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 dimming less severe than (1 + z)⁴. Lubin and Sandage attributed the difference to the evolution of galaxies and concluded that expansion is supported; others, such as Lerner and colleagues (2014), argue the data favor a static universe. RSI calls the evolution correction an unobserved compensating factor, and its own dimming law still needs to be stated as an exponent and tested.

The theory holds instead that redshift reflects field condition, not recession. Galaxies are stationary nodes in a toroidal fluid field, and their light loses energy because the medium attenuates it over a long path. That process does not impose the same brightness penalty as expansion.