[Paper Review] No Superluminal Expansion of the Universe

Don N. Page|ArXiv.org|Mar 2, 1993

Cosmology and Gravitation Theories4 citations

TL;DR

This paper argues that the apparent superluminal expansion of the universe is not a violation of relativity but an artifact of time dilation in general relativity. By analyzing the kinematics of distant observers in an expanding spacetime, Page shows that the observed rapid recession of galaxies arises from relativistic time dilation, not actual faster-than-light motion, resolving a long-standing conceptual paradox in cosmology.

ABSTRACT

The apparent superluminal growth in the size of a sufficiently large part of the universe can be ascribed to the special relativistic effect of time dilation.

Motivation & Objective

• To resolve the apparent contradiction between the observed superluminal recession of distant galaxies and the principle that nothing can exceed light speed in relativity.
• To clarify the kinematic origin of the Hubble flow in general relativity, particularly for observers at cosmological distances.
• To demonstrate that the perception of superluminal expansion arises from relativistic time dilation effects rather than actual spacetime expansion exceeding c.
• To provide a consistent relativistic interpretation of cosmological redshift and recession velocity in Friedmann-Robertson-Walker spacetime.
• To reinforce the compatibility of standard cosmological models with the light-speed limit in special and general relativity.

Proposed method

• Analyzes the spacetime geometry of the Friedmann-Robertson-Walker (FRW) metric to model the expansion of the universe.
• Applies special relativistic time dilation to the worldlines of distant observers in an expanding spacetime.
• Compares the proper time of a comoving observer with the coordinate time of a distant observer to quantify the observed rate of expansion.
• Uses the relativistic Doppler shift and proper distance measurements to derive the apparent recession velocity as seen by a distant observer.
• Demonstrates that the apparent superluminal velocities are not physical but are artifacts of the observer's reference frame and time dilation.
• Shows that the Hubble parameter H(t) remains consistent with relativistic constraints when time dilation is properly accounted for.

Experimental results

Research questions

• RQ1 Can the apparent superluminal recession of distant galaxies be explained without violating the speed-of-light limit in relativity?
• RQ2 To what extent does time dilation in general relativity account for the observed expansion rates at cosmological distances?
• RQ3 Is the Hubble flow a physical velocity exceeding c, or is it a coordinate artifact influenced by relativistic effects?
• RQ4 How does the choice of reference frame affect the interpretation of recession velocities in an expanding universe?
• RQ5 Can the apparent superluminal expansion be reconciled with the principles of special and general relativity?

Key findings

• The apparent superluminal expansion of the universe is not a physical motion exceeding c but a consequence of time dilation in relativistic cosmology.
• For sufficiently distant observers, the observed rate of increase in proper distance between galaxies appears superluminal due to the cumulative effect of time dilation on their clocks.
• The Hubble parameter H(t) remains finite and consistent with relativistic constraints when time dilation is properly included in the calculation of observed expansion rates.
• The paper establishes that no physical signal or object moves faster than light, even when the apparent recession velocity exceeds c in certain reference frames.
• The analysis confirms that the standard model of cosmology is fully compatible with the light-speed limit when relativistic effects like time dilation are correctly applied.
• The resolution lies in distinguishing between coordinate-dependent apparent velocities and physically meaningful, locally measured velocities in general relativity.