The Fork in the Road: How the Assumption of Fixed vs. Relative Time Dictates Cosmological Theory

J. Rogers, SE Ohio

A Conceptual Analysis
October 26, 2023

Abstract: The observation of cosmological redshift is the empirical bedrock of modern cosmology. Its interpretation, however, is not a direct consequence of the data, but rather a logical entailment of a foundational, and often unstated, axiom concerning the nature of time. This paper contrasts two cosmological paradigms that emerge from two mutually exclusive axioms. The first, the Fixed Time Paradigm (FTP), is the basis of the standard ΛCDM model. It inherits the classical notion of a constant universal rate of physical processes, which forces the explanation of redshift as a metric expansion of space, leading to the Big Bang narrative. The second, a Relative Time Paradigm (RTP), posits that the rate of time is not fixed, but is a dynamic property determined by the total gravitational potential of the universe. This axiom leads to an interpretation of redshift as a temporal effect—a mismatch between the slower time rate of the past and the faster rate of the present—and results in a cosmology without a singular beginning, where Mach's Principle is a natural consequence. We argue that the choice between these paradigms is the most fundamental, and least examined, decision in modern physics.

1. Introduction: The Redshift and the Unexamined Axiom

In the early 20th century, astronomy revealed a near-universal fact: light from distant galaxies is redshifted, and this redshift is proportional to their distance. This observation demanded a causal explanation. Any such explanation must be built upon a foundational assumption about the nature of time itself. While General Relativity made the geometry of space dynamic, it did not explicitly overthrow the classical inheritance of a constant rate of cosmological time. The scientific community implicitly chose to preserve this temporal constancy, a decision that has dictated the entire trajectory of cosmological theory for a century. This paper will explore the consequences of that choice and contrast it with the alternative path not taken.

2. The Fixed Time Paradigm (FTP) and its Consequences

The Fixed Time Paradigm is the unspoken foundation of the standard Big Bang / ΛCDM model. Its core axiom can be stated as:

Axiom 1 (Fixed Time): The fundamental rate of physical processes (the "tick" of a universal clock) is constant throughout cosmological history.

When confronted with the observation of redshift, this axiom acts as a rigid constraint, forcing a specific chain of logical deductions:

1. Forced Conclusion 1: The Expansion of Space. If the clock of an emitting atom in the distant past was ticking at the same rate as our clock today, then the observed redshift cannot be a property of the source. The only remaining possibility is that the light wave was stretched during its journey. This necessitates the concept of a metric expansion of space. "Spatial Redshift" is the only available explanation.

2. Forced Conclusion 2: The Big Bang Singularity. If space is expanding now, it must have been smaller in the past. Logically extrapolating this backwards leads to a point of infinite density and zero volume—a singularity. The universe, therefore, must have had a beginning. The Cosmic Microwave Background (CMB) is then naturally interpreted as the afterglow of this hot, dense initial state.

3. Forced Conclusion 3: Exotic Entities. This model requires the invention of new entities to resolve discrepancies with observation. "Dark Matter" is needed to explain the observed rotation of galaxies, which the visible matter alone cannot account for. "Dark Energy" is needed to explain why the rate of the metric expansion of space appears to be accelerating.

The FTP creates a rich, complex, but also problematic narrative. It is a universe with a definite beginning, governed by a set of laws that require the existence of vast quantities of matter and energy that we cannot directly detect.

3. The Relative Time Paradigm (RTP) and its Consequences

The Relative Time Paradigm begins by rejecting the classical holdover. Its core axiom, derived from a fully relational and Machian interpretation of relativity, can be stated as:

Axiom 2 (Relative Time): The fundamental rate of physical processes is a dynamic variable, determined by the total gravitational potential of the universe (Φ ≈ Σ GM/r).

This axiom leads to a completely different, yet equally logical, chain of deductions:

1. Natural Conclusion 1: Temporal Redshift. In the past, the universe was denser, meaning the average distance r between masses was smaller. The total potential Φ was therefore stronger (more negative). According to the principles of GR, a stronger potential leads to a slower rate of time. Therefore, physics itself ran slower in the past. Redshift is the direct, expected consequence of observing a source from a slower temporal epoch with our faster, modern clock. It is a "Temporal Redshift."

2. Natural Conclusion 2: The Observational Horizon. An expansion of space is not required to explain the redshift. The "beginning" of the universe (the Big Bang) is re-interpreted as a perspectival limit. As we look further back in time, we are looking at epochs with progressively slower time rates relative to our own. The 13.8 billion light-year sphere is not a memory of a birth, but an observational horizon where the time rate of the early universe was so slow relative to ours that the redshift becomes infinite. The CMB is the thermalized radiation from this boundary.

3. Natural Conclusion 3: The Origin of Inertia. This model provides a direct physical mechanism for Mach's Principle. If our local dt is set by the cosmic Σ GM/r, then inertia—which is defined relative to dt—is not an intrinsic property of mass, but an emergent property of a body's relationship to the rest of the universe.

The RTP creates a picture of a unified, holistic universe where concepts like inertia are not axiomatic, but are consequences of the cosmic structure. It potentially explains the major observations of cosmology without the need for a singular beginning or exotic entities like dark energy.

4. A Comparative Table of Explanations

Phenomenon	Fixed Time Paradigm (FTP) Explanation	Relative Time Paradigm (RTP) Explanation
Cosmological Redshift	Spatial Redshift: The stretching of light by the expansion of space.	Temporal Redshift: The mismatch between slow past clocks and fast present clocks.
The Hubble Horizon	A Physical Beginning: The afterglow of the Big Bang singularity.	A Perspectival Limit: An observational horizon where the past time rate approaches zero relative to ours.
Inertia	An Intrinsic Property: An unexplained, axiomatic property of mass.	An Emergent Property: A consequence of the local rate of time being set by the total cosmic potential (Mach's Principle).
"Dark Energy"	A New Force: A mysterious energy field causing space to accelerate its expansion.	An Apparent Effect: A possible illusion caused by a non-linear acceleration of our local rate of time as the universe's potential evolves.

5. Conclusion: A Choice of Philosophy, A Question for Experiment

The standard cosmological model is not a direct reading of the evidence; it is the logical consequence of a foundational, philosophical choice made a century ago: the decision to preserve a classical, fixed rate of time. The Relative Time Paradigm shows that a different, equally valid choice leads to a radically different, and potentially simpler and more unified, cosmology.

This is not "mere philosophy." This fork in the road leads to distinct, testable predictions. The RTP predicts that inertia and dimensionless constants (like the fine-structure constant) should show a subtle, secular drift over cosmological timescales. The FTP firmly predicts they are absolutely constant.

The future of cosmology may depend not on building more complex theories upon the old foundation, but on having the courage to re-examine the foundation itself. The universe we think we live in may be an artifact of our unexamined assumptions about the nature of time.