Say I have light moving in a spaceship that travels at velocity $v$ perpendicular to the light ray, as shown in the diagram below. Now due to relativity the shape ship appears length contracted in the direction of $v$ and therefore the light wave in my reference frame appears squished together. Does this mean from my POV that the electric field oscillations that are perpendicular to the light ray are also squished and therefore would the light I see have different properties(i.e less energy or power) as the amplitude of the wave appears to be squished in my frame of reference?
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1$\begingroup$ The lengths of the sources of the electric field would be contracted, and the electric field would change appropriately. en.wikipedia.org/wiki/…. The electric field itself is not a length, and does not transform in the same way length of a rod gets contracted. $\endgroup$– Archisman PanigrahiCommented Oct 18 at 19:55
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$\begingroup$ @ArchismanPanigrahi so is there any measurement or property about the light that would change if the source of electric field is contracted? $\endgroup$– GunnarCommented Oct 18 at 22:11
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$\begingroup$ The intensity of the light (proportional to $E^2 + B^2$ (in Gaussian units)) will change. $\endgroup$– Archisman PanigrahiCommented Oct 19 at 0:22
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$\begingroup$ Related: physics.stackexchange.com/q/115070/123208 but I don't think it's a duplicate. $\endgroup$– PM 2RingCommented Oct 19 at 1:24
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1$\begingroup$ This question is completely unclear. Pls rephrase with a plane wave with electric field $\vec E$ and wavevector $\vec k \propto \vec S \propto \vec E \times B$ (pic one) in frame $S$ that is then viewed from $S'$, which is boosted by $\vec \beta = \vec v/c$. Now I don't mean the general case of arbitrary direction, but pick a Cartesian coordinate system that works, and explain along which axis each relevant vector aligns. $\endgroup$– JEBCommented Oct 19 at 3:08
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No. Although you have drawn the light wave as if the amplitude is a displacement over distance, it is not. The amplitude is a measure of field strength, not distance, so it will not be subject to length contraction.
answered Oct 18 at 20:07
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$\begingroup$ One of my physics profs said to imagine a light bulb flying through space that brightens and dims periodically. $\endgroup$ Commented Oct 18 at 23:21