Maxwell's equations and determinism

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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?
 

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  • #2
Andrew Mason
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vidmar said:
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?
Maxwell's equations alone are not sufficient to determine H and E for any observer at any time. You would have to apply special and general relativity.

AM
 
  • #3
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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?
In free space, Maxwell's Equations reduce to a wave equation for E and a wave equation for H. The solutions are guranteed to be unique, and exist for all time. The equations are even linear, so will not display chaotic behavior (so that prediction is not just theoretically possible, but somewhere in the ballpark of actually possible). But if we include free charges the system becomes extremely nonlinear.
 
  • #4
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Yes, they are deterministic- but they may not be sufficient as in the case of
a chaotic system. It's no different than the 3-body 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
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vidmar said:
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?
Yes, Maxwell equations are deterministic, but determinism is only valid for the average of the physical ensemble.

If Einstant = <E> + Efluctuation

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(t-t')

can be predicted.
 
  • #6
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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
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do Maxwell's allow for the formation of matter out of this form of energy
As far as I know, the only theories in which particles can be created from energy are relativistic Quantum Field theories.
 
  • #8
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vidmar said:
Thanks for the answers. I tend to like determinism :)
Then you like an unphysical issue :-)

Determinism does not work.

vidmar said:
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.
Maxwell equations, like the rest of classical physics, are for constant number of particles,.
 
  • #9
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Juan R. said:
Then you like an unphysical issue :-)

Determinism does not work.
Why wouldn't determinism work. As far as I know Newton as well as Einstein are both deterministic. The only physical theory which is not is Quantum theory and I read (heard, I'm no longer sure) somewhere that even this one can be put on a deterministic footing just that then it doesn't sound that natural or something along does lines.
 
  • #10
reilly
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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 source-field 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 self-energy issues, put some of the determinism in doubt -- the self-energy 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 non-linear, and all bets are off.

Purely free fields are trivially deterministic, as are particles with no forces involved..

Regards,
Reilly Atkinson
 
  • #11
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Then you like an unphysical issue :-)

Determinism does not work.
If you think that Determinism is invalidated by Quantum Mechanics, then you should read about Bohmian Mechanics.

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
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Crosson said:
If you think that Determinism is invalidated by Quantum Mechanics, then you should read about Bohmian Mechanics.

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.
The failure of determinism goes beyond QM.

moreover Bohm formulation is incomplete and non scientific, since claim unobserved things.
 
  • #13
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vidmar said:
Why wouldn't determinism work. As far as I know Newton as well as Einstein are both deterministic. The only physical theory which is not is Quantum theory and I read (heard, I'm no longer sure) somewhere that even this one can be put on a deterministic footing just that then it doesn't sound that natural or something along does lines.
The most simple reply "because world is not determinism."

Determinism is a phylosophical option cannot be shown from physics. But undeterminism can be proved. E.g. QM.
 
  • #14
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moreover Bohm formulation is incomplete and non scientific, since claim unobserved things.
No one ever observed a keplarian orbit either (they can't be directly observed from the earth), and this doesn't stop Kepler's theory of orbits from being a scientific theory.

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
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moreover Bohm formulation is incomplete and non scientific, since claim unobserved things.
No one ever observed a keplarian orbit either (they can't be directly observed from the earth), and this doesn't stop Kepler's theory of orbits from being a scientific theory.

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).

But undeterminism can be proved. E.g. QM.
The predictive power of QM doesn't prove that the world is indeterminate. Determinism says that given the current universe state, there is one and only one future universe-state. Knowing the initial wave function does not allow us calculate one and only one definite universe state, but perhaps the wave function is not a complete description of the state i.e. Hidden Variable theories.
 
