# Is wavefunction collapse limited by the speed of light?

1. Aug 28, 2004

### Loren Booda

Doesn't complete information about a probability distribution presuppose a physically determined wavefunction collapse? How can we have knowledge about statistics of all existent quanta for the wavefunction except by light signals in the first place, whose correspondent reversed process should be a collapse to a point in nonzero time?

Would a theoretical infinity of states then evolve gradually to a finite number to an eventual singleton? After each measurement, how do all of the other points reestablish their expectation value for the subsequent measurement?

2. Aug 29, 2004

### Fredrik

Staff Emeritus
Wavefunction collapse is not limited by the speed of light. This result is know as the Einstein-Podolsky-Rosen (EPR) paradox. It's not really a paradox, but it's one of the strangest things in all of quantum mechanics.

Suppose a spin-0 particle decays into two spin-½ particles. Because of conservation of momentum, the two particles will go in opposite directions, and because of conservation of angular momentum, their spins will be in a state like this one:

$$\frac{1}{\sqrt{2}}\big(\lvert\uparrow\rangle\lvert\downarrow\rangle-\lvert\downarrow\rangle\lvert\uparrow\rangle\big)$$

This state has the property that if an observer measures the spin of the first particle along the z axis and finds it to be "up", he knows with certainty that an observer who measures the spin of the second particle along the z axis will get the result "down".

The funny thing is that quantum mechanics predicts that this will be the case even when the two measurements are spacelike separated. When they are, it's not correct to say that the "earlier" measurement caused the collapse, because one can always do a Lorentz transformation to a frame in which the time order of the two measurements are reversed.