I've been following your answers. This is a fascinating subject.
Indeed - how does one even begin to study something that does not rely on cause and effect or something similar? It's the quantum physics of philosophy (and some rather over-zealous types have postulated that the analogy is no coincidence).
Roger Penrose proposed a whole 'thesis' on conscious freewill and it's possible relation to QM. As I understand it this has been largely refuted. Do you know of any more recent QM based theories or speculations regarding conscious freewill? Is this area considered as much of a dead end by most as you seem to imply?
But still, what does it even mean for a decision to be made in a non-deterministic way? Doesn't imply that some or even all decisions are made at least partly for no rhyme or reason? Isn't this almost random decision making just as terrible as its absence?
What can we learn of freewill from experimentation on brains and human subjects. The link below relates to experiments that seem to show the brain having "decided" simple choices before the subject was consciously aware of the choice that they had apparently made freely. Scientists could seemingly predict whether a test subject would press a left or right button based on brain activity before the subject themself "knew" or had "decided".
Also I understand that split brain patients can be shown to make "decisions" that they consider to be of their own free violition by providing stimuli to one half of the brain but not the other. Have you heard of these cases and what implications, in your opinion, do these cases have for the subject of conscious freewill?
Any quantum system is inherently probabalistic so no matter what information is known we can only ever make statistical predictions.
Radioactive decay for example. There is no amount of information that will tell us which atoms will decay. Only how many.
So quantum systems are not really deterministic.
The uncertainty principle, that we can never know both the exact position and momentum of a particle, would lead to a limit on the accuracy and the completeness of the initial conditions that we can ever have access to.
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.
Cheers for the typically informative and well pitched reply.
Quantum chaos would be where changes in the initial conditions of a quantum system result in a large change in the final conditions of that system. However the weird thing is that, a side from certain well known and now heavily studied systems, this does not happen. Quantum mechanics does not "like" chaos at all and it is very difficult to make any purely QM system exhibit chaotic effects.
Why is this? Is it just the fact that small changes in initial conditions have a relatively small effect on things that are probabalistic anyway? E.g. A tiny change in a a particles possible initial position has little effect on the possible position that the particle has at some time later. The effects of small changes are effectively absorbed by the 'smudginess' of the system. Is that correct?