16 Feb 10
Originally posted by FabianFnasTo add to my previous comments:
It's impossible to predict the future more than statistically. We have a free will. These two statements hold hands.
Not only can we only predict the future via statistics, but the same applies to the past.
Much more interestingly, the same applies to the present. That is what quantum mechanics is all about.
If a photon of light could be in two places at once, then it is. It even affects the statistics of both the past and the future. It can even interfere with itself.
Free will is another mater altogether.
16 Feb 10
Originally posted by twhiteheadFree will is indeed an elusive matter.
To add to my previous comments:
Not only can we only predict the future via statistics, but the same applies to the past.
Much more interestingly, the same applies to the present. That is what quantum mechanics is all about.
If a photon of light could be in two places at once, then it is. It even affects the statistics of both the past and the future. It can even interfere with itself.
Free will is another mater altogether.
(Did I write that?)
16 Feb 10
Originally posted by KazetNagorraCan we? Even if it was possible to know all the positions of all particle in the system, we wouldn't know the velocities of them. So there will always be an uncertainty. In macrosystems, a collection of particle tends to cancel eachothers uncertainty, but in the level of particles we cannot. And thoughts originates in particles, i.e. electrical currents in our nervous system, so we cannot really predict our human actions.
Actually, in a closed system, you can deterministically calculate the future even if only in theory. The question remains: is the universe as a whole a closed system? And if it is, is it possible to write down a closed expression for the Hamiltonian (even if only in theory)?
Newtonally, yes, but quantumally, no.
16 Feb 10
Originally posted by KazetNagorraEven without God rolling the quantum dice doesnt Chaos theory tell us that we will can never measure initial conditions accurately enough to predict the future?
Actually, in a closed system, you can deterministically calculate the future even if only in theory. The question remains: is the universe as a whole a closed system? And if it is, is it possible to write down a closed expression for the Hamiltonian (even if only in theory)?
16 Feb 10
Originally posted by KazetNagorraI would be interested to know why a closed system would be deterministic. I could understand that the wavefunction itself may evolve in a deterministic fashion, but according to my understanding, we could not measure this without disturbing the system.
Actually, in a closed system, you can deterministically calculate the future even if only in theory. The question remains: is the universe as a whole a closed system? And if it is, is it possible to write down a closed expression for the Hamiltonian (even if only in theory)?
17 Feb 10
Originally posted by amolv06Sure, you disturb the system, but you can still get information. For instance, if you have a paddle wheel with a small generator that has a linear voltage out for linear change in paddle wheel RPM's, you can measure the velocity of flow of a stream, but if it is the same size as the stream, you would really disturb the reading. If it was the size of a bee, in the same stream, the reading would be more accurate because it would not be sucking much energy out of the flowing water.
I would be interested to know why a closed system would be deterministic. I could understand that the wavefunction itself may evolve in a deterministic fashion, but according to my understanding, we could not measure this without disturbing the system.
A bit simplistic but that is my take on it.
17 Feb 10
Originally posted by sonhouseBut the information you can get is not sufficiently accurate to predict the future. That is what Chaos theory is all about ie a small change in initial conditions may result in a large change later on meaning that if you don't know where every molecule of air is now, you cannot predict the weather in one week.
Sure, you disturb the system, but you can still get information.
17 Feb 10
Originally posted by FabianFnasThe quantum description of a closed system contains neither positions nor velocities of particles. It just contains the wavefunction of the system.
Can we? Even if it was possible to know all the positions of all particle in the system, we wouldn't know the velocities of them. So there will always be an uncertainty. In macrosystems, a collection of particle tends to cancel eachothers uncertainty, but in the level of particles we cannot. And thoughts originates in particles, i.e. electrical currents i ...[text shortened]... system, so we cannot really predict our human actions.
Newtonally, yes, but quantumally, no.
17 Feb 10
Originally posted by amolv06Well, if you "disturb" a system it's obviously not closed anymore. You would need a quantum description of the measuring apparatus/method as well, which would not be able to interact with anything else, and then you get a deterministic evolution of the system, at least in theory.
I would be interested to know why a closed system would be deterministic. I could understand that the wavefunction itself may evolve in a deterministic fashion, but according to my understanding, we could not measure this without disturbing the system.
I'm not sure how nuclear/particle decay fits into the picture, though.
17 Feb 10
Originally posted by wolfgang59Yes, but since chaos theory involves deterministic problems, that's just a practical reason why it's not possible to determine the future deterministically, not a theoretical one.
Even without God rolling the quantum dice doesnt Chaos theory tell us that we will can never measure initial conditions accurately enough to predict the future?
17 Feb 10
Originally posted by KazetNagorraA more important question is whether or not the universe is deterministic at all. For example, if certain events are essentially random does that mean there is some unknown input from 'outside' the system?
Actually, in a closed system, you can deterministically calculate the future even if only in theory. The question remains: is the universe as a whole a closed system? And if it is, is it possible to write down a closed expression for the Hamiltonian (even if only in theory)?
17 Feb 10
Originally posted by KazetNagorraThat is a theoretical barrier though, isn't it? Chaos theory tells us that small uncertainties in the initial conditions of many simple systems lead to large uncertainties in future states, and quantum mechanics tells us that the exact position and momentum of a particle cannot be known simultaneously. Taken together, it would be impossible (both practically and theoretically) to accurately predict the future state of any chaotic system involving both the positions and momenta of particles.
Yes, but since chaos theory involves deterministic problems, that's just a practical reason why it's not possible to determine the future deterministically, not a theoretical one.
18 Feb 10
Originally posted by PBE6Actually, my understanding of Quantum Mechanics so far, is that particles do not have an exact position and momentum. They have every possible position and momentum in a sort of probability cloud. If this is so, then the universe is not fully deterministic.
... and quantum mechanics tells us that the exact position and momentum of a particle cannot be known simultaneously.
20 Feb 10
Originally posted by twhiteheadYou shouldn't look at a particle as having a position and momentum with a certain uncertainty. Rather, the position and momentum of particles are not well-defined as in a classical sense (I hope the distinction is clear).
Actually, my understanding of Quantum Mechanics so far, is that particles do not have an exact position and momentum. They have every possible position and momentum in a sort of probability cloud. If this is so, then the universe is not fully deterministic.