The Meaning of the Wave Function
What is the Wave Function?
As Einstein’s blackboard drawing at the fifth Solvay Conference shows us, the wave function propagates like a light wave, but when the particle appears, it is found at a single point P.
In 1905 Einstein's wave was the energy in a light wave radiating out in all directions, but then
instantly gathering all its energy at one location to eject a photoelectron carrying all that energy.
Is this perhaps the origin of seeing the event as a
collapse"? Einstein already in 1905 saw something
nonlocal about the photon and that there is both a wave aspect and a particle aspect to electromagnetic radiation. He will make those aspects more clear and in 1909 describe the wave-particle relationship more clearly than it is usually presented today, with all the confusion about whether photons and electrons are waves or particles or both.
Louis de Broglie in 1924 suggested there is a matter wave associated with any material particle. For
Erwin Schrodinger, the wave was the distributed mass of the electron, or perhaps its "smeared out" charge?
Today the wave is an abstract complex wave function Ψ whose square gives us the probability of finding a particle. Many locations have some probability of being the position until the moment when the particle is found somewhere. At that moment, the probability of its being anywhere else goes instantly to zero.
This abrupt change of probability to unity at one location and zero everywhere else has been interpreted as a “collapse.” If the wave had been carrying energy in all directions, or matter/charge as de Broglie and Schrödinger thought, energy and matter would indeed have had to “collapse” to the point.
But
nothing substantial is moving in the "collapse" of an abstract probability to one of many possibilities. Only
immaterial information (our
knowledge ) has changed.
Note that should another particle enter through one of the slits, its wave function Ψ would be the same, since the boundary conditions used to calculate Ψ have not changed.
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