"Big Bang" or "Steady State"?
| Scientific Paper | |
|---|---|
| Title | "Big Bang" or "Steady State"? |
| Read in full | Link to paper |
| Author(s) | Mogens True Wegener |
| Keywords | Steady State Theory, Big Bang, Redshift, Special Relativity |
| Published | 2007 |
| No. of pages | 15 |
Read the full paper here
Abstract
Revised version (30.12.2008). In the present paper it is shown how it is possible to use the strict "light principle" as a point of departure for deriving three new "steady state" models of the universe which are at variance with the Robertson Walker Metric but fulfill Milne's cosmological principle.
Contents
A. Introduction
- A simple derivation of LT
- Importance of the gamma-factor
- The formal reduction of LT to GT
- From "big bang" to "steady state"
- Our basis: the strict "light principle"
- The cosmological principle of Milne
- A new model of continuous creation
- Two asymptotic approximations
- The gamma-factor in disguise
O. Conclusion
Overview
The archived file is the revised (2011) version of a paper the Danish philosopher of science Mogens True Wegener presented at the PIRT conference "Mathematics, Physics and Philosophy in the Interpretations of Relativity Theory" at Loránd Eötvös University, Budapest, in 2007. Its title poses the classic cosmological alternative — "Big Bang" versus "Steady State": are these ideas incompatible? — and answers, in effect, that they need not be, provided one abandons the Robertson–Walker metric rather than the light principle.
The strategy is to follow E. A. Milne rather than A. G. Walker. Milne's kinematic relativity built its uniformly expanding universe directly on the integral Lorentz transformations; Walker showed the model could be restated with a cosmic time and then generalised it into the Robertson–Walker metric (RWM), dς2 = dτ2 − f(τ)2dζ2, which is compatible with the Lorentz transformations only in the Milne case. When Bondi and Gold built their steady state model on the RWM with scale factor f1(τ) ≡ eτ, they noted explicitly that it was incompatible with the Lorentz transformations. Wegener's move is to observe that incompatibility of a scale factor with the integral transformations does not entail incompatibility with the differential ones, and so to ask whether a steady-state cosmology can be built from the strong differential light principle dς2 = dt2 − dr2 = invariant together with Milne's cosmological principle, discarding the RWM instead. He derives three such models, and argues they dissolve the standard Big Bang difficulties without inflation.
The argument
From the light principle to a common time
Sections 1–3 rebuild Special Relativity in a way designed to expose one particular feature. Starting from the Galilean transformations and insisting on c ≡ c′ ≡ 1, Wegener introduces a single multiplicative factor γ, shows it must act on time as well as on x, and recovers γ = 1/√(1 − v2) and the Lorentz transformations. He then reproduces the Milne–Whitrow "signal function" derivation, in which the Doppler factor s = 1 + z = √[(1 + v)/(1 − v)] = eartanh v is constant and reciprocal.
The pivot is section 3. Defining τ ≡ t − x(1 − 1/γ2)/v and substituting into the Lorentz transformations, the transformations collapse to a Galilean-looking form x′ = x − vγτ. Differentiating shows dτ = dt/γ = √(dt2 − dr2), so τ runs at the rate of the master clocks of both observers and agrees with them at τ = 0. Wegener therefore calls τ "the common time of S and S′" — "the great no!!-no of SR" — and, citing Winnie, notes that a simple additive adjustment of time-zero for each slave clock suffices to keep the whole co-moving networks of two frames in agreement permanently. He extends this to a "midway observer" M equidistant from both, and then to any collinear family. The cosmological generalisation is a conjecture: a triply infinite set of particle-observers such that every non-collinear triple has a fourth member equidistant from all three constitutes a Milne substratum, obeying Milne's cosmological principle (CP), with all proper distances e governed by one scale function f(τ). Remarkably, such a substratum is an inhomogeneous centroid that is nevertheless everywhere isotropic.
