A wave function does not collapse upon detection?

A wave function does not collapse upon detection?
physics.stackexchange.com

For simplicity, let's assume that it's the wave function of an electron, but this applies to any particle.

The first problem is the question. What does "detection" means?

The technical term is "measurement", and the most important idea is that you can measure different things, for example the position of the electron, or the speed of the electron, or the energy of the electron, or ...

If you measure the exact position of an electron, the wave function collapses to a point.

But you can measure other thing, for example if it's inside a box or outside the box. In this case the wave function that initially is spread perhaps in all the universe, will collapse to a smaller wave function. In some cases to one that is completely inside the box, and in other cases one that is completely outside the box.

Knowing the initial wave function it's possible to know how the wave functions inside or outside the box will be, but the details are quite technical.

What is not possible to know if after the measurement you will get the wave function that is inside or outside the box. As fas as we know this is a random choice. Nobody likes it, some people thing there are not random rules, but most people think it's sadly random.

Note that the probability to get the wave function that is inside or outside the box are not equal. It may be la loaded "dice". The exact numbers can be calculated if you know the initial wave functions, but the details are quite technical.

Very informally, if the box is small, the probability of getting the wave function that is inside is small. If you have an electron inside the box and open it for a very short time and close it, then the probability of getting the wave function that is inside is big. To get a formal definition, you must read all the nasty technical details.

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The idea is that you can somehow detect that the electron is inside or outside the box, but it does not collapse the wave function completely. You still have a complicated wave function inside or outside the box. And you can make this wave function colide with other wave functions and get some weird quantum mechanics results that are impossible if you assume that the wave function has collapsed for a very short time to a single point inside or outside the box.

Or you can generalize this with two boxes and the rest of the universe. It's possible to measure if the electron is in box A, box B or outside. It's also possible to measure if the electron is in any box or outside. In this case you get entangled boxes that are even weirder.

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The experiment in the link use photon in a one or two slits experiment. The physical details are very different but the calculations and the idea is very similar. The box is the slide, and outside the box is the screen.

This is especially the case with entanglement. By measuring one entangled observable, we often increase our knowledge but not absolutely like in the naive explanations that have you believe it is always an entangled pair of spin up and spin down..

All measurement does is reduce uncertainty/entropy of the wavefunction. The strange part is that one can actually undo this restriction by erasing any traces of the measurement. See the Delayed choice quantum eraser experiment. Collapse doesn't really exist.. It's more like expressions that can be reduced, appear reduced, until they cannot be reduced..thus they appear expanded. Imo, entanglement is evidence that all interactions are lazily computed and are copy-on-read or lisp expressions that gradually become larger as interactions continue, and are beta or alpha reduced when possible.

That's the whole point of the experiment - you can't get an interference pattern if it does not.

> and the act of detecting which slit the photon could go through, if it were a particle

The whole point of the double slit experiment is that there is only one photon, and which slit it goes through is irrelevant.

Whether a photon is a wave-function is missing the point entirely - the point is how do you get an interference pattern if the photon/wave-function only goes through one slot?

The point of this experiment is to show that sometimes light behaves like a continuous wave, while other times it behaves like a particle of sorts.

And if you think QM has actually provided answers to any of this, you might want to read up... https://en.wikipedia.org/wiki/Wave%E2%80%93particle_duality https://en.wikipedia.org/wiki/Interpretations_of_quantum_mec...

In short, QM might have produced some nice mathematics models, but it's claims about objective reality are contested. Some people don't agree there is any paradox, and that the double-slit experiment correctly identifies light as a wave, and that claims that the photoeletric effect proves light is a "particle" are based on false inference (particularly that energy quantization implies packetization). Some people still seriously propose that consciousness affects basic particle physics (as if particle know when they are being measured).

Despite all that the cool smarty pants brigade who have read some 1st year QM books (while understanding only a fraction) come away all puffed up that QM actually provides deep insight and wide consensus as to the underlying interpretation of reality. The fact is, it's as paradoxical today as when the great physicists up to the last of them (Feynman) correctly identified it as such. Quite sad really.

Note, though, that in reality you can never measure the exact position of an electron (or anything else); the best you can do is to measure that the electron is inside some finite-sized (possibly very small) region. The "exact position" measurement is an idealization that can be useful for pedagogy but can't be realized in any actual experiment.