What Is the Meaning of Simultaneous Reality in the EPR Paradox?

[victor94]

I'm reading the paper of the EPR paradox and I'm confused in the meaning of this:

"The elements of the physical reality cannot be determined by a priori philosophical considerations, but must be found by an appeal to results of experiments and measurements......when the operators corresponding to two physical quantities do not commute the two quantities cannot have simultaneous reality".

What it means "simultaneous reality"?

Paper: https://journals.aps.org/pr/abstract/10.1103/PhysRev.47.777

Any help will be apreciated.
Thanks.

 

[zonde]

What it means "simultaneous reality"?

In the context of the paper it means that position and momentum is certain at the same time (which of course contradicts Heisenberg's uncertainty principle).

 

[Denis]

In the context of the paper it means that position and momentum is certain at the same time (which of course contradicts Heisenberg's uncertainty principle).

Wrong, it is not in contradiction with the uncertainty principle. They could be well-defined and certain in reality, but it could be impossible, with the means of quantum theory, to prepare states which violate the uncertainty relations. So, in every repetition of the experiment the same preparation procedure would give different positions and momentum values, but in each repetition they could be well-defined.

So, you have to refer here to other things, like Kochen-Specker or Bell.

 

[vanhees71]

I'm reading the paper of the EPR paradox and I'm confused in the meaning of this:

"The elements of the physical reality cannot be determined by a priori philosophical considerations, but must be found by an appeal to results of experiments and measurements......when the operators corresponding to two physical quantities do not commute the two quantities cannot have simultaneous reality".

What it means "simultaneous reality"?

Paper: https://journals.aps.org/pr/abstract/10.1103/PhysRev.47.777

Any help will be apreciated.
Thanks.

For EPR (the paper is quite enigmatic, and Einstein himself didn't like it too much) observables have a reality if they have a determined value. If you like to get completely confused read Bohr's answer (with the same title) ;-)).

This means for an observable to have a determined value you have to be able to prepare a system in a state that is described by an eigenstate of the self-adjoint operator that represents the observable. Note that it must be a true normalizable Hilbert-space vector to be a proper state, and thus according to EPR position and momentum are never "real", because there is no normalizable eigenstate for either of them.

It also implies that for being able to make two observables "real simultaneously" you have to be able to always prepare a common eigenstate of the corresponding self-adjoint operators and this is, in this generality, only possible, if these operators commute.

Note that for the complete determination of the quantum state you have to prepare the system in a state described by a simultaneous eigenvector of a complete set of compatible self-adjoint operators, describing corresponding compatible observables.