Unsure about the wave function

[Achilles762]

I have been trying to figure out what the wave function is. I think the wave function describes the probability of a particle being in a certain place once the wave function collapses, but as far as the math goes, I am pretty lost.

[KipIngram]

The wave function is a complex value at every point, and to determine the probability you "square it" (multiply the complex number by its complex conjugate) and then integrate that over a volume. If you've normalized the wave function so that the integral over all of space is 1.0, then the integral over a limited volume is the probability that the particle will be found in that volume.

 

There's a ton of debate about what the wave function "really" is, and a lot of physicists preach the "shut up and calculate" methodology. There's also a lot of debate about what "collapse" is, or if it even really happens.

 

I may be a tad ahead of you in this struggle with learning more about quantum theory, but probably not all that far. Good luck with it!

[Achilles762]

It's a lot to digest, especially since I don't have a teacher/professor. Your reply is definitely helpful, though, so thanks a lot for your input.

[KipIngram]

Sure thing. Let me tell you one more thing. It may be a while before you're fully prepared to really dig into this, but I recently read a paper by Art Hobson called "There Are No Particles, There Are Only Fields." After reading it and digesting it, I decided that I think that truly is correct. He makes a very solid case for the notion that ultimately all there is in physical reality is a set of quantum fields that interact with one another. Some of those interactions give rise to what we perceive as "particle like behavior," but nonetheless it's still all fields. If you know anything about the Fourier transform you know that the right set of sinusoidal waves spreading out over all of space can add up to something that looks like a lump in one spot, and that lump can move around.

 

The reason I'm bringing this up is because some of the classic "paradoxes" in quantum theory, like the double slit experiment, cease to be paradoxical if you study them from the "fields only" perspective. The "quanta" of these fields is like one sinusoidal component of the Fourier decomposition of the field. Each quanta is spread out over all of space. When an interaction between two fields occurs, each field may lose or gain quanta - and that means that each field changes everywhere in space at the instant of the interaction. That's how the whole "spooky action at a distance" finds its way into things.

 

Anyway, terribly sorry if that is unhelpful - I just found that particular paper to be a "milestone" in my own understanding of all this stuff.

 

Also, pay a lot of attention to the stuff the user on this forum named Mordred has to say - he's top drawer.

[Achilles762]

Yeah I must say I'm at a kind of existential crisis thanks to quantum physics, and when I learned about string theory things took a turn for the weird. Again thanks for everything.

[KipIngram]

String theory is still hotly debated - it doesn't have nearly the sound basis in experimental proof that quantum theory does.

By that I mean that yes, you really do have to accept quantum theory - there's little doubt about it these days. But string theory is still in the "maybe / maybe not" category.

[imatfaal]

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