If I were to take a “frame by frame” video of a hydrogen atom and its electron, would I find the electron moving along a trajectory or teleporting randomly throughout the cloud?

No. It wouldn’t.

This question reveals the fundamental problem humans face when trying to understand the small. Perhaps Richard Feynman, a physicist, suggested that the fundamental problem in teaching schoolchildren complex topics is by simplifying them so much it’s simply wrong.

They are much more than little balls. They are not waves in the same sense that we refer to ocean waves and sound pressure waves. We humans cannot understand electrons and other quanta. They are not what we think they are. We must remember, however, that these are not the metaphors we use to describe them.

You would be able to examine a hydrogen atom with the exact detail you want, but it would all depend on how you did it.

One way you can see the nucleus enclosed by an electron wave above it in a three-dimensional standing waves.

This is incorrect. Although electrons are not three-dimensional standing waves wrapped around a nucleus, they do possess a property called wavelength that limits them to only exist in multiples of their wavelength. The question is “Why don’t negatively charged electrons stick with the positive protons?” This answer answers the question. They can only reach as close to their inner electron shell as they cannot get any further. Any closer would mean that there wouldn’t be enough room for a multiple of their wavelength.

Simple, yes? But that’s just one view. Another way to look at it, the electrons can be viewed as a cloud-like probability function that is distributed around the nucleus.

In this view, an electron can be thought of as essentially a point of unknowable location and momentum, the exact properties of which can be described using probability mathematics.

This is also false. They aren’t little balls that have uncertain locations. They are electrons.

All things are the same: electrons, photons and protons. They don’t have any metaphors that we can use to describe them. They seem strange and paradoxical because of this. You cannot describe an electron by using phrases like “moving along the trajectory” or “teleporting randomly”. An electron is not a tiny ball that can move along an imaginary trajectory or teleport randomly. It’s a quantum, which can appear to do other things depending on what we poke or prod. You can make it appear to move but not to move, wave without waving and travel backwards in its time to interact with other elements. It can even exchange part of its reality “spookily”, at a distance.

None of this is likely to be true if taken in isolation. It all helps to create a model of something that we are fundamentally ill-equipped to comprehend.

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