# Are Modal interpretations emprically Lorentz invariant?

• A
• JG11
Unfortunately in the QM Foundations literature, the term "interpretation" is being used more generally to mean "different theory", even in cases where the theory being proposed is an outgrowth of an interpretation of QM. This is a serious problem, because it means that the QM Foundations literature is not really providing us with a systematic guide to understanding the various interpretations of QM.

#### JG11

Modal interpretations are a class of realist non local hidden variable theories. However, they cannot be made fundamentally lorentz invariant. However, neither can bohmian mechanics but BH is still emprically lorentz invariant. So are modal interpretation empirically lorentz invariant as well?

Yes.

Demystifier said:
Yes.
I wasn't able to find much on this. How do they achieve Lorentz invariance?

I'm not sure I understand the question. "Empirically Lorentz invariant" means "experimental results confirm Lorentz invariance". But experimental results aren't results about a particular interpretation of QM; all interpretations make the same experimental predictions, so you can't use experiments to distinguish one from the other. All experiments can do is tell you that the basic math, which all interpretations have in common, is making correct predictions.

PeterDonis said:
I'm not sure I understand the question. "Empirically Lorentz invariant" means "experimental results confirm Lorentz invariance". But experimental results aren't results about a particular interpretation of QM; all interpretations make the same experimental predictions, so you can't use experiments to distinguish one from the other. All experiments can do is tell you that the basic math, which all interpretations have in common, is making correct predictions.
Many interpretations break a symmetry that QM possesses at their ontological level, but restore it at the empirical level via fine-tuning or thermalization. There have been problems getting modal interpretations to do this for Lorentz invariance.

Other variations on this would be them predicting effects that we don't see in experiments (and that QM doesn't predict). Again they need fine-tuning or thermalization.

PeterDonis said:
all interpretations make the same experimental predictions
This is said a lot on this forum, but from my reading (papers of Fuchs, Leifer, Pusey, Spekkens and others) this isn't clearly the case.

It's what they aim to do, but in fact most are not at that stage yet. Bohmian Mechanics seems to be headed that way thus far, but the Many-Worlds interpretation and the Transactional interpretation (and other retrocausal intepretations) cannot be clearly said to as of yet. It's quite possible that when they are fully fleshed out they will have slight or even large deviations from QM. Many-Worlds for example needs fine-tuning to reproduce ontological time symmetry (as discussed here: https://arxiv.org/abs/1607.07871) however it has not been shown that such a fine-tuning is possible. So it may only reproduce the symmetry partially, possibly having a detectable difference from QM.

Even in the case of Bohmian Mechanics there has been some discussion of diverging from QM in light of the Frauchiger-Renner theorem. See Renato Renner's talk here:
https://www.video.ethz.ch/conferences/2017/quantum/681416e0-be7b-4958-9d79-9b9ef9333136.html

DarMM said:
It's what they aim to do, but in fact most are not at that stage yet.

If they don't make the same predictions for experimental results, they're not interpretations; they're different theories.

I think the papers you refer to are not talking about interpretations of QM; they are talking about proposed different theories that are outgrowths of interpretations of QM.

PeterDonis said:
If they don't make the same predictions for experimental results, they're not interpretations; they're different theories.
I would agree when being strict about the meaning of "interpretation". However it isn't used in such a fashion within Foundations literature and under that criteria most of the so called interpretations of QM might be interpretations or different theories depending on what we learn about them in future research.

To use your language, Many-Worlds without fine-tuning of the intial conditions of the multiverse is a different theory to standard QM, it remains to be seen if it can be made into an interpretation of QM by appropriate fine tuning.

This is already the case with Bohmian Mechanics where without quantum equilibrium it is a different theory in general. In fact a major theme emerging in modern Foundational work is that realist interpretations seem to be a knife-edge from becoming different theories. As Matt Leifer says "All realist theories are fine tuned".

(Quote is on a slide in the talk, he doesn't discuss it there)

PeterDonis said:
I think the papers you refer to are not talking about interpretations of QM; they are talking about proposed different theories that are outgrowths of interpretations of QM.
The Pusey-Leifer paper discusses standard Many-Worlds and Bohmian Mechanics. In some cases they are talking about outgrowths as you say, in some cases not.

DarMM said:
However it isn't used in such a fashion within Foundations literature

Unfortunately not. To me this means the QM Foundations literature is being sloppy. Also it's not paying attention to how the term "interpretation" is used more generally when talking about scientific theories. The whole point of the term "interpretation" is supposed to be that you already know what the theory is and what it predicts; you're just trying to construct a description of "what's going on"--what the already known theory with its already known predictions is telling you about "what's really happening". The known theory and known predictions are supposed to be the fixed point that any "interpretation" has to start with. (See, for example, discussions of the "curved spacetime" vs. "flat spacetime with a spin-2 field that distorts clocks and rulers" interpretations of GR in the GR literature; those discussions are very clear that both interpretations share the same math and the same experimental predictions.)

Mentz114 and DarMM