- #1
Anamitra
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A plane electromagnetic wave[traveling in the x-direction in an inertial frame]in vacuum is usually represented by an equation of the form:
[tex]{E}{=}{E_{0}}{exp{[}{i}{(}{k}{x}{-}{\omega}{t}{)}{]}}[/tex]
The wave velocity[phase velocity] is given by:
[tex]{c}{=}{\frac{\omega}{k}}[/tex]
We can perform Lorentz transformation on t and x[and y,z] to some other inertial frame moving in the x-x' direction.
The value [tex]{\frac{\omega}{k}}[/tex] changes after transformation.But the value of c [wave velocity=phase velocity]should not change.
How does one explain this?
[If one considers a wave packet in vacuum each component should have the same speed=c]
[tex]{E}{=}{E_{0}}{exp{[}{i}{(}{k}{x}{-}{\omega}{t}{)}{]}}[/tex]
The wave velocity[phase velocity] is given by:
[tex]{c}{=}{\frac{\omega}{k}}[/tex]
We can perform Lorentz transformation on t and x[and y,z] to some other inertial frame moving in the x-x' direction.
The value [tex]{\frac{\omega}{k}}[/tex] changes after transformation.But the value of c [wave velocity=phase velocity]should not change.
How does one explain this?
[If one considers a wave packet in vacuum each component should have the same speed=c]
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