Many years ago, I heard that a group proved that the collapse speed of the wave function is many times faster than the speed of light. After hearing it, I laughed, didn't take it seriously, and never read the original paper.

So what exactly is the collapse speed of the wave function in quantum mechanics? Is this even a valid question?

We first discuss this issue within the theoretical framework of the Copenhagen Interpretation.

The Copenhagen school believes that the wave function of quantum mechanics is the probability amplitude of the eigenvalues. The wave function itself is not an observable or even a real number. A wave function is a complex function or a collection of complex numbers. According to the definition of measurement and probability, the collapse speed of the wave function must be infinite. It is meaningless to measure the collapse speed of the wave function because it's not real.

A quantum wave function is a collection of eigenvalue probability amplitudes. The probability amplitude is a complex value with an imaginary part, and the square of its modulus gives the probability of the corresponding eigenvalue. Or, a wave function is a set. As defined by the Copenhagen Interpretation, measurement is to select a member from a set. It is a probabilistic selection, a mathematical sampling process, not an actual physical interaction. Nothing physical happens except the collapsing.

Discussing the nature of a virtual (complex, imaginary) thing is just as meaningless as conferring how many angels can stand on the tip of a needle and how ghosts and people communicate because this is a scientifically untenable proposition.

Another easy-to-understand example is the glove metaphor.

Put a pair of gloves separately in two boxes. Nothing can see through the box. That is to say, in each box, the gloves are in a superimposed state of being left and right. Separate the two boxes far away. Open one of the boxes and immediately know the left and right sides of the gloves in the other box. Here, the collapse of the superposition state of the glove to the specific state has nothing to do with the distance between the boxes and is always instantaneous. But this probabilistic collapse has no actual physical process nor interaction, so it is impossible to determine the collapse speed. In other words, it can only be infinite. If you get any value that is not infinite, no matter how many times the speed of light, it does not meet the definition of the wave function in the Copenhagen Interpretation.

The collapse measured in the Copenhagen Interpretation is the "collapse", or the change, from indefinite to definite, not the sudden collapse of a real particle from a diffuse physical wave into a point-like particle. That is to say, in Copenhagen Interpretation, the collapse of the wave function is not a physical process. The collapse speed of the wave function is meaningless, and even the concept itself is invalid. The concept originates from the misunderstanding of the definition of the wave function in the Copenhagen Interpretation and confusing the mathematical set (probability distribution) with the physical wave (the oscillating distribution of a particular physical quantity).

In Global Approximation Interpretation (GAI), how should we understand the collapse of the wave function?

GAI holds that the quantum wave function is an abstracted actual physical wave. To ensure the validity of the quantumness of the wave, that is, its close-to-ideal coherence, it must have sufficient establishment time or favorable coherence conditions. Measurements are the result of interactions. The measurement itself changes the system's state, so there is no concept of the collapse of the wave function, but there is a concept of the extent of influence of the measurement on the object. If quantum coherence is ensured, simultaneous measurements of the quantum system at different locations will meet the coherence condition. If there are multiple measurements, all measurements are correlated.

In GAI, the glove metaphor is not a natural quantum system but an association probability system or Einstein's hidden variable situation.

The reason people think the glove metaphor is a quantum system in Copenhagen Interpretation is because of the probabilistic nature of the Copenhagen Interpretation. Probability, or probability amplitude, is not a physical quantity, has no dimension, and cannot be directly measured. The normality of quantum systems and the definition of measurements lead to the concept of "collapse". "Collapse" is not a physical process. No actual physical process happens. Therefore, there can be no concept of a "speed". We can regard or define it as infinity, though.

The glove analogy, like Schrödinger's cat, is a definite macroscopic state. The measurement (opening the box) does not change the glove or the cat's actual state but changes the system's description from a superposition state to a deterministic state. Initially, there was a half probability for each, becoming a specific state afterward.