The Idea of a Cosmic Time
| Scientific Paper | |
|---|---|
| Title | The Idea of a Cosmic Time |
| Read in full | Link to paper |
| Author(s) | Mogens True Wegener |
| Keywords | cosmic time, simultaneity, kinematic relativity, substratum, Milne, cosmological principle |
| Published | 2004 |
| Journal | Foundations of Physics |
| Volume | 34 |
| No. of pages | 16 |
| Pages | 1777-1799 |
Read the full paper here
Abstract
Revised version. This paper was written in honour of Franco Selleri, faithful defender of reason in physics, who committed his efforts to "the liberation of time from the enslavement to space". - Pointing to the cleft between the idea of a temporal evolution, central to modern biology, and the idea of the timelessness of reality derived from the relativization of simultaneity and followed by the fusion of space and time into space-time, both fundamental to modern physics, the paper demonstrates that the standard definition of time at a distance is beset with ambiguities that might be solved by making a fresh start which takes its point of departure in the idea of a Cosmic Time, as proposed by the British Tradition of relativistic cosmology.
Overview
The version archived here is Wegener's own 2011 revision of the paper published in Foundations of Physics 34 (2004), and it carries the subtitle "Debunking the Einsteinian Revolution". It is dedicated to Franco Selleri. The paper is a work of philosophy of physics rather than of physics proper: it contains almost no calculation, but it makes a sustained argument that the standard definition of distant simultaneity is ambiguous, that the ambiguity has been mistaken for a discovery about nature, and that a genuine universal time is both definable and already implicit in modern cosmology.
Wegener opens on what he takes to be an intolerable split. Biology, history and every other narrative science presuppose the passage of time and would "lack all scientific legitimacy" if that passage were meaningless; physics, following Einstein, increasingly denies it — the extreme case being J. Barbour's The End of Time, which Wegener calls "the final apotheosis of Einstein's programme: to reduce everything in physics to 'spacelike concepts'". Worse, the split runs within physics, since big bang cosmology dates the universe at some fourteen billion years while relativity is invoked to argue that time is illusion. His response is not to reject relativity's mathematics but to relocate its interpretation inside a cosmological setting, drawing on what he calls the British Tradition of relativistic cosmology — E. A. Milne, A. G. Walker and G. J. Whitrow — and behind them Poincaré.
The argument
Einstein's answer, and what it leaves out
Einstein answered "what is time?" by pointing to clock readings, which Wegener grants is "just as ingenious as it is natural and simple". But it says nothing about whether the observed clock shows the right time, and still less about the prior question of how we distinguish a working clock from a stopped one — "since a standing clock is right once or twice a day". From Einstein's own texts Wegener extracts the distinction between local time (observer near the event) and time at a distance (observer far from it, corrected by the finite speed of light).
He then presses a point about Einstein's own premises. In the 1920 exposition, before defining simultaneity but after the train-and-embankment thought experiment, Einstein writes: "It (is) assumed that all these clocks go at the same rate if they are of identical construction." Wegener reads this as a frank admission of time's flow and as the source of a paradox: a theory explicitly premised on identically constructed clocks keeping the same rate concludes that clocks in relative motion do not count the same intervals after all. He is careful to concede that the theory is mathematically consistent and supported "not merely by a lot of experiments, but even by the most diverse kinds of experiment", entering two Popperian reservations instead — that consistency is necessary but not sufficient for truth, and that no amount of confirmation excludes the possibility that other premises yield more plausible consequences.
The ambiguity in the definition of simultaneity
The technical core of the paper concerns Einstein's radar definition: the epoch of reflection is the arithmetic mean of the epochs of emission and reception. Einstein assumed synchronism to be both reciprocal and transitive, and later admitted in a footnote that transitivity "is a physical hypothesis about the law of light propagation; it must certainly be fulfilled if we are to maintain the law of the constancy of the velocity of light in vacuo". Wegener turns this admission against the theory. Under special relativity transitivity of simultaneity holds within a single inertial frame but not between frames; by Einstein's own footnote, then, light-speed invariance would hold only within a frame, so that data referring to more than one frame appear incomparable. He notes that Einstein never confronted whether the same photon retains the same speed relative to two different frames at once, "quite a feat", or only relative to the frame in which it is observed.
His diagnosis is that Einstein used two different synchronizations without saying so. Wegener distinguishes proper time, read off an observer's master clock, from frame time, shown by the slave clocks fixed to that observer's comoving frame — "a frame is a cloud of clocks associated with an observer". Simultaneity within frames is defined explicitly by the arithmetic mean of the emission and reception epochs; simultaneity between frames, he argues, is defined implicitly by their geometric mean, in order to calibrate the master clocks of different observers. Master clocks and slave clocks are therefore synchronized by different methods, and the resulting "retardation" is an artefact of comparing the two. Stated correctly, he says, the master clock of one observer always appears retarded relative to the slave clocks of another's comoving frame — but two properly synchronized master clocks of fundamental observers in collinear inertial motion never disagree, because "if the clock of one observer deviates from that of another, at least one of them is not fundamental". He supports this with the radar method of Milne and Whitrow, the analyses of Stephenson and Kilmister, Törnebohm and Prokhovnik, and Bondi's k-calculus, concluding: "the claim that moving clocks do not agree is based on a convention, nothing else!"
