Scale Expanding Cosmos Theory I – An introduction: Difference between revisions

Scientific Paper
Title	Scale Expanding Cosmos Theory I – An introduction
Read in full	Link to paper
Author(s)	C Johan Masreliez
Keywords	Space and time expansion, Space and time Equivalence, Scale expansion, Space and time symmetry, Cosmic drag, Tired light, Pioneer anomaly
Published	2004
Journal	Apeiron
Volume	11
Number	3
No. of pages	35
Pages	99-133

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Abstract

A new cosmological theory is presented based on the proposition that all four metrical coefficients of space and time change with the cosmological expansion. Such a universal scale expansion would preserve the four-dimensional spacetime geometry and therefore by general relativity most physical relationships. In addition, if the scale expansion were exponential with time, all epochs would be equivalent. The theory resolves several outstanding problems with the Big Bang theory and better agrees with four observational programs. It also provides a simple explanation to the Pioneer anomaly.

Overview

This is the first of a projected four-part series in Apeiron in which C Johan Masreliez sets out the Scale Expanding Cosmos (SEC) theory. Its founding proposition is a single change to the standard cosmological line element: instead of expanding only the three spatial metrical coefficients, as Friedmann's choice of coordinates does, let all four — space and time together — expand by a common exponential factor. The result is the SEC line element ds² = e^2t/T(dt² − dx² − dy² − dz²), where T is the Hubble time. Masreliez stresses that Friedmann himself was careful to note that a fixed temporal coefficient with time-varying spatial metric "merely is a convenient choice of coordinates, since there are innumerable GR-equivalent line elements related by continuous variable transformations"; the SEC takes a different branch from that same fork.

The motivation is as much philosophical as observational. Masreliez opens with Parmenides — "only being is; non-being is not" — and argues that a creation event is unpalatable because it implies "the breakdown of physics at the time of creation, which would make the origin of the universe forever incomprehensible." Since Einstein's equations are unchanged by a constant rescaling of the metric, no physical process can fix the cosmological scale; Masreliez asks, "if the scale of bodies in the universe were fixed, what could determine this fixed scale?" If no answer exists, the scale may change with time, and an exponential change makes every epoch physically equivalent. The universe is then eternal, without beginning, end, or cosmological evolution — and the redshift becomes a tired light effect derived from the geodesic rather than a recession. The theory has one free parameter, the Hubble time.

The argument

Scale invariance as a gauge symmetry

An obvious objection is that the SEC line element is just the FRW element in disguise, reachable by t′ = Texp(t/T). Masreliez answers that the SEC form is physically equivalent under translations in both space and time. Under t = t′ + t₀ the line element acquires a constant factor e^2t₀/T, and since Einstein's equations are identical for any ds² = S²g_μνdx^μdx^ν with constant S, all physical relationships survive a discrete scale change. Four-dimensional scale invariance is thus treated as "a fundamental, universal, gauge invariance."

The move that takes the theory "beyond GR" is to generalize relativity to include discrete scale transformations. On Masreliez's reading, general relativity models four-dimensional geometry but not the progression of time — it does not distinguish past from present, and it has no provision for a changing pace of proper time, since proper time is the reference increment ds. In the SEC the discretely changing scale supplies what geometry cannot. To use the GR machinery at all, the pace of proper time must be held fixed at the present rate; with that convention the modelled universe appears denser and the CMB hotter in the past, and the age of the universe equals the Hubble time — but this is equally true for every observer in every epoch.

Cosmic drag

The most testable consequence follows directly from the geodesic of the SEC line element: relative velocities of freely moving objects decay exponentially with a time constant equal to the Hubble time, and angular momenta dissipate likewise. Masreliez names this cosmic drag and calls it a new phenomenon. It predicts that planets slowly spiral toward the Sun with accelerating angular velocities, and he claims optical observations since the introduction of atomic time have detected this. He is explicit that this "would invalidate basic laws of physics, for example Newton's first law of motion," and equally explicit that it makes the theory falsifiable: "cosmic drag will soon either confirm or falsify the theory," since positional deviations from post-Newtonian predictions grow quadratically with time.

