Lorentz invariance of quantum theory

[Narasoma]

I read Lucien Hardy's paper whose tittle was "Quantum Mechanics, Local Realistic Theories, and Lorentz Invariant Relativistic Theories". There, he argued that lorentz invariant observables which involved locality assumption contradict quantum mechanics.

I tried to follow his argument, but got stuck on the paragraph right after eq. num. (17).

Looks like he mixed outputs from different experiments (replaced/removed beam splitter). I couldn't understand why that was allowed and seemed logic on the paper.

So, if anybody gets a better understanding on this, please explain to me.

 

[Demystifier]

Looks like he mixed outputs from different experiments (replaced/removed beam splitter). I couldn't understand why that was allowed and seemed logic on the paper.

That's how science works, you do different experiments to see how the outcomes will differ, and from that you learn something about general laws of nature. If you always repeat the same experiment, you cannot learn anything about the general laws. Without variations in the experimental setup you cannot learn what are the causes of the final outcomes, and without learning about the causes you cannot tell whether the causes are local or non-local, Lorentz invariant or Lorentz non-invariant, etc.

 

[bhobba]

There, he argued that lorentz invariant observables which involved locality assumption contradict quantum mechanics.

He is correct. If you read chapter 3 of Ballentine you see the dynamics can be fully derived from the Galilean transformations which are manifestly non local. It isn't usually pointed out but classical mechanics is manifestly non local because its based on the Galilean transformations. An exception is Landau - Mechanics but due to his terse style he doesn't spend a lot of time on it which IMHO requires more emphasis and discussion.

To rectify it you must go to QFT. But there locality is replaced by the so called cluster decomposition property:
https://www.physicsforums.com/threads/cluster-decomposition-in-qft.547574/

This has implications for Bells theorem (it doesn't disprove it or anything like that - simply allows a different viewpoint) - but that needs a whole new thread.

Thanks
Bill