# What's the invariance quantity under EPR and Bell's inequality?

I was reading and writing a study report about EPR and Bell's inequality.

As the hidden variable and local realism was proven to be "false", and from many posts in physics exchange websites such as EPR paradox and uncertainty principle I learned that (quote John Rennie)

"the measurement to the entangled system affect the system in a whole, and was not constrained by the speed of light".

However, the entangled system that was dealt with was a physical system, and it must still followed some physical laws.

Further, I was taking nonlinear dynamic these days where we learnt the idea of conserved system. It's practically saying that, without interaction, the trajectories of object must be in the constant surface or line of some conservatives quantities, if there was one or more.

Therefore I had the following questions:

1. What's the invariance quantities in the EPR and Bell's inequality?

(i.e. the particle's four speed was conserved, and, in this case, the uncertainty principle was followed. Thus in a scene $\Delta x\Delta p\ge \hbar/2$. But the uncertainty was an inequality, and it's kind of tricky to see what exactly was the conserved quantity.)(Asked for functional description)

1. What's the path of information such "simultaneous interaction" of the entangled system took?

(i.e. what's the possible or preferred geometry of the EPR?)(Asked for geometrical description)

• Question 1 seems to suppose hidden variables (else what kind of non-trivial "quantities" are you talking about?); question 2 seems to suppose realism (by considering EPR correlations as the effect of a physical process carrying information). But as you rightly say at the start of the post, both local realism and hidden variables are precisely what are ruled out by Bell's results. So these questions are ill-posed and do not make much sense in the EPR context. – Stéphane Rollandin Apr 27 '18 at 9:22
• @StéphaneRollandin I wasn't assuming hidden variable. The uncertainty was in a sense "an equivalence/invariance " relation that must be followed and thus created the paradox. I was just wondering if there was a proper equivalence relations(i.e. equal sign, like that of the four speed.) that demonstrated the experiment. (i.e. the entanglement itself was also an equivalence relation that changes one another, as the system was changed in a whole and the affect to one affects all.) – J C Apr 27 '18 at 13:31