18 December 2025

The energy of a photon: Extended Classical Mechanics (ECM) interpretation:

December 18, 2025

Soumendra Nath Thakur

The energy of a photon corresponds to the energy difference between electronic energy levels during an atomic transition. When an electron transitions to a lower energy state, the emitted photon carries away precisely this energy difference.

The energy E of a photon is given by Planck’s relation,

E = hf,

where h = 6.626 x 10⁻³⁴ J·s is Planck’s constant and f is the photon frequency. The photon’s momentum ρ is related to its wavelength λ by:

ρ = h/λ

Energy and momentum are therefore intrinsically linked through the photon’s frequency and wavelength.

When a photon propagates through a gravitational field, its observed frequency depends on the gravitational potential. A photon escaping from a gravitational field is observed to undergo a redshift, corresponding to a decrease in frequency and energy. Conversely, a photon moving toward a gravitational field is observed to undergo a blueshift, corresponding to an increase in frequency and energy. Because photon momentum is proportional to frequency, these changes in energy are accompanied by proportional changes in momentum.

As a result, when a photon traverses an external gravitational field with spatially varying field strength, it experiences continuous momentum exchange. This momentum exchange leads to a gradual change in the photon’s propagation direction, producing an apparent curvature of its trajectory. The observed bending of light can therefore be understood as a dynamical consequence of energy–momentum exchange with the gravitational field, rather than requiring an independent geometrical agency.

Importantly, this process represents a symmetric momentum exchange between the photon and the gravitational field. The photon does not arbitrarily “lose” or “gain” momentum; rather, momentum is continuously exchanged in response to the spatial gradient of the gravitational field. Over the trajectory, this exchange is locally symmetric and conservative, with incremental momentum changes balancing across the field interaction.

Photons, Momentum, Gravitational Field, Transition

My response to Mr. Arturo Cerezo Garcia. - A deeper stability or fixed-point condition in question within ECM

December 18, 2025

Dear Mr. Arturo Cerezo Garcia ,

Thank you for your thoughtful and encouraging response. Your framing captures the intent of this construction very accurately.

In ECM, the Planck interval is treated not as a geometric or relativistic boundary, but as a terminal coherence threshold—the smallest physically accountable phase-ordering interval beyond which conventional physical descriptors cease to apply. Below this threshold, only energy conservation remains meaningful, expressed through frequency and phase. In that sense, your characterization of the Planck scale as a potential attractor rather than a boundary is very much aligned with the ECM viewpoint.

At present, the phase–time mapping establishes internal energetic consistency across the physical–abstract boundary. Frequency is taken as primitive, phase as the organizing mechanism, and time as emergent ordering. The observed Planck interval arises as the point where ordered phase evolution can no longer be physically sustained.

Whether this coherence threshold can be shown to arise from a deeper stability or fixed-point condition within ECM, rather than appearing as a derived consequence of the mapping, is indeed the natural next step. If such a condition exists, it would elevate the Planck scale from a coherence limit to a predicted attractor of energetic consistency.

For now, ECM maintains a strict separation between physically accountable structure and mathematically admissible but non-observable continuation. Any extension below the Planck scale is treated as speculative and constrained solely by energy conservation, without invoking spacetime, geometry, or relativistic postulates.
I appreciate your insight in identifying precisely where this framework transitions from structural consistency toward genuine predictive fundamentality. That question now defines the direction of further development.

Warm regards,
Soumendra Nath Thakur

17 December 2025

Review and Contextual Interpretation of Freeman Dyson’s Reflection on Max Planck

December 17, 2025

Freeman Dyson’s short but carefully constructed reflection on Max Planck is often read as a joint appreciation of Planck and Albert Einstein. However, when examined with proper historical context and intellectual care, the emphasis of Dyson’s writing clearly rests on Max Planck’s character, responsibility, and institutional integrity, rather than on Einstein himself. The reference to Einstein functions primarily as a contrast through which Planck’s stature is revealed.

