Quote:t ultimately quantum mechanics does not incorporate determinism.[/quote]Quote:So it is not determinate insofar as you cannot determine what variable A is now, nor can you know what it will be. Indeed, because of these fuzzy positions, momenta, energy, etc, the particle's future position (such that it is) is random: its associated wavefunction assigns it future possible positions, but nothing determines where it will be.
(January 9, 2009 at 1:00 pm)josef rosenkranz Wrote: In other words the uncertainity principle is an expression of a dual form a physical laws including determinism as well as indeterminism.I disagree. At a stretch, you could say that quantum indeterminism approximates to classical determinism (as per the Bohr correspondence principle), buquote]So it is not determinate insofar as you cannot determine what variable A is now, nor can you know what it will be. Indeed, because of these fuzzy positions, momenta, energy, etc, the particle's future position (such that it is) is random: its associated wavefunction assigns it future possible positions, but nothing determines where it will be.
Here is a quotation from Stephen Hawking's book A brief history of time, chapter The uncertainity principle:
" In general quantum mechanics does not predict a single definite result
for an observation.Instead it predicts a number of different possible outcomes and tells us how likely each of these is".( unquote)
So quantum mechanics does predict outcomes but they are fuzzy as you put it.
May I ask on what base is this prediction done if not on physical laws which are per se an expression of determinism.The fuzzyness or the randomness of the outcomes is the second part of this equation expressed statistically or as Hawking puts it "how likely each of these is".
One can express that duality of determinism and indeterminism in many philosophical forms but one can not deny their simultaneous coexistence in the most basical laws of nature.
Here is another quotation from the same book ,the same chapter:
"We could still imagine that there is a set of laws that determines events completely for some supranatural being,who could observe the present state of the universe without disturbing it.However such models of the universe are not of much interest to us ordinary mortals.It seems better to employ the principle of economy known as Occam's razor and cut out all the features of the theory that cannot be observed.(unquote)
In his concise scientifical but also popular style Hawking cuts the limits of determinism and throughs the remainig features away to randomness.
That's,in other words, just the characteristics of statistical laws.
Let's take for instance a law which says :A+B =C, but where C has not a definite value but a statistical one of let's say 60%.
Now if we will repeat the experiment A+B for a 100 times we will get only in 60 cases the result C in at least 2 conditions:
- before each experiment we will not know if the result is exact C for the reason as put by Hawking ( in generally, not in the particular case of quantum mechanics)
-after achieving the value C in 60 experiments before the number of 100 the next results will be highly random.
Here we see the same dualty :the value C is predictable (say determined) for a certain number of experiments but is in the same time random for all the others.
I have used in this thread the case of the uncertainity principle only as a classical example for it's well known position in the debate over indeterminism without any pretention of competing with members who are skilled in the prolems of modern physics.