Thirteen problems with the standard model

Section 5, drawing largely on Van Flandern's 2002 summary, lists the difficulties the SEC claims to dissolve. Among them: the creation event disappears in an eternal universe; the horizon problem vanishes because all regions have always communicated, with infinite distance corresponding to infinite redshift; the flatness or "Omega" fine-tuning problem does not arise because scale expansion preserves all relative distances and the mass density never changes; the age problem and the excess of large-scale structure are relieved because objects may be far older than the Hubble time; the absence of evident evolution in high-redshift Hubble Deep Field galaxies is expected, since "all epochs are equivalent"; and flat spiral-galaxy rotation curves follow from a steady inward flow of matter driven by cosmic drag. On dark energy, Masreliez argues the SEC vacuum energy-momentum tensor does not vanish, comprising a cosmological constant of negative energy density from spatial expansion exactly balanced by positive energy density from temporal expansion, so that the net gravitating energy disappears while spacetime still contains vacuum energy.

Defending tired light

Section 6 confronts the three standard objections. To the charge that no interaction degrades photon energy without also changing momentum — which would blur distant objects — Masreliez replies that in the SEC the redshift is not an interaction at all but a spacetime effect derived from the geodesic, as in the de Sitter model, and so involves no scattering.

To the charge that tired light cannot preserve the CMB blackbody spectrum, he offers the paper's most specific technical argument. A Planck spectrum survives expansion if energy density is diluted by 1/(1+z)⁴ while temperature falls as 1/(1+z). In the SEC the three spatial dimensions expand by (z+1), giving volume dilution 1/(z+1)³; the fourth factor comes from the temporal expansion. Working through the momentum scalar product, he finds that in the SEC the photon energy carries E(t) → E₀·e^−t/T where the corresponding de Sitter (spatial-only) line element gives e^−t/2T — "the additional factor e^−t/T ... is due to the temporal expansion and provides the fourth dilution factor." Hence, he concludes, the Planck spectrum is preserved much as in a classical cavity, with the CMB representing equilibrium between radiated energy and energy dissipated by tired-light redshift.

To the charge that tired light predicts no time dilation of supernova light curves, he asserts that the SEC has both redshift and time dilation (Appendix 1), so that the two dimming factors of 1/(z+1) present in the standard model are present here too, without any recession velocity.

The Pioneer anomaly and four observational tests

Masreliez treats the Pioneer anomaly as "direct evidence for tired light redshift." What JPL measures, he notes, is a discrepancy between the directly measured frequency shift of the returned signal and a modelled Doppler shift based on ranging; interpreting the discrepancy as acceleration is a choice. If solar-system light is subject to tired-light redshift, the SEC predicts an apparent a = c/T, and the observed 7.5 × 10⁻⁸ cm/s² gives T = 12.7 billion years, close to independent Hubble-time estimates. He adds that the annual modulation JPL noticed, with extrema at solar conjunction and opposition, "obviously ... cannot be a Doppler effect" but follows from a distance-dependent tired-light shift as the Earth orbits.

Four further tests are cited, following LaViolette's 1986 work. The galaxy number-count test (sixteen programs summarized by Metcalf et al. 1995), the angular-size test (Djorgovski and Spinrad 1981) — where the standard model predicts angular size to turn upward beyond a minimum while the SEC predicts monotonic decrease — the Tolman surface-brightness test, and the Type Ia supernova data. On surface brightness the SEC predicts 1/(1+z)² rather than 1/(1+z)⁴, since distances and viewing angles remain constant under scale expansion; Masreliez reads Lubin and Sandage (2001) at z = 0.75 and 0.90 as favouring the SEC. On the supernovae, he claims agreement "without any adjustable parameters" and therefore no need for accelerating expansion. Counting Pioneer, he concludes that five independent programs agree with the SEC while the standard model disagrees with all five.

