The Cosmological Principle: Theoretical and Empirical Foundations
| Scientific Paper | |
|---|---|
| Title | The Cosmological Principle: Theoretical and Empirical Foundations |
| Read in full | Link to paper |
| Author(s) | Toivo Jaakkola |
| Keywords | Cosmological, Principle |
| Published | 1989 |
| Journal | Apeiron |
| Volume | 4 |
| No. of pages | 36 |
| Pages | 9-31 |
Read the full paper here
Abstract
The idea of the (perfect) cosmological principle (CP), viz. that the Universe presents the same aspect from any place at any time, is traced to the ancient Greek philosophers, who also suggested how such a cosmic order might work. The antithesis of this view, i.e. the Aristotelian-Ptolemaic world-picture, was to become the hallmark of the Dark Ages. The Copernican revolution constitutes the first step by science in a modern direction, and the advance of science is thus seen as a succession of world pictures, all entred on local systems, in a hierarchical progression. We demonstrate that the prevailing picture of the Universe as an evolving system is still trapped in a local mode of thinking: the Copernican revolution is unfinished.
Overview
Toivo Jaakkola of the University of Helsinki opens the fourth issue of Apeiron (February 1989) with a wide-ranging review arguing that cosmology has never properly adopted its own founding principle. His subject is the perfect cosmological principle — that the Universe "presents the same aspect from any place at any time" — which he takes to be the only genuinely cosmological standpoint, the prefix "perfect" having in his view "only historical value". The restricted principle of the standard model, which imposes uniformity in space but permits evolution in time, is for Jaakkola a half-measure: it treats the Universe as one more evolving system among systems, and so remains "trapped in a local mode of thinking". His central historical claim is that the Copernican revolution — the successive dethronement of Earth, Sun and Galaxy from the centre — is unfinished, because the modern picture still places us at a privileged moment even if not at a privileged place.
Two arguments carry the paper. The first, philosophical, is that the Universe is not a system at all: "Physical systems are not homogeneous: they contain central bodies, other different constituents, density gradients, etc. The universe is homogeneous, structureless. It is more than the sum of its contents." Inferring that the whole evolves because its parts do is therefore a category error, and Jaakkola offers a memorable analogy: "while individuals age, the mean age of people living on earth does not increase one year every year". The second argument is empirical and is the heart of the paper: whether the observed portion of the Universe — Jaakkola's metagalaxy — actually satisfies the principle is a question for observation, and he reviews the evidence, concluding that on both the expansion tests and the tests for evolution of discrete objects "the Universe appears as non-evolving". If so, the metagalaxy is a fair sample of the infinite whole, and cosmology becomes possible without ever-deeper surveys: "it would be vain to cross the sea in order to catch fish." A final section sketches his own "quasistatic" model, in which Redshift arises from a coupling of gravitation and electromagnetism rather than from expansion.
The argument
History: an unfinished revolution
Jaakkola traces the principle to the Greek materialists as transmitted by Lucretius: "The universe then is not limited along any of its paths... Nor does it matter in which of its quarters you stand"; and "unless matter had been everlasting, before this all things would have returned utterly to nothing". Against it he sets the Aristotelian–Ptolemaic scheme, "rooted in theology and anthropocentrism", which by the end of the fifteenth century required more than eighty crystal spheres and still failed to save appearances — and which he compares directly to the modern standard model, which in his view "demands an increasing number of 'epicycles' to avoid breakdown".
The pivotal moment he identifies is Hubble's 1930s galaxy counts, whose slope of 0.6 is what a distribution uniform in depth requires, prompting Hubble's remark that "for the first time, the region now observable with existing telescopes may possibly be a fair sample of the universe as a whole". Jaakkola holds that science "missed this opportunity", taking instead the route of Lemaître, Eddington, Jeans and Gamow. Three errors are alleged: the hasty reading of redshift as Doppler, "despite the fact that the latter is a symmetrical effect while the former is asymmetrical"; the identification of expansion with the second law of thermodynamics; and the habit of supposing "that everything that is possible in mathematical models must also be possible in physical reality". He stresses that the observers closest to the data — Edwin Hubble himself, Humason, Mayall, Zwicky — were markedly less convinced of expansion than the theorists, Hubble concluding in 1937 that an expanding model "can be obtained only as a forced solution".
