What should hidden variables explain?

[PeterDonis]

The standard model is not known to have exact Lorentz symmetry.

I will agree that we can't rule out the presence of operators in the standard model that violate exact Lorentz symmetry; the best we can do is to constrain their magnitude based on experimental data.

However, AFAIK it is still true that a QFT with exact Lorentz symmetry (i.e., not including any operators that could violate that symmetry) predicts violation of the Bell inequalities. That's really the primary point I was trying to make in response to Ilja.

 

[stevendaryl]

Perhaps I should have said "direct observables". I'm not try to get into issues involved with measurement in QM.

But I think that when people doubt whether quantum field theory is relativistic, they are thinking specifically about measurements.

 

[PeterDonis]

I think that when people doubt whether quantum field theory is relativistic, they are thinking specifically about measurements.

I can't say what other people are thinking in this connection. I agree with you that there is no principled distinction in QM between "measurements" and other interactions. But there is a distinction between observables and theoretical quantities that aren't observables.

 

[Ilja]

I don't know what you're talking about here. QFT has Lorentz symmetry as an exact symmetry.

I disagree. It has Lorentz symmetry as a symmetry of observable effects. As a symmetry for observable effects, it is exact. As far as the theory is well-defined (see Haag's theorem for reasons to doubt it is.)

If we built a theory with Lorentz symmetry as only an approximate symmetry, it would not be QFT, it would be some different theory.

I doubt. QFT can be understood as well as defined as a limit of regularized theories, with each regularized theory having Lorentz symmetry only approximately. This is what is done in the conceptually simplest case - lattice regularizations. Given that the limit itself is problematic, one can understand QFT as well as a theory which describes a lattice regularization with a critical length so small that violations of Lorentz symmetry becomes unobservable. Given that we anyway do not believe that QFT holds below Planck length, what would be the difference between QFT as a (well-defined) lattice theory with $h=10^{-100} l_{Pl}$ and the (hypothetically existing despite Haag's theorem) theory with exact Lorentz symmetry?

And, anyway, the difference between fundamental and weak relativistic symmetry is not at all about exact or approximate Lorentz symmetry. It is allowing for a hidden preferred frame which is the key difference. The Lorentz ether has exact Lorentz symmetry.

 

[PeterDonis]

Given that we anyway do not believe that QFT holds below Planck length, what would be the difference between QFT as a (well-defined) lattice theory with $h=10^{-100} l_{Pl}$ and the (hypothetically existing despite Haag's theorem) theory with exact Lorentz symmetry?

Observably, nothing, by hypothesis, unless and until we were able to make measurements at distance scales of $10^{-100} l_{Pl}$. If measurements at that scale are taken to be impossible in principle, then there is no measurable difference at all between the two theories; they both predict the same observables. But they are still obviously different theories conceptually and mathematically. The differences just can never be experimentally tested. See below.

It is allowing for a hidden preferred frame which is the key difference.

This "hidden preferred frame" has nothing to do with observable effects; it's purely an internal aspect of the theory. As my other posts have made clear, I don't think a "relativistic" theory has to have exact Lorentz symmetry of purely internal aspects of the theory. It only has to have exact Lorentz symmetry of observable effects. More precisely, it has to have that as predicted by the theory. It might be impossible, as above, to distinguish exact Lorentz symmetry from some approximate version due to finite limits on measurement accuracy.

 

[Ilja]

This "hidden preferred frame" has nothing to do with observable effects;

It has, because its existence allows violations of Bell's inequality. Which a fundamentally Einstein-causal theory would not allow. And violations of BI are observable.

 

[stevendaryl]

It has, because its existence allows violations of Bell's inequality. Which a fundamentally Einstein-causal theory would not allow. And violations of BI are observable.

I think you've blurred the distinction between two different things:

1. Einstein causality
2. Lorentz invariance

No Einstein causal theory can violate Bell's inequalities. But it's much less clear that no Lorentz invariant theory can. Lorentz invariance does not directly imply that there can be no FTL effects. What you can prove is that FTL signal propagation, together with relativity, leads to a contradiction, because you could then set up a closed loop in which you receive a reply to a message before you send the message. The type of nonlocal correlation implied by violations of Bell's inequality does not allow FTL signals to be sent, so the proof that it leads to a contradiction with relativity fails.

 

[PeterDonis]

It has, because its existence allows violations of Bell's inequality.

I understand that this is what your preferred theory says. But experiment does not say this. Experiment cannot detect your "hidden preferred frame", so there is no way of showing experimentally that that is what allows violations of BI. And since there are theories that do not have a "hidden preferred frame" but still predict violations of BI, you cannot justify this claim on theoretical grounds either. All it is is your personal preference.

