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Suppose you have two entangled particles. Particle A, and Particle B. If the spin of particle A is up, then the spin of particle B must be down and vice versa.

Now suppose you measure the spin of A at $(xA, tA)$, and measure the spin of B at $(xB, tB)$.

We usually say that the wave function collapsed at $t=tA$, if $tA<tB$ and at $t=tB$, if $tB<tA$.

However, in a different reference frame, if the separation between $(xA, tA)$ and $(xB, tB)$ is spacelike, $tA<tB$ or $tA>tB$ is not uniquely determined.

So, when exactly a wave function collapsed is not clear.

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This is one of the things that shows that the collapse of the wavefunction is a problematic concept. Some say there isnt even a collapse. Its just that the measurements of both of the particles are correlated even though the individual measurements are completely random. This correlation is injected into the system when they become entangled, not when either A or B are measured. The bottom line is that the measurement on one of the particles is undetectable for some observer who only has access to the other particle. Only when the two observers exchange their information, the "spooky correlation" becomes visible.

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