# Is the total amount of light today the same as it was 13.8 billion years ago?

Is the total amount of light today the same as it was 13.8 billion years ago? Is it fair to assume that the total background photon flux (ignoring local deviations) given by $\ cm^{-2}s^{−1}sr^{−1}$ unchanging globally. Electron/photon exchange, not withstanding, is there such a thing as a conservation of light?

• Can you expand upon your question. I think it's quite unclear. Jul 5 '17 at 2:17
• I'm at least as religious as most, but this is a science site. The title to this post should probably be modified. Jul 5 '17 at 2:53
• @DavidWhite Indeed, and in cases like this I would encourage you (or anyone) to make that edit yourself. Edits that change titles to clearly represent what the question is asking are especially useful. Jul 5 '17 at 4:08

When you say "amount of light", first be careful about what you mean.

1.) Do you mean total number of photons in the entire universe? (Here I mean not only inside our horizon, but in the universe as a whole, if that has meaning.) If this is what you mean, then the total number of photons should be pretty close to what it was shortly after the universe became transparent (e.g. right after the surface of last scattering was formed (which we see as the CMB)). There will be a few processes that can change this number (various scatterings off particles, collection by CMB satellites, etc), but at the surface of last scattering the mean free path of a photon is larger than the size of the visible universe. Most of the photons created then will still be around today.

2.) Do you mean photon number density (# photons per cubic meter)? Since the CMB was formed, space has expanded and the number of photons per cubic meter has diluted very much.

3.) Do you mean photon energy density (energy carried by photons per cubic meter)? This will also be much smaller due to both space expanding (fewer photons per cubic meter, as mentioned above) and photons redshifting, which causes them to lose energy as space expands their wavelength too.

Hope this helps.

• To be precise please note that there is no conservation of photon number. These are bosons, photon photon interactions do exist and can multiply the number of photons also, but it is true that the burst at the photon decoupling era floods out any new generations. Jul 8 '17 at 5:27
• Agreed. From a particle physics perspective, photon number conservation is not strictly true. From a cosmology perspective, photon number conservation is usually assumed since the mean free path is greater than the Hubble distance (unless interstellar/intergalactic dust is important in your model).
– Bob
Jul 8 '17 at 14:15

Photons are far from conserved. Firstly, any particle can decay, or be created or annihilated during inelastic collision. For example, $$\pi^0\rightarrow2\gamma.$$ Secondly, even in elastic collision, such as the energy level transition of electrons in an atom, photons are not conserved.

Generally, from Noether's theorem, each conserved quantity is associated with a one dimensional continuous global symmetry. Unfortunately, there is no such symmetry for photon to be conserved.

In order for the number of photons to be conserved,a new photon would have to be produced every time one was absorbed. Since there are processes that do not follow this rule, there is no reason to believe that the total number is conserved. For example, when an electron is ejected from a metal via the photoelectric effect, a photon is absorbed (which turns into the energy required to overcome the work function and, afterward, the electron's kinetic energy), and another one is not produced.

But maybe you meant that, on average, the number of photons in the universe is conserved. Unfortunately, this also should not be true. To begin with, it is reasonable to assume that the photon flux of the universe is dominated by the cosmic microwave background (which it is, to 1 part in 100, as per Number density of CMB photons?), which are very well approximated by a blackbody of a certain temperature $T$ (currently 2.7 K). This temperature has gradually decreased since the Big Bang. The number of photons emitted per second by a blackbody is proportional to $T^3$ (see pg. 9 of http://www.spectralcalc.com/blackbody/CalculatingBlackbodyRadianceV2.pdf). Thus, decreasing blackbody temperature means decreasing numbers of photons in the universe over time.

• The CMB isn't really a cooling blackbody emitting fewer photons, the original photons are just redshifted by the expanding universe. The total number of CMB photons should be approximately conserved - less the tiny proportion that happen to hit some object in a pretty empty universe. Jul 5 '17 at 3:18
• @MartinBeckett Photon flux per frequency bin and spectral radiance are related in a straightforward way (see the second source in my above answer). We know that the spectral radiance (hence the photon flux per frequency bin) for the CMB today matches a blackbody to a very high degree. At some point in the past, the photons' wavelengths were contracted relative to what they are now. Assuming that the number of photons is the same, there is no possible way to match the spectral radiance of a blackbody of a higher temperature. So are you saying that the CMB was not a blackbody in the past? Jul 5 '17 at 3:44
• I'm saying that the photons emitted per second by a blackbody is not a useful model of the CMB. It isn't emitting new photons longer wavelenght photons as "it" cools Jul 5 '17 at 16:17
• @MartinBeckett If it isn't a blackbody, then why is it so well modeled as a blackbody? Jul 6 '17 at 18:34
• It is a blackbody because it started as a black body and redshift shifts all wavelengths equally. But it is wrong to think of it as a current blackbody that is "emitting" fewer photons now than when it was hotter. It hasn't emitting any new photons since the photon era Jul 6 '17 at 20:57