The Tolman surface brightness test

In 1930, Richard Tolman proposed a test to tell an expanding universe from a static one. If space expands, a distant galaxy's surface brightness (its light per unit of sky area) should fall as (1 + z)⁴, where z is the redshift. A galaxy at z = 1 should look sixteen times fainter per unit area, and one at z = 2 eighty-one times fainter.

Surveys, most notably by Lubin and Sandage (2001) and later Hubble deep fields, have found the raw dimming less severe. Lubin and Sandage measured it as (1 + z) raised to about 2.6 in red light and 3.4 in near-infrared light. They attributed the difference from 4 to the evolution of galaxies, concluded that expansion is supported, and ruled out the simplest tired-light model, which predicts a power of only 1, at more than 10 standard deviations. Others, such as Lerner and colleagues (2014), argue the data favor a static universe. Galaxy evolution is seen independently in colors and spectra, though the exact size of the correction is still debated.

RSI reads the same measurements through the breathing medium of Chapter VI. Galaxies are not receding. Their light keeps its energy in flight and is compared with atoms whose rhythm has risen since it left. Because Christof Wetterich's (2013) equivalence leaves every observable ratio unchanged, that comparison reproduces every factor in Tolman's count, so unchanging galaxies would dim as (1 + z)⁴, exactly as in an expanding universe. Distant galaxies are seen closer to the trough of the breathing, younger and brighter, which accounts for the milder measured dimming just as in standard cosmology. The ruled-out tired-light model is not RSI's account: in RSI nothing is lost on the way.

So the Tolman test does not distinguish RSI from the standard model. Both predict the same dimming and both credit the shortfall to galaxy evolution. It is a consistency check that RSI passes, provided the history of the medium's breathing reproduces the measured relation between redshift and distance.