On the Fundamental Origin and Upper Bound of the Speed of Light:

May 12, 2025

The historical derivation of the speed of light from Maxwell’s equations establishes its value in terms of the vacuum permittivity and permeability (c = 1/√(ε₀μ₀)). This result, while mathematically robust within classical electrodynamics, does not account for the invariance of the speed of light across all inertial frames. That invariance is not derived from Maxwell’s theory but is adopted as a foundational postulate in the formulation of special relativity.

Moreover, Maxwell’s framework operates within specific reference frames and does not inherently explain the physical origin or upper bound of the speed of light. In contrast, the Planck scale—introduced in 1899—offers a more fundamental perspective. The smallest physically meaningful units, the Planck length (Lₚ) and Planck time (Tₚ), define a natural upper bound on velocity, expressed as:

   c = Lₚ / Tₚ

This expression arises from dimensional analysis within quantum gravity and not from classical field equations. It provides a boundary condition that limits all propagation processes, including those involving particles or wave phenomena associated with effective or apparent mass.

As such, the value of c is not explained within the frameworks of classical electromagnetism or special relativity, but rather bounded by physical constraints implied at the Planck scale. Reintroducing the classical derivation of c without acknowledging the quantum-gravitational context overlooks the deeper issue: neither Maxwell’s equations nor special relativity explain why the speed of light is c—they either compute or assume it. The Planck scale offers a more foundational interpretation by establishing the physical boundary that constrains this value.

Sincerely,

Soumendra Nath Thakur

Photon Behaviour Under Negative Apparent Mass in ECM:

Soumendra Nath Thakur

May 11, 2025

In the Extended Classical Mechanics (ECM) framework, the photon—being perpetually in motion—is modelled as a massless particle with a dynamic negative apparent mass (−Mᵃᵖᵖ), distinguishing it fundamentally from ordinary matter. This −Mᵃᵖᵖ accounts for the photon's repulsive interaction with massive bodies and its resistance to gravitational attraction, balanced by an intrinsic energy expenditure.

The effective acceleration (aᵉᶠᶠ) of the photon is state-dependent:

* Upon emission within a gravitationally bound system, the photon exhibits aᵉᶠᶠ = 2c, leading to an effective force of Fₚₕₒₜₒₙ = −2Mᵃᵖᵖ · aᵉᶠᶠ.

* As the photon escapes the gravitational influence of the source, aᵉᶠᶠ reduces to c, and the force becomes Fₚₕₒₜₒₙ = −Mᵃᵖᵖ · aᵉᶠᶠ, reflecting the energetic cost of decoupling from the source's gravitational field.

Although the photon tends toward infinite velocity and frequency due to its −Mᵃᵖᵖ-driven dynamics, this behaviour is constrained by the Planck thresholds:

    f < fₚ ; λ > lₚ and Δt > Tₚ.

These bounds define the photon's maximum frequency and minimum wavelength, stabilizing its propagation speed at c—the maximum permissible speed under ECM, assuming vacuum conditions.

In refractive or reflective media, photons are entirely absorbed and re-emitted by bound electrons. This interaction introduces a time delay between incidence and re-emission, lowering the photon’s effective frequency and causing a transient reduction in speed. Nevertheless, these effects are environmental and do not contradict the constancy of photon speed in free space.

Thus, under ECM, the photon's behaviour—including its effective acceleration, energy dissipation, and Planck-limited oscillation—is a direct consequence of its negative apparent mass (−Mᵃᵖᵖ) and the fundamental constraints of the vacuum medium.

Can Spinning a Crystal Distort Time? This Experiment Says Yes—Without Einstein

Soumendra Nath Thakur

Tagore's Electronic Lab, India

May 10, 2025

In a laboratory experiment, scientists spun a special type of crystal called a piezoelectric—a material known for generating electricity when it's squeezed or stretched. But here’s the twist: they didn’t apply any power at all. They simply rotated the crystal, and it began to generate a clean 50 Hz electrical signal entirely on its own.

Even more curious? That signal started to drift in time. Imagine a metronome ticking, but each tick slowly shifting forward. This steady “phase shift” wasn’t noise or error—it was perfectly matched to how fast the crystal was spinning. That means the act of rotating the crystal was somehow affecting the timing of the signal it produced.

So what’s going on?

This surprising behaviour actually fits beautifully with the fundamental principles of piezoelectricity: the internal structure of the crystal responds to mechanical stress—in this case, the stresses caused by rotation. But there’s a deeper message. The experiment points to a bold new idea called Extended Classical Mechanics (ECM), which suggests that motion—especially acceleration—can change how time flows inside matter.

