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
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