^{*}

The author has declared that no competing interests exist.

Conceived and designed the experiments: ETK. Performed the experiments: ETK. Analyzed the data: ETK. Contributed reagents/materials/analysis tools: ETK. Wrote the paper: ETK.

An alternate Lorentz transformation, Absolute Lorentz Transformation (ALT), has similar kinematics to special relativity yet maintains absolute simultaneity in the context of a preferred reference frame. In this study, it is shown that ALT is compatible with current experiments to test Lorentz invariance only if the proposed preferred reference frame is locally equivalent to the Earth-centered non-rotating inertial reference frame, with the inference that in an ALT framework, preferred reference frames are associated with centers of gravitational mass. Applying this theoretical framework to cosmological data produces a scenario of universal time contraction in the past. In this scenario, past time contraction would be associated with increased levels of blueshifted light emissions from cosmological objects when viewed from our current perspective. The observation that distant Type Ia supernovae are dimmer than predicted by linear Hubble expansion currently provides the most direct evidence for an accelerating universe. Adjusting for the effects of time contraction on a redshift–distance modulus diagram produces a linear distribution of supernovae over the full redshift spectrum that is consistent with a non-accelerating universe.

The Absolute Lorentz Transformation (ALT) is an alternate Lorentz transformation that has similar kinematics to special relativity (SR), but is distinct in describing absolute simultaneity and invoking a preferred reference frame (PRF) relative to which time dilation and length contraction occur in a directional manner

The Lorentz transformation equations were first described by J. Larmor

R. Mansouri & R.U. Sexl created a widely-used test theory for SR

In the MS test theory convention, the Lorentz transformation has: 1/^{2}/^{2})^{1/2}; and ^{2}

A. Eagle, F.R. Tangherlini, and Mansouri & Sexl described a modified Lorentz transformation that maintains absolute simultaneity ^{2}/^{2})^{1/2}; and

SR and ALT have similar kinematics. The form of the Lorentz transformation equation that is generally used in experimental settings to calculate time dilation is identical to the ALT time dilation equation. As described in Einstein's 1905 paper ^{2})/(1 - ^{2}/^{2})^{1/2} with the value ^{2}/^{2})^{1/2}, which is the ALT equation (3). Mansouri & Sexl noted that ALT is the very relation one would write down if one has to formulate a theory in which rods shrink by a factor (1 - ^{2}/^{2}^{1/2} and clocks are slow by a factor (1 - ^{2}/^{2}^{1/2} when moving with respect to a PRF

ALT differs from SR in several respects. ALT maintains absolute simultaneity for all observers, while SR implies local differential simultaneity

SR does not preclude an absolute reference frame. Lorentz and Poincaré believed in the existence of an absolute reference frame in the context of the Lorentz transformation

Throughout the remainder of this study, ‘PRF’ will not be used in the sense of an absolute reference frame, but rather in the broader sense to refer to any reference frame relative to which Lorentz/ALT transformations occur in a directional manner.

Experimental evidence from Hafele & Keating indicates that the Earth-centered non-rotating inertial reference frame (ECI) can act as a local reference frame to direct time dilation (i.e., a PRF in the broader sense). In their experiment, atomic clocks were flown in airplanes eastward and westward around the Earth, and time dilation was calculated relative to the ECI

In the Hafele & Keating experiment, the time dilation was absolute and directional, as the flying and ground-based clocks showed different elapsed times when brought together for side-by-side comparisons. Hafele & Keating suggested that the directional time dilation arose within the context of SR because objects in non-inertial reference frames experience directional time dilation relative to inertial reference frames

Satellites of the global positioning system (GPS) are in inertial reference frames because they are in free-fall orbits around the Earth, similar to the inertial reference frame of the ECI that arises from its free-fall orbit around the Sun. It is well established that the ECI functions as a PRF for GPS satellites, with the satellites experiencing directional time dilation based on their velocity relative to the ECI

In 1929, Edwin Hubble provided evidence that the recession velocities of galaxies increase linearly with distance, thereby inferring that the Universe is expanding

Cosmological redshift (

Cosmological redshift can be interpreted as kinematic relativistic Doppler shift by a mathematical treatment of transporting the velocity four-vector from the source to the observer

There is a large body of published data that shows no violations of Lorentz invariance for experiments carried out on the Earth or in the local Earth environment

Mansouri & Sexl suggested that the CMB frame is the obvious candidate for a possible “ether frame”

The requirement for the PRF to be locally centered on the ECI has implications for the concept of the ether. The ether is defined as the medium for the propagation of electromagnetic radiation

The observation of directional time dilation relative to the ECI indicates that the ECI functions locally as a PRF (broadly defined). Both the ECI and GPS satellites are in “free fall” inertial reference frames, and yet GPS satellites experience directional time dilation relative to the ECI. This indicates that directional time dilation is not limited to the interaction of non-inertial and inertial reference frames but is also observed between inertial reference frames. It therefore raises the issue of why the ECI functions as a PRF. The force of gravity connects the ECI and the objects that experience directional time dilation as a result of motion relative to the ECI. A plausible hypothesis is that the ECI functions as a PRF because it is the local center of mass with the dominant gravitational field in its local environment. The combination of ALT and PRFs linked to local centers of gravitational mass will be referred to as absolute simultaneity theory (AST).

