[Paper Review] Derivation of the Lorentz transformation without the use of Einstein's second postulate

Andrei Galiautdinov|arXiv (Cornell University)|Jan 1, 2017

Relativity and Gravitational Theory2 references3 citations

TL;DR

This paper derives the Lorentz transformation using only the principles of relativity, isotropy, homogeneity, and the operational definition of clock synchronization—without invoking Einstein’s second postulate (constancy of the speed of light). It shows that the Lorentz transformation and its key features—such as time dilation, length contraction, and the invariance of the speed of light—follow from symmetry and operational definitions alone, resolving the faster-than-light neutrino controversy by demonstrating that superluminal particles would violate causality in a statistical, macroscopic sense.

ABSTRACT

Derivation of the Lorentz transformation without the use of Einstein's Second Postulate is provided along the lines of Ignatowsky, Terletskii, and others. This is a write-up of the lecture first delivered in PHYS 4202 E&M class during the Spring semester of 2014 at the University of Georgia. The main motivation for pursuing this approach was to develop a better understanding of why the faster-than-light neutrino controversy (OPERA experiment, 2011) was much ado about nothing.

Motivation & Objective

• To provide a derivation of the Lorentz transformation that does not rely on Einstein’s second postulate (constancy of the speed of light).
• To clarify the foundational assumptions underlying special relativity, emphasizing symmetry principles and operational definitions.
• To resolve the misconception behind the 2011 OPERA faster-than-light neutrino anomaly by showing that such particles would violate causality in macroscopic systems.
• To demonstrate that the invariance of the speed of light and the structure of spacetime emerge naturally from symmetry and synchronization procedures.

Proposed method

• Uses the principle of relativity, spatial and temporal homogeneity, isotropy, and continuity as foundational symmetries.
• Defines inertial frames via floating-ball detectors that remain at rest when unforced, ensuring no external influences.
• Introduces operational clock synchronization using light signals or identical balls released from a midpoint, ensuring simultaneity is defined, not assumed.
• Applies the Lorentz transformation to events in two inertial frames, K and K′, using the transformation equations derived from symmetry and synchronization.
• Derives the transformation of time and space intervals between events using the gamma factor γ = 1/√(1−v²/c²), showing that it arises from symmetry, not postulate.
• Demonstrates that the speed of light c is invariant across frames as a consequence of the transformation, not a postulate.

Experimental results

Research questions

• RQ1 Can the Lorentz transformation be derived without assuming the constancy of the speed of light as a postulate?
• RQ2 What fundamental symmetries and operational definitions are sufficient to derive the structure of spacetime in special relativity?
• RQ3 Why was the faster-than-light neutrino result from the OPERA experiment physically implausible?
• RQ4 How does the relativity of simultaneity and time dilation emerge from symmetry and synchronization alone?
• RQ5 What is the role of causality in ruling out tachyons, and how does it relate to thermodynamic principles?

Key findings

• The Lorentz transformation can be derived from symmetry principles—homogeneity, isotropy, continuity, and the relativity principle—without invoking Einstein’s second postulate.
• Clock synchronization via light signals or identical balls leads to the same transformation equations, showing that the structure of spacetime is operationally defined.
• The speed of light c is invariant across all inertial frames as a consequence of the transformation, not a starting assumption.
• Time dilation and length contraction emerge naturally from the transformation: moving clocks run slow by a factor of 1/γ, and moving rods contract by a factor of 1/γ.
• Events that are simultaneous in one frame are not simultaneous in another, demonstrating the relativity of simultaneity.
• Tachyons (faster-than-light particles) would violate causality in macroscopic systems, which is ruled out by the second law of thermodynamics, thus making superluminal neutrinos impossible.