The Bondi–Gold–Hoyle steady state is credited with keeping the full principle alive, and its seven advantages (as Bondi listed them) are reproduced; but Jaakkola rejects continuous creation, which "violates the conservation principle and is unacceptable from the materialist point of view", and holds that the theory cannot survive modern tests of expansion. He notes the convergence of many independent non-expanding proposals — Pecker's redshifting boson medium, the Pecker–Vigier material ether, Broberg's elementary quanta, Kipper's photon-energy transfer to the vacuum, Segal's properties of time, Roscoe's Machian wave gravitation, his own electro-gravitational coupling — and finds it "especially noteworthy... that the same result emerges from so many directions".
Philosophy: the Universe is not a system
The philosophical section argues that "cosmological" means the opposite of "local", so no study of a single system is cosmology proper. Spinoza's single substance, "eternal and infinite, cause and effect at the same time", is equated with the Universe, and its lack of diversity is taken to exclude evolution; Hegel's denial of the evolution of nature as a whole is defended as "not the hallmark of an idealist"; Engels is quoted at length on the indestructibility of matter "not only in the quantitative but also in the qualitative sense". A separate argument from eternity is offered: if the Universe were infinite in past time and evolving one way, cosmic parameters would already have reached their limiting values — "there would already have been enough time for the 'heat death of the universe'". Since the Universe is not dead, it does not evolve one way.
Jaakkola is careful, however, to keep the philosophical and empirical questions apart: "no demands can be made upon nature — much less the cosmos as a whole. Whether the CP is valid in the metagalaxy is an empirical question, not a philosophical question."
Observations
On the spatial aspect he finds structural hierarchy ending "at the level of second-order clusters of galaxies", with the isotropy of the 3 K and X-ray backgrounds (fluctuations below 0.1% and 1.3% respectively) indicating that a cosmological distribution of matter has been reached. On the temporal aspect he cites four groups of tests. Redshift is stronger within systems than between them, with strength scaling as h ∝ ρ½ — which he says contradicts Doppler and points to an interaction mechanism. Classical global and local tests he reads as internally inconsistent within the standard model: "the Hubble diagrams always give a closed model, while local tests point to an open one; optical (θ,z) tests imply a positive cosmological constant, while the radio (θ,z) diagrams contradict the whole range of relativistic predictions." The Hubble–Tolman surface-brightness test, applied to galaxies, clusters, QSO host galaxies and extended radio sources, he reports as supporting the non-expanding model in all four cases. Finally he reviews the claimed evolutionary effects — quasar space density, radio and X-ray source counts, the Butcher–Oemler colour effect, the 4000 Å break amplitude in ellipticals — and attributes each to a selection effect, a luminosity-class effect or an underestimated K-term: "even the 'compelling evidence' of cosmic evolution is a false scent."
The quasistatic model
Jaakkola derives redshift a priori from the principle: if photon energy did not decrease in transit, radiation energy would accumulate without limit, violating the steady state; and if z depended on rest wavelength, the spectrum of universal radiation would change continuously. Redshift is an absorption effect cancelling emission, so its positive sign follows from the theory, whereas Doppler "is inherently symmetrical" and the standard model must "adopt an additional ad hoc hypothesis, namely the Big Bang". The distance relation is r = ln(1 + z)c/H, giving
- m = 5log(1 + z) + 2.5log(1 + z) + K(z) + C,
whose non-linearities nearly cancel to reproduce Hubble's linear law. Angular diameter is θ = Dc/[H ln(1 + z)], and — the sharpest prediction in the paper — surface brightness falls as SB(z) = SB(0)/(1 + z), against the standard (1 + z)−4. Jaakkola rightly calls "the pronounced difference" between these a powerful test. He also states the general test condition p(z) = constant for any absolute parameter p, which "points to dozens of different possible tests".
The mechanism proposed is electro-gravitational coupling, following Zwicky, in which both photon energy and gravitation are weakened by the same exponential factor exp(−Hr/c). This gives the Machian interaction of cosmic masses a finite acceleration ac = 4πGρc/H ≈ 6.4 × 10−9 cm s−2, resolving the gravity paradox; and the condition as ≥ ac for individual systems is offered as a basic law explaining why supergalaxies and their chains are the largest structures and why the universe is stable. The microwave background is the re-emission of the absorbed redshift energy E0z/(1 + z), with the tired-light relation h = cAT3 bounding the temperature to 1 K ≤ T ≤ 5 K. Olbers' paradox is resolved by the remainder of the redshift energy going into particle production at rate Cm = L/c2 ≈ 3 × 10−53 g s−1 cm−3, about one galaxy per Mpc3 per 1016 years.
