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Maxwells Equations being non-invariant with Galilean transformations

  1. Jun 28, 2012 #1
    I just purchased a book on the introduction of special relativity and I seem to be stuck on a simple mathematical step. For some reason I just cant see this!

    This is what it says:
    Gotta love getting stuck on something when the book says its "Easy to see." Confidence -1.
  2. jcsd
  3. Jun 28, 2012 #2


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    Staff: Mentor

    The Galilean transformation in this case is x' = x - vt; y' = y; z' = z; t' = t.

    Apply the chain rule for partial derivatives, e.g.

    $$\frac{\partial}{\partial t} =
    \frac{\partial x^\prime}{\partial t} \frac{\partial}{\partial x^\prime} +
    \frac{\partial y^\prime}{\partial t} \frac{\partial}{\partial y^\prime} +
    \frac{\partial z^\prime}{\partial t} \frac{\partial}{\partial z^\prime} +
    \frac{\partial t^\prime}{\partial t} \frac{\partial}{\partial t^\prime}$$
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