Assessment

The theory's genuine attraction is its economy and its symmetry argument. Masreliez asks a question that is not easy to dismiss — what fixes the cosmological scale, given that the field equations are indifferent to it? — and builds from a symmetry principle rather than from parameter fitting. With one free parameter, the Hubble time, the model is far more constrained than the standard model with its density parameters and dark-energy equation of state, and Masreliez deserves credit for making the theory falsifiable in the near term: cosmic drag predicts a specific, cumulative, quadratically growing deviation in planetary ephemerides. He is also right that Friedmann's coordinate choice was a choice, and right that the exact-blackbody character of the CMB is the classic difficulty for tired-light models — the attempt to derive the fourth dilution factor from temporal expansion is the most serious technical work in the paper.

The difficulties are correspondingly deep. The largest is the status of the "beyond GR" step. Discrete scale adjustments are introduced because continuous transformations cannot change the pace of proper time, but they are placed precisely where Einstein's equations are invariant and therefore blind — which means they are, by construction, unable to produce any signature the field equations can see. The paper does not say what triggers a discrete step, how large it is, or what fixes its rate; "new physics" is announced rather than specified. Similarly, the SEC-to-FRW coordinate equivalence is conceded and then set aside on the ground that the SEC form is translation-invariant. That is a statement about the form of the line element, not about observables, and the paper does not identify a measurement that distinguishes the two beyond the aesthetic preference for a metric that looks the same at every epoch.

Several observational claims are considerably weaker than presented. The time-dilation claim is the critical one: the (1+z) stretching of Type Ia supernova light curves is a direct kinematic measurement, subsequently confirmed to z ≈ 1 and beyond and, more recently, in quasar variability, and it is exactly what a static-space tired-light model cannot produce. Masreliez asserts that the SEC has time dilation and refers the reader to an appendix, but a scale factor multiplying all four coordinates equally rescales the observed period and the observed wavelength together, so it is not obvious — and is nowhere shown in the main text — how the theory yields the same (1+z) light-curve stretch alongside a non-Doppler redshift without double-counting. Since two of his five "independent" programs (surface brightness, supernovae) depend on this factor, the claim carries a great deal of weight for the argument it is given.

The surface-brightness case has similar problems: the Lubin and Sandage result is presented as favouring the SEC, but the analysis requires "the radii adjusted to the SEC model," which is a model-dependent correction on the very quantity in dispute, and Lubin and Sandage themselves concluded the opposite. The number-count and angular-size figures are from 1981 and 1995, and the observational landscape has since changed substantially — deep surveys now show clear galaxy evolution with redshift, which is precisely what "all epochs are equivalent" forbids. The Pioneer coincidence is elegant, but a = cH is a coincidence that many tired-light and modified-inertia models reproduce, and the anomaly has since been accounted for by anisotropic thermal recoil from the spacecraft's own radioisotope generators — an explanation that also accommodates the observed decay of the anomaly with time, which the SEC's constant c/T does not. Finally, if cosmic drag is real and universal, the same argument that predicts planetary in-spiral should also apply within the solar system to the highest-precision dynamics available, where lunar laser ranging and planetary radar have long since reached sensitivities that constrain such a term severely.

Masreliez is unusually candid about all of this — "the SEC theory is quite unorthodox since it would invalidate basic laws of physics," "the reader might still feel somewhat uneasy" — and presents the paper as an introduction to a programme rather than a finished case. As an introduction it succeeds: it states a clear proposition, derives a testable consequence, and identifies what would falsify it. Whether the observational support survives the two decades of data since 2004 is a different question, and on the evidence of the light-curve stretching in particular, it does not.

