The Redshift and the Zero Point Energy

Scientific Paper
Title	The Redshift and the Zero Point Energy
Read in full	Link to paper
Author(s)	Barry John Setterfield
Keywords	Redshift, Redshift quantization, Zero Point Energy
Published	2003
Journal	Journal of Theoretics
No. of pages	23

Read the full paper here

Abstract

The history of the redshift is traced and a variety of problems listed in addition to two major anomalies. One of these anomalies is the quantized redshift, which was first noted by Tifft in 1976 and has been confirmed a number of times, most recently by Bell in 2003. The second anomaly is the breakdown in the redshift/distance relationship, evidenced by the observations of distant Type Ia supernovae, that has revived interest in the existence of the cosmological constant. These problems and anomalies admit a resolution if the energy density of the electromagnetic fields making up the vacuum Zero Point Energy (ZPE) is increasing with time. This approach predicts that light emitted from distant galaxies should have a basic redshift quantization of 2.671 km/s, which is in good agreement with Tifft's basic quantum of 2.667 km/s. In addition, the standard redshift/distance relationship is shown to derive from known physical processes that produced the ZPE rather than the expansion of space-time or the motion of galaxies. The equations governing these processes readily allow an alternate explanation for the deviation from the standard formula at high redshifts without recourse to the action of a cosmological constant or so-called 'dark energy'.

Overview

This 2003 paper by Barry John Setterfield and Daniel Dzimano, written for the Journal of Theoretics, argues that the cosmological redshift is not a signature of recession or of expanding space at all, but a record of a changing property of the vacuum — a rising Zero Point Energy (ZPE). The authors begin from the observation that z = Δλ/λ is a dimensionless number, and that its conversion into a velocity by multiplication with c was Hubble's interpretive choice rather than a measurement. They quote Malcolm Longair — "It is a great pity that Hubble multiplied z by c. I hope we will eventually get rid of the c" — and note that Misner, Thorne and Wheeler reject both Doppler and gravitational origins for quasar redshifts, leaving only a "cosmological redshift" by elimination.

Against that background the paper presses two observational anomalies: the quantization of galaxy redshifts reported by Tifft and confirmed by others, and the breakdown of the redshift/distance relation revealed by distant Type Ia supernova photometry. Both, the authors claim, are fatal to expansion interpretations and both fall out naturally if atomic emitters themselves shift with epoch, in step with the energy density of the vacuum that sustains their electron orbits. The proposal is therefore an intrinsic redshift model in the tradition of John Gribbin's suggestion, embedded in a static cosmos and grounded in stochastic electrodynamics rather than in general relativity.

The argument

From dimensionless ratio to recession velocity

The historical section traces Slipher and Pease's forty-two galaxy redshifts, Shapley's 1919 note that nearly all are positive, and Hubble's use of Cepheid variables to obtain distances, giving r = z/h. Hubble's later step zc = v produced r = cz/H_o, and by the mid-1960s the departure from linearity beyond z ≈ 0.4 required the relativistic Doppler form

(1 + z) = [1 + (v/c)] / √[1 − (v²/c²)]

The Friedmann–Lemaitre alternative replaces this with (1 + z) = R₂/R₁, the ratio of the space-time expansion factor at reception and emission. Setterfield and Dzimano make the point that since both formulae describe the same data, the two right-hand sides must be numerically equal — so the expansion factor "must be behaving in a way that mimics the relativistic Doppler formula." Whatever produces the redshift, the relativistic Doppler expression is a good approximation to it, and reproducing that expression is the target the paper sets itself.

They add two objections to expansion. First, following W. Q. Sumner's 1994 analysis in the Astrophysical Journal, cosmological expansion acting on the atom would produce an observable blue-shift, so a redshift requires that galaxies, stars and atoms be exempted from the expansion — a proviso they call a "vital necessity" rather than a derivation. Second, they quote Robert Gentry's remark that the expansion factor R has never been verified experimentally and that no method has been proposed to measure it.

The quantized redshift

The first anomaly is Tifft's finding, from 1976 onward, that redshift differences between galaxies go in steps rather than varying smoothly, with bands running through the Coma cluster and jumps appearing within individual galaxies. The paper tracks the confirmations: Tifft and Cocke's 1984 reanalysis of the Fisher–Tully catalogue after subtracting the Solar System's own motion, which produced quantization globally across the sky; Sulentic and Arp's 1985 radio measurements of over 260 galaxies, in which the same periodicity appeared unsought with measurement error one-ninth the quantization; and Guthrie and Napier at Edinburgh, who set out to disprove Tifft and instead found 37.5 km/s in 106 spirals, 37.2 km/s in 89 more, and 37.5 km/s again in two further sets, with a Fourier spike at one-in-a-million significance across all 399 data points. Morley Bell's 2003 abstracts on 55 spirals and 36 Type Ia supernova galaxies are cited as the most recent confirmation.

