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Homework Statement
Not really a homework/coursework problem, I'm just trying to make sense of some class notes from our chapter on special relativity. I'm trying to find the expression for electromagnetic wave propagation in a reference frame S' that is moving at a constant velocity with respect to an inertial reference frame S.
[PLAIN]http://img193.imageshack.us/img193/4058/p1000897f.jpg
Where capital phi is either the B or E vector (see relevant equations).
Homework Equations
[URL]http://upload.wikimedia.org/math/4/5/a/45adde5635abaf78b4b9174bf210f504.png[/URL]
[URL]http://upload.wikimedia.org/math/d/a/4/da48cd00768a325141e38f519b4ca55e.png[/URL]
or more generally:
[URL]http://upload.wikimedia.org/math/6/7/0/670fa614a400a15236d39ece735e6f14.png[/URL]
Just need to find the 2nd order partials with respect to x, y, z for the Laplacian and the 2nd order partial with respect to t.
The Attempt at a Solution
I have no trouble finding the first order partial derivatives of phi with respect to all 4 variables (note the red checkmark), nor the 2nd order partial derivatives with respect to x, y and z. But I don't know what happened with the 2nd derivative with respect to time, I don't know where the two middle terms came from. (see arrows)
2nd question: What does the solution imply? I didn't understand/am missing the bit of theory that came afterwards (I'm not studying in my native language and my lecturer speaks blazingly fast lol), supposedly the solution for this equation in a moving reference frame gives an answer of 0, which implies that their is no preferential reference frame.
Sorry for posing a question so convoluted but I'd appreciate any help.
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