@@ Line 6: / Line 6: @@
 | published = 2004
 | journal = [[Apeiron]]
-| volume = [[11]]
+| volume = 11
-| number = [[3]]
+| number = 3
-| num_pages = 6
+| num_pages = 35
 | pages = 99-133
 }}
@@ Line 17: / Line 17: @@
 A new cosmological theory is presented based on the proposition that all four metrical coefficients of space and time change with the cosmological expansion. Such a universal scale expansion would preserve the four-dimensional spacetime geometry and therefore by general relativity most physical relationships. In addition, if the scale expansion were exponential with time, all epochs would be equivalent. The theory resolves several outstanding problems with the Big Bang theory and better agrees with four observational programs. It also provides a simple explanation to the Pioneer anomaly.
+==Overview==
+This is the first of a projected four-part series in ''[[Apeiron]]'' in which [[C Johan Masreliez]] sets out the Scale Expanding Cosmos (SEC) theory. Its founding proposition is a single change to the standard cosmological line element: instead of expanding only the three spatial metrical coefficients, as Friedmann's choice of coordinates does, let ''all four'' — space and time together — expand by a common exponential factor. The result is the SEC line element ''ds''<sup>2</sup> = ''e''<sup>2''t''/''T''</sup>(''dt''<sup>2</sup> − ''dx''<sup>2</sup> − ''dy''<sup>2</sup> − ''dz''<sup>2</sup>), where ''T'' is the Hubble time. Masreliez stresses that Friedmann himself was careful to note that a fixed temporal coefficient with time-varying spatial metric "merely is a convenient choice of coordinates, since there are innumerable GR-equivalent line elements related by continuous variable transformations"; the SEC takes a different branch from that same fork.
+The motivation is as much philosophical as observational. Masreliez opens with Parmenides — "only being is; non-being is not" — and argues that a creation event is unpalatable because it implies "the breakdown of physics at the time of creation, which would make the origin of the universe forever incomprehensible." Since Einstein's equations are unchanged by a constant rescaling of the metric, no physical process can fix the cosmological scale; Masreliez asks, "if the scale of bodies in the universe were fixed, what could determine this fixed scale?" If no answer exists, the scale may change with time, and an exponential change makes every epoch physically equivalent. The universe is then eternal, without beginning, end, or cosmological evolution — and the redshift becomes a [[Tired Light|tired light]] effect derived from the geodesic rather than a recession. The theory has one free parameter, the Hubble time.
+==The argument==
+===Scale invariance as a gauge symmetry===
+An obvious objection is that the SEC line element is just the FRW element in disguise, reachable by ''t''′ = ''T''exp(''t''/''T''). Masreliez answers that the SEC form is physically equivalent under ''translations'' in both space and time. Under ''t'' = ''t''′ + ''t''<sub>0</sub> the line element acquires a constant factor ''e''<sup>2''t''<sub>0</sub>/''T''</sup>, and since Einstein's equations are identical for any ''ds''<sup>2</sup> = ''S''<sup>2</sup>''g''<sub>μν</sub>''dx''<sup>μ</sup>''dx''<sup>ν</sup> with constant ''S'', all physical relationships survive a discrete scale change. Four-dimensional scale invariance is thus treated as "a fundamental, universal, gauge invariance."
+The move that takes the theory "beyond GR" is to generalize relativity to include ''discrete'' scale transformations. On Masreliez's reading, general relativity models four-dimensional geometry but not the progression of time — it does not distinguish past from present, and it has no provision for a changing pace of proper time, since proper time ''is'' the reference increment ''ds''. In the SEC the discretely changing scale supplies what geometry cannot. To use the GR machinery at all, the pace of proper time must be held fixed at the present rate; with that convention the modelled universe appears denser and the CMB hotter in the past, and the age of the universe equals the Hubble time — but this is equally true for every observer in every epoch.
+===Cosmic drag===
+The most testable consequence follows directly from the geodesic of the SEC line element: relative velocities of freely moving objects decay exponentially with a time constant equal to the Hubble time, and angular momenta dissipate likewise. Masreliez names this cosmic drag and calls it a new phenomenon. It predicts that planets slowly spiral toward the Sun with accelerating angular velocities, and he claims optical observations since the introduction of atomic time have detected this. He is explicit that this "would invalidate basic laws of physics, for example Newton's first law of motion," and equally explicit that it makes the theory falsifiable: "cosmic drag will soon either confirm or falsify the theory," since positional deviations from post-Newtonian predictions grow quadratically with time.
