MNRAS 000, 1–8 (2025) Preprint 20 April 2025 Compiled using MNRAS L A T E X style file v3.0 Reassessment of Hubble’s 1929 claim of a velocity-distance relation Sergio Torres-Arzayus International Center for Relativistic Astrophysics Network, Piazza della Repubblica 10, 1-65122, Pescara, Italy 20 April 2025 ABSTRACT This paper revisits Hubble’s 1929 “discovery paper” using more accurate measurements and modern statistical tools that were unavailable at the time. The aim is to reassess Hubble’s data to determine whether the paper’s claims were justified or premature. This analysis sheds light on the process of scientific discovery and reveals extra-scientific factors that influence the acceptance of new paradigms. Key words: Hubble, cosmology, big bang, sociology of science, falsifiabiliy 1 INTRODUCTION The foundation of the standard cosmological model is the realization that the fabric of space itself is expanding, causing galaxies to re- cede from one another. The first observational evidence supporting this concept came in 1929, when Edwin Hubble published a paper demonstrating a correlation between the spectral shifts of galaxies, interpreted as radial velocities, and their distances from Earth. Al- though Hubble himself did not interpret this velocity–distance rela- tion as evidence of expanding space, subsequent work by astronomers engaged in relativistic cosmology provided that interpretation. How- ever, Hubble’s 1929 paper (Hubble 1929, hereafter H1929) is widely regarded as one of the most significant and impactful astronomical publications in history. As we approach the 100th anniversary of Hubble’s observation of cosmological expansion - and considering the ongoing disagreement over the value of the Hubble constant ( 0 ) - it is of considerable educational value to revisit Hubble’s 1929 pa- per. Doing so offers insight into the nature of scientific discovery and the mechanisms by which science progresses. In 1931, Hubble, together with Milton Humason, published an expanded data set that extended the velocity-distance relations to greater distances, further supporting the initial findings (Hubble & Humason 1931, hereafter H1931). Hubble’s results were instrumental in convincing a previously skeptical scientific community to take relativistic cosmology seriously. Although the history of the big bang model has been extensively studied (Kragh 1999), certain aspects of this foundational period warrant further scrutiny, especially given the profound influence of H1929, despite its methodological flaws and possibly premature con- clusions. Several reviews have discussed Hubble’s role in the devel- opment of the standard cosmological model (Kirshner 2004; Bahcall 2015). By taking a focused look at this pivotal scientific result, we have the opportunity to explore the dynamics of the scientific process and the interplay between data and theory, an interaction that lies at the heart of modern scientific practice. This study focuses specifically on the 1929 paper, which is widely considered Hubble’s ’discovery paper’ despite the later publication in 1931 that provided a more robust confirmation of the velocity- distance relationship. Before proceeding with the analysis, it is important to note that, contrary to the convention of avoiding anachronism, I will use mod- ern terminology such as galaxy, Hubble flow, and Hubble constant for clarity. Prior to Hubble’s work, terms like cluster, nebula, and spiral nebula were used ambiguously. Beyond the planets and the Sun, telescopes revealed two general types of celestial objects: point sources and diffuse patches of light. The former were associated with stars, while the latter were broadly categorized as nebulae. With in- creasingly powerful telescopes, some of these nebulae were resolved into individual stars, though it remained unclear whether they were part of the Milky Way or separate systems altogether. In 1925, Knut Lundmark, and later in 1926, Edwin Hubble, deter- mined the distance to the spiral nebula M31 (Andromeda), placing it well beyond the Milky Way. This confirmed the existence of in- dependent stellar systems — then referred to as ’island universes.’ Today, we recognize that objects previously labeled as nebulae fall into one of three categories: planetary nebulae or globular clusters within the Milky Way, or external galaxies beyond it. Throughout this paper, I will use the term galaxy in place of the historical spiral nebulae for consistency with modern usage. By the early twentieth century, astrophotography had matured enough to be adopted by professional astronomers for routine mea- surements of brightness and spectra of celestial objects. According to the Doppler effect, the velocity of an astronomical object can be inferred from the shift in the wavelength () of absorption lines in its spectrum. This shift is quantified by the parameter  =Δ/, where  is positive (redshift) when the object is receding and negative (blueshift) when it is approaching. To measure distances to stars within the Milky Way, astronomers used the method of parallax. However, for objects beyond the Milky Way, alternative techniques were required. If the intrinsic luminosity of a star (or galaxy) is known, its distance can be derived by compar- ing the observed (apparent) brightness with the expected brightness, using the inverse-square law for electromagnetic radiation. Lumi- nosity and brightness are quantified through the magnitude system: absolute magnitude ( ) represents intrinsic luminosity, while appar- ent magnitude () represents observed brightness. The relationship between them is given by the distance modulus: © 2025 The Authors