What question did this study set out to answer?

To provide a new logical framework for understanding light speed within Time Field Theory, challenging classical views.

July 5, 2026Open Access

Light is Not Motion: The Logical Foundations of Light Speed, Calculus of Variations, and Calculus — The Ontological Position of Light in Mathematical Structure from the Perspective of Metric Self-Consistency

Key Points

To provide a new logical framework for understanding light speed within Time Field Theory, challenging classical views.
Re-examine speed of light using Time Field Theory (TFT).
Demonstrate that light functions as a geodesic based on Fermat's principle.
Establish logical connections between speed of light and variational calculus.
Proves light satisfies first-order vanishing variation conditions, indicating its geodesic nature.
Identifies zero intrinsic time of photons as essential for calculations related to light speed.
Establishes metric self-consistency as the foundation of light's constant speed in path space.

Abstract

This paper re-examines the fundamental physical connotation of the speed of light under the framework of Time Field Theory (TFT). Contrary to classical physics that regards light as a material entity moving at constant c, this paper ontologically proves that light is a geodesic satisfying the first-order vanishing variation condition of Fermat’s principle: ds / =0. The zero intrinsic time of photons vₓ=0 is not a negative physical feature of light, but a precondition that legitimizes the calculus of variations for physical research. This paper constructs a closed logical chain: metric self-consistency flux conservation () =0 Fermat’s principle ds / =0 vanishing first variation zero intrinsic time of photons locally unique constant speed of light differential relation ds=c dt calculus as a valid language for physical description. If any link in this chain breaks (variable light speed or non-zero intrinsic time for photons), the underlying logic supporting calculus and variational calculus as physical tools will fully collapse. The speed of light is not an inherent property of moving substances; it is the mathematical signature of metric self-consistency in path space. Metric Self-Consistency → ∇· (γ∇γ) =0 → δ∫ (ds/γ) =0 → Vanishing First Variation → Zero Intrinsic Time of Photons (vₜ=0) → uniquely defined local γ → Constant Speed of Light ds = cγ dt well-defined → Calculus Valid for Physical Analysis

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