That "combined-only" requirement is referred to sometimes as Lorentz(Poincare) covariance in relativistic quantum theory. This follows the requisite of local gauge invariance, from local quantum fields, which is not explicitly enforced in the case of classical SR in Minkowski spacetime, that is determined only by its spacetime symmetries rather than also by the "internal' ones of quantum relativistic gauge theory.atyy said:Assuming classical relativistic spacetime (which is assumed in both classical and quantum relativistic theory), the violation of a Bell inequality is not compatible with classical relativistic causality. Classical relativistic causality does have a "special" speed, which is commonly called the speed of light.
Note that a Bell inequality is a statement about classical relativistic causality, and does not depend on relativistic quantum theory. Relativistic quantum theory does violate Bell inequalities, showing that relativistic quantum theory is not compatible with classical relativistic causality. The "Bell operator" or "Bell observable" mentioned in the paper is a part of relativistic quantum theory, and is not needed in the derivation of the Bell inequality. The Bell operator or Bell observable is used to show that relativistic quantum theory violates a Bell inequality in any reference frame.
In relativistic quantum theory, neither operators (including the Bell operator or Bell observable) nor states need to be separately Lorentz invariant, only the combined use of operators and states to predict the probabilities of measurement outcomes needs to be Lorentz invariant.
Bell's inequality is a mathematical expression that was proposed by physicist John Stewart Bell in 1964. It is used to test whether quantum mechanics, which describes the behavior of particles at the subatomic level, is consistent with classical physics.
Lorentz invariance is a fundamental principle in physics that states that the laws of physics should be the same for all observers in uniform motion. This means that the laws of physics should not change depending on the observer's frame of reference.
Bell's inequality is used to test the validity of quantum mechanics, which is based on the principles of Lorentz invariance. If Bell's inequality is violated, it would suggest that quantum mechanics is not consistent with Lorentz invariance and therefore may not accurately describe the behavior of particles at the subatomic level.
Yes, Bell's inequality has been tested for Lorentz invariance in several experiments, including the Aspect experiment in 1982 and the Hensen experiment in 2015. These experiments have shown that Bell's inequality is violated, indicating that quantum mechanics is not consistent with classical physics and Lorentz invariance.
If Bell's inequality is violated, it would suggest that there may be a need for a new theory that can reconcile quantum mechanics with classical physics and Lorentz invariance. This could potentially lead to a better understanding of the fundamental laws of physics and have significant implications for our understanding of the universe.