The authors' reading is blunt: expanding space cannot expand in jumps, and galaxies are unlikely to move in fixed velocity steps — least of all when the steps run through a single galaxy. They add a corroborating detail from the 1996 Tucson conference: in the inner regions of the Virgo cluster, "deeper in the potential well, [galaxies] were moving fast enough to wash out the periodicity." Genuine motion smears quantization, so real peculiar velocities must be a secondary effect on top of a primary, non-kinematic redshift.

The supernova anomaly

The second anomaly is the Type Ia data. Perlmutter's 1998 supernovae at z ≈ 0.83–1.2 were about 20% fainter than predicted, 0.2 magnitudes corresponding to an intensity reduction of 1.2 and hence a distance greater than the redshift implied by √1.2 ≈ 1.1. The interstellar-dust explanation failed; the surviving interpretation required accelerating expansion and thus a cosmological constant. The paper presses the fine-tuning objection through Barrow and Magueijo ("There is no theoretical motivation for a value of Λ of currently observable magnitude") and Greene's statement that vacuum-fluctuation calculations give a value "some 120 orders of magnitude larger than experiment allows". Riess's 2001 supernova at z = 1.7, and ten more announced in October 2003, were brighter than expected — and dust can dim but never brighten. For Setterfield and Dzimano, the natural reading is not a Λ that switches sign of influence near z = 1.5 but the failure of the Doppler formula itself as an exact description.

A static cosmos

If the formula is only approximate and the redshift is quantized, the universe may be static. The paper cites Narlikar and Arp's 1993 result that a static matter-filled universe is stable against gravitational collapse without Λ provided mass increases with time — "stability is guaranteed by the mass-dependent terms" — together with Troitskii's 1987 constant-curvature cosmos in which other constants evolve synchronously with the speed of light, and Tom Van Flandern's 1984 remark that constant linear dimensions in both dynamical and atomic units would imply a larger c at past epochs. A static cosmos with intrinsic redshifts also removes Hubble's own energy-conservation worry, since wavelengths fixed at emission never lose energy in transit.

Zero Point Energy and atomic orbits

The physical mechanism rests on Puthoff's 1987 Physical Review D result that the ground state of hydrogen is a dynamic equilibrium: the power an orbiting electron radiates equals the power it absorbs from the zero-point field, "just as you would keep a kid swinging on a swing by resonantly-timed pushes". If atomic orbit energies are sustained by the ZPE, a changing ZPE changes those energies. Because orbit radii appear fixed (otherwise crystal dislocations would betray changing atom sizes) while orbit energies are quantized, a slowly rising ZPE would move atoms through quantum thresholds in discrete steps, and emitted light would be redder in jumps the further back one looks. With hc invariant, this gives

U₂/U₁ = E₂/E₁ = λ₁/λ₂ = 1/(1 + z)

so (1 + z) is inversely proportional to the strength of the ZPE.

Deriving the basic quantum

The paper's most concrete prediction comes from Puthoff's expression for the power absorbable by a charged harmonic oscillator from the zero-point field, P_a = e²hω³/(24π²εm₀c³), reduced by a factor of three to the utilizable power because only one third of the field's energy is absorbed. Writing P₁ = P₂ + zP₂, the fractional jump z is identified with the dimensionless content of that expression: 1/(72π²) from the denominator, and 1/(4π) from a dimensional decomposition of the electronic charge in terms of the "bare" electron surface area a = 4πr₀². The product gives

Δz = (1/4π)² × 1/(72π²) = 1/(1152π⁴) = 8.91144 × 10⁻⁶

cΔz = 299792 × 8.91144 × 10⁻⁶ = 2.671 km/s

against Tifft's basic quantum of 8/3 = 2.667 km/s.

Origin of the ZPE and recovery of the Doppler form

For the trend itself the authors appeal to statistical histories of the constants: officially declared values of Planck's constant rising with time (Sanders, 1965, finding instrumental improvement quantitatively inadequate to explain it), measured lightspeed declining from Newcomb (1886) to Birge (1941), and declared electron rest masses increasing — 638 measurements by 41 methods, catalogued in the 1987 Norman–Setterfield report and re-examined by Montgomery and Dolphin in 1993.

The origin story is stochastic-electrodynamic rather than relativistic. An initial rapid expansion fed energy into the vacuum as Planck particle pairs (PPP), whose dimensions equal their own Compton wavelengths and which are charge-balanced overall. Separation gave electric fields, spin gave magnetic fields, and turbulence and vorticity — following Gibson's treatment of early-universe turbulence, with Bizon's result that inelastic systems have stronger and longer-lived vortices — spawned further pairs. Recombination of the pairs then released a pulse of radiation of the same energy, augmenting the primordial fields. The authors take the absence of the "fuzziness" that granular space would impose on distant astronomical images as evidence that the pairs have now nearly all recombined.