Discarding the Robertson–Walker metric
Section 4 sets out the choice. Bondi and Gold's f1(τ) = eτ, and its two asymptotic relatives f2(τ) = sinh τ and f3(τ) = cosh τ, are each incompatible with a strong light principle when embedded in the RWM. One may keep the RWM and abandon the universality of the light principle, or keep the light principle and abandon the RWM; Wegener takes the second option, where Bondi and Gold took the first. He is also explicit about the theoretical cost and benefit: neither Milne nor Bondi and Gold accepted the Einstein field equations, and on the Friedmann–Lemaître analysis both their models are empty of matter. Milne's own gravitation theory he describes as "turning Mach's principle upside down" — explaining gravitation as a kind of inertia, reduced to local deviations from global cosmic symmetry, rather than inertia as a kind of gravitation. On that view a model is its scale function, there is no global gravitational field braking the expansion, and hence no motive for filling the universe with dark anti-gravitational energy.
The privileged frame and the Tangherlini transformations
Section 5 works with hyperbolic rapidity r, writing the transformations as dt′ = dt cosh r − dr sinh r and so on, and notes that the Lorentz transformations follow from the hyperbolic addition formulae if and only if dτ′ ≡ dτ. Introducing non-standard frame times referred to a privileged frame, he obtains the differential Tangherlini transformations "as generalized by Selleri", and observes that these reduce to the Galilean form when everything is referred to the midway observer. The point is methodological: in standard relativity it is a single moving clock that is retarded relative to a network at rest, but if inertial motion is referred to a privileged frame the Tangherlini form is the appropriate one.
A model of continued creation
Sections 6–7 carry Milne's velocity-distribution analysis through with one change: in Milne's uniformly expanding model the relative velocities between fundamental observers are constant, whereas in Wegener's steady-state substratum they increase with distance. Milne's distribution f(vx,vy,vz)dvxdvydvz = Bγ4dvxdvydvz is retained, but exploiting γ = 1/√(1 − tanh2r) = cosh r and the invariant dς = dt/cosh r = dr/sinh r gives a new spatial distribution. The resulting "continued creation" (CC) model has proper distance e ≡ 2 tanh(r/2), so that light-time distance r is simply additive while proper distance adds hyperbolically. The world-map — the universe as simultaneous co-existence — is a hyperboloid of infinite 3-space, dς2 = dt2 − ds2; the world-view — the universe as it appears — is a pseudo-sphere of finite 3-space made of shells of increasing age. Wegener leans on Milne's distinction between world-map and world-view to make his central claim: a steady-state world looks the same as it is (world-view = world-map), whereas an evolving Big Bang world does not, and as world-map his SS model "has exactly the same structure as the BB-model of Milne". The cosmic redshift is the ordinary Doppler shift corrected by a hyperbolic factor, 1 + z = er = 1/{1 − ½e}2, and equation (21) converts the distribution into a number–redshift relation. The model satisfies Milne's dimensional postulate that no dimensional constant of nature may enter the definition of the substratum.
Section 8 gives two asymptotic approximations: model M2, a "Fiery Blow" built on ρ ≡ sinh r/sinh t, and model M3, a "Gentle Flow" built on ρ ≡ sinh r/cosh t, each with its own corrected redshift law. Section 9 adds an energetic layer: the substratum is a "compass of inertia" (Weyl, Gödel) fixing rest and motion; kinetic energy relative to one fundamental observer appears as potential energy relative to another; a Lagrangian L = T − V = m(γv + γφ − 2) is proposed, and with the principle of least action Wegener claims to recover the perihelion advance of Mercury. Following Prokhovnik on rod contraction in an aether, an angle-dependent light speed is assumed, from which the radar-echo delay and, by a Fermat principle, the deflection of light near a massive body are said to follow.