  • #16
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vidmar said:
Why wouldn't determinism work. As far as I know Newton as well as Einstein are both deterministic. The only physical theory which is not is Quantum theory and I read (heard, I'm no longer sure) somewhere that even this one can be put on a deterministic footing just that then it doesn't sound that natural or something along does lines.
Determinism only works in simple systems. Like Einstein theory applied to one idealized body system, Newtonian mechanics applied to celestial bodies, etc. When Newton mechanics is applied to condensed matter does not work fine and is generalized by Langevin type equations. Almost all of statistical mechanics is not determinist, thermodynamics is not, chemical kinetics, of course is not, etc. At higher levels, biochemistry, ecology, medicine, sociology, dynamics of human populations, etc. determinism fails completely.

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.

*****************************

Crosson said:
No one ever observed a keplarian orbit either (they can't be directly observed from the earth), and this doesn't stop Kepler's theory of orbits from being a scientific theory.

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).
Kepler orbits are observed (Kepler theory does not say that orbits are unobservable items) and the theory tested by direct measure of position of planets which follows from Newton gravitation. I already said why Bohm mechanics is incomplete. Any theory to be taken seriously may be based in observed things. Bohm postulates the existence of things cannot be measured, even in principle.

Crosson said:
The predictive power of QM doesn't prove that the world is indeterminate. Determinism says that given the current universe state, there is one and only one future universe-state. Knowing the initial wave function does not allow us calculate one and only one definite universe state, but perhaps the wave function is not a complete description of the state i.e. Hidden Variable theories.
No QM alone, but scientific experiments prove (in a strict scientific sense) that world is not determinist. Do you know some single experimental proof of that world is determinist? Of course, the wave function is not a complete description of the state. That is already known. Wave functions work only for pure quantum states, it does not work for quantum mixtures. Another aspect ignored by Bohm...
 
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  • #17
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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
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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/orbits-trans.gif

Do you know some single experimental proof of that world is determinist?
Why don't you take a look at the rest of the universe? For thousands of years western astronomers held the doctrine that the heavens were immutable, unchanging. The combined astronomical observations of all the humans who ever lived before the 15th century, considering that Astronomy was as important a skill in those days as driving a car is today, tend to support determinism.
 
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  • #20
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I'm lost. The motion of the planets is indeed observable, in principle and in reality, and has been for a great deal of time.
Think harder. The picture I showed you is a cartoon. This is important because you will not find a photograph of the solar system from that perspective. The cartoon is a theoretical model, it is impossible (in principle, considering optics) to actually observe the exact scene that that cartoon depicts. Yet the predictions of the model are correct, and we accept the existence of orbits as a fact even though no has ever observed them as depicted in that cartoon.

The point is that we can infer the existence of things that we don't see, if it makes our world view more conceptually pleasant.
 
  • #21
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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 1024particles in an ideal gas. Therefore experiments prove that Ftotal = Fdeterm + Frandom

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.
 
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  • #22
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Crosson said:
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/orbits-trans.gif
I think that you are a bit confounded.

http://uts.cc.utexas.edu/~setreal/Pics/ny/empire%20state%20building.jpg [Broken]

You are claiming basically that Empire tate does not exist because i cannot see it entire. I am sited at north i only can see a side, if i am at west i can see another side but like i cannot see all togheter it cannot exist. Moreover like i cannot see a guy sited in the floor 25 from the street but i can the guy if i am inside the Emipre, in the 25 (and then cannot see the Empire), them both Empire state and the guy both do not exist.

:bugeye:

I cannot see the entire solar system once (in principle I believe that one could) but i can see parts of them at each time and then reconstruct the entire system in a graphical from. Like i can obtain a collection of photos of the Empire and reconstruct it with a graphical package.

Crosson said:
Why don't you take a look at the rest of the universe? For thousands of years western astronomers held the doctrine that the heavens were immutable, unchanging. The combined astronomical observations of all the humans who ever lived before the 15th century, considering that Astronomy was as important a skill in those days as driving a car is today, tend to support determinism.
For classical mechanics

a = Fdeterm + Frandom

Random components is related to Temperature and strengh "gamma" of interactions, inverse of mass, etc.

