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Electromagnetic wave equation not invariant under galilean trans.

  • Thread starter bfusco
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  • #1
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Homework Statement


Prove that the electromagnetic wave equation: 
(d^2ψ)/(dx^2) + (d^2ψ)/dy^2) + (d^2ψ)/(dz^2) − (1/c^2) * [(d^2ψ)/(dt^2)]= 0 is NOT invariant under Galilean transformation. (i.e., the equation does NOT have the same form for a moving observer moving at speed of, say, v in the x direction).

*note: all the "d"s in this equation are the partial derivatives.


Homework Equations


galilean transformation:
t'=t, x'=x-vt, y'=y, z'=z

The Attempt at a Solution


-from what i understand to solve this involves the chain rule for partial derivatives.
-looking at the equation i cant help but jump to something with the gradient of ∇ψ, but i dont know where to go from there.
 

Answers and Replies

  • #2
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The y,z,t components in the equation just stay the same, you can ignore them. You just have to change the x-component.
Hint: It will get an additional t-component afterwards.
 
  • #3
128
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d/dx(dψ/dx' * dx'/dt + dψ/dt' * dt'/d(something)) ?
 
  • #4
128
1
d/dx(dψ/dx' * dx'/dt + dψ/dt' * dt'/d(something)) ?
wait is it d/dx(dψ/dx' * dx'/dx + dψ/dt' * dt'/dx), which equals d/dx(dψ/dx' * 1 + dψ/dt' * 0)?
 

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