Soumendra Nath Thakur
April 09. 2025
Mr. Vikram Zaveri’s statement, “Fundamentally, time is periodic in nature. It is not linear like in modern science,” distorts the functional and empirical interpretation of time within physical frameworks—both classical and quantum—as well as observational cosmology. Time, in its operational sense, is defined through sequential events and causality. While periodicity is an inherent characteristic of oscillatory systems (such as wave mechanics), this does not imply that time itself is periodic. Periodicity applies to physical processes within time, not time as a dimension of measurement.
1. On the Definition of Speed of Light:
The claim that “the accurate definition of speed of light is c = λ/T and not d/t” unnecessarily restricts the concept of speed to wave periodicity and overlooks the broader physical definition of speed:
c = d/t
This classical definition remains valid and fundamental. The equation c = λ/T is a specific case of d/t, when considering a periodic wave. As such, both formulations are compatible. In fact, I have shown in the ECM framework:
ΔS = Δd/Δt ⇨ c = λ/Δt
This makes your equation c = λ/T a subset of a more general and foundational expression of speed. There is no contradiction, only contextual application.
2. On the ‘Periodic Invariant’ and Null Geodesic Argument:
Your reference to the “periodic invariant” s² = λ² - c² T² and the condition s² = 0 for photons indeed mimics the relativistic null geodesic condition. However, the Extended Classical Mechanics (ECM) approach intentionally moves beyond relativistic assumptions, particularly those that involve spacetime curvature or geodesics.
ECM posits that light's constant speed can be understood non-relativistically, by considering:
• the anti-gravitational nature of photons (via negative apparent mass),
• the negligible influence of observer motion in a dominant anti-gravitational frame, and
• the physical limits imposed by Planck-scale constraints, which cap wavelength and frequency at known extremes.
The assertion that light must satisfy a periodic invariant assumes the primacy of wave periodicity over the energetic and gravitational character of photon dynamics. ECM, on the other hand, recognizes that the speed of light emerges from energy-frequency-distance consistency within a mass-energy dominated framework, not necessarily from relativistic invariants.
3. On the Role of Observer’s Mass and Motion:
Your claim that “discussion on mass of the observer is irrelevant” misses a key point. The ECM framework treats observer dynamics not merely as a mathematical abstraction but as physically significant in interpreting measurement reference frames.
In a universe where negative apparent mass (-Mᵃᵖᵖ) and effective anti-gravitational dynamics dominate, the motion of an observer (with positive matter mass) becomes negligible in contrast. This is not a metaphysical notion but a measurable consequence of mass-energy interaction and frame dominance.
Hence, dismissing the mass-energy structure of the observer as irrelevant fails to acknowledge the measurement system’s physical embedding in the universe’s gravitational architecture.
4. On the Planck Scale and the Existence of Light:
The claim “Planck scale is questionable because light did not exist at Planck time” conflates existence of photons with the validity of Planck limits.
The Planck time (≈ 5.39 × 10⁻⁴⁴ s) marks the limit of meaningful physical measurements, not the emergence of specific particles like photons. Whether or not light existed at that instant is irrelevant to the fact that wavelengths shorter than ℓₚ and frequencies higher than fₚ lose physical meaning.
Planck limits define boundaries of physical resolution, not the actual timeline of photon creation.
Furthermore, ECM accommodates the emergence of light after the Planck era—especially near the symmetry-breaking scales—while still employing Planck boundaries as fundamental constraints on physical observables, including light.
5. On the Status of Dark Matter and Dark Energy:
While you state “dark matter and dark energy are not discovered”, this overlooks strong indirect empirical evidence:
• Galaxy rotation curves (Zwicky, Rubin),
• CMB anisotropies (Planck, WMAP),
• Large-scale structure and baryon acoustic oscillations,
• Supernovae redshift observations (Riess, Perlmutter).
Although not directly detected, their gravitational and energetic effects are measurable. ECM integrates these observations within a coherent force-energy framework, utilizing negative effective mass (-Mᵉᶠᶠ) and apparent mass displacement to rationalize cosmic acceleration and photon dynamics.
Summary:
Your assertion of time’s periodicity, the absolute supremacy of relativistic invariants, and dismissal of the Planck scale or observer mass ignores the measurable, energy-based structure of the universe that ECM emphasizes.
ECM does not deny periodicity, nor does it conflict with wave mechanics. Instead, it enhances our understanding by interpreting the speed of light through:
• anti-gravitational motion of photons (via −Mᵃᵖᵖ),
• negligible gravitational motion of observers (positive Mᴍ),
• Planck constraints as limits of observable quantum motion,
• and a dominant measurement system dictated by effective mass-energy distributions, not solely geodesics or classical periodic invariants.
