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If special relativity causes magnetism to arise from the electric force, how does light work?

My understanding of light was perturbations in the electric field that cause perturbations in the magnetic field, which caused perturbations in the electric field and so on, resulting in a packet of energy that travels through space.

If, however, magnetism can be viewed as arising from relativistic length contractions due to different reference frames of moving objects (which I just stumbled across from Veritasium's video), how do we explain electromagnetic waves under that model? As I understand it, for relativistic effects to come into play there have to be two different reference frames moving at different speeds / directions. What are the reference frames at play here? As I see it, there's only the reference frame of the photon.

Also note, from How Special Relativity causes magnetism I understand there are different ways to view the relationship between magnetism, electricity, and relativity. I'm specifically asking about how light works from the perspective of "magnetism is just charges + relativity," even if there's a better way to frame how light works in general.

S. Sobell
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From the point of view of Special Relativity, there are no two separate electric and magnetic fields, and charge and current densities are not independent when passing from one reference frame to another.

$E^2-B^2$ is a relativistic invariant (I use units such as $c=1$). Its value must be the same in every inertial reference frame, although the intensity of the electric and magnetic fields may vary separately. This fact puts an essential constraint on the possible changes of electric and magnetic fields from one reference frame to another. In particular, if only an electric field exists in one reference frame, a magnetic field may appear in other frames. Still, in no frame, the electric component of the electromagnetic field may vanish (that would reverse the sign of the relativistic invariant).

The invariance of $E^2-B^2$ helps to understand that the argument showing the magnetic field as an effect of a change of reference frame, when staring with a reference where only the electric field is present, can be reversed. It is equally possible to show that an electric field must appear in another reference frame if only a magnetic field is present in the original. In any case, Vweritasium's video is not showing that the electric field is more fundamental than the magnetic field. It just shows how the unitary description of the electromagnetic fields introduced by SR allows us to understand the deep link existing between electric and magnetic forces. Without a hierarchy among them.

In the case of an electromagnetic wave, the invariant is zero, and then it remains zero in all inertial frames. Said in another way, there is no possibility of converting an electromagnetic wave into a purely electric or magnetic wave.

GiorgioP-DoomsdayClockIsAt-89
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In any given frame, you have an electric field, a magnetic field, and disturbances related via Maxwell's equations. If you Lorentz transform to a different frame, you get electric and magnetic fields that are linear combinations of the old ones, and disturbances that are combinations of the old ones, and Maxwell's equations still apply.

WillO
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If we trust relativity, light is pure kinetic energy. I mean, if light has no rest mass, then light is pure kinetic energy according to relativity.

So light is kinetic energy, which can become electric field energy. (Or alternatively mechanical pushing energy (radiation pressure).

stuffu
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