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One could potentially suggest observations of atomic locations partly with chaos theory by suggesting that the seemingly random pattern simply results from a sufficiently small Lyapunov time that allows nearby trajectories to diverge very quickly, making randomness and chaotic trajectories indistinguishable.

However, the inverse of Lyapunov time should not be faster enough such that trajectories diverge faster than the speed of light, but this is very difficult to assess with individual particles that are either entangled or which cannot have simultaneous position and momentum determined.

In the observational constraints and in seeing the simpler explanation of deterministic chaos, why can't quantum randomness potentially be explained by chaotic motion? It seems physicists already possess the capability to predict the exact future state of single particles at a time at least.

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  • $\begingroup$ How would you use chaos to explain, e.g., the interference pattern observed in the one-electron-at-a-time double-slit experiment? $\endgroup$
    – stafusa
    Dec 19, 2020 at 16:34
  • $\begingroup$ Can waves not exhibit chaotic motion? $\endgroup$
    – PhiEarl
    Dec 19, 2020 at 21:12
  • $\begingroup$ Yes, they can -- but my take from your post was that you wanted to replace the description by wave functions and (e.g.) collapse by a description based on chaotic particles, maybe hidden-variables-like. If not, your question might be to vague/broad to be on topic. So, please, what exactly do you have in mind? $\endgroup$
    – stafusa
    Dec 19, 2020 at 22:56
  • $\begingroup$ I don't "want" to replace anything, that is your own confrontational prejudice in an elitist physics community that you are projecting onto me. I am simply asking on why it is/isn't possible given that seemingly random observations seem to be capable of explanation through chaotic behavior. Bell's inequality experiments, as far as I know, also do not rule out hidden non-local variables. $\endgroup$
    – PhiEarl
    Dec 20, 2020 at 0:32
  • $\begingroup$ Hey, PhiEarl, I am by no means looking for confront, nor, I hope, being prejudiced - my "want to" should perhaps have been "suggest to". So, please, answer my question, because your post is still not clear to me. Is chaotic classical particles instead of mainstream QM what you have in mind? How could that describe interference? $\endgroup$
    – stafusa
    Dec 20, 2020 at 0:39

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Let's postulate that every possible physical observable follows a chaotic (but deterministic) evolution rule such that, over any "reasonable" amount of time, their "long-term" behavior is effectively random with statistics that precisely match the predictions made by quantum mechanics.

A notable challenge to such a description of physical behavior is relativity, notably the universal speed limit. To see this, consider a particle in free space whose chaotic behavior is consistent with a probability density that is uniform over a small, finite region of space. As time goes on, the probability density is predicted to keep spreading out by quantum mechanics—inevitably to the point where the underlying chaotic dynamics of the particle would have to make the particle travel faster than light in order for its statistics to be consistent with the quantum mechanical prediction (i.e. for the particle to "visit" all regions of its nonzero probability density function). You might say that the underlying chaotic behavior of the particle is exempt from relativity to adjust for this, but you can imagine the can of worms that such an assumption would open.

Ultimately, even if some convoluted version of this was viable, it would still only be a worthy contender for a novel physical theory if it generated novel testable behavior, which would be impossible at any time scale that we can currently test at. (This is by construction—we postulate that the chaotic evolution rule matches all current quantum mechanical predictions by definition.)

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  • $\begingroup$ I don't quite see how this follows. Trajectories of particles in chaotic motion would be just as affected by length contraction and time dilation as any other trajectory, the Lyapunov time itself would be adjusted based on the relativity of observations. There's nothing special about chaotic motion, it is only that in a closed system it possess an inherent unpredictability. $\endgroup$
    – PhiEarl
    Dec 20, 2020 at 23:20

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