In Astronomy, "gamma" --> 0, and T --> 0, and (1/m) --> 0... and

a --> Fdeterm

But is only an approximation. For example, T is not zero in space, but is so small that effects are not measured in usual astronomical experiments.

The problem of physics is that began with Astronomy and the myth of determinism arised because in astronomy things appears to be deterministic. Chemistry began with condensed matter and newer claimed that world was deterministic. Chemistry always was based in uncertainlty, therein that was did arise like science 100 years after than physics.
 
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  • #23
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QM doesn't disprove determinism at least for inanimate objects.
It only proves it is incapable of determining specific causes and making non-statistical predictions for itself.

Bohmian Mechanics is of course an excellent formal interpretation of QM theory. Science is after all based upon causality, not witchcraft, and Bohm succeeded in offering a logically rational interpretation of QM effects, carrying out Einstein's hope. The latest installment, the Transactional Interpretation of QM, is also an extension of Einstein's deterministic and logical program, only this time picking up from Feynman's projected agenda.

Thus:

Einstein --> Bohm --> Feynman --> Cramer --> Mead.

Offering the best and most scientifically cogent interpretation of QM yet conceived. Mead carried off Feynman's hope of formulating QED without using Maxwell's Equations at all! (and he succeeded where Feynman failed)
The final result is Collective Electrodynamics, a short but awesome feat.
 
  • #24
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Nam_Sapper said:
QM doesn't disprove determinism at least for inanimate objects.
It only proves it is incapable of determining specific causes and making non-statistical predictions for itself.
False, QM stablishs that classical determinism does not work. In fact, any attempt to introduce determinism on QM is based in hidden variables, doing clear that if pure determinism exists, it cannot be observed, and if cannot be observed then it cannot be proved, doing determinisitc interpretations a field of phylosophy or methaphysics.

In a more thecnical side, still nobody has shown like probabilities of QM arises from an underliyng -phylosophical- deterministic evolution.

Nam_Sapper said:
Bohmian Mechanics is of course an excellent formal interpretation of QM theory.
False, this is the reason that is not followed by physicists, except by some guys with a distorted view of reality. Even Bohm claimed that quantum potential is "strange".

The best example of that Bohm mechanics is not complete or consistent is that there is dozens of different versions of it. E.g. Hilley version of Bohm (Broglie/Bohm) emphasizes that quantum potential is the key, whereas the Dürr School (named Bohmian mechanics) regards the guidance condition as the fundamental equation and avoids the quantum potential.

Nam_Sapper said:
Science is after all based upon causality, not witchcraft, and Bohm succeeded in offering a logically rational interpretation of QM effects, carrying out Einstein's hope.
False, chemistry (e.g. chemical kinetics) is not deterministic being causal. Statistical mechanics is causal being no determinisitc, Langevin equations are causal being no deterministic, etc.

You are confounding causality with determinism.

Bohm offered a posibility which was studied but is rather discredited today. There is not logical rationality on Bohm theory. In fact, is more "weird" that usual QM claiming for misterious effects that are hidden and cannot be observed (even in principle). The idea that Bohm theory is carrying out Einstein's hope is complete nonsense. Einstein claimed for a complete determinism based in observable reality. Einsten waited reduce QM to classical physics. Einstein said about Bohm mechanics

it was unnecessary superstructure
Bohm claim for a unobserved reality: a new mechanics that is not classical mechanics, is based in hidden variables (therefore is not physical) and obtain less results that from standard approaches.
 
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  • #25
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In fact, is more "weird" that usual QM claiming for misterious effects that are hidden and cannot be observed (even in principle).
How ironic it is that standard QM makes use of "hidden variables" .When is the last time anyone measured a wave function? Wave functions are inobservable in principle and so it is they which are the true hidden variables.

Bohm's theory is much more concrete then standard QM, since it speaks of particles as having trajectories.
 

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