Is the wave-function collapse real or an interpretation?

Question

Consider the double slit experiment in which the position of the particle is in a superposition of the 'eigenfunctions' of the position operator before they reach the detector. This process is completely determined by the Schrodinger equation and the wavefunction of the particle evolves according to it. However, we can measure the position of the particle using a detector placed behind the slits and the electron is observed at a single location. This is normally thought of as the 'wavefunction collapse' as the wavefunction collapsing to a single position eigenfunction. However, I haven't seen any textbooks or theory talk about the method of detection or what causes the collapse. The detector is composed of atoms and molecules which interact with the wave function of the particle. This process, I believe, can be explained using the Schrodinger equation if we already know enough details about the state of the detector. In other words, it can be thought of as an interaction between particles and be solved using the Schrodinger equation.

So why do we ever need the concept of wavefunction collapse?. And if the concept of a wavefunction collapse is not necessary, why does a distributed wavefunction become localized when it interacts with the screen?

EDIT:

Now, in this case, I could argue that the wavefunction collapse is only an interpretation and that the wavefunction can only describe the probability of obtaining a certain outcome. However, it cannot describe the particle after measurement. Therefore, the wave function doesn't collapse because I only see a specific outcome with a probability predicted by the wavefunction before measurement.

But let's consider a different system in which there is an unknown apparatus which can somehow measure the position of a particle to a certain precision (pretty high precision). When I use this device to measure the position of the particle, I find out out it's at a certain location. Theory tells us that if we measure the position almost immediately after the first measurement, the position of the particle should be pretty much the same as before. This means that using the logic from the above paragraph, if the wavefunction is simply the probability of getting a certain outcome before the measurement, since the second measurement finds the particle at approximately the same location as the previous measurement, it must mean that the first measurement has somehow localized the wavefunction. That is the only reason why we would find the particle at the same position the second time.

This must mean that the concept of wavefunction collapse is somehow real.

It is an interpretation. Another interpretation need not include it. See Does the collapse of the wave function happen immediately everywhere? — mmesser314, Oct 17 '21 at 01:46
"why does a distributed wavefunction become localized when it interacts with the screen?" This is pretty much exactly what all the fuss about different interpretations of quantum mechanics is all about. Basically, no one knows, except to say that if you measure the screen you always see one particle located at one point on the screen. And, decoherence is almost certaintly part of the story. — Andrew, Oct 17 '21 at 04:40
A related question can be... suppose there are 2 dice and we shake them while hidden within a dice shaker, then leave them covered on the table. Can we say that the 2 dice exist in a superposition of probability clouds between 1 and 12, and this superposition will collapse once we unveil the shaker to reveal the value of the dice in it? In what ways is this similar/different from electrons dice in QM? — , Oct 17 '21 at 09:37
Related: I'm not seeing any measurement/wave function collapse issue in quantum mechanics — benrg, Oct 17 '21 at 21:05

score 4 · Accepted Answer · answered Oct 17 '21 at 10:33

The so-called collapse of the wave function seems somewhat less mysterious when you consider that quantum mechanics provides a collection of methods for modelling the behaviour of particles by finding approximate solutions to the Schrodinger equation, usually with a number of simplifying assumptions.

If you model the 'before' and 'after' states of an electron that has passed through two slits and been detected on a screen, the 'after' wave function is more localised, so clearly some sort of change has taken place. However, the idea of an instantaneous 'collapse' is almost certainly a misleading simplification.

The local environment in which the electron finds itself after detection is clearly quite different from the environment in which it existed before it reached the slits. We might model the experiment by assuming that the wave-function of the electron before it reached the slits was a plane wave, and we would treat the slits themselves as simply gaps a classical barrier that blocked the propagation of the wavefront- the wave function then propagates only through the slits, giving rise to the characteristic interference effects that are observed.

The precise nature of the wave function of the electron after detection will depend upon the nature of the detecting apparatus. In a microchannel plate detector, for example, the electron will interact very locally with atoms within a channel of the detector, causing them to emit a cascade of other electrons. Clearly the wave function is not an eigenfunction of position (a Dirac delta function).

If we were to model the behaviour of the electron in the detector, we would try to find a solution again to the Schrodinger equation, but it would be a quite different Schrodinger equation to that which would have described the electron before it passed through the slits, the difference being that the nature of the potential term in the equation would now have to reflect all the complexities of the environment within the detector.

It should be clear from the foregoing that physicists rarely try to model an end-to-end experiment by solving a single end-to-end Schrodinger equation that takes account of the all of the many-body interactions between the particle being measured and all the particles that make up the surrounding environment- that would be impossibly complicated. Instead physicists make as many simplifying assumptions as they can, consistent with predicting results that agree with experiment.

When we say they electron wave function 'collapses' in a two-slit experiment, what we really mean is that the 'after' wave function is more localised than the 'before'. How does that change come about? Is it an instantaneous collapse? Is it an instantaneous branching into multiple universes? Is it the result of interactions with the local environment causing 'decoherence'? Is it the result of non-linear terms in the Schrodinger equation that are too hard to calculate? Is it really the result of a smoothly evolving multi-body wave function of the electron and all the particles in the detector- a wavefunction that is so impossibly complicated that we can never hope to model it? We just don't know yet, and there are adherents of all those competing interpretations of what is 'really' happening.

score 1 · Answer 2 · answered Oct 17 '21 at 07:48

1

It is an interpretation. There are many interpretations of quantum physics which don't include wave function collapse. For instance, the many worlds interpretation says that wave function collapse does not happen.

answered Oct 17 '21 at 07:48

MathGeek

234

Is the wave-function collapse real or an interpretation?

2 Answers2