Einstein's "Zur Elektrodynamik..." (1905) Revisited, with Some Consequences

Einstein, in his "Zur Elektrodynamik bewegter Korper", gave a physical (operational) meaning to "time" of a remote event in describing "motion" by introducing the concept of "synchronous stationary clocks located at different places". But with regard to "place" in describing motion, he assumed without analysis the concept of a system of co-ordinates. In the present paper, we propose a way of giving physical (operational) meaning to the concepts of "place" and "co-ordinate system", and show how the observer can define both the place and time of a remote event. Following Einstein, we consider another system "in uniform motion of translation relatively to the former". Without assuming "the properties of homogeneity which we attribute to space and time", we show that the definitions of space and time in the two systems are linearly related. We deduce some novel consequences of our approach regarding faster-than-light observers and particles, "one-way" and "two-way" velocities of light, symmetry, the "group property" of inertial reference frames, length contraction and time dilatation, and the "twin paradox". Finally, we point out a flaw in Einstein's argument in the "Electrodynamical Part" of his paper and show that the Lorentz force formula and Einstein's formula for transformation of field quantities are mutually consistent. We show that for faster-than-light bodies, a simple modification of Planck's formula for mass suffices. (Except for the reference to Planck's formula, we restrict ourselves to Physics of 1905.)Comment: 55 pages, 4 figures, accepted for publication in "Foundations of Physics

Observational constraints on conformal time symmetry, missing matter and double dark energy

The current concordance model of cosmology is dominated by two mysterious ingredients: dark matter and dark energy. In this paper, we explore the possibility that, in fact, there exist two dark-energy components: the cosmological constant $\Lambda$, with equation-of-state parameter $w_\Lambda=-1$, and a `missing matter' component $X$ with $w_X=-2/3$, which we introduce here to allow the evolution of the universal scale factor as a function of conformal time to exhibit a symmetry that relates the big bang to the future conformal singularity, such as in Penrose's conformal cyclic cosmology. Using recent cosmological observations, we constrain the present-day energy density of missing matter to be $\Omega_{X,0}=-0.034 \pm 0.075$. This is consistent with the standard $\Lambda$CDM model, but constraints on the energy densities of all the components are considerably broadened by the introduction of missing matter; significant relative probability exists even for $\Omega_{X,0} \sim 0.1$, and so the presence of a missing matter component cannot be ruled out. As a result, a Bayesian model selection analysis only slightly disfavours its introduction by 1.1 log-units of evidence. Foregoing our symmetry requirement on the conformal time evolution of the universe, we extend our analysis by allowing $w_X$ to be a free parameter. For this more generic `double dark energy' model, we find $w_X = -1.01 \pm 0.16$ and $\Omega_{X,0} = -0.10 \pm 0.56$, which is again consistent with the standard $\Lambda$CDM model, although once more the posterior distributions are sufficiently broad that the existence of a second dark-energy component cannot be ruled out. The model including the second dark energy component also has an equivalent Bayesian evidence to $\Lambda$CDM, within the estimation error, and is indistinguishable according to the Jeffreys guideline.Comment: Revised version emphasising a different version of the underlying symmetry, as published in JCA