The equation  (derived from ) conceptually implies that the frequency of a quantum object (like a photon) can be related to an effective mass via the equivalence of energy and mass.
5. Reconciling GR and QFT Through
This relation can offer several possible insights into bridging GR and QFT:
(a) Quantum Interpretation of Gravity:
In GR, gravity is sourced by mass and energy, which curve spacetime. If we treat frequency as being equivalent to mass via , this implies that quantum properties (like the frequency of a photon) can have a gravitational effect, even though we usually think of mass as the gravitational source.
This formalism hints at the idea that gravitational effects can be linked to quantum frequencies, which might help us develop a quantum theory of gravity. In such a theory, not only mass but also the quantum properties (like frequency and energy) of particles would influence the curvature of spacetime.
(b) Photon as a Bridge Between Mass and Energy:
Photons, despite being massless, carry energy through their frequency. The relation  can be viewed as a way of treating the photon’s frequency as a type of "effective mass" in the context of gravitational interactions.
If we interpret frequency as mass, then the bending of light (photon interaction with gravity) could be seen as a manifestation of the photon's "effective mass" curving spacetime in the same way that normal mass does. This interpretation could provide a way to understand gravity at the quantum level, where particles do not have mass in the traditional sense, but still carry energy and frequency.
(c) Energy and Geometry:
The relation  could potentially lead to a new way of thinking about spacetime curvature. In GR, spacetime is curved by the presence of mass and energy. If frequency (a quantum property) is analogous to mass, this could imply that quantum properties, like frequency, curve spacetime in the same way mass does.
This might open up the possibility of describing spacetime geometry using quantum field theory language, where the curvature of spacetime is influenced not just by classical mass-energy, but by the quantum fields (with associated frequencies) themselves.
6. Implications for Quantum Gravity:
The formalism  hints at a duality between mass-energy in classical GR and quantum properties (frequency) in QFT. This duality could potentially be developed into a consistent framework for quantum gravity, where:
Mass and frequency (or energy) are treated as equivalent sources of gravitational interaction.
Spacetime curvature in GR could be linked to quantum properties (like frequency) through some quantum version of the Einstein field equations.
