CptBork:
May be you can have this with water waves but I challenge to achieve them with electric and magnetic fields. Remember that the solutions imply constant electrci and magnetic fields in entire planes parallel to that planes!
Wrong, the solutions are superpositions of plane waves, and such superpositions need not have the unphysical characteristics you specify. If you want to set up oscillating boundary conditions, you can do things like having capacitors on the boundary rapidly charge and discharge, or set up wires on the boundary carrying oscillating electric currents. If you can do it with water, you can do it with electromagnetism too. Don't ask me for specific details, that's for electrical engineers to worry about, I'm not an expert on this stuff. Naturally these conditions won't produce perfect finite plane waves, but they can come pretty close if you set it up right. It's irrelevant though- no physical solutions to Maxwell's equations produce infinite plane waves, only superpositions of such waves.
Maxwell's equations are not aproximations of nothing, they must be verified exactly or the fields are not what it is said they are and so the solutions must also be exactly that suggested by them. Some experiments don't match exactly due to practical conditions but I challenge again: give me a good aproximation of plane waves with electric and magnetic fields as described above, I mean as suggested by the Maxwell's equations.
Point sources of light such as the individual points of a flashlight bulb emit spherical waves, which at large distances become almost identical to plane waves. Approximating these waves as plane waves gives very accurate solutions to many problems in optics, such as Fraunhofer diffraction. If you think Maxwell's equations can be verified exactly, past the millionth decimal point, using real life lab experimentation, then you don't know squat about physics. All we can do is verify that the equations give the correct predictions to within the bounds of experimental error, and this has been verified thoroughly, aside from quantum and relativistic corrections when the experiments get precise enough.
I don't know what Fourier's series have to do here since they are a transformation from a time-domain function to a frequency-domain function. I don't know how you will solve the problem with Fourier Transformations. I think your idea is to sum an infinite number (a series) of the plane solutions to achieve some other solution (something more related to Taylor's series), may be more "practical" but sincerely I don't believe that adding the infinite parallel planes (allocating one by one in front of each other?) you will get a feasible solution.
Who cares what you believe? It's called a Fourier spatial transform, look it up. Clearly you don't know what you're talking about here, because I never said Fourier transforms had to be restricted to the time domain. I said you add up plane wave solutions for various different
wave numbers, which means spatial frequencies, not time. I assumed that since you were seeking to disprove Maxwell's equations, while treating me like some kind of grade school jackass, you would have already been familiar with how to solve them. Evidently I was mistaken.
I have a feeling whatever I post here is going to be futile, because I can see from your website that you've spent a long portion of your life trying to prove Maxwell and co. wrong, and it'll take more than a 5 minute argument to get you to see the futility of your efforts. At least I tried to give you some serious and accurate information on this subject, so you're welcome.
P.S.
On top of all that, the plane wave solutions you speak of only apply when the entire universe is devoid of all charges and currents, except for some initial fields set up at the beginning. Realistic solutions produced by real, physical charges and currents come from methods such as Green's functions and retarded potentials, not plane wave superposition. So even if your argument was correct for an empty universe (and it's not), it still would have no bearing on the validity of Maxwell's equations.