# Discrete movement vs wave function collapse

I remember once, as a child, thinking that objects do not really "move," but that at a very small scale they would have to "disappear" and then "appear" again at their newly shifted position, just the way computers render moving particles based on refresh rates. This relates to Zeno's paradox which is solved by infinite sums.

Then I heard about quantum wave function collapse and the double slit experiment, and then thought: oh, maybe nature solved the problem by turning anything that wants to move into a wave instead of making a single particle "appear" and "disappear" in new positions as it moves. Waves is by the way a very elegant solution in comparison.

My question is: was my thinking correct? are waves (and wave collapse) nature's way to make particles move around?

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I don't think so, there are conservation laws which don't let you destroy matter. – jinawee Dec 29 '13 at 9:31
why the downvote for question? – user117325 Dec 29 '13 at 18:01
@jinawee in quantum mechanics there is Heisenberg uncertainty principle which allows the total energy of a system to diverge for a short time. – Anixx Dec 29 '13 at 20:18
I think it's wrong to think of the particle as having an exact location. If you view the particle as a probability distribution centered at some point in space you can imagine the probability distribution moving continuously by decreasing the probability of the particle on one side and increasing it on the other side. – Brandon Enright Sep 9 '14 at 1:58

This is an excellent question! The nature of “motion” has always been mysterious. People have wondered how a rigid object can move at all, noting that it at one time is in one location and at some later time in another location, but how does it transit between these locations? Does it do it in a stepwise manner, or does it somehow change its shape and move like an inchworm? This question is not generally posed, but it is important, since the mystery of motion still remains unresolved and appears to defy detailed analysis. If motion of a rigid object proceeds in a stepwise manner that mimics continuous transition these steps must be very small, and the smaller they are the higher their frequency must be. If such motion approaches a smooth continuous state this frequency increases beyond any limit. The ancient Greeks thought that this is impossible, and now we know that they actually were right, because Heisenberg’s uncertainty relation prevents the incremental steps from becoming arbitrary small; stepwise motion dissolves in a fuzziness of uncertainty. In the past people thought that this objection might be overcome by differential calculus, originally developed by Isaac Newton and Gottfried Leibnitz, which allowed the increments to become “infinitely small”, but in the beginning of 20th century we learned In fact, this issue has never been resolved and movement is still mysterious. Some think that General Relativity can model motion but this is not true because GR cannot explain the progression of time. The explanation to motion requires new physics.

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Perhaps it is just me, but I don't think that this really answers the question. – Kyle Kanos Sep 9 '14 at 0:00

Particles move continuously. There is no "disappear" and "reappear". If such discrete movements were the case than we should be able to detect it by scattering experiments and find that certain regions of space always seemed to be empty (similar to how they detected that atoms were mostly empty space). No experiment has detected this phenomena.

Also, the wording you chose is misleading. "Nature" doesn't solve any problem. People make the problems, and people solve them.

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Why the downvote? – mcFreid Dec 29 '13 at 17:35
see my answer. Particles continuously appear and annihilate in vacuum. – Anixx Dec 29 '13 at 17:38
there is no "continuous move" in quantum mechanics. – Anixx Dec 29 '13 at 17:55
I don't think that has much to do with the OP's question. There is no "spatial" aspect to the loop effects in a propagating particle. Taking your example, we could never measure the positron in the virtual electron-positron pair, else it wouldn't be virtual. So it's not like the electron dissapears at x=0 and then reappears at x=1. – mcFreid Dec 29 '13 at 17:59
Also, the confusion with loop effects comes from the fact that the electron is never purely an electron since it's charge disturbs the vacuum state of the EM field and this disturbance propagates. Either way, the result remains that the electron and its disturbance do move continuously. With regards to QM, free particles move continuously. I don't know what you're saying by "there is no continuous move". – mcFreid Dec 29 '13 at 18:01

Motion of the particles indeed can be described as in your first point: for example, propagation of electron can be seen as a creation of a virtual electron-positron pair ahead of the propagating electron, and later annihilation of the first electron with the positron so the newly-created electron remains.

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Isn't this rather philosophical? Virtual particles cannot be detected and there are theories which don't use them (for example, QFT in the lattice). By that reasoning you should say that when a particle goes from A to B there are infinite particles created-destroyed all over the Universe. And the OP's vision of wavefunction collapse and movement seems incorrect, but I don't know enough QM to be sure. – jinawee Dec 29 '13 at 20:25
@jinawee everything concerning the interpretation of quantum mechanics is quite philosophical. But this model explains for example, why in certain circumstances particles can seemingly move faster than light en.wikipedia.org/wiki/Hartman_effect – Anixx Dec 29 '13 at 20:28
@jinawee of course one can interpret it in another way: that is the particle's velocity varies as the particle propagates, sometimes reaching faster-than-light values, remaining constant only on average. But this interpretation is equivalent to that with virtual particles because an antiparticle can be actually viewed as a particle moving backwards in time. That is anti-particle moving from B to A is particle moving from A to B at super-infinite velocity. – Anixx Dec 29 '13 at 20:35

## protected by Qmechanic♦Sep 8 '14 at 22:05

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