I think this guy proved that even in classical mechanics, there is indeterminism:
http://arxiv.org/abs/1311.5349
It is a billiard experiment, he says that at one point, when there are too much balls, there is a loss of information, so it is not possible to predict the positions and speeds of all the balls at one time in the future. If I remember, the number of balls must be higher than 4000. He had to use powerful computers and ingenious algorithms to do that.
This has blown my mind, thank you so much frederic!
Reading the abstract it suddenly and immediately
seemed to make total sense to me how non-deterministic behaviour
must arrive from any deterministic system, given enough time/objects...but I now seriously doubt whether the way I was thinking about it had ever so much to do with what the paper is actually about.
The key quote for me is this, from the abstract: "...our fundamental hypothesis that physical information has a finite and limited density, responsible for the irreversibility..."
I'm almost certainly misunderstanding this completely, by reading "information density" in terms of "granularity" (completely different I
think), so what I took from this is probably a different argument entirely, but how I understood it is this: in this system of hundreds of balls pinging around on a billiard table, we do understand from chaos maths that the tiniest change in position of any one of them at the start - however small - will completely change the behaviour of the whole. But what is the granularity of the cartesian grid within which we are going to define the positions of these balls, when we translate them into our deterministic mathematical model? Are we defining those positions down as far as the planck length, as the smallest possible distance between grid lines, or are we going to go beyond the planck length in our precision? And how far down, in precision, would we have to go, to determine the positions of all the balls accurately enough to predict their future behaviour for ever?
This is not making as much sense in writing as it did in my head this afternoon, but putting it another way: The idea of a deterministic machine, from the beginning, has started from the thought experiment "if we knew the exact position of everything in the universe" but the problem with that premise is the concept of all the things actually having an 'exact' position that can be measured to
infinite precision - and that (for reasons I can't yet articulate) seems impossible. Our precision in measuring all the positions would seemingly have to go
beyond the planck length...way beyond...for ever...
That
may only be enough to explain why it is impossible in practice for
us to measure a sufficiently complex real-world system with sufficient precision to predict its behaviour over an infinite time period. But I think what I'm pointing at with introducing the planck length is that reality itself must have the same problem that we would have in trying to pin down the position of objects, and the distances between them, with infinite precision.
I'm still thinking all that through, but I think the matter may hinge on whether or not there is some grid system (which would be a bit like the 'ether' which relativity supposedly forbids) within which all the objects in the universe exist. If we're in a grid, if we're in a computer simulation, then
maybe everything would all be deterministic. But if the objects don't exist in an 'ether' - if the 'somethings' just exist within a 'nothing' - then there is an infinite granularity which can't be measured. My hunch is that while the
objects seem to have a minimum scale (the planck length) the 'nothing' around them surely doesn't. And no, I can't hold in my head the something and the nothing and the relationship between them, and it all still twists my head, but hopefully something I'm saying is pointing at the moon for someone...
Anyway, that's not what I meant to write about in this reply really; I just wanted to mention this:
http://www.sciencealert.com/physicists-just-figured-out-how-quantum-mechanics-pops-up-in-game-theory
...in which it is mentioned that mathematical models of a school of fish give rise to Schrodinger's equation, and also Couder's oil droplets, eg:
http://www.wired.com/2014/06/the-new-quantum-reality/
(I see there's
loads more great stuff about this now, since I was last looking, if you search for eg "quantum oil droplet").
I suspect I'm actually making no sense at all here (so don't take it personally!) but what I think
is simple and true connecting all of these angles on the problem is that the supposedly spooky and bizarre quantum behaviours and equations that supposedly apply only at the microscopic level, are now emerging all over the place both in experimental and purely mathematical systems!
What this says to me is that Einstein was right all along, and should have stuck to his guns (and trusted his instincts regarding de Broglie and Bohm's "pilot waves" rather than throwing them under the bus because their theory didn't seem to be compatible with relativity), whereas the Copenhagen interpretation was a disastrous historical error (that's what you get for resolving scientific questions by majority vote!). It now seems clear that it is, after all, quite possible for 'hidden variables', and some kind of description/model of the sub-subatomic world, to give rise to all the quantum phenomena we observe. We don't necessarily have to treat what's inside the quantum system as a 'black box'; we can now start to postulate and describe models of what's inside subatomic 'particles' that would produce all of the maths and the phenomena that we know from quantum mechanics.
The two examples of systems, suggested by the shoals of fish and the quantum droplet, that could explain where quantum mechanical phenomena come from would be, very roughly:
- what we call a subatomic 'particle' is actually a cloud of tinier 'fish' that are bound together
- what we call a subatomic 'particle' is actually a 'particle' coupled with the 'wave' it creates in the ether (or the 'nothing').
Either model can now potentially explain where quantum phenomena come from.
Until yesterday, I was purely focused on the second of these two options, and then I heard about the game theory mathematical model and the shoals of fish...and now, thanks to frederic, I learn of this argument about information density - again, Schrodinger's equation arising from a deterministic mathematical model - and my mind is going a little nuts about this right now (in case you can't tell that from the above!
).
Anyway, since I last read about the bouncing oil droplet a couple of years ago, and saw its devastatingly simple and compelling explanation of wave-particle duality (the 'particle' is a particle riding on a wave, and whereas the 'particle' goes only through one slit, the wave goes through both and creates the interference pattern on the other side, which the particle's trajectory is then affected by), the whole thing appears to have become quite fashionable. That being the case, I think we are now on the cusp of a monumental breakthrough in the understanding of all the weirdness of quantum physics...there's real hope, I think, that all of this is solvable and explainable, and that we'll see that explanation arrive in the next few years.
Since I've got this far without my head exploding, I'll just note that I don't think any of the argument about determinism actually impacts on the free will / consciousness problem at all, even though it appears obvious that it would. I see the question itself as a kind of error of circular reasoning (in a way that I
totally can't articulate), because the reason why we are asking the question is to worry about whether we really have moral responsibility and how this should affect our reasoning about ethics, but if we
don't have free will then all of our reasoning is out of our control too, meaning that whether we do, or whether we don't have free will, makes zero difference to anything we could ever possibly think about, and we can never know the answer to that anyway. I do really like this idea of meditation and 'degrees of freedom' though...there's something in that. The only place where absolute freedom exists would be a state of being and doing absolutely nothing. As soon as you make a choice you form patterns and constraints which come to control you.
Sheesh, what possessed me to write this almost certainly nonsensical post and make such a fool of myself, at this time of night?
I should have just posted the links above and gone back to lurking, so you could all blow my mind some more. I suppose I must have done it because I thought this thread hadn't gone off-topic enough.