What are some of the explanations as to why the wave function of electrons collapses when interacting with an observer?

Question

What are some of the explanations as to why the wave function of electrons collapses when interacting with an observer? Is there a specific reason why the wave function collapses, what are some of the proposed explanation. I read that it's because when observed an electron may hit the electron emitted thus causing the collapse, but why would such a collision cause a collapse?

Answer 1

The wavefunction $Ψ$ is not a balloon, and collapse is a misleading terminology invented in the popularization of quantum mechanics.

$Ψ$ is a solution of the quantum mechanical equation describing a stable, non interacting system of quantum mechanical particles. It is characterized by the boundary conditions of the particular problem,and $Ψ^*Ψ$ is the probability of finding the system at a particular state at a given time, according to the postulates of quantum mechanics.

If the system interacts, new solutions will apply and new boundary condition, thus the old $Ψ$ is no longer valid and a new one will describe the sysem after the interaction. That is the "collapse" the need to change the mathematics describing the system.

When there is an interaction, a new wavefunction will describe the system, the old one is invalid, and that invalidation is called "collapse".

Answer 2

The wave function is perhaps more accurately also called a probability amplitude. It is related to probability by the Born rule, and is equivalent to the probability of a particular result in an measurement given known initial conditions (this approach to quantum mechanics was taken by Dirac and von Neumann). This means that there is nothing more mysterious to wave function collapse than there is in the change to a probability once a result is known.

Probabilities always "collapse" with a change of information. If you throw a dice then the probability of getting a $6$ changes from $1/6$ to either $1$ or $0$ when you see the result. The change in probability depends on information. If your friend throws a dice behind a screen where you cannot see it, then the probability (for you) remains $1/6$ until the screen is removed. But your friend can see the dice when it lands, so for him the change in probability takes place earlier. (We may compare this to Wigner's friend, who has a different knowledge of a quantum result from Wigner, who is outside the room, and to Alice and Bob in Bell tests. When Alice observes her result, she obtains a different wave function for Bob's particle, but Bob observes no change as he cannot know Alice's result).

The real question is "Why should the wave function obey the Schrödinger equation?" from which follows the mathematics of wave mechanics. The answer is buried in the mathematical foundations of quantum mechanics. This is not generally covered in physics courses which are usually more concerned with practical application than with mathematical structure, but the general form of Schrödinger's equation can be derived from the Dirac–von Neumann axioms. An outline of the derivation is given at Derivation of the Schrödinger equation. I have given a detailed derivation in The Hilbert Space of Conditional Clauses.

The key postulate is that probabilities are given by the Born rule (or expectations given by the inner product). One also requires that the fundamental physical behaviour of matter does not change. This enables one to show that the probability interpretation requires unitary time evolution satisfying the conditions of Stone's theorem, and the general form of the Schrödinger equation follows as a simple corollary.

The key reason for this difference in mathematics from classical probability is that classically probabilities are determined by unknown variables, whereas in quantum theory probabilities result from the absence of determinism in the fundamental interactions of matter.

Answer 3

It is easy enough to explain away the collapse as a feature of the way we model quanta, a change of physical conditions requiring a new equation. Were that all there was to it, nobody would bother with all the other explanations. Quantum reality is much weirder than that.

Experimentalists have sent the spin of a "particle" down one path and its momentum down another, combining them back together at the far end. They use very sophisticated techniques of what one might call partial or pseudo-measurement to draw statistical information about the properties of many such "particles" without collapsing their wave functions. It is hard to justify the wave equations for each path as mere mathematical artefacts, there appears to be some physical reality underlying the phenomenon.

Given that the wave equation models something real which is physically distributed in some such way, we may note that the collapse is instantaneous and therefore nonlocal.

Consider a photon emitted by a star and travelling for a billion years. Its wavefront is vast beyond comprehension, yet collapses to nothing the instant it hits the astronomer's camera. Millions of almost identical photon waves pass by the camera as if it did not exist. Why this particular "hit" and not another one?

Some people have suggested that the photon is actually a tiny particle, whose trajectory is governed by hidden variables and if we knew those variables we would know its path. Provided such a hidden-variable theory respects nonlocality (which most don't), the idea can be made to work. But it tends to make the maths more complicated, as for example with Bohm & Hiley's pilot-wave model.

Others have claimed that it just looks like it happened that way because the Universe split into all possible outcomes and your particular copy of you just happens to be in the universe where the photon hit the camera; all the other parallel worlds left that particular camera dark.

There are various other ideas, such as quantum handshakes, but most just push the probability around, they don't explain the mechanism for its collapse. Or at least, I can't think of any others off hand.

If you feel that the proffered examples are on a par with the Flying Spaghetti Monster, you are far from alone. Fundamentally, it is one of the biggest and most long-standing conundrums of quantum physics and we have not the slightest idea what is going on. Hence the wide popularity (reflected in some other answers here) of seeking sanity in a simple mathematical sleight of hand; "Shut up and calculate".