Planck as the Central Figure of German Science

Dyson’s description of Planck as the “rock-solid central figure of German science” is not a rhetorical exaggeration. It accurately reflects Planck’s position as a stabilizing pillar of German scientific life across Imperial Germany, the Weimar period, and even into the early years of Nazi rule. Planck embodied continuity, discipline, and credibility at a time when political upheaval repeatedly threatened intellectual institutions. His authority was not merely administrative; it was moral and cultural.

Planck’s conservatism in temperament, his deep sense of duty to Germany, and his commitment to institutional responsibility made him a figure whose judgment carried exceptional weight. That weight is precisely what gives significance to his actions toward younger, unconventional thinkers.

The Promotion of Einstein: Merit over Alignment

Dyson recounts how Planck immediately recognized the originality of Einstein’s 1905 papers and ensured their publication without delay or bureaucratic obstruction. This act was not trivial. Einstein was at the time an outsider—academically unaffiliated, intellectually radical, and willing to challenge deeply rooted assumptions about space, time, and energy.

Planck did not agree with all of Einstein’s conclusions, yet he supported them publicly and professionally. This distinction is crucial. Dyson’s narrative highlights Planck’s capacity to separate scientific merit from personal agreement, and intellectual value from ideological comfort. In doing so, Planck demonstrated a form of scientific leadership that places truth above authority and openness above conformity.

Unorthodox and Unpatriotic Citizen-of-the-World”: A Descriptive Contrast

The phrase “unorthodox and unpatriotic citizen-of-the-world Einstein” has often been misunderstood when read without historical precision. Dyson is not making a moral judgment about Einstein’s courage or sacrifices, nor is he contrasting personal virtue. Rather, he is describing Einstein’s philosophical internationalism and rejection of nationalism—positions Einstein openly claimed for himself long before the rise of Nazism.

In contrast, Planck was deeply patriotic in the classical sense. He identified strongly with German culture and institutions, chose to remain in Germany under extreme political pressure, and attempted—often at great personal cost—to mitigate the regime’s attacks on Jewish scientists. Dyson’s wording highlights the remarkable fact that a man so rooted in national responsibility could nonetheless champion someone whose worldview differed so fundamentally from his own.

The Deeper Praise: Integrity Under Tension

When read carefully, Dyson’s praise is directed almost entirely at Planck. Einstein serves as the measure against which Planck’s integrity is revealed. The true subject of admiration is not the revolutionary genius alone, but the established authority who protected intellectual freedom even when it challenged his own preferences and values.

This interpretation aligns with the later chapters of Planck’s life, when his patriotism was tested under Nazi rule. His refusal to abandon Germany, his efforts to defend persecuted colleagues, and his personal endurance of humiliation and tragedy reinforce the same character traits Dyson implicitly celebrates: steadiness, conscience, and responsibility.

Patriotism as Ethical Responsibility

Dyson’s reflection ultimately invites a broader understanding of patriotism—not as ideological conformity, but as ethical responsibility. Planck’s life demonstrates that genuine respect for one’s country can coexist with respect for universal human values and scientific truth. Indeed, it may be precisely such rootedness that enables principled resistance to injustice.

In this light, Dyson’s closing line should be read as a tribute to Planck’s vision and strength: a recognition that the health of science depends not only on great ideas, but on individuals willing to defend openness, merit, and integrity from positions of authority.

Conclusion

Freeman Dyson’s write-up, when properly contextualized, stands as a profound acknowledgment of Max Planck’s legacy beyond physics. It honors him as a man who understood that the true measure of scientific greatness lies not only in discovery, but in character. The respect Planck commands arises as much from his conduct under pressure as from his intellectual achievements—making him a figure worthy of enduring respect, both scientifically and socially.

