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