In all these cases, the goal is to extend the classical geometry of GR (Ricci tensor, metric) to a quantum regime where spacetime is no longer smooth and continuous but instead exhibits quantum fluctuations and discrete structures at the Planck scale. This approach could ultimately lead to a unified theory of quantum gravity, reconciling the successes of both QFT and GR.
Consider these some points:1. Energy of photon E = hf. 2. Photon interacts with gravity. 3. Mass energy equivalent equation  E = mc^2. When we can find mathematic bridge by formalism f = m in which derived from hf = mc^2, is it alternative way to reconcile GR = QFT?
Yes, exploring the formalism where , derived from , could be an interesting alternative approach to reconciling General Relativity (GR) and Quantum Field Theory (QFT). Let's walk through the physical meaning of this relationship and how it might help bridge the gap between these two foundational theories of physics.
1. Photon Energy and Frequency:
In quantum mechanics, the energy of a photon is given by Planck’s relation:
E = hf
h is Planck’s constant,
f is the frequency of the photon.
This equation connects a quantum property (frequency ) with energy, and it is central to quantum mechanics and quantum field theory (QFT). It emphasizes the particle-wave duality of photons, where their energy is directly tied to their frequency.
2. Mass-Energy Equivalence:
In Einstein’s special theory of relativity, the famous mass-energy equivalence formula is:
E = mc^2
m is the rest mass,
c is the speed of light.
This equation connects mass to energy and highlights that mass is a form of energy. This is crucial for general relativity (GR), where the presence of energy (including mass) causes spacetime to curve, as described by the Einstein field equations.
3. Photon Interaction with Gravity (General Relativity)
Even though photons are massless, they interact with gravity because they carry energy and momentum, which, according to GR, still contribute to spacetime curvature. This is why light is bent by gravity (gravitational lensing) and why photons can lose energy (redshift) in the presence of a strong gravitational field.
In this context, both energy and mass influence spacetime curvature, meaning photons, despite being massless, still feel the effects of gravity.
4. The Formalism
Let’s now combine the equations:
hf = mc^2
f = \frac{mc^2}{h}
What Could  Imply?
