Hardy's Paradox and lorentz invariant realist interpretation

[JG11]

Does Hardy's paradox show that all realist interpretations cannot be made lorentz invariant? Or is it just realist hidden variable theories?

 

[Demystifier]

It depends on what exactly do you mean by a realist theory which is not a hidden variable theory. If by realist theory you mean a theory of objects existing out there irrespective of our observations, then the theorem refers to all realist theories.

 

[JG11]

It depends on what exactly do you mean by a realist theory which is not a hidden variable theory. If by realist theory you mean a theory of objects existing out there irrespective of our observations, then the theorem refers to all realist theories.

So this would even apply to the many world interpretation and the GRW theories?

 

[Demystifier]

So this would even apply to the many world interpretation and the GRW theories?

Yes, provided that "Lorentz invariant" is replaced with the word "local". GRW theories are explicitly non-local. MWI is also not local, but in a somewhat subtle sense explained in https://lanl.arxiv.org/abs/1703.08341 .

 

[JG11]

Yes, provided that "Lorentz invariant" is replaced with the word "non-local". GRW theories are explicitly non-local. MWI is also not local, but in a somewhat subtle sense explained in https://lanl.arxiv.org/abs/1703.08341 .

Can the MWI be made lorentz invariant then? GRW? I guess not because of what Hardys paradox shows...?

 

[Demystifier]

Can the MWI be made lorentz invariant then? GRW? I guess not because of what Hardys paradox shows...?

As I said (but perhaps not sufficiently clearly), this theorem should actually be interpreted as the statement that MWI and GRW cannnot be made local. For a non-local but Lorentz invariant GRW-like theory see https://arxiv.org/abs/quant-ph/0406094

 

[JG11]

As I said (but perhaps not sufficiently clearly), this theorem should actually be interpreted as the statement that MWI and GRW cannnot be made local. For a non-local but Lorentz invariant GRW-like theory see https://arxiv.org/abs/quant-ph/0406094

Interesting. Say that one formulates the MWI to be as non local as bohmian mechanics (I guess by inserting the non locality by hand), would it still be empirically lorentz invariant like bohmian mechanics?

 

[Demystifier]

would it still be empirically lorentz invariant like bohmian mechanics?

Not only empirically Lorentz invariant, but even fundamentally Lorentz invariant.

 

[JG11]

Not only empirically Lorentz invariant, but even fundamentally Lorentz invariant.

Does Lucien Hardy come to the wrong conclusion that realist lorentz invariant models make the wrong predictions?

 

[Demystifier]

Does Lucien Hardy come to the wrong conclusion that realist lorentz invariant models make the wrong predictions?

Yes. If you want to see what exactly the Hardy's error is, see Sec. A.1.1 of my https://lanl.arxiv.org/abs/1309.0400 .

 

[A. Neumaier]

provided that "Lorentz invariant" is replaced with the word "local".

"Lorentz invariant" and "local" are two very different properties of a theory. Nonrelativistic QFT is often local. On the other hand, classical relativistic kinetic theory is Lorentz invariant but nonlocal.

 

[Demystifier]

classical relativistic kinetic theory is Lorentz invariant but nonlocal.

Why is it nonlocal? Where does the nonlocality come from?

 

[A. Neumaier]

Why is it nonlocal? Where does the nonlocality come from?

because kinetic fields are functions of position and momentum.

There are also lots of nonlocal but Lorentz invariant multiparticle models; see also my theoretical physics FAQ.