# Maxwell equations invariant under Lorentz transformation but not Galilean transformations

Why Maxwell equations are not invariant under Galilean transformations, but invariant under Lorentz transformations? What is the deep physical meaning behind it?

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Are you looking for an explicit demonstration of these properties, or what....I mean, that set of equation simple has those mathematical properties. It's sort of like asking why a square ninety degree angles and not sixty degree one. The deep physical meaning is that physics is Einsteinian and not Galilean. –  dmckee Sep 11 '12 at 0:52

The simplest answer is that Galilean transformations do not preserve the invariance of light's speed but Lorentz transformations do. Are you looking for something deeper?

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It tells you that the phenomena of electromagnetism are inherently relativistic and unlike mechanics there is no "Newtonian" low-velocity non-relativistic limit. Hence the equations have Lorentz structure built into them.

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You can make a quasistatic approximation when the timescale of the sources $T$ and the size of the system $L$ are such that $L/T \ll c$, or $L/c \ll T$. This means that the field propagates through the entire system much faster than the sources vary. This is a non-relativistic approximation since we get action at a distance. Of course, we can't capture all EM phenomena in this approximation. In particular, radiation is usually studied in the opposite regime $r/c \gg T$ where $r$ is the distance to the source. –  Robin Ekman Jul 6 '14 at 18:05

This is because electromagnetic radiation is a manifestation of some properties of the spacetime, consequently it has to be invariant under those transformations which preserves the spacetime interval invariant.

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