The closing sections set out the equilibrium processes that must hold each cosmic parameter fixed — density, angular momentum, photon–baryon ratio, element abundances, spiral structure and stellar populations — with galactic nuclei ("smelting furnaces") and the Machian pull of distant masses as the two opposed agents. Jaakkola follows Ambartsumian and Halton Arp in giving ejection from galactic nuclei a central role in galaxy formation. The consequences for physics are drawn without hedging: G becomes "a physical variable which is constant only over the homogeneous distribution on the cosmological scale"; if electro-gravitational coupling is confirmed, "the special and general theories of relativity become untenable"; and "there is no cosmic time. In a sense, when the arrow of time approaches infinity, it ceases its flight."
Assessment
The paper's real strength is that it does not stop at criticism. Jaakkola states a quantitative alternative with, as he says, "no free parameters (arising from evolution, expansion rate or geometry)", and he identifies the observation that would decide between it and the standard model: the scaling of surface brightness with redshift, (1 + z)−1 against (1 + z)−4. That is a proper falsifiable claim, and his insistence that a theory with fewer adjustable knobs deserves a hearing is methodologically sound. The historical section is well informed and its central observation is correct and underappreciated: Hubble himself remained sceptical of the expansion reading of his own relation to the end, and the sociological point that the restricted principle was adopted while the temporal half was quietly dropped is fairly made. The demand that we not privilege our own epoch is a genuine extension of the Copernican move, and the analogy of individual ageing versus mean population age is a sharp piece of reasoning against sloppy inference from parts to whole.
The difficulties are correspondingly serious, and several of the paper's key claims have since been settled against it by measurements that did not exist in 1989. The surface-brightness test Jaakkola nominated as decisive has been performed: the Tolman dimming of galaxies is observed to follow (1 + z)−4 once evolution in the stellar populations is modelled, not (1 + z)−1. More directly, the time dilation of Type Ia supernova light curves scales as (1 + z), a result confirmed both in photometric light-curve widths and in the ageing rate of supernova spectra — an effect that follows from expansion and that no tired-light mechanism reproduces, since a photon-energy-loss process affects wavelength but not the arrival-time spacing of events at the source. The blackbody spectrum of the microwave background, measured by COBE/FIRAS to a fractional deviation below 10−4, is also fatal to the re-emission account offered here: Jaakkola in fact welcomes "a slight deviation of the observed spectrum from the blackbody curve" as evidence for redshift distortion of the re-emission spectrum, and that deviation does not exist. His temperature bound 1 K ≤ T ≤ 5 K is honest but so loose as to have little discriminating power.
Second, much of the empirical case rests on the author's own earlier work. Of the four groups of expansion tests, three are supported by citations to Jaakkola 1977, 1983, 1986 and 1988; each of the five claimed evolutionary effects is dismissed by reference to a Jaakkola paper identifying a selection effect. This may be right in every instance, but the reader of this review has no independent purchase on it, and the pattern — every contrary result explained away by an artefact, every supporting result taken at face value — is the shape an argument takes when the conclusion is not genuinely at risk. The paper announces that the principle "seems to be reasonably well established empirically", which is stronger than the evidence marshalled here supports.
Third, the philosophical sections do work they cannot do. Spinoza, Hegel and Engels are cited as authorities on whether the physical Universe evolves, and the eternity argument — that infinite past time would already have produced heat death — assumes both that the relevant thermodynamic reasoning applies to an infinite self-gravitating system and that the present state is not itself an intermediate one. Jaakkola's own methodological rule, that "no demands can be made upon nature", tells against these passages. The claim that the Universe is "homogeneous, structureless" is likewise asserted where it should be argued: modern redshift surveys find structure — filaments, walls, voids — on scales well beyond the second-order clusters at which he places the end of hierarchy, and although the transition to homogeneity is now measured at roughly 100 Mpc, the intervening structure is real and its statistics are the primary evidence for a specific growth history.
Finally, the electro-gravitational coupling that carries the whole model is a hypothesis, not a theory. The exponential factor exp(−Hr/c) is asserted rather than derived, and no field equations, no coupling constant and no independent laboratory or solar-system consequence are given beyond the appeal to anomalous solar redshift and light deflection within 3–4 solar radii. A gravitational interaction attenuated over cosmic distances would have consequences for cluster dynamics and for the timing of binary pulsars that are not addressed. Jaakkola's willingness to accept that "the special and general theories of relativity become untenable" is at least consistent, but general relativity's precision tests — the Hulse–Taylor binary's orbital decay, matched to the quadrupole prediction at better than one part in a thousand — set a bar the sketch here does not approach.
Read as what it announces itself to be — a review essay setting out a research programme and the philosophical case for it — the paper is coherent, unusually literate and admirably specific about what would refute it. That specificity is its best quality, and it is also the reason its central prediction can now be judged.