Lorentz invariance of quantum theory

In summary, Lucien Hardy's paper "Quantum Mechanics, Local Realistic Theories, and Lorentz Invariant Relativistic Theories" argues that Lorentz invariant observables, which rely on locality assumption, contradict quantum mechanics. This is because in order to understand the general laws of nature, it is necessary to conduct experiments with variations in the setup. This leads to the concept of cluster decomposition in QFT, which has implications for Bells theorem.
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Narasoma
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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.
 
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Narasoma said:
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.
 
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  • #3
Narasoma said:
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
 
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1. What is Lorentz invariance of quantum theory?

Lorentz invariance of quantum theory is the principle that states that the laws of quantum mechanics should not change under Lorentz transformations, which are mathematical transformations that describe how measurements of space and time change according to an observer's relative motion.

2. Why is Lorentz invariance important in quantum theory?

Lorentz invariance is important because it is a fundamental symmetry of the universe, and it has been confirmed by numerous experiments. It also allows for the consistent description of physical phenomena at different reference frames, which is necessary for the validity of quantum mechanics.

3. How does Lorentz invariance affect the behavior of particles in quantum theory?

Lorentz invariance dictates that the behavior of particles should remain the same regardless of the observer's relative motion. This means that particles should behave in the same way regardless of their speed or the speed of the observer.

4. Can Lorentz invariance be violated in quantum theory?

There is currently no experimental evidence to suggest that Lorentz invariance is violated in quantum theory. However, some theoretical models, such as string theory, suggest that it may be possible in certain extreme conditions, such as near the Planck scale. But, this is still a topic of ongoing research and debate.

5. How does Lorentz invariance relate to other fundamental principles in physics?

Lorentz invariance is closely related to other fundamental principles in physics, such as the principle of relativity and the speed of light being constant in all reference frames. These principles are all interconnected and form the basis of our understanding of the universe through theories like general relativity and quantum mechanics.

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