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We review a sample of the early literature in which the reality of theexpansion is discussed, explain Hubble's reticence to accept the expansion asreal, and contrast the Tolman surface brightness test with three other moderntests. We search for the Tolman surface brightness depression with redshiftusing the Hubble Space Telescope (HST) data from Paper III for 34 early-typegalaxies from the three clusters Cl 1324+3011 (z=0.76), Cl 1604+4304 (z=0.90),and Cl 1604+4321 (z=0.92). Depressions of the surface brightness relative tothe zero-redshift fiducial lines in the mean surface brightness, log linearradius diagrams of Paper I are found for all three clusters. Expressed as theexponent, n, in 2.5 log (1 + z)^n mag, the value of n for all three clusters isn = 2.59 +/- 0.17 in the R band and 3.37 +/- 0.13 in the I band for a q_o = 1/2model. The sensitivity of the result to the assumed value of q_o is shown to beless than 23% between q_o = 0 and +1. For a true Tolman signal with n = 4, theluminosity evolution in the look-back time, expressed as the exponent in 2.5log (1+z)^(4-n) mag, must then be between 1.72 to 1.19 in the R band and 0.94to 0.45 in the I band. We show that this is precisely the range expected fromthe evolutionary models of Bruzual & Charlot. We conclude that the Tolmansurface brightness test is consistent with the reality of the expansion. Wehave also used the high-redshift HST data to test the ``tired light''speculation for a non-expansion model for the redshift. The HST data rule outthe ``tired light'' model at a significance level of better than 10 sigma.Comment: 36 pages, 6 figures; accepted for publication in the Astronomical  Journa

the astronomical journal

The Tolman Surface Brightness Test for the Reality of the Expansion. IV. A Measurement of the Tolman Signal and the Luminosity Evolution of Early-Type Galaxies