Recent content by ObsessiveMathsFreak

I'm actually reading through this at the moment, so I'll throw my hat in here for a second. Here's the summary of the paper's position after the derivation of the transformation rule between EM fields in the stationary and moving reference frames To my understanding, this is basically a summary...

Eventually I managed to figure this out. It turn out that you do use the chain rule, but you also have to use the EM conditions to derive the result. For the sake of making the thread a potentially useful resource, I'll give the result for the first of the equations, but I'll use primed...

That was the first thing I tried, but I couldn't see how it would work. Perhaps it is based on the galilean/linear transformations of the equations. Does anyone have a reference for the raw Newtonian/Galilean transformation of Maxwell's equations?

To clarify, I'm not talking about the derivation of Lorentz transforms. I'm asking about the transformation of Maxwell's equations in special relativity. How are these derived without using 4-vectors?

But he doesn't give a derivation, and seems to rely on existing principals. How exactly did he go about it without four-vectors, etc?

Could you give links to the relevant threads, for future googlers if nothing else.

What is the simplest derivation of the transformation rules for Maxwell's equations in special relativity? I'm working through Einstein's original 1905 paper(available here), and I'm having trouble with the section on the transformation of Maxwell's equations from rest to moving frame. The...

The first notation only really makes sense if you consider 'x' to be a complex variable. In this case, taking the limit at infinity means asking whether the function approaches a fixed value no matter which direction you approach infinity from. The second notion on the other hand can be used...

It depends on what you mean by infinite. You really have to think about this one.

This is what happens when you restrict yourself to the latin Alphabet. Try using Greek and Cyrillic letters if you run out.

In "Mathematical Aspects of Classical and Celestial Mechanics", Arnold & co. claim that this problem was solved by Legendre for a wide class of power law resistance terms of the form c v^\gamma. The extract is attached. Arnold claims that the 1st order equation which the system reduces to is...

In general 4d space time, the Riemann tensor has 20 independent components. However, in a more symmetric metric, does the number of independent components reduce? Specifically, for the Schwartzchild metric, how many IC does the corresponding Riemann tensor have? (I think it is 4, but I...

The Schrödinger equation is a fairly big lump to swallow undigested. The photoelectric effect is a trifle by comparision. I'd prefer to keep the basic assumptions simple if I could, but I'm wondering whether this is really valid in this case.

The first apparently comes from the photoelectric effect, and the second from the de Broige wave/particle duality. Whether this is valid or not I really don't know.

One derivation I have seen works by considering a free wave-particle of energy E=h\omega, momentum \mathbf{p}=h \mathbf{k}, and relates the two by E=\tfrac{|\mathbf{p}|^2}{2m}+V. Then the wave is assummed to have the form \Phi=e^{i(\mathbf{k}\cdot\mathbf{x}-\omega t)} The equation is then...