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Maxwell's equations and determinism 
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#1
Sep405, 06:36 AM

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Are Maxwell's equations deterministic in the sense that e.g. if given free space with H and E defined for any point at time t0, then Maxwell's equations are sufficient to determine H and E for any t>t0?



#2
Sep405, 09:45 AM

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#3
Sep405, 12:19 PM

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#4
Sep405, 03:52 PM

P: 1,781

Maxwell's equations and determinism
Yes, they are deterministic but they may not be sufficient as in the case of
a chaotic system. It's no different than the 3body celectial mechanics problem. And I beleive you do not need special relativity since ME are already Lorentz invariant. You may in fact need GR if you want to solve problems near massive bodies. 


#5
Sep505, 06:07 AM

P: 416

If E_{instant} = <E> + E_{fluctuation} Determinism works only for the average <E>. Molecular noise is not determinist. For example, fluctuations f in the electric field measured in a macroscopic solution of ions (near equilibrium) is indeterminist, only average behavior <f> = 0 <f f'>= delta(tt') can be predicted. 


#6
Sep505, 09:59 AM

P: 11

Thanks for the answers. I tend to like determinism :) I have another question, namely: gieven ab initio free space with E and H do Maxwell's allow for the formation of matter out of this form of energy (energy of the electromagnetic waves). Arguablly Einstein says E=mc^2, so they probably should. I know I'm probbaly asking questions in a way one with a more detailed knowledge of the theories would not but I'd be happy of any comments on them anyway.



#7
Sep505, 07:15 PM

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#8
Sep605, 05:29 AM

P: 416

Determinism does not work. 


#9
Sep605, 10:00 AM

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#10
Sep605, 10:49 AM

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The answer to your initial question is yes, but .... Don't forget that M's equations involve sources, which can have their own dynamics. Technically the combined sourcefield equations are, in classical circumstances, deterministic. All this means is that second order differential equations, partial included, are fully determined for all t by the system of equations together with initial conditions. (See most any text on E&M) Note that selfenergy issues, put some of the determinism in doubt  the selfenergy problem has never been satisfactorily solved.
One could, I suppose, add a source in which the number of particles is a function of, say E*E + B*B. But now the set of equations is horribly nonlinear, and all bets are off. Purely free fields are trivially deterministic, as are particles with no forces involved.. Regards, Reilly Atkinson 


#11
Sep605, 12:42 PM

P: 1,295

Even besides the existence of the purely deterministic Bohmian interpretation of quantum mechanics, you should remember that no one suspects that the ill understood field of quantum mechanics is a description of true reality. 


#12
Sep605, 01:14 PM

P: 416

moreover Bohm formulation is incomplete and non scientific, since claim unobserved things. 


#13
Sep605, 01:16 PM

P: 416

Determinism is a phylosophical option cannot be shown from physics. But undeterminism can be proved. E.g. QM. 


#14
Sep705, 02:11 AM

P: 1,295

How is Bohmian mechanics incomplete? Bohmian mechanics, like any theory, postulates the existence of theoretical entities (things that cannot be observed, but can be infered to explain observations). 


#15
Sep705, 02:17 AM

P: 1,295

How is Bohmian mechanics incomplete? Bohmian mechanics, like any theory, postulates the existence of theoretical entities (things that cannot be observed, but can be infered to explain observations). 


#16
Sep805, 07:11 AM

P: 416

It is not true that Quantum mechanics can be rewritten in a deterministic form. In fact, nobody has newer developed any deterministic consistent formulation of quantum mechanics. The problem of some people is that does not understand probability and think that probabilities of QM are some kind of measure of ignorance of some fundamental underlying formulation, which is, by ad hoc definition in those theories, unobservable. As said, determinism is a philosophical option with no solid link with pure physics because is not a testable scientific hypothesis. Moreover, there are further difficulties with idea of determinism regarding human matters (free well, ethic, etc.) Einstein theory is deterministic just like approximation, when stochastic (random) components vanish. That determinism does not work is not a philosophical issue, it is a fact of science. The problem of physics is that begin focusing in simple systems where determinism work at first approximation. There is no a culture of determinism on chemistry for example. ***************************** 


#17
Sep805, 10:03 AM

P: 11

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. 


#18
Sep805, 03:22 PM

P: 1,295

This is the twentieth century dichotomy in physics: Physicist want their scientific models to help them "really know" what's happening, but they have all bought the party line which says "all that matters in physics are observables".
I dare you to look at the following picture of a theoretical model that could NEVER be observed, even in principle, but can only ever be infered INDIRECTLY from routine observations. This model is accepted as a practical fact today: http://eos.uom.gr/~hatzifot/orbitstrans.gif 


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