Are Maxwell's Equations satisfying?

[jslam]

Excuse me if this is a stupid question.
I'm now studying Electricity and Magnetism, and I'm coming toward the end of the course. The thought has been crossing my mind recently of what a shame it is that Maxwell's Equations turned out not to be correct, seeing as they are so beautiful and elegant. But thinking about it now, it occurred to me that the classical model is, really, very unsatisfying. Gauss' law - that is, the interaction of charges - I think, one can swallow pretty easily. But all the magnetism stuff, and especially all the induction stuff, is really very counter-intuitive, and to me seemingly too convoluted to be correct. Why should charge moving relative to another charge experience a force perpendicular to it in a certain direction? Why should one changing field produce another field? Somehow, the model seems to me very un-nature-y.
Now, I know that modern physics are purported to be maximally counter-intuitve, but I feel (without really knowing too much about the subject) that they at least have a deep inner-consistency and simplicity at some level which is lacking in all this right-hand-rule stuff.
My question is, then, what do you (general public) think about this matter? Am I wrong?

 

[fluidistic]

I just finished my intro to EM course so I might be wrong and I think I enter the "general public" you are seeking with your questions.
Indeed, Maxwell equations aren't easy to grasp within a very short time. I don't think you can call something unsatisfying because it's not intuitive for you. As far as now these 4 equations are thought to be true and have been "tested"/used thousands of times and they are in agreement with the experiments.
However one of these equations might change the day that magnetic monopoles would be confirmed. But I don't think it's a big deal. (I personally don't see any beauty in a possible symmetry of Maxwell's equations, but it may be because I'm not yet a physicist.)

About the right hand rule that seems to be counter intuitive to you : Do you remember in classical mechanics the angular velocity? The torque? The angular momentum? Some experiments in CM were counter intuitive for many people, but the right hand rule was there to save them!

 

[Phrak]

I have similar questions too.

--Why do the E and B fields act on their first derivatives (charge) through the Lorentz force (Classical).

Or alternately why do the potentials act upon their second derivatives (P.A.M. Dirac)?

--Why are the second derivatives of potential always associated with mass (why must charge have mass?) while first derivates (photons) must have strictly zero mass?

 

[Born2bwire]

Maxwell's equations, on the whole, are still probably one of the greatest achievements in physics. For over 130 years, we have had what is essentially a complete picture of electromagnetics that satisfies the classical and special relativity regimes. It was only with the maturity of quantum electrodynamics that we have found a better theory and a way to extend our understanding to the quantum world. Still, the precipitation of relativity out of Maxwell's equations and their experimental results have also been groundbreaking.

As for the relation between fields and moving charges, some of this can be explained by special relativity. By using Lorentz transformations, we can see how the electric field from a static charge changes into a magnetic field due to its movement. In essence, we come to find that electric and magnetic fields are very intimately connected. Not only that but except in the static case, they always exist together. It isn't that a changing field truly produces the other, it is that they always exist together. Jefimenko's equations help demonstrate the duality that the two fields exist together, http://en.wikipedia.org/wiki/Jefimenko's_equations . In a way, this becomes less surpising in light of the treatment of electrodynamics in quantum electrodynamics. In quantum electrodynamics, the primitives are the scalar and vector potentials, not the electric and magnetic fields themselves. In this way, our manipulation of the potentials involves manipulation of both the electric and magnetic field observables since they both share a dependence upon the vector potential.

Now the Lorentz transformations, Jefimenko's equations and stuff like this are all based upon Maxwell's equations still. Sometimes a lot of the underlying physics can be hidden behind the simplicity of Maxwell's equations. It should be no surprise then that after all these many years we still have a very active research community in electromagnetics.

 

[jslam]

Hmm...
Thanks alot. I didn't realize how relevant Maxwell's equations still are. I was under the impression that they just get superseded when you move on to non-classical physics, as does Newtonian gravity (in my understanding).

 

[Born2bwire]

Hmm...
Thanks alot. I didn't realize how relevant Maxwell's equations still are. I was under the impression that they just get superseded when you move on to non-classical physics, as does Newtonian gravity (in my understanding).

Well, to the best of my knowledge we still perform astronomical calculations using Newtonian physics for the most part. Using general relativity for complicated bodies of the heavens is usually too computationally costly to be done for many problems. But I digress, as to electrodynamics, you will find that the classical calculations are valid for a very large range of problems and frequencies. Just about any low frequency problem can be solved to high accuracy using classical electrodynamics. It is only around the terahertz region that we get to areas where quantum explanations become applicable. For example, how do we create a visible light antenna? Classical electrodynamic would say you need to create a wire antenna on the scale of a few hundred nanometers and then feed it with a terahertz signal. Basic quantum physics says you create a black body radiator, like say a piece of tungsten metal, and heat it to around 5800K. The quantum physics solution that gives us the incadescent light bulb is the physically realizable solution here. But even in the terahertz range we often do a mix of quantum and classical. For example, the radiation of light from our light bulb. We explain the mechanism for the creation of the light using quantum physics but we can calculate the radiated path and behavior of the light using classical electromagnetics. The other regime where quantum electrodynamics takes precedence is in the quantum world, on very microscopic levels and when we talk about solid state devices like semiconductors. But again, it is not uncommon to mix in classical equations to help simplify the quantum calculations.

 

[diazona]

Hmm...
Thanks alot. I didn't realize how relevant Maxwell's equations still are. I was under the impression that they just get superseded when you move on to non-classical physics, as does Newtonian gravity (in my understanding).

Whoever told you that? Maxwell's equations are indeed alive and well and very relevant. I imagine you wouldn't find many physicists who would be willing to call them "incorrect."

In fact, even Newtonian gravity still finds applications these days. They use Newton's law of gravity to calculate rocket trajectories and predict eclipses, and to keep our calendar in sync with the Earth's orbit. And if you're going to aim a probe at, say, a comet millions of miles away and have it hit dead-on, your physics had better be correct ;-) General relativity only makes a significant difference in certain specialized situations, like GPS (needs to be accurate to the nanosecond), modeling the universe at large scales, and, well, designing experiments to test general relativity.