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We are learning about the wave/particle duality of electrons, and how electron orbitals are just standing waves each with a different discrete amount of energy, which got me wondering, is quantum mechanics just a mathematical trick?

That is, are electrons just a particle but move around like waves due to the forces acting on it, a phenomenon that just happens to be explainable by waves? Or, is there any deeper, more fundamental physics governing the physics of elementary particles?

I watched a Veratasium video on pilot-wave theory, which I think kind of explains my answer, but I had one problem with it, which was the existence of physical waves. Where would such waves exist in real life(in the video, it was in a tub of some kind of oil)? Also, Veratasium said that this is not actually how elementary particles behave in real life, so I also wanted to know if we actually know that to be true.

So basically my question is: what are elementary particles, and why is their behavior described by wave functions?

Sorry if this is a really basic/bad question. I don't really know much about quantum mechanics and I'm just trying to understand why things are the way they are.

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So basically my question is: what are elementary particles, and why is their behavior described by wave functions?

The reason they are described by wave functions has a lot of historical background, but a major inspiration is the double slit experiment, which shows wave-like behavior for matter which was once thought to behave like a point particle. It has not been proven (and probably cannot be proven) whether matter really is described by point-particles or not, fundamentally. There are flavors of quantum mechanics which explain its results through a notion of point particles (Bohmian Mechanics), and those which don't (textbook Quantum Mechanics), and both are mostly equivalent in their predictions. Note that both make use of the wave function, $\psi(x)$, as well.

As for what elementary particles actually are, we also can't quite answer; we can do experiments which allow us to attempt to make inferences about what we see, but there is always limited accuracy and the possibility that if we dig deeper, we will see something different. This seems unavoidable regardless of the state of experimental technology.

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  • $\begingroup$ Why is it not possible to get a more accurate description of what is going on? $\endgroup$ Oct 14 '20 at 13:33
  • $\begingroup$ @SagarPatil We are always limited by: (1) Experiments, setting up sufficiently high-energy and large-scale experiments costs a lot of money which isn't always available. (2) Theoretical ignorance, it's not clear which theories in theoretical physics will ultimately be the most accurate or useful so a lot of theoretical work ends up not being very useful. $\endgroup$
    – Charlie
    Oct 14 '20 at 13:37
  • $\begingroup$ There is the question of "what is REALLY going on in nature?" and the separate question of "how does the framework of QM explain what is going on?". The QM framework is created by humans to match nature as well as possible, but one never knows that it is correct, as experiments have limited accuracy, and there are always more possible things to experiment which haven't yet been checked. $\endgroup$ Oct 14 '20 at 14:14
  • $\begingroup$ I can give a more accurate description of what is going on, but it is within a framework of QM, so although the framework matches nature in a variety of existing experiments, there is no guarantee that it is really how nature works. I guess a succinct answer to the question in your comment is: certain questions can't really be experimentally tested, like "what is matter, fundamentally". String theorists would tell you it is strings, Bohmians would tell you it is point particles and waves. $\endgroup$ Oct 14 '20 at 14:19
  • $\begingroup$ The best we can do is "within the possible experiments we have technologically been able to perform, a theory with consituents X is consistent with the data". Whether consituent X is actually how nature is, doesn't seem to be testable scientifically. X here could be particles, waves, strings, or combinations thereof, for example. $\endgroup$ Oct 14 '20 at 14:21
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Quantum mechanics is mainly concerned with describing the behavior of the wave packets associated with small bits of matter or energy. The problem is that it appears that the packets only inter-act with each other at some point where they overlap. The subsequent behavior may depend on the location of that point and the best we can do is calculate the probability of where that point may be.

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Ultimately, we use the wave function because it accurately predicts the results of a huge number of experiments, such as Young's slits. On the other hand, a particle model can better predict other observed phenomena, such as the photoelectric effect. Quantum mechanics is a kind of unhappy marriage between the two models, in which the wave dominates until a measurement is taken and it "collapses" into a particle.

This approach has an extraordinary ability to predict the outcomes of the most complex, weird, subtle and counter-intuitive experiments, sometimes to a staggering level of precision (for example we can use the quantum properties of light to detect the gravity wave emitted when two large stars collide).

It is possible to recast or reinterpret the equations in various ways to give different models of the underlying reality, such as pilot waves or many diverging worlds or quantum handshakes or whatever. All of these variations yield the same experimental predictions, so it is impossible to tell which might be right.

The standard approach is to ignore these interpretations as meaningless babble, to just "shut up and calculate". To claim that any one interpretation is somehow better is just pseudoscience.

Of course, sometimes we make an advance and modify or clarify our standard model. For example Bell's theorem allowed us to demonstrate experimentally that nonlocal or faster-than-light quantum entanglement exists. Some of the pilot wave models had been developed specifically in order to avoid such implications, so-called local realist theories, so demonstrating that reality really is nonlocal dealt them a lethal blow; they have had to be either modified or abandoned, but all too many adherents still try to cling to outdated ideas.

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