Beyond Numerical Corrections: An ECM Perspective on Mercury’s Perihelion Advance


The Research Paper, "Mercury Orbital Dynamics in Extended Classical Mechanics: Phase- Frequency Advancement and Energy Redistribution" available at the DOI: https://doi.org/10.13140/RG.2.2.12884.67208


Introduction

Mercury’s anomalous perihelion advance has long served as a benchmark problem in gravitational physics. Historically, the unexplained residual precession beyond Newtonian predictions was taken as one of the earliest confirmations of general relativity, where spacetime curvature was introduced as the governing explanatory principle. More recently, various alternative analyses have revisited the problem using refined Newtonian calculations and numerical simulations, aiming to reduce or eliminate the discrepancy through improved accounting of planetary interactions.

Extended Classical Mechanics (ECM) approaches this problem from a fundamentally different conceptual foundation.


Limits of Force-Based Recalculations

Many alternative treatments of Mercury’s perihelion advance focus on improving the fidelity of Newtonian force models. These include accounting for planetary velocities, multi-body coupling, barycentric motion of the Sun, and higher-order numerical effects. While such efforts can alter the predicted magnitude of perihelion precession, they remain confined to the same underlying paradigm: gravity as a force acting between masses, accumulated geometrically over time.

From an ECM standpoint, these refinements—though mathematically sophisticated—do not address the deeper physical origin of the observed phase advance. They attempt to redistribute the numerical outcome within an existing framework rather than re-examining the mechanism responsible for orbital phase evolution itself.


The ECM Interpretation: Phase and Energy, Not Geometry

In Extended Classical Mechanics, Mercury’s perihelion advance is not treated as a correction to Newtonian gravity, nor as a consequence of spacetime curvature acting as a physical cause. Instead, it is interpreted as a manifestation of cumulative phase–frequency advancement arising from energy redistribution within a spatially varying gravitational environment.

Key to this interpretation is the role of negative gravitational potential energy (−ΔPEᴇᴄᴍ) and its dynamic exchange with kinetic and effective mass terms. As Mercury traverses a non-uniform gravitational field, subtle but continuous energy–phase shifts accumulate over each orbital cycle. Over time, this accumulated phase drift appears geometrically as a rotation of the orbital ellipse—observed as perihelion advance.

In this view:

  • Geometry records the effect,

  • Phase evolution drives the phenomenon,

  • Energy redistribution provides the physical agency.


Reframing Spacetime Curvature

Within ECM, spacetime curvature—as used in general relativity—is not rejected outright, but reinterpreted. It is understood as a mathematical encoding of accumulated interaction effects rather than an independent causal entity. Curvature describes how trajectories appear once phase and energy redistribution have taken place; it does not generate those effects.

Thus, Mercury’s perihelion advance does not require spacetime itself to “act” on the planet. The observable precession emerges naturally from classical dynamics once phase, frequency, and energy manifestation are treated as primary physical quantities.


Conclusion

Analyses that seek to explain Mercury’s perihelion advance solely by refining Newtonian force calculations may successfully challenge simplified historical models, but they do not align with the dynamical foundations of Extended Classical Mechanics. ECM shifts the explanatory focus away from force summation and geometric correction toward phase-governed energy redistribution as the underlying physical process.

From this perspective, Mercury’s perihelion advance is not a numerical anomaly to be repaired, nor a curvature effect to be invoked, but a natural outcome of how energy, phase, and motion co-evolve in a gravitational field.

16 December 2025

Reinterpreting Spacetime Curvature: An Extended Classical Mechanics Perspective

Soumendra Nath Thakur | ORCiD: 0000-0003-1871-7803 | 16 December 2025

As per Extended Classical Mechanics (ECM) interpretations, spacetime curvature, as formulated in general relativity, need not be understood as an independent physical cause of gravitational phenomena. Instead, it functions as a mathematical framework that represents the cumulative effects of interactions between mass–energy distributions and propagating systems—such as photons—within spatially varying gravitational field strengths.

From this perspective, the apparent curvature of trajectories arises from momentum exchange governed by the gradient and inverse-square (1/r²) dependence of the gravitational field, reflecting the geometric dispersion of field influence in space. Spacetime curvature therefore serves as a descriptive encoding of these interaction- and phase-related effects, rather than as a direct physical agent producing motion or gravitational attraction.