The final section works backwards from (1 + z) = (1 + T)/√(1 − T²), where T is a dynamical time ratio running from 1 at the origin to 0 now, setting M = N₁ − N equal to the number of recombined pairs. Differentiating and substituting T = (1 − M²)/(1 + M²) yields dN/dt = k{q − rN²}, the standard recombination equation, with r = 1/(2N) carrying units of cm³/(PPP-seconds). A binomial expansion near small t gives M = t^1/2/√2, so q ∝ t^−1/2 — a turbulence decay law L = t⁻ⁿ with n = 0.5, which the authors argue is plausible for spatially free incompressible turbulence, confined systems reaching as low as n = 0.66. Allowing n to vary, they suggest, would let the curve be fitted to the supernova data beyond z ≈ 0.8 without Λ or dark energy.

Assessment

The paper's attraction is that it takes seriously a body of data the standard account largely sets aside, and it commits to a number. The quantization literature it surveys is real and was published in refereed journals; the Guthrie–Napier history, in which sceptics repeated their analysis on fresh samples at referees' insistence and recovered the same 37.5 km/s, is a fair account of how that work proceeded. The observation that peculiar motion washes out periodicity is a genuinely sharp argument, because it makes quantization and kinematics compete rather than coexist. And the derivation of 2.671 km/s from Puthoff's absorbed-power expression is falsifiable in a way that most alternative-redshift proposals are not: it predicts one specific quantum from constants of the vacuum, and it lands within 0.15% of Tifft's 8/3 km/s.

The difficulties are equally clear. The central derivation of Δz is not a derivation but an identification. Equation (16) shows only that the fractional change in utilizable power is z; the step from there to "this requires z to be a dimensionless component of (14)" asserts that the fraction must equal a particular numerical factor extracted from the formula, which does not follow from the physics of the equation. The treatment of the electronic charge compounds this: charge is decomposed into "energy per area times time squared", proportionality constants are swept into undetermined symbols d and D, and the 1/(4π) is retained while D is discarded. Since the result is a pure number of order 10⁻⁶, the agreement with 8/3 km/s rests entirely on which factors of π are kept — and the same procedure applied with slightly different bookkeeping would give a different quantum. The recombination derivation has the same character in reverse: the authors begin from the answer, equation (22), and manipulate it until it takes the form dN/dt = k(q − rN²). Recovering an equation you started from is algebra, not prediction, and the identification of r = 1/(2N) as a recombination coefficient is dimensional analogy rather than derived kinetics. The turbulence exponent is likewise argued to be "not unreasonable" at n = 0.5 by comparison with a confined-system value of 0.66 that does not bound it.

Two internal tensions deserve note. The model is presented as a static cosmos, yet its entire mechanism is powered by an "initial rapid expansion or inflation" that converted expansion energy into Planck particle pairs — expansion is denied as an explanation of redshift while being retained as the source of the vacuum energy that replaces it. And the case for a rising ZPE rests on trends in declared values of h, c and the electron mass, which is a claim about the history of metrology, not directly about nature; Sanders is cited as finding instrumental improvement insufficient, but modern determinations of c ceased in 1983 when the metre was defined from a fixed c, so the trend cannot be extended or tested by later data.

The sharpest external difficulty is one the paper does not address. If the redshift is imprinted at emission by the energy state of atomic orbits, then it carries no information about the rate at which distant events unfold. But Type Ia supernova light curves at high redshift are observed to be stretched in time by exactly the factor (1 + z) — the same supernovae whose brightness the paper discusses at length. A purely intrinsic, emission-side redshift predicts no such time dilation, and the effect is measured in the same datasets from Perlmutter and Riess that the paper draws on for its second anomaly. Similarly, the fit of the Cosmic Microwave Background to a blackbody spectrum, and the (1 + z) scaling of its temperature measured in absorbing clouds at high redshift, are not accounted for here. On the quantization side, the effect has become harder rather than easier to sustain since 2003: large redshift surveys with far more objects than the few hundred galaxies in the Guthrie–Napier samples have not confirmed a global periodicity, and much of the debate has turned on the correction for solar motion, which the paper treats as a settled preliminary step rather than a contested one. Readers should also be aware that the constancy-of-c work underlying the atomic-constants trend was developed by Setterfield in a young-earth context and has been contested on that ground as well as on statistical ones.

Taken on its own terms, the paper is a coherent programme: it names the observations it thinks the standard model cannot absorb, offers a single physical cause for both, and produces a number. Its weakness is that the number is reached by selecting dimensionless factors rather than by solving the physics, and that the model is not confronted with the time-dilation and CMB measurements that most directly test whether a redshift can be intrinsic.

See also

• Barry John Setterfield
• Redshift
• Redshift quantization
• Zero Point Energy
• Cosmological Constant
• Dark Energy
• Expanding Universe
• Steady State Theory
• Halton Arp
• Tom Van Flandern
• Casimir Effect
• Variable Speed of Light
• Tired Light
• Hubble Constant