Mansouri & Sexl state that there is the impossibility of an ‘experimentum crucis’ that can distinguish between SR and ALT because both have similar kinematics

The first experimentally distinguishable difference between the two theories is that ALT allows anisotropies in the one-way speed of light, while light speed is isotropic with SR

Experimental approaches using one-way light paths have demonstrated that light speeds are anisotropic when measured from the rotating Earth surface; these approaches include the Michelson-Gale experiment

It is possible to design experiments that would be capable of detecting light speed anisotropies predicted by AST in the context of a proposed gravitational mass-based PRF moving relative to an inertial reference frame. Consider two observers at rest in the heliocentric reference frame who are separated from each other parallel to and near Earth's orbit. When the Earth is next to the observers, they send light signals between themselves so that the light signals move in the direction of the Earth's orbital motion or opposite to the Earth's motion. Viewed from the ECI perspective, the observers are in an inertial reference frame moving past the ECI, and one observer appears to move toward the light signal sent in the direction of Earth's orbital motion, while the other observer moves away from the light signal sent in the other direction. This situation can be considered analogous to the AST perspective on the Sagnac effect, where observers on the rotating Earth move toward or away from light beams that propagate isotropically in the ECI. Just as observers on the Earth surface or in orbit around the Earth calculate light speed anisotropies when sending light signals among themselves

The second experimentally distinguishable difference between the two theories is that AST predicts directional time dilation for inertial reference frames moving relative to a proposed PRF

Experiments that utilize atomic clocks traveling in inertial reference frames near a proposed gravitational mass-based PRF can be used to probe for differences in time dilation. For example, clocks could be sent past the Earth in the direction of and opposite to the Earth's orbital motion in linear inertial paths. For each clock, the time dilation due to gravitational effects would be calculated and subtracted from the total observed time dilation to determine the time dilation due to motion. This can be accomplished because time dilation due to gravity (calculated using general relativity, GR) and motion (calculated using the Lorentz transformation/ALT) are, in practice, independent and additive

Historically, SR has not been used extensively in general relativistic cosmology (GRC). This can be attributed in part to the historical view that Minkowski spacetime applies only in situations devoid of mass and energy

The Lorentz transformation/ALT time dilation equation functions robustly in conditions that have classically not been associated with Minkowski spacetime. The Lorentz transformation/ALT equation can accurately calculate the time dilation of objects traveling in non-inertial frames

The convention in cosmology is to use a comoving universe coordinate system that expands in sync with the Hubble expansion

Time contraction would have effects on both redshift and luminosity. From the vantage point of our present time scale, photons emitted in the past under time-contracted conditions would have been emitted at a faster rate, with blueshifted wavelengths (as the frequency of the emitted light was increased relative to our time scale).

Type Ia supernovae (SNe Ia) function as standard candles, and the analysis of their redshift and luminosity has provided unique insights into universe evolution

The relativistic Doppler shift formula is used to calculate the effective recession velocity (_{er}

The ALT time dilation formula (3) is used to calculate the time-contraction ratio (_{e}_{o}

_{er}_{er}_{er}

Substituting the definition of _{er}

_{TC}_{e}_{o}

_{e}

_{o}

_{TC}

Top: Diagrams of SNe plotted for _{TC}_{TC}

Under time-contraction conditions, the rates of photon emissions for SNe Ia in the past were increased when viewed from our current, time-dilated perspective. To compensate for the increased emission rates, SNe Ia are shifted to higher distance modulus values (upward) on the diagram to reflect the lower level of luminosity that would have occurred if the SNe Ia were emitting at the current (non-time contracted) rate (_{x}_{x0}_{TC}

In 1998 and 1999, two groups showed that SNe Ia with redshifts greater than 0.3–0.4 are dimmer than predicted from the linear application of the Hubble constant

Statistical analysis was performed to determine if the distribution of the TC-adjusted SNe Ia is consistent with a linear distribution. In agreement with previous reports

To further confirm that the TC-adjusted high-redshift SNe Ia are linear with low-redshift SNe Ia, the high-redshift SNe Ia were compared to a line derived from linear regression of low-redshift SNe Ia. The cut-off for low redshift SNe Ia was set to

SNe Ia have characteristic light curves that increase and decrease in intensity over a set time period. Cosmological time dilation alters the duration of the light curves that are observed on Earth by a factor of 1+

