[Paper Review] The Theory of Relativity - Galileo's Child

Mitchell J. Feigenbaum|ArXiv.org|Jun 6, 2008

Relativity and Gravitational Theory10 references15 citations

TL;DR

This paper demonstrates that the Lorentz transformations and the full kinematic structure of special relativity emerge purely from Galileo's principle of relativity and the isotropy and homogeneity of space, without any reference to the speed of light. The key result is that relativity is logically independent of light's properties, with the constant $1/c^2$ arising as a universal parameter from spacetime symmetry alone.

ABSTRACT

We determine the Lorentz transformations and the kinematic content and dynamical framework of special relativity as purely an extension of Galileo's thoughts. No reference to light is ever required: The theories of relativity are logically independent of any properties of light. The thoughts of Galileo are fully realized in a system of Lorentz transformations with a parameter 1/c^2, some undetermined, universal constant of nature; and are realizable in no other. Isotropy of space plays a deep and pivotal role in all of this, since here three-dimensional space appears at first blush, and persists until the conclusion: Relativity can never correctly be fully developed in just one spatial dimension.

Motivation & Objective

• To establish that special relativity can be derived solely from Galileo's principle of relativity and spacetime symmetries, without invoking light or its speed.
• To refute the widespread belief that the constancy of light speed is a necessary postulate for relativity.
• To clarify that isotropy and homogeneity of space are essential and non-negotiable in deriving the Lorentz transformations.
• To show that the mathematical structure of relativity is uniquely determined by Galilean thought when extended to three spatial dimensions.
• To correct the misconception that relativity depends on electromagnetic theory or light-based experiments, by proving its foundation is kinematic and geometric.

Proposed method

• Derive the most general linear transformation between inertial frames using only Galileo's principle of relativity and the isotropy of space.
• Impose homogeneity of space and time to enforce linearity of the transformation, ensuring consistent dynamics across all spacetime points.
• Use rotational invariance (isotropy) in three spatial dimensions to constrain the form of the transformation, excluding one-dimensional solutions.
• Introduce a universal constant parameter $1/c^2$ as the only free parameter in the transformation, derived from symmetry alone.
• Show that the resulting transformation is uniquely the Lorentz transformation, with no alternative forms possible under the given constraints.
• Demonstrate that the constancy of light speed is a consequence, not a postulate, of this symmetric framework.

Experimental results

Research questions

• RQ1 Can the Lorentz transformations be derived from Galileo’s principle of relativity and spacetime symmetries without assuming the constancy of light speed?
• RQ2 Why is isotropy of space essential for deriving three-dimensional relativity, and why do one-dimensional derivations fail to capture the full structure?
• RQ3 Is the speed of light a fundamental postulate of relativity, or is it a derived property of the spacetime symmetry framework?
• RQ4 What role does homogeneity of space and time play in ensuring the linearity and consistency of the Lorentz transformation?
• RQ5 Can the entire framework of special relativity be reconstructed as a natural extension of Galilean kinematics, independent of electromagnetic theory?

Key findings

• The Lorentz transformations are uniquely determined by Galileo’s principle of relativity, isotropy, and homogeneity of space and time, with no reference to light required.
• The parameter $1/c^2$ emerges as a universal constant of nature from spacetime symmetry, not from electromagnetic properties.
• Isotropy in three spatial dimensions is essential; the theory cannot be consistently formulated in one dimension without violating rotational symmetry.
• The constancy of the speed of light is not a postulate but a consequence of the symmetric structure of spacetime, making it logically independent of relativity’s foundations.
• The theory of relativity is epistemologically and mathematically self-contained, with no dependence on the physical properties of light or photons.
• Even if light were found to be composite or massive, the kinematic framework of relativity—defined by $1/c^2$—would remain valid, as it is rooted in symmetry, not in light itself.