distinguishable from that which uses the fields as physical and the potentials as irrelevant mathematics.

Terms like "physical" or "not physical" or "irrelevant mathematics" are interpretation; they are not part of the math. The math just says: do these mathematical operations to obtain predictions. It doesn't say anything about what is "real" or "physical".

One can reasonably argue that many of those things named interpretations are in fact different theories. This would be, in fact, a natural way of theory development.

It is in the sense that different interpretations suggest different ways of extending or modifying an existing theory.

One starts with inventing a new interpretation, being unaware that there exist empirical differences given that the equations are the same.

There can't be empirical differences if the equations are the same. Same equations = same predictions.

 

[PeterDonis]

In dBB theory as well as other realistic interpretations there exists no measurement problem.

dBB theory could be considered a different theory, since the mathematical description of the configuration space trajectories does not, as far as I can see, appear in the math of the minimal interpretation of QM.

 

[Quantum Alchemy]

If MWI and collapse-theory are both possible interpretations of QM, then both of them are not a fact, right? If MWI is a fact then collapse isn't and vice versa, you could say the least. So, shut up and calculate, i.e. the minimal interpretation, makes no inference about the realness of these two interpretations. So could I then be allowed to suggest many world are not really 'many' worlds, but rather mathematical semantics?

Good question and I think the truth lies in Godel's Incompleteness Theorem and Ontological Proof. This is a Platonic view of the universe and it's what Physicist like Tegmark calls a landscape of mathematical structures.

So in this case, all of these interpretations of QM would be true. They would make up the landscape of mathematical structures and mathematical truths would be metaphysical and exist independently of the physical universe.

If you you talk to 10 proponents of 10 different interpretations of QM they will each make a convincing argument as to why their interpretation is the correct one.

If you look at it from the standpoint of a landscape of mathematical structures, then we need to look at which part of the landscape are we residing in. Are we residing in a many worlds part of the landscape? Are we residing in a Quantum Bayesian part of the landscape or a Copenhagen part of the landscape?

I think Tegmark is onto something when you incorporate Godel's Incompleteness and Ontological proof.

 

[PeterDonis]

in this case, all of these interpretations of QM would be true. They would make up the landscape of mathematical structures

The different interpretations of QM all use the same mathematical structure. So there would not be different "parts of the landscape" for different interpretations; there would just be a "QM landscape" for the mathematical structure of QM.

 

[Elias1960]

dBB theory could be considered a different theory, since the mathematical description of the configuration space trajectories does not, as far as I can see, appear in the math of the minimal interpretation of QM.

Indeed, this is one of the examples of additional math. The other examples have similar properties. The preferred coordinates do not appear in the math of SR and GR. SR and GR do not have equations that define preferred coordinates. The Lorenz gauge does not appear in the mathematics of EM theory based on the E and H fields, because the gauge potential does not appear in these equations. The quantum Hamilton-Jacobi equation of Nelsonian stochastics is not an equation of quantum theory, because the phase function $S(q)$ does not even exist in general in QT.

There can't be empirical differences if the equations are the same. Same equations = same predictions.

Wrong. Examples:
1.) The Einstein equations in harmonic coordinates are, clearly, the equations of GR. Even if this excludes the Einstein equations in other coordinates, this is not an essential restriction. But once we give the preferred coordinates a physical meaning as defining the Newtonian background, only solutions on $\mathbb{R}^4$ remain valid solutions. Wormholes would become unphysical, despite being solutions of the equations at every place.

2.) If we, then, interpret the harmonic condition for the preferred time coordinate as the continuity equation for the ether density, this gives the additional restriction $g^{00}\sqrt{-g}=\rho> 0$ with forces the preferred time to be time-like, adding the condition of existence of a global time-like coordinate. Now, Goedel's rotating universe becomes unphysical, despite being a solution of the equations. Observing wormholes or a rotating universe would empirically falsify the interpretation without falsifying GR itself.

3.) The Wallstrom objection against Nelsonian stochastics. The fundamental equations are equations for $\rho(q)=|\psi(q)|^2$ and the potential field $S(q)$. They define the wave function by $\psi(q)=\sqrt{q}e^{iS/\hbar}$ and follows the Schrödinger equation, which also defines completely the evolution equations for $\rho(q)$ and $S(q)$. But all the solutions of Nelsonian stochastics fulfill the additional condition $\rho(q)=|\psi(q)|^2>0$. Observing or preparing a state with a wave function that has necessarily zeros in the configuration space representation (even if we take into account unavoidable uncertainties) would empirically falsify Nelsonian stochastics.

4.) Variants of EM theory, with different gauge conditions interpreted as fundamental physical equations, define different theories. Each may be empirically falsified by observing solutions which do not allow a gauge potential with that particular gauge. So, if we add the radiation gauge, observing a field with some charged particles as sources would be sufficient.

