Do quantum particles follow geodesics?

[orange31]

Hello, read up on space-time how throwing a stone here on earth high up, long hang time, vs throwing it the same distance but low and quick; if you plotted them on the space-time geodesic graph they would be superimposed on the same curve.

The double slit quantum experiment with 'single shot' photons or electrons, at first the hits look random and scattered. But over time and thousands of shots, you see the interference pattern of a wave function develop.

Similar to the default geodesic for throwing rocks in space-time on the earth's surface, is there some recognized 'inevitable' geodesic that quantum particles are following which leads to the wave interference pattern? thanks!

[sol invictus]

Hello, read up on space-time how throwing a stone here on earth high up, long hang time, vs throwing it the same distance but low and quick; if you plotted them on the space-time geodesic graph they would be superimposed on the same curve.

Hmm... maybe if you only plot one space direction?


Similar to the default geodesic for throwing rocks in space-time on the earth's surface, is there some recognized 'inevitable' geodesic that quantum particles are following which leads to the wave interference pattern? thanks!

In QM particles follow every possible path all at once, but they follow geodesics much "more" than other paths. And yes, one way to understand that pattern is as interference between those paths.

[orange31]

Thanks- re space-time, yes, one direction point A to point B, for both rocks thrown.



For the individual QM particles, all evidence still implies that, for example, a probability distribution for direction is truly a random event and not a compensation for an unknown hidden variable?
(for those unfamiliar with the concept, it's theoretically possible that you could throw a dice - or a coin- and always get the side you wanted if you mastered the technique with superhuman motor skills. The lack of those skills imparts the "hidden variables" to the coin toss and why we call it 'random'.)

[Vorpal]

For the individual QM particles, all evidence still implies that, for example, a probability distribution for direction is truly a random event and not a compensation for an unknown hidden variable?
Bell's theorem mathematically proves that if the predictions of QM are correct, any hidden variables cannot be local. In that sense, it's just the same as asking whether there is any evidence that potentially falsifies QM.


At least, under the assumption that it's meaningful to talk about counter-factually about experiments different from the ones you performed, even in principle... but hidden-variable theories assume this anyway.

[epepke]

Hello, read up on space-time how throwing a stone here on earth high up, long hang time, vs throwing it the same distance but low and quick; if you plotted them on the space-time geodesic graph they would be superimposed on the same curve.

The double slit quantum experiment with 'single shot' photons or electrons, at first the hits look random and scattered. But over time and thousands of shots, you see the interference pattern of a wave function develop.

Similar to the default geodesic for throwing rocks in space-time on the earth's surface, is there some recognized 'inevitable' geodesic that quantum particles are following which leads to the wave interference pattern? thanks!


Well, not quite, but it's not a dumb question.

Classical geodesics are (usually, but not always) the maximal probability path under Quantum Electrodynamics. The interference patterns are due to the fact that when there isn't a state change, there is no single classical path for the particle, and all possible paths interfere. The classical geodesic appears because nearby, the possible paths interfere constructively, whereas elsewhere they interfere destructively.

This is why light usually goes in a straight line. Near that straight line, the paths are very similar, and the possible paths reinforce each other.

You add up all the possible paths in a certain way, and you get a probability for each path that the particle will go that way. Each particle has a probability of going along a path given by the results of that calculation.

You get the interference pattern in the double slit because there are two nearby paths, but the path between them is blocked. So the path between doesn't interfere, and it changes what happens.

If you ignore polarization, it's really easy to get a feel for what happens. Picture a wheel rolling along a path with a radial arrow painted on it. Roll the wheel along a path, and the arrow moves. Another path, and the arrow move more or less. If you compare all the wheels rolled by different paths, they're pointing in different directions. Put all the arrows head-to-tail (vector addition), and the are of the circle that is formed is a measure of the probability of the particle being found there.

Most paths will just cancel each other out. Near a straight line, there will be a lot of paths with about the same length. So there will be a bunch of arrows pointing in about the same direction, and so the circle will be big.