Conclusion
Two definite predictions are stated. In light-time distance the Hubble function is non-linear, v/r → tanh r/r, equal to tanh 1 at r = 1; in proper measure de/e dς → unity. And the velocity distribution tends asymptotically to a steady state. All three models are non-Friedmannian, obey Milne's no-horizon principle, and so escape the flatness and horizon problems — "There is no reason to invoke the idea of inflation." Because the world-view is confined within a pseudo-sphere of radius e0 = 2, a constant universal mass–energy is definable; a receding particle reaches that border in finite time ς ≈ ln(2/ρ) and thereafter "leaves the universe, it no longer exists". Energy lost at the periphery is balanced by a steady gain at the centre, "from which a steady aethereal stream of matter and light is pouring out towards all possible directions". Wegener closes with Nicholas of Cusa's world machine whose "center is everywhere and circumference nowhere", and claims his models as a synthesis of Parmenides and Herakleitos.
Assessment
The paper's genuine originality lies in its diagnosis, which is sharper than the usual dissident complaint. Wegener identifies exactly where the standard cosmological framework parts company with special relativity — the Robertson–Walker metric, not the light principle — and observes correctly that Bondi and Gold themselves conceded the incompatibility. His distinction between the integral and differential Lorentz transformations is a real one, and the demonstration in section 3 that a common time τ exists for any pair of collinearly moving frames, with clock networks brought into permanent agreement by a mere adjustment of time-zeros, is sound and instructive: it exhibits how much of relativistic Simultaneity is conventional. Reviving Milne's world-map / world-view distinction is also valuable, since much confusion in popular cosmology comes from conflating the two. And the scholarship is serious — Milne, Whitrow, Walker, Winnie, Lucas, Prokhovnik, Selleri and Tangherlini are used accurately, not name-dropped.
The difficulties are correspondingly large. The most serious is that the models are, by the paper's own admission, empty: on the Friedmann–Lemaître analysis both Milne's model and Bondi–Gold's are devoid of matter, and Wegener's answer is not to supply a matter content but to reject the field equations. What remains is a kinematic substratum of test particles with a prescribed velocity distribution — which cannot address why the universe has the density it does, nor produce a theory of structure formation, nor say anything about nucleosynthesis. This is the point at which the classical steady-state programme foundered, and nothing here re-opens it. The energy section makes matters worse rather than better: the Lagrangian m(γv + γφ − 2) is written down by analogy, the identification of "velocity of escape with gravitational potential" is asserted as "the classical equivalence", and the claims to recover Mercury's perihelion advance, the Shapiro delay and light deflection are stated in three lines each with no numbers computed. Given that these are the tests general relativity passes to parts in 105 and better, asserting agreement without a single figure is not an argument.
Two of the paper's key steps are conjectures wearing the clothes of results. The substratum construction — that a set in which every non-collinear triple has an equidistant fourth member realises Milne's cosmological principle — is explicitly labelled "my conjecture", yet everything downstream depends on it. And the claim that a model's world-map being structurally identical to Milne's Big Bang model makes the two views compatible trades on an ambiguity: identical world-maps with different world-views is precisely the situation in which the models are observationally distinguishable, so the "synthesis" is verbal rather than physical.
Finally, the predictions the paper does make can be checked, and they do not fare well. The non-linear Hubble function v/r → tanh r/r is a specific curve, and modern distance-ladder plus supernova data constrain the redshift–distance relation tightly enough that a fixed hyperbolic form with no free density parameters is difficult to accommodate. More decisively, a strictly stationary world-view predicts no cosmic evolution, yet the (1 + z) stretching of Type Ia supernova light curves, the (1 + z) scaling of the Cosmic Microwave Background temperature measured from molecular excitation in absorbers, the strong evolution of radio-source and quasar counts with redshift, and the primordial deuterium and helium abundances all record a universe that was denser, hotter and different in the past. The paper's number–redshift relation (21) is the natural place to confront the source counts that first told against Bondi–Gold, and it is not confronted. The claim that particles crossing e0 = 2 "no longer exist", with energy replenished at the centre, is also a substantial physical assertion — an aetherial stream sourced at the observer's own position — presented without any mechanism, and it sits awkwardly with the isotropy the model otherwise insists on. As a philosophical reconstruction of relativistic kinematics on a preferred-frame basis the essay is careful and worth reading; as a cosmology it remains, as Wegener effectively concedes, a family of scale functions in search of a matter content.