+===Thirteen problems with the standard model===
+Section 5, drawing largely on Van Flandern's 2002 summary, lists the difficulties the SEC claims to dissolve. Among them: the creation event disappears in an eternal universe; the horizon problem vanishes because all regions have always communicated, with infinite distance corresponding to infinite redshift; the flatness or "Omega" fine-tuning problem does not arise because scale expansion preserves all relative distances and the mass density never changes; the age problem and the excess of large-scale structure are relieved because objects may be far older than the Hubble time; the absence of evident evolution in high-redshift Hubble Deep Field galaxies is expected, since "all epochs are equivalent"; and flat spiral-galaxy rotation curves follow from a steady inward flow of matter driven by cosmic drag. On dark energy, Masreliez argues the SEC vacuum energy-momentum tensor does not vanish, comprising a cosmological constant of negative energy density from spatial expansion exactly balanced by positive energy density from temporal expansion, so that the net gravitating energy disappears while spacetime still contains vacuum energy.
+===Defending tired light===
+Section 6 confronts the three standard objections. To the charge that no interaction degrades photon energy without also changing momentum — which would blur distant objects — Masreliez replies that in the SEC the redshift is not an interaction at all but a spacetime effect derived from the geodesic, as in the de Sitter model, and so involves no scattering.
+To the charge that tired light cannot preserve the CMB blackbody spectrum, he offers the paper's most specific technical argument. A Planck spectrum survives expansion if energy density is diluted by 1/(1+''z'')<sup>4</sup> while temperature falls as 1/(1+''z''). In the SEC the three spatial dimensions expand by (''z''+1), giving volume dilution 1/(''z''+1)<sup>3</sup>; the fourth factor comes from the temporal expansion. Working through the momentum scalar product, he finds that in the SEC the photon energy carries ''E''(''t'') → ''E''<sub>0</sub>·''e''<sup>−''t''/''T''</sup> where the corresponding de Sitter (spatial-only) line element gives ''e''<sup>−''t''/2''T''</sup> — "the additional factor ''e''<sup>−''t''/''T''</sup> ... is due to the temporal expansion and provides the fourth dilution factor." Hence, he concludes, the Planck spectrum is preserved much as in a classical cavity, with the CMB representing equilibrium between radiated energy and energy dissipated by tired-light redshift.
+To the charge that tired light predicts no time dilation of supernova light curves, he asserts that the SEC has ''both'' redshift and time dilation (Appendix 1), so that the two dimming factors of 1/(''z''+1) present in the standard model are present here too, without any recession velocity.
+===The Pioneer anomaly and four observational tests===
+Masreliez treats the Pioneer anomaly as "direct evidence for tired light redshift." What JPL measures, he notes, is a discrepancy between the directly measured frequency shift of the returned signal and a modelled Doppler shift based on ranging; interpreting the discrepancy as acceleration is a choice. If solar-system light is subject to tired-light redshift, the SEC predicts an apparent ''a'' = ''c''/''T'', and the observed 7.5 × 10<sup>−8</sup> cm/s<sup>2</sup> gives ''T'' = 12.7 billion years, close to independent Hubble-time estimates. He adds that the annual modulation JPL noticed, with extrema at solar conjunction and opposition, "obviously ... cannot be a Doppler effect" but follows from a distance-dependent tired-light shift as the Earth orbits.
+Four further tests are cited, following LaViolette's 1986 work. The galaxy number-count test (sixteen programs summarized by Metcalf et al. 1995), the angular-size test (Djorgovski and Spinrad 1981) — where the standard model predicts angular size to turn upward beyond a minimum while the SEC predicts monotonic decrease — the Tolman surface-brightness test, and the Type Ia supernova data. On surface brightness the SEC predicts 1/(1+''z'')<sup>2</sup> rather than 1/(1+''z'')<sup>4</sup>, since distances and viewing angles remain constant under scale expansion; Masreliez reads Lubin and Sandage (2001) at ''z'' = 0.75 and 0.90 as favouring the SEC. On the supernovae, he claims agreement "without any adjustable parameters" and therefore no need for accelerating expansion. Counting Pioneer, he concludes that five independent programs agree with the SEC while the standard model disagrees with all five.
+==Assessment==
