# Why You Should Ignore IAU Resolution B4

The problem with this resolution's proposal to rename the Hubble law is that it blurs together multiple concepts that need to be kept separate.

First, Hubble's law refers to observational data - measurement of velocities and distances. The data have two properties - the functional relationship (i.e., linear or otherwise) between velocity and distance and the slope. To which does "Hubble's law" apply? Normally we think of the functional relationship as being the "law", while the slope is the Hubble "constant".

The "expanding universe" is the theoretical explanation for the velocity-distance relation. The age of the universe gives H_0 (the slope), while the geometry of the universe would give the functional relationship (linear at low redshift, but deviating at high.)

Not all models of the universe predict a linear relation between velocity and distance; Segal's Chronometric Cosmology predicted a quadratic relation (v ~ r^2). Not all models that predict a linear relationship are expanding universes: e.g. Zwicky's "tired light" model.

What did Lemaitre's 1927 paper cover? Obviously, it presented the theoretical model (expanding universe) and it provided the Hubble constant. While it predicted a linear relationship between distance and velocity, it did not (and could not) demonstrate that the relationship actual existed based on the limited observational data available at that time.

Hubble's 1929 paper did cover both aspects of the observational data. Note that the Hubble-Humason 1931 paper focused almost exclusively on the functional relationship aspect (demonstrating that the relationship stayed linear to much higher redshifts.)

Thus, Lemaitre actually made no direct contribution to what we call the "Hubble law". If one wanted to rename something, it should be the "Hubble Lemaitre constant." However, we need to first ask the following. If someone publishes a result that has no impact because it wasn't read or was read but ignored by the relevant people, should that person still get credit?

Concerning Lemaitre's 1927 paper, it is useful to remember the following:

• He was not the first to derive the dynamical equations for an expanding universe (Eq. 11 in his paper). Friedmann did it in 1922 (Zeitschr. Phy. 10, 377; Eq. 7 in his paper.) Lemaitre's model is called a monotonic world of the second kind by Friedmann.
• He was not the first to propose a linear relation between redshift and distance. Weyl did it in 1923 (Raum Zeit, Materie; Phys. Zeitschr, 24, 230).
• He was not the first to measure the slope of the velocity-distance relation for galaxies. Lundmark did it in 1925 (MNRAS, 85, 865; see also Line 20.)
• He was not the first person to use the term "expanding universe" (multiple prior references in the literature.) In 1922, Carl Wirtz described the "expansion of the system of spiral nebulae" (Astr. Nach. 216, 451) (at least according to Virginia Trimble https://arxiv.org/abs/1307.2289).
• Robertson (1928, Phil. Mag., 7, 835) being unaware of Lemaitre's work, independently rederived many of his results, including predicting a linear velocity-distance relation and determining the slope. (expressed as a radius); what he failed do was to use the word "expansion" to describe this model (just calling it relativistic cosmology).
When Lemaitre's paper was finally "discovered" by Eddington and de Sitter in 1930, it was the expanding universe model that had a big impact (a really big impact). The slope (Hubble constant) was ignored. Eddington quoted Hubble's 1929 value, while de Sitter had derived his own.

Suppose tired light had turned out to be the correct theory. We would still have the Hubble law, but Lemaitre would be forgotten.

Suppose Lemaitre had included the paragraph describing the derivation of his (by now) old value of the slope in his 1931 English translation, what would have been the reaction? It would likely also have been ignored. Only historians and scientists coming much later would have been interested. Would that have caused the nomenclature of the "Hubble law" or "Hubble constant" to be different? Probably not. Let us remember that Lundmark is universally recognized as having created the first rendition of what we call a "Hubble diagram". Is there any call to change its name to a "Lundmark diagram"?