- #1
PhysyCola
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Homework Statement
For a plane, monochromatic wave, define the width of a wavefront to be the distance between two points on a given wavefront at a given instant in time in some reference frame. Show that this width is the same in all frames using 4-vectors and
in-variants.
Homework Equations
- $$ \vec{X} = (ct, \vec{x}) $$
- $$ \vec{K} = (\omega/c, \vec{k})$$
- $$ \vec{U} = (\gamma_u c, \gamma_u \vec{u})$$
The Attempt at a Solution
I have tried in vein to create an appropriate invariant quantity to show that this 'width' is invariant. I know that this question can also be done by writing equations for the movement of the two ends of the width, and taking a Lorentz transform, but I am also struggling to set this up. Any help would be greatly appreciated.