echidna

No starboy, prior to the development of CT and QM, classical determinism claimed prediction over even very simple systems. Expanding these systems then became purely a practical issue of scale and accuracy.

However CT (is it even necessary to call this a theory anymore ?) subsequently explains that even simple systems can be exponentially sensitive to initial conditions, but again it only comes down to a question of scale (albeit exponentially massive) to become theoretically deterministic.

But then the QM element removes determinism even as a theoretical possibility.

Thanks ohwilleke. In lieu of any further protests I’ll take this as widely accepted. It seems bleeding obvious, but I suddenly wondered how solidly the reasoning was based …

As fando says, I’m also a little uncertain how confidently I can state this position & whether there is hard mathematics to support it. Even text books and journals seem to relegate it to only anecdotal mention.

I remain dissatisfied.

Starboy

echidna, think what you want, but the n-body problem remains unsolved to this day and is as theoretically intractable as turbulent flow. The best solutions are approximations. Classical physics claimed determinism only in principle. I don’t think there was a classical physicist on the face of the earth that thought it could be done in practice.

As to whether QM removed determinism, it depends on what you mean by determinism. In a completely described QM system one can shown that certain outcomes will have zero probability. What kind of determinism is that? It doesn't predict with certainty what will happen but it does predict with certainty what will not happen.

Starboy

[ August 26, 2002: Message edited by: Starboy ]</p>

Mark_Chid

"It's unsolved" isn't really the true picture. It has been solved, as long as you accept "We have shown that this is a system so dependent on initial conditions that its behaviour cannot be predicted because in any attempt to measure the starting conditions the margin of error in our measurements is enough to totally change that behaviour extremely rapdidly" as a solution.

i.e. "It's Chaotic" is useful information and therefore a kind of solution.

Starboy

Mark_Chid, Are you saying that the n-body problem has been solved in exact form?

Starboy

[ August 26, 2002: Message edited by: Starboy ]</p>

Mark_Chid

No - I'm saying its been shown to be insoluble in reality which in a very real sense IS a solution - i.e. Its time to stop trying!

Starboy

Mark_Chid,

Stop trying what? My point was that classical determinism is possible only in principle but not in practice. As stated before in this thread, I say this for two reasons,

1. Initial conditions cannot be determined to sufficient accuracy.
2. There are no exact general solutions to the n-body problem.

As such classical determinism was and is a red herring. I also wanted to raise the question of determinacy in general, in particular as it applies to QM. What kind of determinacy is it when a theory doesn't predict exactly what will happen but does predict exactly what will not happen? Any ideas?

Starboy

[ August 26, 2002: Message edited by: Starboy ]</p>

Mark_Chid

I didn't mean YOU should 'stop trying', I meant that it is in general pointless to attempt to solve the problem since in practice any exact solution cannot be applied to make predictions. the statistical predictions of Chaos theory are the best we can do and hence ARE the solution.

I agree with your main point except that classical determinism only APPEARS to work in theory. The flaw in it is the assumption that exact measurement is possible or that minor errors in measurements are negligable. This isn't true, so the whole thing is a house of cards. A theory that doesn't model reality isn't much use!

echidna

Starboy, let me start again. It’s been a while since I studied & my grounding is somewhat fragmented.

My loose understanding of the n-body problem is that a system of n-bodies behaves in an unusual and complex fashion which increases its complexity exponentially, making prediction practically impossible.

Yes, the complexity increases exponentially such that it quickly becomes practically impossible to attain, but there is no theoretical limit to this complexity & complexity remains finite as long as time remains finite. But to my understanding classical physics does not assert a limit to the actual existence of such complexity, it does not demonstrate that there is an exact point when causality becomes unknowable. To my understanding, classical physics only shows that it becomes more complex, but not impossibly complex in a theoretical sense (I'm not discussing the practicality of ever being able to measure to such accuracies of course).

The difference which QM introduces is that there is indeed such a point at which deterministic causality breaks down.

Starboy

Echidna, the n-body problem becomes intractable as early as going from 2 to 3 bodies. The problem lies in the mathematical apparatus of classical mechanics. For all but the simplest systems, the equations of motion cannot be solved exactly. If they are solved at all it is done by applying special cases, simplifications and approximations.

Chaotic behavior is a different mathematical phenomenon. It occurs when the solution to an equation changes wildly with very small changes in initial values. It is seen quite often in n-body systems, but IIRC it can occur in very simple systems.

Quantum behavior is not the result of chaotic equations. It is due to a completely different formulation of motion. It has nothing to do with the complexity of a physical system. In many physical systems, if you can write the classical Hamiltonian it can be converted directly into the quantum description. It is the result of this conversion and its physical interpretation from which quantum phenomena is predicted.

It appears that your physical conceptual framework is not anchored in modern physics. You would be well served by remedial study.

Starboy