File:Tolman surface brightness test.png

English: According to the tired light hypothesis, given a simple (static and flat) universe, the photons per second received from an object drops proportional to the square of its distance and the apparent area of the object also drops proportional to the square of the distance, so the photons received per surface area per unit time would be constant, independent of the distance, even though the surface brightness is reduced because of tired light reddening. In an expanding universe, however, there are two effects that change this relation. First, the rate at which photons are received is reduced because each photon has to travel a little farther than the one before. Second, the energy of each photon observed is reduced by the redshift. At the same time, distant objects appear larger than they really are because the photons observed were emitted at a time when the object was closer. Adding these effects together, the surface brightness in a simple expanding universe (flat geometry and uniform expansion over the range of redshifts observed) should decrease with the fourth power of (1+z).