[later contribution] One can add as 5.) also EPR-realistic SR and the EPR-realistic Lorentz ether (SR with preferred frame) to the list of examples (EPR-realistic means, the EPR criterion of reality holds). In EPR-realistic SR one can prove the Bell inequality, so it is empirically falsified, in the EPR-realistic Lorentz ether, where causality is defined using the preferred frame, one cannot, thus, it is not falsified by violations of the Bell inequality. The equations are, nonetheless, the same.

Terms like "physical" or "not physical" or "irrelevant mathematics" are interpretation; they are not part of the math. The math just says: do these mathematical operations to obtain predictions. It doesn't say anything about what is "real" or "physical".

Yes. But the interpretation, by naming some of these parts of legitimate math "physical", make them obligatory. Harmonic coordinates are not forbidden in GR, but not obligatory. In an interpretation with preferred coordinates, they define obligatory global objects. Wave functions without zeros are not forbidden in QT, but not obligatory, in Nelsonian stochastics they are.

It is in the sense that different interpretations suggest different ways of extending or modifying an existing theory.

Yes. And, given that they usually have weak points, which will be criticized by proponents of other interpretations, these weak points also suggest the places where one has to start to modify them.

Say, a weak point of dBB is that the Bohmian velocity becomes infinite if one approaches the zeros of the wave functions. This is nothing interesting for other interpretations, which do not assign any physical meaning to this "velocity". But dBB gives it a physical meaning. Thus, becoming infinite, even if only in some limit where it means nothing given that the density is zero, defines a problem. Thus, dBB also identifies places where one could look for a modification of QT.

Nelsonian stochastics with accepted Wallstrom objection - the theory that there are no such wave functions with zeros - would be a quite radical way to modify QT in this direction.

 

[PeterDonis]

The preferred coordinates do not appear in the math of SR and GR.

Coordinates do. Calling them "preferred coordinates" is an interpretation, not math. Mathematically they work the same as any other coordinates.

The Lorenz gauge does not appear in the mathematics of EM theory based on the E and H fields

And calling it the "Lorenz gauge" and giving it some kind of special status is an interpretation, not math. Mathematically it works the same as any other gauge choice.

once we give the preferred coordinates a physical meaning as defining the Newtonian background, only solutions on $\mathbb{R}^4$ remain valid solutions.

Which solutions are considered physically valid is not a prediction of GR. It's an interpretation. You can only extract predictions from GR after you choose a solution.

Similar comments apply to your other examples.

 

[Elias1960]

Which solutions are considered physically valid is not a prediction of GR. It's an interpretation. You can only extract predictions from GR after you choose a solution.

To reject a particular solution of the GR equations as unphysical is, indeed, part of the interpretation. But if it appears that the universe we live in is described by solutions of the GR equations which are rejected by the interpretation as unphysical, like solutions with wormholes or a rotating universe, it follows that by observing our universe we have falsified that interpretation.

Which makes this interpretation a physically (empirically) different theory, even if the equations are the same.

 

[PeterDonis]

if it appears that the universe we live in is described by solutions of the GR equations which are rejected by the interpretation as unphysical, like solutions with wormholes or a rotating universe, it follows that by observing our universe we have falsified that interpretation.

Which makes this interpretation a physically (empirically) different theory, even if the equations are the same.

Hm. I'm actually not sure, in the light of this, that different restrictions on which sets of solutions of the EFE are physically valid would just be different interpretations, since, as you say, different claims about which sets of solutions are physical can be empirically distinguished. In the meaning of "interpretation" vs. "different theory" that I have been using, that would make them different theories, not interpretations of the same theory. And on this view, "GR" itself would not be a single theory, but more like a framework for constructing theories. "QM" can be viewed similarly: "the Schrodinger Equation" does not define a single theory, because different configuration spaces and different Hamiltonians will lead to different empirical predictions and therefore count as different theories.

 

[PeterDonis]

"QM" can be viewed similarly: "the Schrodinger Equation" does not define a single theory, because different configuration spaces and different Hamiltonians will lead to different empirical predictions and therefore count as different theories.

To expand on this a bit in the context of the thread topic, if "QM" is not one single theory but a theory framework, then "interpretations of QM", like Copenhagen or the MWI, are not really single interpretations but interpretation frameworks, that can be used to construct interpretations of particular theories constructed using "QM".

But this does not change the fact that, once you have a particular theory constructed using QM--in terms of the Schrodinger Equation, you have picked a particular configuration space (or Hilbert space) and a particular Hamiltonian--then all interpretations of that particular theory, constructed using the different interpretation frameworks--Copenhagen, MWI, etc.--will agree on all empirical predictions for that particular theory, and therefore cannot be empirically distinguished.

