# Is light scale invariant?

Are the equations that describe light's behavior unbounded to its energy and unrelated to the dimensions of the Universe (in which light exists)?

• Who is the dumb who downvoted? Aug 30, 2021 at 14:28

No, the energy of radiation (e.g., light and anything else massless) does scale during the expansion of the universe. It goes like the inverse fourth power of the scale factor a, of the universe, in the general relativistic standard Lambda CDM model. That is, $\rho_{rad}$ ~ $a^{-4}$.

The $a^{-3}$ issue is due to the fact that the universe is expanding and it's volume increases like the cube of a, so density decreases like its inverse. One factor of the inverse of a is due to the redshift. That last factor means every photon looses energy, and is lowered in frequent, by that factor due to the redshift. The cube factor is due to the space expanding, so fewer photons per unit volume.

Don't know if this answers your question, it was not totally clear, but it tells you how light energy scales in the universe. Keep in mind that in the reference frame in which it is emitted, say by an atom or electron scattering or some nuclear or particle emission, it is the same as it would be here on earth. As it propagates in the spacetime it reduces in each photon's energy due to redshift, and in the density of photons per unit volume.

As @Victor noted in his answer, electromagnetic radiation without any matter present is scale free. It is matter, or in the case of cosmology the universe scale factor and expansion that provides the scale.

According to wikipedia concerning the theory of classical electromagnetism, light without matter interaction is scale invariant. This is because the Maxwell equations are invariant under the transformation:

$$x \mapsto \lambda x$$

$$t \mapsto \lambda t$$