In short, this crystal didn’t just make electricity—it acted like a clock whose rhythm was bent by motion. No need for satellites or speed-of-light travel—just an ordinary device showing that even here on Earth, motion can subtly reshape time.

This ground breaking result opens new doors for precision sensors, navigation tech, and even how we understand time itself. Sometimes, spinning a crystal is all it takes to shake up physics.

Experimental Phase Shift in Rotating Piezoelectric Device

Soumendra Nath Thakur
Tagore's Electronic Lab, India
May 10, 2025

This experiment used a piezoelectric crystal—materials that can turn mechanical pressure into electrical signals—to explore how motion affects time. Normally, piezoelectric devices need electricity to work, but here, no electricity was applied. Instead, the crystal was simply rotated.

Surprisingly, the crystal started producing a clear 50 Hz electrical signal all on its own, and more importantly, that signal began to slowly drift in phase, meaning its timing was shifting little by little—like a second hand running slightly ahead or behind on a clock. This shift wasn’t random; it matched the speed of rotation, showing that the motion itself was causing a change in the crystal’s internal behaviour.

This lines up perfectly with how piezoelectric materials work: when they're squeezed, stretched, or rotated, their structure changes in ways that can generate electricity. The experiment showed that rotation was enough to create internal stresses in the crystal that made it behave like a tiny self-powered clock—one whose timing was subtly altered just by being spun.

These findings support a new physics idea called Extended Classical Mechanics (ECM), which says that motion—especially acceleration—can directly affect how time flows inside matter. The phase drift we saw in the experiment is like a fingerprint of this effect. So in simple terms: spinning the crystal made it create its own voltage and shift its timing, proving that motion can affect time in a measurable, physical way—without needing relativity or space travel.

Relativity does not have a mathematical explanation for why the speed of light is c:

May 09, 2025

The assertion that "Relativity does not have a mathematical explanation for why the speed of light is c" is fundamentally correct. In special relativity, the invariance of the speed of light is not derived from first principles but postulated as a foundational axiom. While Maxwell’s equations predict that electromagnetic waves propagate at a fixed speed c in vacuum, these equations are formulated within particular reference frames and do not inherently explain why this speed should remain invariant across all inertial observers. Special relativity adopts this invariance as its second postulate: that the speed of light in a vacuum is the same for all observers, regardless of their relative motion. As such, the value of c is not mathematically deduced from within relativity—it is assumed.

In standard relativity, photons are treated as massless (rest mass m = 0), yet they carry energy and momentum, implying an effective inertial influence. In Extended Classical Mechanics (ECM), this leads to a re-interpretation: photons and other massless particles can exhibit negative apparent mass (Mᵃᵖᵖ < 0) due to their kinetic energy characteristics. This challenges the conventional notion of masslessness by introducing a dynamical interpretation tied to acceleration and force. Similarly, in cosmological contexts, dark energy—such as that inferred in studies by A. D. Chernin et al. on the Coma Cluster—is interpreted as having negative effective mass, a view consistent with ECM’s framework.

Within ECM, particles exhibiting negative apparent mass—such as photons emitted from gravitationally bound systems—tend toward unbounded propagation speeds. This provides an alternative explanation for the observed superluminal recession of distant galaxies, where the recession is not merely a relativistic artifact of metric expansion, but a real, force-driven phenomenon resulting from gravitational–antigravitational interaction. Specifically, such recession occurs when the negative effective mass component dominates over the matter mass, producing a net repulsive dynamic. Here, "unbounded" refers to the mathematical tendency of speed to diverge as apparent mass becomes increasingly negative or frequency increases without bound.

However, ECM also acknowledges that physical unboundedness is constrained by fundamental quantum limits. The Planck scale introduces the smallest meaningful physical quantities—the Planck length (Lₚ) and Planck time (Tₚ)—which naturally impose an upper bound on velocity. This bound is expressed through the ratio:

  c = Lₚ / Tₚ

This expression does not emerge from relativity itself but from dimensional considerations in quantum gravity. It defines the maximum attainable speed for any propagation process, including those involving particles with Mᵃᵖᵖ < 0. While mathematical models may suggest speeds approaching infinity, the Planck scale sets a physical boundary, beyond which further acceleration or frequency increase ceases to be meaningful or measurable. In this way, ECM preserves causal consistency and enforces a speed limit—not as a postulate of relativity or a consequence of spacetime curvature, but as a boundary arising from the discrete, physical limits imposed by the Planck scale.

Regards,

Soumendra Nath Thakur