Directly observed relations in complete galaxy samples and the predictions of redshift-distance power laws.
Directly observed relations in complete galaxy samples (apparent magnitude or diameter vs. redshift) are compared with the predictions of redshift-distance power laws. The predictions are obtained by an objective, nonparametric, statistically uniform, and fully reproducible procedure. In all cases the linear law fits even more poorly than a cubic law, and the optimal law is approximately quadratic. Even a 1.2 power law is conspicuously better-fitting than a linear law. The results of the present study in terms of directly measured quantities are consistent with and confirm earlier studies in terms of theoretical quantities such as absolute magnitudes and diameters. They show that there is no positive evidence for the Hubble law in manifestly fair galaxy samples and that the law can be reconciled with the data in complete samples only, if at all, by the adjunction of a tissue of ancillary hypotheses, none of which is capable of direct observational substantiation.
Segal
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Massachusetts Institute of Technology, Cambridge, MA 02139.