In classical QM, when I measure the wave function of a system, e.g. the position of an electron somewhere in a box, its wave function collapses instantaneously to some classical position. But how fast does this collapse spread? If it is a very large box (i.e. light years across), would the electron wave function on the far end still exist in its original shape, whereas on my end it had converged against a point? How is the wave function collapse modeled in QFT?
Collapse is just one way to use quantum mathematics and there are more ways to understand this collapse. For example, one of those is:
In non-relativistic theory, the collapse is instantaneous. The collapse is just a change in description from one function to another when the result of measurement is learned.
In QFT this is probably the same, the preferred frame of reference being that of the reference system used to measure the position.
The wave function collapse is instantaneous. Measuring the value of one dynamic variable forces all other linked variables to collapse into specific values instantaneously.
You need to understand three postulates of quantum mechanics.
If y1 and y2 are two solutions for a wave equation( I don't know how to write 'psi' here), then a linear combination of y1 and y2 is also a solution. Say y = Ay1 + By is also a solution.
- The result of measurement of any dynamic variable is one of the possible values allowed.
When the result of measurement of a dynamic variable P is the value p, then the system collapses to a state where P has the value p.
Before measurement the system staysin a state of superposition of all the states possible. It is the act of mmeasurement that forces the system to collapse to one state.
And as the system collapses to one state all the dynamic variables assume a value allowed in that state.
The idea of spreading of collapse is nonsensical in quantum mechanics. A system cannot be in one state somewhere and another state somewhere else.
An example of this is quantum entanglement. For example , if you have two particles with entangled wave functions and you try to measure the spin of one particle, the act of measuremt will force the system to collapse to a state to give you a result of the measurement. But due to entanglement the other particle will also collapse to a particular value of spin allowed by that state. And this happens instantaneously no matter bywhat distance the particles are saperated. They could be at opposite ends of the uuniverse ( figure of speech).
The wave function cannot be measured as it does not represent any physical quantity.