My understanding is that quantum mechanics can predict only the probabilities of various outcomes of an experiment; the actual outcome is a random choice amongst the potential outcomes when the state of the system is observed.
There is also the phenomenon of chaotic behavior in which a system can behave in a deterministic but inherently unpredictable way due to extreme sensitivity to initial conditions.
Is there any possibility that chaos could be the underlying reason for the indeterminacy of quantum effects, or has this been ruled out via theory or experiment?
The inedterminancy of quantum mechanics comes from the uncertainty principle which is a fundamental property of waves. Essentially, the shorter the wave, the more defined it is in location and the less defined it is in frequency. The longer the wave, the more defined it is in frequency the less defined it is in location. Remember that the wavelength is equal to plancks constant devided by momentum. So the more you know about its velocity, the less you know about where it is.
A simple analogy is made with sound. If you play a note for a long time you know exactly what note is being played, but it exists throught the entire time you are playing so it’s time is undefined. On the other hand, a drum beat is defined very well in time, but has no well defined frequency.
Chaos may have a use in quantum mechanics, but the indeterminacy is not chaotic.
If I may interpret the OP here? Certain phenomena in quantum mechanics are unpredictable. Chaotic systems are very difficult to predict, because they require extremely precise measurements for any given amount of time, and as the time increases, the precision required increases very rapidly-- In the famous example, predicting the weather a couple of weeks in advance would require precise enough measurements that you’d need to know about every butterfly flapping its wings.
The OP seems to be asking whether the unpredictable things in quantum mechanics might be of the same nature: That our inability to predict them stems solely from our lack of ability to make sufficiently precise measurements. The answer to that is no: That would be an example of what’s called “local hidden variables”, and Bell found a set of mathematical relationships that any such theory must obey, no matter how complicated the hidden variables are. The thing is, quantum mechanics, both as predicted by theory and confirmed by experiment, does not follow those mathematical relationships.
You can still salvage hidden variable theories, if you allow the variables to be non-local: That is to say, the particles which have these hidden variables can communicate instantaneously across any distance. But in this case, you want the variables to be truly, inherently impossible to measure, not just very difficult, or you run into a mess of other quandaries.
More precisely, quantum effects can act as a seed for chaos. So, for instance, there’s some threshhold beyond which it’s absolutely completely impossible to predict the weather, since even if it’s hypothetically theoretically possible to watch the wingflaps of all the butterflies, it’s not possible to measure all the subatomic particles to enough precision.
But you still need an inherently chaotic system for this to matter, and whether the system is inherently chaotic doesn’t depend on quantum mechanics.
I would say no, there are two very different things in the two cases…
Quantum uncertainty is an intrinsic property of the universe. Its not a failing in our ability to measure something or our our ability to solve equations, irregardless of how good our measurments or our maths skills get we will NEVER be able to accurately measure both the position and velocity of an electron.
“Chaos” on the other hand IS just a math problem. We cannot, with our current understanding of math predict the behaviour of a complex system far into the future, this is not some fundamental barrier as our maths get better we are able to predict further into the future (of course the exponential nature of these problems means our maths has to get MUCH better to predict a little further into the future).
Prediction of a chaotic system is an issue of measurement, not math. We can predict a system’s behavior as far ahead as you want, as long as we have sufficiently precise measurements of the initial conditions and we don’t lose precision due to computer arithmetic. Our limitations come from the fact that we can’t do either of those things, not from our lack of mathematical understanding.