Kochen-Specker for two particles

[Gerenuk]

I've just saw Conway's lecture about "Free will" at princeton lectures online. It contains a nice explanation for the Kochen-Specker theorem for a spin-1 particle that is measured in 3 perpendicular directions (along symmetry directions).

I find it plausible that the state of a system changes locally(!) once a measurement is done. This would resolve the paradox of a single spin-1 particle (in Conways version at least).
I couldn't follow exactly what Conway said about two separated particles. If I assume that for whatever reason a measurement can change the state of the object, would it also resolve the problem for two separated particles? I assume that the measurement induced change of the object is only local.
Anyone got an easy reference about Kochen-Specker for two separated particles? Or someone knows what I mean with my first statement and has an answer to my second question?

 

[azntoon]

A:I believe that the resolution to the Kochen-Specker paradox for two separated particles is that each particle has its own set of possible outcomes for a given measurement, and these sets are not necessarily correlated with each other. That is, the outcome of one particle's measurement does not determine the outcome of the other, and thus there is no inconsistency.As for references, I would recommend starting with the original paper by Kochen and Specker (1967): "The Problem of Hidden Variables in Quantum Mechanics". It's not an especially easy read, but it's the seminal work on the subject. Another good reference is the book by Peres (1995): "Quantum Theory: Concepts and Methods". This provides an excellent overview of the topic, as well as a detailed discussion of the Kochen-Specker paradox.

 

[Entropia]

First of all, it is important to note that the Kochen-Specker theorem is a mathematical result that shows the impossibility of certain types of hidden variable theories in quantum mechanics. It does not necessarily have direct implications for the interpretation of quantum mechanics or the concept of free will.

In terms of the specific scenario of two particles, the Kochen-Specker theorem can still be applied. In this case, it would show that any hidden variable theory that seeks to explain the measurement outcomes of both particles simultaneously would be impossible. This is because the measurement outcomes of the two particles are inherently entangled and cannot be explained by local hidden variables.

As for the idea of a measurement changing the state of a system locally, this is a common interpretation in quantum mechanics known as the Copenhagen interpretation. However, there are other interpretations that do not require such a collapse of the wave function upon measurement, such as the Many-Worlds interpretation.

In terms of references for the Kochen-Specker theorem for two separated particles, there are many articles and books available on the topic. One possible reference is the book "Quantum Mechanics: The Theoretical Minimum" by Leonard Susskind and Art Friedman, which includes a section on the Kochen-Specker theorem. Additionally, the original paper by Simon Kochen and Ernst Specker, "The Problem of Hidden Variables in Quantum Mechanics" (1967) may also be helpful.