He is explicit that this argument covers only inertial clocks. The cosmic-ray meson lifetime evidence, he says, shows nothing in isolation about internal clocks being retarded — it could equally be read as permitting superluminal velocities — and the real move is to separate the one-way light speed, which may vary, from the two-way radar speed, which is constant. He reports his own attempt at a unitary definition of distant time reducible in some cases to the arithmetic and in others to the geometric mean, and then concedes its weakness: like special relativity, "the theory may be unable to explain the experiment of Sagnac", so one should perhaps rather return to the theories of Poincaré and Lorentz.
The British Tradition
Milne's kinematic relativity was built as an explicit alternative to Einstein's theories, deducing a mathematical cosmology from a few definitions and principles and generalizing the radar technique into a full cosmology. Walker freed it from Milne's particular uniform-dispersion model, so that the Robertson–Walker metric became a technique applicable to any world model subject to cosmic isotropy. Whitrow contributed to the radar method and later wrote The Natural Philosophy of Time.
Milne, a nominalist, denied that reference frames are real things — they are "abstract constructions of the human intellect" — and so asked how to construct them. A clock, for him, is a one-one relation between the events constituting an observer and an increasing series of numbers, so that having a clock means being "able to count his own experiences". Two clocks are congruent if their signal functions are reciprocal; infinitely many are congruent if their signal functions are commutative, which implies that although mutual distances change, relative angles are preserved. Congruence partitions observers into equivalence classes, and Milne held that one privileged class — the substratum, whose members are the fundamental observers — fixes the structure of the universe and constitutes, accidentally, a universal frame for rest and motion. All directions are equivalent: this is the principle of cosmic isotropy, which Wegener notes was first coined by Milne although often ascribed to Einstein.
The key result is that a universal time is definable within any world model satisfying the isotropy principle — whether one comes at it through Milne's cosmological principle read with Whitrow's signal-function argument, or through general relativity read through the Robertson–Walker metric, "whose basic parameter is the very same cosmic time". Wegener treats this as a criterion: models for which cosmic time is undefinable, such as Gödel's rotating universe or Smolin's multiverse, may be excluded.
One universe only
The paper's second half is frankly metaphysical. Wegener invokes Kant's first antinomy — that reason represents the universe as both finite and infinite in space and time — and argues that Milne's model dissolves it, because the same model admits two mathematical representations: a t-scale on which fundamental observers recede with constant velocities from a finite past, and a τ-scale, logarithmically related, on which they are at rest while their atoms shrink and the past extends infinitely. "A finite past starting at t = 0 does not exclude an infinite past"; on t-time the substratum is a sphere of finite radius R = ct with infinite contents, on τ-time the stationary contents of infinite hyperbolic space. He cites Eddington's remark that "the theory of the expanding universe is equivalent to the theory of the shrinking atom", and Walker's T-scale as the public proper time of the master clocks.
From Leibniz and Plato he takes the principle of the unity of the world — there is one world only — which he uses against the many-worlds reading of quantum mechanics ("the collapse of modal distinctions") and against inflationary bubbles. The principle entails a single unique world time, and equivalently Milne's no-horizon postulate: since all fundamental particles share the substratum's time, the universe cannot be divided into horizon-bounded enclaves, and "world map" and "world view" are formally identical, so the observable universe coincides in principle with the whole of it. Nicolaus Cusanus' sphere "having its centre everywhere and its periphery nowhere" is invoked, as is tense logic — from his own work with Øhrstrøm — as the proper formal instrument for time's passage.
On the cosmological evidence Wegener is deliberately non-committal. Hubble's redshift he prefers to describe not as expansion of the universe but as "a simultaneous and proportional expansion of all distances between galaxies". The 2.7 K background radiation is usually taken as proof of a big bang, but he notes alternatives — re-radiation of starlight by interstellar graphite grains, or emission from a zero-point field, citing Narlikar — and says only that both observations show universal space to have no privileged directions, which is what makes the Robertson–Walker metric appropriate.