 

[Elias1960]

To expand on this a bit in the context of the thread topic, if "QM" is not one single theory but a theory framework, then "interpretations of QM", like Copenhagen or the MWI, are not really single interpretations but interpretation frameworks, that can be used to construct interpretations of particular theories constructed using "QM".

But this does not change the fact that, once you have a particular theory constructed using QM--in terms of the Schrodinger Equation, you have picked a particular configuration space (or Hilbert space) and a particular Hamiltonian--then all interpretations of that particular theory, constructed using the different interpretation frameworks--Copenhagen, MWI, etc.--will agree on all empirical predictions for that particular theory, and therefore cannot be empirically distinguished.

I fully agree with this distinction of theory frameworks and interpretation frameworks. There is the additional point that the interpretation framework requires sometimes more, the dBB framework of the Nelsonian framework require that you specify the configuration space, with nontrivial choices for fields theories (field ontology vs. particle ontology) while the QM framework does not require this. Then, the QM framework is more general, in principle there simply may be Hamiltonians so that you cannot define canonical operators so that $\hat{H} = \frac12 \hat{p}^2 + V(q)$ is quadratic in the momentum variables. Living in a world described by such a Hamiltonian would falsify those interpretations too.

But even if this is unproblematic, the examples remain valid counterexamples to your claim that from identical equations it follows that the theories are identical too (thus, only interpretations).

BTW, let's add EPR-realistic SR and the EPR-realistic Lorentz ether to the list of examples (EPR-realistic means, the EPR criterion of reality holds). In EPR-realistic SR one can prove the Bell inequality, so it is empirically falsified, in the EPR-realistic Lorentz ether one cannot, thus, it is not falsified by violations of the Bell inequality. The equations are, nonetheless, the same.

Hm. I'm actually not sure, in the light of this, that different restrictions on which sets of solutions of the EFE are physically valid would just be different interpretations, since, as you say, different claims about which sets of solutions are physical can be empirically distinguished. In the meaning of "interpretation" vs. "different theory" that I have been using, that would make them different theories, not interpretations of the same theory.

Correct, and unproblematic.

But what remains is that they have the same equations, but make nonetheless different empirical predictions, thus, are different as physical theories.

What makes Nelsonian stochastics interesting is that it was invented as an interpretation, but only later, and by another person, Wallstrom, it was argued that it is a different theory (in this sense).

Given that to distinguish empirically theories which are different but have the same equations, it makes sense to have a special name for such theories, and, given that "interpretation" has been used for many such different theories, I think to use "interpretations" for such a class of different theories is fine. The meaning would be "interpretation of the equations" instead of "interpretation of the theory".

 

[PeterDonis]

the examples remain valid counterexamples to your claim that from identical equations it follows that the theories are identical too

No, they aren't, because "identical equations" on the view I described means identical particular solutions to the EFE (for GR) or identical Hilbert spaces and Hamiltonians in the Schrodinger Equation (for QM).

let's add EPR-realistic SR and the EPR-realistic Lorentz ether to the list of examples (EPR-realistic means, the EPR criterion of reality holds). In EPR-realistic SR one can prove the Bell inequality, so it is empirically falsified, in the EPR-realistic Lorentz ether one cannot, thus, it is not falsified by violations of the Bell inequality.

Where are you getting all this from? Do you have a reference?

what remains is that they have the same equations, but make nonetheless different empirical predictions

They don't have the same equations. See above.

 

[Elias1960]

No, they aren't, because "identical equations" on the view I described means identical particular solutions to the EFE (for GR) or identical Hilbert spaces and Hamiltonians in the Schrodinger Equation (for QM).
...,
They don't have the same equations. See above.

One can, of course, define that theories have "the same equations" if they have the same set of solutions accepted as complete physical solutions by the interpretation. In this case, those different interpretations do not have the same equations. But, sorry, this would be simply misleading. Is this what you propose, or do you propose something else for "having the same equations" which I have not yet understood?

The equations in our examples are the Einstein equations in harmonic coordinates resp. the Schroedinger equation. They are the same. But differently interpreted, with the consequence that some solutions are not accepted as viable physical solutions. Observing such solutions empirically falsifies those interpretations which reject them as non-physical. But even the proponents of these interpretations would not doubt that they fulfill the equations.

Where are you getting all this from? Do you have a reference?

I thought these are well-known trivialities. But, ok, let's look for "aether" in Bell, speakable and unspeakable:

It may well be that a relativistic version of the theory, while Lorentz invariant and local at the observational level, may be necessarily non-local and with a preferred frame (or aether) at the fundamental level.

The role of Lorentz invariance in the completed theory would then be very problematic. An 'aether' would be the cheapest solution. But the unobservability of this aether would be disturbing.

