On Wed, May 25, 2011 at 7:33 PM, Mark Iverson <zeropo...@charter.net> wrote:
> Robin hits the nail on the head... Anything mathematical is the MODEL, and is supposed to reflect physical reality. My question was about the physical world -- what I was asking got was a rational, qualitative, cause and effect sort of explanation. Nothing is more rational than a mathematical description of reality, and it provides cause and effect. I'll grant that it is not a qualitative explanation, and doesn't give the answer to the ultimate question of life, the universe, and everything (42), but science starts from observation, and uses that to predict consequences. For any explanation, you can always keep asking, as a child does, "but why?". Why gravity? Why Newton's law? Why general relativity? The best we can do is find the most fundamental observation, and until more fundamental ones come along, try to explain what we see based on those. So, I took it back to Coulomb's law and special relativity. All of the laws of electromagnetism can be derived from those two concepts, including the reason for the perpendicular fields in an em wave. But it is a mathematical development. The language of physics is math. > The perpendicular nature of E and B fields existed PRIOR to Maxwell, or even cavemen, or even life on this planet! Obviously. I certainly didn't say anything different. I said Maxwell's equations were developed from laboratory experiments, and they predict that the fields in electromagnetic waves are perpendicular. (Not that E and B field are always perpendicular, because they aren't.) > I'm afraid that this reflects very poorly on JC's understanding of what is more fundamental, the experiment (physical reality, facts) or model (theory). I'm sorry you misunderstood what I wrote. I was not suggesting that reality was a consequence of theory. But when you ask why something is so, without specifying what can be taken as understood, then it is a little difficult to answer. For example, one can ask why are planetary orbits elliptical. And another might answer because of the inverse-square law of gravity, and proceed to prove the connection mathematically. Some questioners, who are satisfied with Newton's law as fundamental, might be happy with the explanation. Others, like you, might object that that is putting theory before reality: "Sure, I know that, but I want a qualitative explanation for why Newton's law exists." That's a very different question, and asking about elliptical orbits is perhaps not the most direct way to get at fundamental origin of gravity. > JC has shown a great ability to regurgitate what he has read in his textbooks, in great detail, but his responses to this simple question seems to indicate that he hasn't any idea of the difference between physical reality and the mathematical models that attempt to explain what is observed. First, if this is a simple question, what is your answer? Second, I regret that I gave the impression that Maxwell's equations are anything but a mathematical description of what we observe. They were developed using certain observations, but then they were used to predict (or explain) other observable phenomena, like the perpendicular nature of the fields in waves. As I said before, the perpendicular nature *in waves* was not known or observed before Maxwell. And fields are not necessarily perpendicular; only induced fields are. Coming back to the elliptical orbits, they were in fact observed and known before Newton, and expressed empirically in Kepler's laws. Before Newton, if someone asked why elliptical, one could cite Kepler's laws, but in this case, the law does little more than state what is observed: orbits are elliptical, so it would really be case of begging the question. There was a mad race to find a more fundamental reason for Kepler's laws, and Newton won that race. More fundamental explanations for gravity would take centuries. As for your question, I started with the superficial answer. Electromagnetic fields can sustain themselves in the absence of sources because of reciprocal induction (changing E induces B, changing B induces E), and in laboratory experiments induction is observed to produce perpendicular fields. But I also went further and said that the existence of those laws of induction stems from Coulomb's inverse-square law and special relativity, but I made no attempt to connect them. And I also made no attempt to explain why Coulomb's law, or why relativity. Evidently, what you wanted was the reason for the laws of induction, for Faraday's law, and for the generalized form of Ampere's law. So let me try a little gedanken experiment that gives some sense of the perpendicular nature of the fields from Coulomb's law and relativity. It kind of explains the origin of magnetism, but is not a perfect explanation for induction. That would be more difficult. Consider two positive charges moving parallel in the laboratory. In the reference frame of the charges, an observer sees only Coulomb repulsion, and therefore they accelerate away from each other. A laboratory observer will see time dilation in the charges' reference frame, and so reduced separation acceleration, and therefore an apparent attractive force. Classically, this attraction is the magnetic attraction of parallel currents. One way to explain attraction of parallel currents is with a magnetic field produced by one moving charge perpendicular to the motion, and the resulting (Lorentz) force on a moving charge due to a magnetic field, perpendicular to the field and the motion. So, a circulating magnetic field perpendicular to the electric field between the charges is one mathematical way to explain the observations. That's the one we've adopted. (Note that all those perpendicular directions would be easier to illustrate with right hand rules and pictures.) Now, if you want to know why Coulomb's law, and why relativity, you're on your own.
