vidmar said:
OK I might as well add some of my own thoughts.
First of all, when I say I like determinism, it does not mean that I don't find theories, which are based on probabilities and are said to be undeterministic, interesting and useful if not beautiful. I just mean that I would prefer a theory at least in principle to allow for only one evolution of an observed system (even if the underlying technical difficulties don't enable us to have closed formed solutions - as for example in the three body problem of Newton - there the movement is determined (except for singularities) even though we can't have closed formed solutions as in the two body case). QM on the other hand is inherently undterministic (as far as I know) in the sense that gievn a system, its future development is not determined.
I also don't think that scientific experiments (can) prove (even if only in the limited strict scientific sense) that the world is undeterministic. What they show is that on a certain level of precision of physical measurments we have theories, which equipt us with tools necessary for the calculations of certin probabilities, that agree with the observed data within the error of measurment. But that doesn't mean that the world need be inherently undeterministic, let alone that we cannot have a deterministic theory, which would describe it. This may easily be seen with the introduction of hidden variables (which in my view don't make the theory incomplete). The succesfullness of a theory in physics may be measured only by its ability to predict the results of measurments and not by a formalism one chooses to have for it. The latter is more a matter of taste (as long as it does not entail that the theory would become less predicitve or make it harder to produce results) as it is a consequence of the world around us.
The problem is that for explaining experimental data one needs formulations with deterministic forces more random forces. Determinism is a phylosophical attitude and i, of course, respect if you like it, but is scientifically unproven. In fact, none even conceivable experiment can prove determinism. Of course, is a phylosophical option.
In classical physics, systems are not deterministic: e.g. thermodynamics or chemical kinetics.
Yes, experiments can prove that the world is undeterministic by measuring random forces, which cannot be reduced to deterministic forces. From a phylosphical view, it is true that nondeterminism is not proved but scientifically it is. You have a random copmponent that cannot be explained in determinisitc terms, that is science. Now you can phylosophically claim that that random component is really caused by an underlying deterministic theory. Yes, phylosophically it is possible. But and scientifically?
If you want your hypotesis to be scientific you may prove that can be verified (falsable) in experiments.
You may formulate the deterministic final EXACT theory, then derivate random components from it and show that coindice with experiments. This is by definition
imposible because by definition the theory may be exact (which may be imposible), you may measure with infinite precision, which is imposible, the proposed state of
all universe (even beyond observable universe!), which is imposible, and may compute the EXACT result, which is imposible (except by the use of a perfect computer more larger than universe itself), then and only then if experiment coincides with theory you could prove that universe is determinist.
But we compute with imperfect computers, measure with finite precision, develop inexact theories, and cannot know the state of the entire universe. In fact, there is further limitations even for measuring positions and momentum of 10
24particles in an ideal gas. Therefore experiments prove that F
total = F
determ + F
random
And that is all science can say.
You cannot apeal to hidden variables because if are hidden. How do you scientifically show that variables are there?
It is like the hyphotesis of "pink elephants" that i said.
Personally, I see not problem with the phylosophical interpretation of a world which is non determinist. That mean free will, and love, and ethics, etc.