Suggestions
In the closing section Wegener accepts that the physically relevant content of special relativity is comprised in the factor γ = 1/√(1 − v2/c2), while denying that it can be applied to the retardation of one fundamental master clock relative to another. He notes that stellar aberration and the Sagnac experiment suggest light behaves as if transmitted by a medium — as Selleri argued — but adds that such an aether "need not be stationary, since it may be expanding", and is best interpreted as a substratum of fundamental particles. Light exchanged between two accidental particles propagates as if exchanged between the fundamental particles they momentarily coincide with, a "transmission by substitute" that presupposes a common time for the two substitutes and a quantum collapse localizing emission and reception. Using Whitrow's suggested analogy between the γ-factor and the Robertson–Walker metric, with v ≡ dr/dt ≡ R(t)dσ/dt, he writes dT2 = dt2 − R2(t)dσ2, an invariant element of "timespace" (Mercier's supertime), and, by setting c−1(τ) ≡ dt/dτ ≡ R(t), converts the expansion of the substratum into a secular shrinking of atoms, equivalently a secular reduction of the differential light speed — "being instantaneous and ubiquitous, it is imperceptible". For fundamental particles dσ = 0 and dt = dT, so their clocks agree; for accidental particles dσ ≠ 0, and this deviation from true cosmic time "might indicate the emergence of spontaneous accelerations, i.e. of 'forces'". The paper ends with Milne's reduction of gravitation to inertia by an inverted Boltzmann equation, contrasted with Einstein's lifelong attempt to reduce inertia to gravitation — "to cram forces into the package of curved space-time is a far cry from explaining them" — and with a jab about the cosmological constant: Einstein called it his biggest blunder, and "one may well wonder whether this was really the worst of his blunders".
Assessment
The paper's best work is exegetical, and it is genuinely good. The observation that Einstein's own footnote makes transitivity of synchronism "a physical hypothesis about the law of light propagation" is correctly sourced and correctly pressed, and the distinction between an observer's master clock and the cloud of slave clocks defining his frame is a real clarification that much popular exposition blurs. Wegener is right that a great deal of loose talk about "moving clocks running slow" conflates a comparison of one clock with many clocks against a comparison of one clock with one clock, and right that the conventionality of distant simultaneity within a single frame is a well-established result rather than a heterodox claim — Poincaré said as much before Einstein. He is also scrupulous where it costs him: he concedes the mathematical consistency and broad experimental support of special relativity, he concedes that the meson evidence can be read either way only "when considered in isolation", and he concedes that his own alternative theory of distant time may fail on Sagnac and that one might therefore have to fall back on Lorentz and Poincaré. Admitting that your own construction may not survive the decisive experiment is rare in this literature. The historical recovery of Milne, Walker and Whitrow is valuable in itself, and the central positive point — that cosmic isotropy makes a preferred cosmic time definable, and that the Robertson–Walker metric already contains it — is simply correct and uncontroversial among cosmologists.
The difficulties lie in what is made of that correct point. That a preferred foliation exists in an isotropic cosmology does not make it dynamically preferred: the field equations remain generally covariant, and the cosmic rest frame is picked out by the matter distribution, not by the geometry. Wegener slides from "definable" to "true time" without an argument that closes the gap, and the phrase "why not regard it as 'the true time'?" is doing the work a derivation should do. Similarly, the claim that Einstein tacitly used a geometric mean to synchronize master clocks between frames is the paper's most important technical assertion and it is never demonstrated — no transformation is written down, no passage of Einstein is cited in which such a synchronization occurs, and the reader is left with an attribution rather than a proof.
The treatment of time dilation is where the argument runs into measurement. Wegener restricts his claim to inertial, collinearly moving master clocks, which insulates it from the twin-paradox cases; but the effects he must then explain away are not confined to conventions of synchronization. Muon lifetimes are one thing, and he is right that the atmospheric case alone underdetermines the interpretation. The CERN muon storage-ring measurements, in which the dilation factor is read from a single closed path returning to its starting point, involve no distant synchronization at all — and Wegener's response, that "the Cern evidence has no bearing whatsoever on the relationship between fundamental observers", is true but beside the point, since the evidence bears on whether γ describes a real change of rate. The same applies to the transverse Doppler shift measured in ion-storage-ring spectroscopy, and to the (1+z) stretching of Type Ia supernova light curves, which is a direct observation of clock rates at cosmological distances. None of these is discussed.
The metaphysical sections, though lively, are argumentatively the weakest. Kant's antinomy is "dissolved" by exhibiting two coordinate descriptions of one model, which shows only that "finite" and "infinite" here are properties of a chart rather than of the world — a point about representation, not a refutation of Kant. The exclusion of Gödel's rotating universe and of multiverse models because cosmic time is undefinable in them is a stipulation dressed as a criterion: undefinability of a global time is a mathematical fact about those models, not evidence against them. And the closing suggestion that gravitation is time, and that forces emerge from accidental particles' deviation from cosmic time, is offered as an aphorism with no dynamics attached — nothing in the paper allows one to compute a force, recover the inverse square law, or reproduce a single gravitational measurement.
Read as what it announces itself to be — a philosophical case that the standard definition of distant time is ambiguous, and that cosmology already supplies a better starting point — the paper is careful, well sourced and worth engaging. Read as the "debunking" its subtitle promises, it does not deliver, because it never confronts the class of measurements that do not depend on the convention it identifies.