[Mock idea] Can quantum mechanical description of physical reality be considered complete?

[andreamari]

Albert Einstein, Boris Podolsky, and Nathan Rosen
Institute for Advanced Study, Princeton, USA

Consider the following wave function describing the quantum state of two distant particles:

$$ \Psi(x_1, x_2) = \int_{-\infty}^{\infty} e^{\frac{i}{\hbar}(x_1 - x_2+ x_0)p} dp $$

• By measuring $\hat x_1$ or $\hat p_1$ of the first particle, one can (with infinite precision) determine $\hat x_2$ or $\hat p_2$ without interacting with the second particle.

• At the same time, according to our friend Heisenberg, $\hat x_2$ and $\hat p_2$ cannot be simultaneously determined with arbitrary precision.

This seems to be a contradiction. Is quantum theory incomplete? 😱

For a more detailed description, see the links below.

• Link to the associated project folder.
• Link to the associated Markdown document.

[egcavalcanti]

Dear Albert,

You raise an interesting question. However, as you say, you can only determine $\hat{x}_2$ OR $\hat{p}_2$, but not both for the same particle. So strictly speaking it does not seem to be in contradiction with Werner's result. Perhaps we could make the assumptions of your argument a little more explicit?

It seems that you are assuming some kind of "sufficient criterion for reality", such as "If, without in any way disturbing a system, we can predict with certainty (i.e. with probability equal to unity) the value of a physical quantity, then there exists an element of physical reality corresponding to this physical quantity". Would that be a fair characterisation?

And what do you mean by "incomplete"? Perhaps you have in mind some "necessary condition for completeness" of the type: "Every element of the physical reality must have a counterpart in the physical theory". Would you agree?