What is so special about the “wave function collapse”?

Question

Im not entirely sure of my intuition behind this topic, so please someone explain to me. Is the “collapse of the wave function” not just a description of observing an outcome? Why is there this notion of a physically seemingly “collapse” when the wave function is just a description of how something that was in a prior state of all possible locations, is finally being found out about? For example, if I throw a ball and aim it at a specific target, the second before it hits the target, probabilistically speaking, has a higher probability of hitting that target vs a farther location. Then, when I finally see the ball hit the target, thats when the “highest probable state” reduces to one state, and is observable to me. Is that not all that the collapse of the wave function is?

TLDR: Is the “collapse of the wave function” not just the observer finally finding out about where the particle actually is? (Indicating that a prior space of possibilities was in fact just a specific location upon our observation”?

Answer 1

Not really. What quantum theory says is that a particle- say an electron- has an associated mathematical function (the wave function), from which you can determine, in a probabilistic way, dynamic properties of the particle, such as its position, spin direction, momentum and so on. The wave function is influenced by the particle's environment (that effect is modelled in quantum theory by terms in the Hamiltonian in the Schrodinger equation). If you measure a property of an object- the spin direction of an electron, say, you have to subject it to some process that has an effect on the object, so that its wave function after the measurement can be different from its wave function before. In the original Copenhagen interpretation, it was simply accepted that such changes happened in a sudden, discontinuous way as a consequence of an observation, since by making that simplifying assumption you can still correctly predict the outcomes of experiments.

If you consider, for an example, an electron coasting in a vacuum tube- it is in a region of effectively constant potential, so according to quantum theory its wave function is a plane wave. If the electron now impinges on a detecting screen, it is no longer in a region of constant potential- so that if you wanted to try to model its wave function, you would have to find solutions of the Schrodinger equation for a complicated potential determined by the chemistry of the screen.

If you like, you can model this in QM by saying that the electron was initially in plane wave state that 'collapsed' when it hit the detecting screen, and you will get accurate predictions that way. But by 'collapse' what you really mean is that it changed as the electron was influenced by the complicated chemical potential in the region of the screen having previously been in a region where the potential was effectively constant.

Finally, you need to be clear about what the wave function represents. When we say the wave function shows how the probability of finding the electron varies over space, we don't mean that the electron at any instant is 'really' at some specific point within the much wider region encompassed by the wave function. The wave function doesn't represent our uncertainty about whether the electron 'really' is. We know that when we detect electrons through localised interaction with other objects they act as point-like particles with a radius less than 10^-18m. However, quantum theory suggests that it isn't meaningful to ask where an electron 'really' is between such localised interactions.

Answer 2

There is no such thing as "wave function collapse". Every measurement on a quantum system requires us to either take a quantum of energy out of the system or to add a quantum of energy to the system. These are irreversible processes that destroy the state of the system and they replace it with a new state. These are perfectly well understood microscopic events, but unfortunately the mathematics of quantum mechanics, especially in the von Neumann formulation using a Hilbert space is completely void of a physical explanation for what really happens during measurement.

Since a wave function is ontologically similar to a probability distribution, the term does not even make any logical sense whatsoever. Both a probability distribution and a wave function are descriptions of the averages of an infinite ensemble (number of independent copies) of a system. No single outcome will every change anything about the average over an infinite number of events. We do, after all, also not claim that a roll of dice "collapses the probability distribution of dice".

I have not been able to find out where the term "wave function collapse" originates. Wikipedia makes a reference to an old paper by Heisenberg where he discusses wave packets that are being reflected forth and back in an interferometer and it seems that the "collapse of the wave packet" is mentioned in there. How the term became so famous is not clear to me. I don't remember even hearing it during my QM 101 class, which was "shut up and calculate" but at least it didn't invoke such misleading terms.

Answer 3

No, it isn't possible to interpret the wave function collapse as a mere gaining of information, because of the uncertainty principle. For example, if you prepare a spin system in the state $\uparrow$, and measure it along the $\updownarrow$ axis, you will always get the result $\uparrow$ (which you already knew). But if you measure it along the $\leftrightarrow$ axis and then along the $\updownarrow$ axis, you may get $\downarrow$ from the second measurement. This can be modeled mathematically by saying that the state is updated/collapses to $\leftarrow$ or $\rightarrow$ after the $\leftrightarrow$ measurement, and measuring $\leftarrow$ or $\rightarrow$ along the $\updownarrow$ axis may result in $\downarrow$. The mathematics of the update/collapse resembles a classical Bayesian update, but Bayesian updates don't invalidate what you previously knew for certain.