He refers to Eberhard, P. H. (1978). Bell’s theorem and the different concepts of locality. Il Nuovo Cimento B Series 11, 46(2), 392–419, where one can read the following:

4"2. The principles of relativity break down. - If so, then all rest frames may not be equivalent. One of them, $R_0$, is fundamental and, in this rest frame $R_0$ only, causality applies. Causal effects can propagate faster than the velocity of light as long as the cause precedes the effect in $R_0$. No causal loop can be made then. In any other rest frame R, the time sequence between events with a timelike separation is the same as in $R_0$. Therefore the usual causal chains in the light-cone are the same as expected from relativity. For events with a spacelike separation, the cause may seem to occur after the effect in R if the time sequences in R and $R_0$ are opposite. However, this may have an interpretation: only the time in the rest frame $R_0$ is the real physical time, and the other rest frames seem to be equivalent to the fundamental one $R_0$ because the laws of Nature just happen to have Lorentz invariance.

 

[PeterDonis]

I thought these are well-known trivialities.

They're not. That's why I asked for a reference. The references you give do not say what you said.

 

[PeterDonis]

One can, of course, define that theories have "the same equations" if they have the same set of solutions accepted as complete physical solutions by the interpretation.

You're missing the point. If GR is not a single theory but a theory framework, then the EFE is not an equation that defines a theory. It's an equation framework. To get equations that define a theory--something you can make actual predictions from--you have to pick a particular solution of the EFE. That means that there is no such thing as "an interpretation of GR" on this view; there are only interpretations of particular solutions of the EFE. A statement like "only solutions of the EFE that can be expressed in harmonic coordinates are physically valid" is not an interpretation on this view; it's a more restrictive theory framework than "GR" by itself, since "GR" by itself does not place any restrictions on which solutions of the EFE can be considered.

Similar remarks apply to the Schrodinger Equation in general, with no specification of a Hilbert space or a Hamiltonian, vs. the general Schrodinger Equation but with some restriction placed on what kinds of Hilbert spaces or Hamiltonians are physically valid.

 

[Elias1960]

They're not. That's why I asked for a reference. The references you give do not say what you said.

The first part - that in EPR-realistic SR one can prove Bell's theorem - is simply Bell's theorem. The quote I have given describes the preferred frame as one of the ways to solve the problem. Once the Lorentz ether has a preferred frame, and causal interactions are those which go not into the past in the preferred time, the solution is the same as in the quote.

Explain which is the point where you have doubt, given that all this is quite straightforward, I will give a proof here if I find no quote. It is quite common that, given the difficulty to publish outside the mainstream, many trivial things which would be separate publications in the mainstream have not been published at all.

You're missing the point. If GR is not a single theory but a theory framework, then the EFE is not an equation that defines a theory. It's an equation framework. To get equations that define a theory--something you can make actual predictions from--you have to pick a particular solution of the EFE.

No, 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.

This well-defined theory, with well-defined equations for all the fields, has, then, following the general scheme, also those interpretations with harmonic coordinates as defining the preferred background and a global timelike harmonic function defining absolute time. So, the framework of the interpretation, applied to the particular theory from the GR framework, creates an interpretation (no longer a framework) of that particular theory. And it does this without picking any particular solution.

Particular solutions become relevant if we try to describe a particular situation we observe with a solution to that theory.

And if we observe a situation that can be described by a solution of the theory, but this solution is named unphysical by the interpretation, then the interpretation is empirically falsified but the theory not.

That means that there is no such thing as "an interpretation of GR" on this view; there are only interpretations of particular solutions of the EFE.

Sorry, this makes no sense. 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.

A statement like "only solutions of the EFE that can be expressed in harmonic coordinates are physically valid" is not an interpretation on this view; it's a more restrictive theory framework than "GR" by itself, since "GR" by itself does not place any restrictions on which solutions of the EFE can be considered.

This would be a strange proposal for renaming.

What is known as a framework - GR without specification of the matter Lagrangian, QM without specification of the configuration space and the Hamilton operator - remains a framework, but particular theories become frameworks too, moreover, even their interpretations become frameworks. The old notions of theory and interpretation will be simply thrown away, they are all frameworks now, and what was a particular solution becomes now a theory or an interpretation or so.

Similar remarks apply to the Schrodinger Equation in general, with no specification of a Hilbert space or a Hamiltonian, vs. the general Schrodinger Equation but with some restriction placed on what kinds of Hilbert spaces or Hamiltonians are physically valid.

And the same criticism applies here too. The reasonable definition of the framework is fine, but 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.

Then comes Nelsonian stochastics and throws away some solutions of this particular equation as unphysical.

 

[PeterDonis]

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?

 

[PeterDonis]

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.

 

[Elias1960]

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.

 

[PeterDonis]

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.

 

[Elias1960]

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.

 

[PeterDonis]

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.

 

[Elias1960]

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.

 

[PeterDonis]

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.

 

[Elias1960]

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.

 

[PeterDonis]

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".

 

[Elias1960]

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.