 

[Ilja]

I understand that this is what your preferred theory says. But experiment does not say this.

No, my preferred theory has nothing to do with this claim.

If you don't go back to mysticism, denying the existence of objective reality even if you see it (the EPR criterion of reality) as well as that observed correlations require causal explanations (Reichenbach's common cause principle, which distinguishes science from astrology), then you have simple theorems.

From Einstein causality one can derive Bell's inequality.

From a theory with a hidden preferred frame, which would allow hidden causal influences, you cannot derive Bell's inequality.

Bell's inequality is testable and tested.

 

[Ilja]

I think you've blurred the distinction between two different things:

1. Einstein causality
2. Lorentz invariance

No Einstein causal theory can violate Bell's inequalities. But it's much less clear that no Lorentz invariant theory can.

Mystical theories (theories which reject as the EPR principle of reality, as Reichenbach's common cause) can violate everything. But for a realistic, causal theory with fundamental Lorentz invariance (that means, where not only observables but everything should have Lorentz invariance) you can derive Einstein causality from the requirement that causality has to preserve Lorentz invariance.

What you can prove is that FTL signal propagation, together with relativity, leads to a contradiction, because you could then set up a closed loop in which you receive a reply to a message before you send the message.

And why would this be a problem if there is no causality? For mysticism causal loops are not a problem at all. There are only some correlations, that's all. Everything is somehow mystically correlated, this is sufficient, once the idea of a necessity of a causal explanation is rejected.

 

[stevendaryl]

Mystical theories (theories which reject as the EPR principle of reality, as Reichenbach's common cause) can violate everything. But for a realistic, causal theory with fundamental Lorentz invariance (that means, where not only observables but everything should have Lorentz invariance) you can derive Einstein causality from the requirement that causality has to preserve Lorentz invariance.

And why would this be a problem if there is no causality? For mysticism causal loops are not a problem at all. There are only some correlations, that's all. Everything is somehow mystically correlated, this is sufficient, once the idea of a necessity of a causal explanation is rejected.

Well, if you have two theories that are empirically indistinguishable, then I don't see how you can call one "mystical" and the other not. The correlations implied by quantum mechanics are not arbitrary, they are very specific. It may be emotionally unsatisfying to have a theory that violates Einstein causality, but to go from there to "all bets are off, we might as well embrace magic and voodoo" is an over-reaction.

 

[Ilja]

Well, if you have two theories that are empirically indistinguishable, then I don't see how you can call one "mystical" and the other not. The correlations implied by quantum mechanics are not arbitrary, they are very specific. It may be emotionally unsatisfying to have a theory that violates Einstein causality, but to go from there to "all bets are off, we might as well embrace magic and voodoo" is an over-reaction.

Ok, we have three theories here:

1.) Fundamental realistic relativity, which gives Einstein causality and, then, Bell's inequality. This theory is empirically falsified by the known experiments.
2.) Realistic and causal Lorentz ether, or dBB interpretation of QM. It allows hidden causal influences into the future as defined by the preferred time coordinate. It does not allow to prove Bell's inequality, thus, is not empirically falsified by a violation of Bell's inequality.
3.) The immunization of (1) against this empirical falsification, by rejection of realism (EPR criterion) and causality (Reichenbach's common cause).

(1) and (2) are empirically distinguishable, by the violation of Bell's inequality, and have been empirically distinguished. (3) is mystical.

Feel free to explain me what is different between magic and voodoo, as long as they make predictions (astrology certainly does). The only remaining difference is that the numbers predicted by quantum theory fit better than those predicted by astrology, or at least we scientists think so. If this is fine with you, ok. But there was another difference between science and astrology in the past: Namely that science has constructed models of reality, models which have explained the numbers by realistic, causal influences.

 

[PeterDonis]

From Einstein causality one can derive Bell's inequality.

From a theory with a hidden preferred frame, which would allow hidden causal influences, you cannot derive Bell's inequality.

So what? There are also theories that do not have a hidden preferred frame, from which you cannot derive Bell's inequality (they predict violations of it). So why should I care that "Einstein causality" allows you to derive Bell's inequality? (That assumes that we even have a rigorous definition of "Einstein causality" plus a theory that exhibits it. As stevendaryl has already pointed out, "Einstein causality" is not the same as Lorentz invariance. See below.)

Fundamental realistic relativity

What theory are you talking about?

(1) and (2) are empirically distinguishable, by the violation of Bell's inequality, and have been empirically distinguished

I have closed this thread for moderation. Please PM me specific references for what you mean by "fundamental realistic relativity" if you want the thread reopened.