Is wavefunction collapse limited by the speed of light?

[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?

 

[Fredrik]

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.

 

[R0man]

The concept of wavefunction collapse is a highly debated topic in quantum mechanics and there is no clear consensus on its limitations or mechanisms. However, one thing that is generally agreed upon is that the collapse of a wavefunction occurs instantaneously, regardless of the distance between the particles involved. This means that the speed of light does not limit the collapse of a wavefunction.

As for the connection between wavefunction collapse and the completeness of information about a probability distribution, it is important to note that the wavefunction itself is a mathematical representation of the probability distribution of a quantum system. This means that the collapse of a wavefunction does not necessarily require complete information about the system, but rather a specific measurement or observation that causes the wavefunction to collapse into a particular state.

It is also worth mentioning that the concept of a physically determined wavefunction collapse is still a matter of debate and there are alternative interpretations of quantum mechanics that do not rely on such a collapse. In these interpretations, the wavefunction is seen as a description of our knowledge or information about a system, rather than a physically real entity that collapses.

As for the role of light signals in establishing knowledge about the statistics of all existent quanta, it is true that our observations and measurements are limited by the speed of light. However, this does not necessarily mean that the collapse of a wavefunction is limited by the speed of light. Our understanding of quantum mechanics suggests that the collapse of a wavefunction is a fundamental process that is not dependent on any external factors.

The idea of a theoretical infinity of states evolving gradually to a finite number and eventually to a singleton is an interesting concept, but it is not supported by current theories and models of quantum mechanics. The wavefunction is a continuous function that describes the probabilities of different states, rather than a discrete set of states that evolve over time.

Finally, after each measurement, the wavefunction does not need to reestablish its expectation value for the subsequent measurement. The collapse of a wavefunction means that the system is in a specific state, and the expectation value for the subsequent measurement will depend on this new state. The collapse of the wavefunction does not affect the previous measurements or their outcomes.