Quantum electrodynamics (QED) is the relativistic quantum field theory of electrodynamics. Its a theoretical framework which combines classical field theory , special relativity and the quantum mechanical properties of particles as excited states of quantum fields , which it assumes are more fundamental than the particles. However, it has not been able to derive gravity as defined in the General Theory of Relativity into that framework.
In S pecial Relativity the exchange energy between particles is derived terms of electromagnetic waves moving though the continuous field properties of space-time. While the General Theory of Relativity derives gravity in terms of distortion or curvature in the “surface” of that field created by an increase in the local energy density.
In Schrödinger’s version of QFT, the wave function defines the mathematical evolution of an ISOLATED quantum system. That along with SUPERPOSITION principle of quantum mechanics allows one to add of all possible outcomes defined by the wave function together to derive the quantum equivalent of the classical and the space-time fields of Relativity.
Putting it another way both QED and Special Relativity derive the evolution of the field properties of their environments in terms of waves. Relativity defines it in terms of the exchange of energy between objects in terms of an electromagnetic wave moving thought the field properties of space-time while QED mathematically defines it in terms of an interaction of the wave function with the field properties of all possible outcomes.
This suggests that the wave function that defines the evolution of field properties of QED may be a MATHEMATICAL representation of an electromagnetic wave that defines it in space-time.
As was mentioned earlier the General Theory of Relativity derives the “evolution” of a gravitational field in terms of distortion or curvature in the “surface” of a space-time field created by an increase in its local energy density while QED derive it in terms of how an interaction of the wave function with all possible outcomes would cause the creation of a particle and therefore an increase the energy density of space.
This suggests one way to integrate gravity into QED may be to define how and why the interaction of the field properties of all possible outcomes with the wave function causes a QUANTIZED increase its energy density.
However, one can show Relativity also define quantum gravity by showing why an interaction of an electromagnetic wave with the field properties of space-time also results in a QUANTIZED increase in the energy density of space.
In other words, one can show gravitational forces may not be quantized but their causality MAY be.
One way of accomplish this would be to use the science of wave mechanics and the fact Relatively tells us the energy of an electromagnetic wave energy would move continuously through space-time unless it is prevented from by moving through time by someone observing or something interacting with it. This would result in its energy being confined to three-dimensional space. The science of wave mechanics also tells us the three-dimensional “walls” of this confinement will result in its energy being reflected back on itself thereby creating a resonant or standing wave in three-dimensional space. This would cause its wave energy to be concentrated at the point in space where a particle would be found thereby increasing it energy density. Additionally, wave mechanics also tells us the energy of a resonant system, such as a standing wave which this confinement would create can only take on the discrete or quantized values associated with its fundamental or a harmonic of its fundamental frequency.
Putting it another way it defines quantum gravity in terms of how and why an electromagnetic wave interacts with field properties of space-time to cause a QUANTIZED increase in energy density and therefore the gravitational potential in a specific region of space.
However, to derive quantum gravity in terms of QED one must show how the interaction of the wave function with the field properties of ALL possible outcomes would result in quantum increase in the energy density of that field.
One way of doing this would be to compare the mathematical oscillations associated with the wave function in the field properties of all possible outcomes to ball oscillating on a rubber diaphragm. Observations of that diaphragm tell us those vibrations will be disturbed over its surface while its magnitude would decrease as one moves away from the focal point of the oscillations.
Similarly, if the assumption that wave function is a mathematical representation of vibrations or oscillations in the field properties of ALL possible outcomes, is correct these oscillations would be distributed the entire field while the magnitude of those oscillations would be greatest at their focal point and decreases as one moves away from it. Putting it another way, the PROBABILITY of QUANTUM increase in its energy density in space due to a particle being there would be related its distance from the focal point of those oscillations.
In other words, it is possible to understand why gravity is quantized in terms of both quantum mechanics and Relativity by assuming it is the result of interaction of a wave moving through their respective fields. For example, as was shown above when an electromagnetic wave interacts with the field properties of space-time it would create a quantized increase in the energy density of space. While, as was also shown above when the mathematical properties of the wave function interacts with the probably field associated QED it creates a particle or quantized increase in the energy density of space would be responsible for gravity.