Of the many cosmological models developed during the past forty years, none is completely satisfactory; so work continues in the development of new models and in the checking of their predictions against the growing mass of experimental evidence. The validity of a model rests on its agreement with experimental data, particularly the data on distribution of galaxies and on redshifts.

In 1909, Ehrenfest published a note in the Physikalische Zeitschrift showing that a Born rigid cylinder could not be set into rotation without stresses, as elements of the circumference would be contracted but not the radius. Ignatowski and Varićak challenged Ehrenfest’s result in the same journal, arguing that the stresses would emerge if length contraction were a real dynamical effect, as in Lorentz’s theory. However, no stresses are expected to arise, according to Einstein’s theory, where length contraction is only an (...) apparent effect due to an arbitrary choice of clock synchronization. Ehrenfest and Einstein considered this line of reasoning dangerously misleading and took a public stance in the Physikalische Zeitschrift, countering that relativistic length contraction is both apparent and real. It is apparent since it disappears for the comoving observer, but it is also real since it can be experimentally verified. By drawing on his lesser-known private correspondence with Varićak, this paper shows how Einstein used the Ehrenfest paradox as a tool for an ‘Einsteinian pedagogy’. Einstein’s argumentative stance is contrasted with Bell’s use of the Dewan-Beran thread-between-spaceships paradox to advocate for a ‘Lorentzian pedagogy’. The paper concludes that the disagreement between the two ways of ‘teaching special relativity’ stems from divergent interpretations of philosophical categories such as ‘reality’ and ‘appearance’. (shrink)

Among the many controversial contributions of E. A. Milne to cosmology, the only one which is taken seriously today (to the extent that it has been absorbed as a premise in most scientific approaches to the problem of the universe as a totality) is his early suggestion that a formal equivalence may be made between Newtonian and Relativistic cosmology. My own paper suggests that, over and above any logical validity in the alleged equivalence, the actual way in which it has (...) subtly insinuated itself into nearly all contemporary speculation reveals as few things could some of the epistemological foundations that underlie the current assumptions in cosmological science. (shrink)

This article seeks to show that E.A. Milne’s philosophy of science has its roots in the philosophy of Aristotle and it could be an inspiration for Popper’s philosophy. The similarities with Aristotle’s concept are as follows: 1) the aim of science is to explain phenomena by discovering general principles; 2) the mind is responsible for discovering them, although experience guides the search; 3) deducing detailed statements from general assumptions is the most important element of research. On the other hand, Milne’s (...) proposal is consistent with Popper’s main ideas: 1) criticism of the principle of induction; 2) preference for the hypothetical-deductive method ; 3) appreciation of falsification and confidence in the effectiveness of deductive logic. (shrink)

In this paper we summarise the constraints that low-redshift data—such as supernovae Ia, baryon acoustic oscillations and cosmic chronometers —are able to set on the concordance model and its extensions, as well as on inhomogeneous but isotropic models. We provide a broad overlook into these cosmological scenarios and several aspects of data analysis. In particular, we review a number of systematic issues of SN Ia analysis that include magnitude correction techniques, selection bias and their influence on the inferred cosmological constraints. (...) Furthermore, we examine the isotropic and anisotropic components of the BAO data and their individual relevance for cosmological model-fitting. We extend the discussion presented in earlier works regarding the inferred dynamics of cosmic expansion and its present rate from the low-redshift data. Specifically, we discuss the cosmological constraints on the accelerated expansion and related model-selections. In addition, we extensively talk about the Hubble constant problem, then focus on the low-redshift data constraint on \ that is based on CC. Finally, we present the way in which this result compares to the high-redshift \ estimate and local measurements that are in tension. (shrink)