You are absolutely right that Cavediver or Son Goku would add a great deal to this. Son Goku in particular has given some really useful and reasonably understandable insights into this sort of topic previously.

However in the meantime I will see if I can answer some of your questions.

We have seen how chaos is defined in classical mechanics. Can chaos also be defined in quantum mechanics?

Well quantum chaos does exist but I must admit that I know nothing really about it at all. So far, not so good......

Is there a connection between the uncertainty principle of quantum mechanics and chaos and if there is, how are they related?

I am not sure that they are related in the way you might be suggesting (as in one is derived from the other). However chaos theory is indeed a classical theory that tells us tiny changes in initial conditions can have dramatic effects on the eventual result. The uncertainty principle tells us that there is a necessary limit on the knowledge that it is possible to have regarding any system. Thus there is a limit to the knowledge we can have of any initial conditions. So we have both a limit on what we can know and an exponential effect of these unknowables. This leads to an inherent and potentially large level of unpredictability of any given system.

Doesn't chaos arise in a classical, non-quantum world on macroscopic phenomena?

Yes. Chaos theory is a classical non-quantum theory. In essence it says that the effects of tiny fluctuations can have exponential effects on the eventual outcome of a system. Chaos theory in itself says nothing about the theoretical limits of knowledge regarding initial conditions. However in most complex classical systems the practical inability to know all of the initial condition info is more than enough to lead to a high degree of unpredictability in any practical sense.

Will the uncertainty principle hold in the future when we will likely have a much more sophisticated and accurate measurements of quantum events than the ones of today?

If current QM theories are correct and not an approximation to some as yet unknown theory then no. The uncertainty principle is not a technological limit. It is an inherent limit of nature.

Is there "true, uncaused" chaos in quantum mechanics(I don't really expect anyone to know that with great certainty)?

Well QM is inherently probabilistic. So causality does go out of the window to some degree. Something like a half life is not just a statistical approximation to caused events. It is inherently probabilistic'

What is causing the phenomenon that prevents us from knowing with accuracy both the position and the momentum of an electron?

How would you measure? By observation? But a photon required to do that measurement would itself change the position and/or momentum of that electron. That is my simplistic understanding anyway.

I am happy to be corrected and/or elaborated upon by anyone with more knowledge regarding any of the above.

To my mind the idea of the many worlds interpretation of QM and the role of (or absence of) freewill is a truly mind-blowing concept. This suggests that all possibilities exist and that whichever possibility we find ourselves living out is just one statistical pathway of many. Thus, as I understand it, there is no freewill as such. There is a "you" who has made every opposite decision and the "you" that you know as "you" is just a statistical path in time. As are the "yous" that are not.

*Edited by Straggler, : No reason given.*

*Edited by Straggler, : No reason given.*