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Vrbic

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## Homework Statement

Professor C. Rank claims that a charge at [itex](r_1, t_1) [/itex] will contribute to the air pressure

at [itex](r_2, t_2) [/itex] by an amount [itex] B \sin[C(|r_2 − r_1|^2− c^2|t_2 − t_1|^2)] [/itex], where B and C are constants.

(A) Is this effect Galilean invariant?

(B) Is this effect Lorentz invariant?

## Homework Equations

Galilean transformation:

[itex]x'=x-vt, t'=t[/itex]

Lorentz transformation:

[itex]'x=\frac{x-vt}{\sqrt{1-(\frac{v}{c})^2}}, t'=\frac{t-\frac{tv}{c}}{\sqrt{1-(\frac{v}{c})^2}}[/itex]

## The Attempt at a Solution

(A) I suppose that part with [itex]t_2,t_1[/itex] is not important for Galilean transformation it is same. And if I transform [itex] r_1, r_2[/itex] to [itex]r'_1=r_1-vt, r'_2=r_2-vt[/itex] the extra terms are deducated.

So it is Galilean invariant? True?

(B) In Lorentz case I have problem with times. Could you suggest some point of view?