Changes in the light period correlate directly to changes in the duration of the light curve. To illustrate that the light periods of distant time-contracted SNe Ia have the normal periods upon observation, a specific SN Ia, sn2002fw, will be used as an example. As listed in _{TC}_{e}_{e}_{,} where _{e}_{o}_{e}

For this calculation, let _{e}

Under non-time-contraction conditions for SN 2002fw:

Time contraction increases the frequency of light at emission by the ratio

The observed light period is thus the same under both non-time-contracted conditions (_{o}_{oTC}

This study explores the potential validity of ALT, an alternate Lorentz transformation that is not widely known, and its implications for cosmology when integrated into the AST framework in which PRFs are linked to centers of gravitational mass. The failure to identify violations of Lorentz invariance has been used to support the widely-accepted SR theory. However, these experiments do not invalidate ALT, but rather act to restrict the localization of a potential PRF. Multiple experiments to test SR (analyzing light or subatomic particles moving at high relative speeds) have had the effect of restricting the localization of a putative PRF to the ECI. Complementary time dilation experiments that studied objects traveling at slower speeds for longer durations (e.g., airplanes and satellites) have provided evidence that the ECI acts as a PRF (broadly defined) to direct Lorentz/ALT transformations. Thus, the first class of experiments provides evidence that the only viable scenario for ALT is a PRF that is locally centered on the ECI, while the second class of experiments shows that the ECI does in fact act as a PRF for Lorentz/ALT transformations. Notably, GPS satellites traveling in inertial reference frames also experience directional time dilation relative to the ECI, and this finding is more compatible with AST than with SR.

The current situation, where there is a lack of compelling experimental evidence that distinguishes between SR and AST, allows one to countenance the possibility and implications of a valid AST. In the context of a valid AST, one can ask why the ECI functions as a PRF. The observation that objects moving in inertial reference frames experience directional time dilation relative to the ECI suggests that inertial reference frame status is not sufficient to confer PRF status. The most compelling hypothesis is that the ECI functions as a PRF because it is the local center of gravitational mass. This suggests that in an AST scenario, PRFs would not have fixed positions in the Universe, but would vary temporally and spatially based on the distribution of gravitational mass. New experimental data is required to definitively distinguish between SR and AST; and if the latter is supported, to inform theoretical models that describe how the effects of PRFs extend spatially and overlap.

The published interpretation of redshifts as kinematic recession velocities suggests that cosmological redshifts arise because cosmological objects in the present Universe move faster than objects in the past due to Hubble expansion. Combining this with ALT leads to a scenario of universal time dilation (UTD) in which the present Universe experiences time dilation relative to the past Universe. When viewed from our present (time-dilated) vantage point, cosmological objects in the past would have experienced time contraction that was associated with increased rates of light emissions and increased frequencies of emitted light. The UTD scenario would apply throughout the Universe, e.g., to observers in other PRFs or at rest with the CMB. The proposed universal nature of UTD is illustrated by

UTD has several implications, foremost of which is that the rate of time is not constant, and is linked to the rate of universe expansion. Because the effect of past time contraction includes the blueshifting of emissions (relative to our current time scale), light from distant cosmological objects would have undergone further changes in wavelength prior to reaching us (a greater redshift value); and therefore cosmological objects at high redshift would be older and more distant than currently envisioned.

Currently, the strongest and most direct evidence for an acceleration in the rate of universe expansion is that distant SNe Ia are less luminous than predicted by a linear regression of the Hubble constant

Dark energy is proposed to drive the accelerated universe expansion, but its composition and mechanism of action are unknown. As stated in a review of dark energy: “… through most of the history of the universe dark matter or radiation dominated dark energy by many orders of magnitude. We happen to live at a time when dark energy has become important.”; “The universe has gone through three distinct eras: radiation dominated,

Experimental support for a role of dark energy in universe acceleration comes from the analysis of four types of data: SNe Ia luminosity and redshift; the distribution of galaxy clusters; baryon acoustic oscillations; and the analysis of cosmic shear caused by gravitational lensing

One argument against UTD is that it has the potential to disrupt current GRC theories, which are able to accurately model cosmological observations. In this regard, it should be noted that GRC theories have substantial inherent flexibilities that allow the theories to model diverse observations. The flexibility in these models derives from the ability to alter parameter values; and it is not unusual for these values to change in response to new experimental observations

In summary, current experimental evidence fails to definitively distinguish between SR and AST. This study shows that a valid AST would have significant implications for cosmology, including universal time dilation, increased ages and distances for high-redshift objects, and a linear, non-accelerating rate of universe expansion during the most recent era.

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I thank K.R. Love-Myers and the University of Georgia Statistical Consulting Center for advice on the statistical analyses; R.S. Balachandran and T.E. Kipreos for helpful discussions; and S.N. Chaudhari for constructive comments on the manuscript.