On Wed, May 25, 2011 at 1:36 PM, Mark Iverson <zeropo...@charter.net> wrote:
> > With all the sophistication and accuracy to umpteen decimal places in > atomic physics/QM, how come we > can't explain WHY they're perpendicular! I think any theory should have to > explain the simple > observations first before delving down into more difficult and esoteric > aspects of physics. > > What do mean by "we"? It's not from observing e-m waves that we know the fields are perpendicular. It follows from Maxwell's equations, which predict the waves. So, certainly some people can explain in arbitrary detail why they are perpendicular, given what we know about the properties of the fields as described by Maxwell's equations. It's basically Faraday's law and the extended Ampere's law that require them to be perpendicular in the absence of sources (i.e. in self-propogating waves). The curl of one field is proportional to the other, and since the curl of a vector is perpendicular to the vector, the fields must be perpendicular. Faraday's law is probably the simplest to imagine. Remember in a solenoidal transformer, a changing magnetic field along the axis produces an electric field that circulates the axis; i.e. it is perpendicular to it. An electromagnetic wave sustains itself because a changing electric field induces a magnetic field, and a changing magnetic field induces an electric field, and so they sustain each other as they oscillate, and according to the induction laws the induced fields are perpendicular. Now, you can ask why induced fields are perpendicular, or what is the reason for Faraday's law. Historically, of course, these laws (Maxwell's laws collectively) were discovered empirically in the laboratory (except for Maxwell's displacement current, which was his stroke of genius). But now we know that magnetism is just a relativistic transformation of the electric field. Maxwell's equations can be derived entirely from Coulomb's law and relativity, as many textbooks demonstrate. That's not an explanation that's easy to visualize, but that's where it all stems from. Now, if you ask why Coulomb's law, or why relativity, the answers become more philosophical, although there are certainly field theories that give a more fundamental basis for these things than just treating them axiomatically.
