Do Wave Functions Really Collapse?
When someone wins the state lottery, it is reasonable to say that the probability has "collapsed."Before the win, you could say the probability was distributed all over the state, in the form of lottery tickets. Just like a wavefunction. As soon as the winner was announced on TV, suddenly every ticket's probability of winning became zero (except the winner). That's a collapse of a spatially distributed probability.
If we think of the wavefunction as pure mathematical probability (not a real actual material wave) then this makes a lot of sense.
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| The concept of wavefunction collapse was introduced by Werner Heisenberg in 1927. [Wikipedia] |
Standard (textbook) quantum mechanics is mainly about the laws of statistical probability. It deals with "statistical ensembles." It is a set of tools that can calculate the exact probability of any particular outcome or event. There is no mystery. No paradoxes or weirdness at all. We can predict that there is a 50% chance that Schrödinger's cat will be alive. It would make no sense to say "the cat is half-dead." Or to say the cat is alive and dead at the same time. In QM there is an initial state and a final state. If you want to know what happened along the way, if you want to see the underlying mechanism, you have to look elsewhere.
On the other hand, some people interpret the wavefunction as a real, physical, material wave carrying energy, momentum, charge, spin, and mass. Similar to a real electromagnetic wave that propagates in space carrying real energy and momentum. Real physical waves don't "collapse." They are absorbed, like electromagnetic waves get absorbed and turned into heat. Think of sunlight shining on a piece of black paper. There is no "collapse" of the light. It is absorbed like any other physical wave. I try to visualize how an ocean wave is absorbed by the sand on the beach. It's not an instant collapse, it's a smooth continuous process. The wave's energy and momentum gets transferred to the sand.
On the other hand, some people interpret the wavefunction as a real, physical, material wave carrying energy, momentum, charge, spin, and mass. Similar to a real electromagnetic wave that propagates in space carrying real energy and momentum. Real physical waves don't "collapse." They are absorbed, like electromagnetic waves get absorbed and turned into heat. Think of sunlight shining on a piece of black paper. There is no "collapse" of the light. It is absorbed like any other physical wave. I try to visualize how an ocean wave is absorbed by the sand on the beach. It's not an instant collapse, it's a smooth continuous process. The wave's energy and momentum gets transferred to the sand.
In summary, there are two views (interpretations) here. In the first picture we have an initial state and several possible final states. Each final state has some probability that it will actually happen. (Think of the cat). In the second picture we have real waves moving along and colliding with things. (Think of the beach).
Is one interpretation better? Is one right, the other wrong? I don't think so. Both pictures are useful. Choose the one that works best for you at the moment, but don't mix them up.
In standard (textbook) quantum mechanics the waves are just probability (amplitudes). There is a sudden, drastic change in probability at the instant the outcome is measured. Probability waves suddenly "collapse" when the result becomes known. That's how probability works.
In the field picture (Quantum Field Theory) the waves are real and physical. Everything is made of waving fields, like electromagnetic waves. These real waves move around and act on each other but they don't "collapse."
More on this subject is here.
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