+The theory's genuine attraction is its economy and its symmetry argument. Masreliez asks a question that is not easy to dismiss — what fixes the cosmological scale, given that the field equations are indifferent to it? — and builds from a symmetry principle rather than from parameter fitting. With one free parameter, the Hubble time, the model is far more constrained than the standard model with its density parameters and dark-energy equation of state, and Masreliez deserves credit for making the theory falsifiable in the near term: cosmic drag predicts a specific, cumulative, quadratically growing deviation in planetary ephemerides. He is also right that Friedmann's coordinate choice was a choice, and right that the exact-blackbody character of the CMB is the classic difficulty for tired-light models — the attempt to derive the fourth dilution factor from temporal expansion is the most serious technical work in the paper.
+The difficulties are correspondingly deep. The largest is the status of the "beyond GR" step. Discrete scale adjustments are introduced because continuous transformations cannot change the pace of proper time, but they are placed precisely where Einstein's equations are invariant and therefore blind — which means they are, by construction, unable to produce any signature the field equations can see. The paper does not say what triggers a discrete step, how large it is, or what fixes its rate; "new physics" is announced rather than specified. Similarly, the SEC-to-FRW coordinate equivalence is conceded and then set aside on the ground that the SEC form is translation-invariant. That is a statement about the ''form'' of the line element, not about observables, and the paper does not identify a measurement that distinguishes the two beyond the aesthetic preference for a metric that looks the same at every epoch.
+Several observational claims are considerably weaker than presented. The time-dilation claim is the critical one: the (1+''z'') stretching of Type Ia supernova light curves is a direct kinematic measurement, subsequently confirmed to ''z'' ≈ 1 and beyond and, more recently, in quasar variability, and it is exactly what a static-space tired-light model cannot produce. Masreliez asserts that the SEC has time dilation and refers the reader to an appendix, but a scale factor multiplying ''all four'' coordinates equally rescales the observed period and the observed wavelength together, so it is not obvious — and is nowhere shown in the main text — how the theory yields the same (1+''z'') light-curve stretch alongside a non-Doppler redshift without double-counting. Since two of his five "independent" programs (surface brightness, supernovae) depend on this factor, the claim carries a great deal of weight for the argument it is given.
+The surface-brightness case has similar problems: the Lubin and Sandage result is presented as favouring the SEC, but the analysis requires "the radii adjusted to the SEC model," which is a model-dependent correction on the very quantity in dispute, and Lubin and Sandage themselves concluded the opposite. The number-count and angular-size figures are from 1981 and 1995, and the observational landscape has since changed substantially — deep surveys now show clear galaxy evolution with redshift, which is precisely what "all epochs are equivalent" forbids. The Pioneer coincidence is elegant, but ''a'' = ''cH'' is a coincidence that many tired-light and modified-inertia models reproduce, and the anomaly has since been accounted for by anisotropic thermal recoil from the spacecraft's own radioisotope generators — an explanation that also accommodates the observed decay of the anomaly with time, which the SEC's constant ''c''/''T'' does not. Finally, if cosmic drag is real and universal, the same argument that predicts planetary in-spiral should also apply within the solar system to the highest-precision dynamics available, where lunar laser ranging and planetary radar have long since reached sensitivities that constrain such a term severely.
+Masreliez is unusually candid about all of this — "the SEC theory is quite unorthodox since it would invalidate basic laws of physics," "the reader might still feel somewhat uneasy" — and presents the paper as an introduction to a programme rather than a finished case. As an introduction it succeeds: it states a clear proposition, derives a testable consequence, and identifies what would falsify it. Whether the observational support survives the two decades of data since 2004 is a different question, and on the evidence of the light-curve stretching in particular, it does not.
+==See also==
+* [[C Johan Masreliez]]
+* [[On the Origin of Inertial Force]]
+* [[Tired Light]]
+* [[Big Bang]]
+* [[redshift]]
+* [[Dark Energy]]
+* [[Cosmology]]
+* [[General Relativity]]
+* [[Tom Van Flandern]]
+* [[Edwin Hubble]]
+* [[Apeiron]]
 [[Category:Scientific Paper|scale expanding cosmos theory introduction]]
 [[Category:Relativity|scale expanding cosmos theory introduction]]
+[[Category:Cosmology|scale expanding cosmos theory introduction]]
+[[Category:Big Bang|scale expanding cosmos theory introduction]]
+[[Category:Redshift|scale expanding cosmos theory introduction]]
+[[Category:Gravity|scale expanding cosmos theory introduction]]