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Background independence is a condition in theoretical physics that requires the defining equations of a theory to be independent of the actual shape of spacetime and the value of various fields within it. In particular this means that it must be possible not to refer to a specific coordinate system—the theory must be coordinate-free. In addition, the different spacetime configurations (or backgrounds) should be obtained as different solutions of the underlying equations.
Einstein defined gravity and the shape or geometry of space in terms of its energy density while defining the interaction of gravitating bodies in terms of a gravity wave moving through space. Therefore, to define a background independent quantum gravity one must first show why its energy is quantized and then show why it is independent of the geometry and the value of the various fields within the spacetime it occupies.
Relatively and the science of wave mechanics tells us wave energy moves continuously through space-time unless it is prevented from doing so by someone 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 were a particle would be found. Additionally, wave mechanics also tells us the energy of a resonant system, such as a standing wave can only take on the discrete or quantized values associated with its fundamental or a harmonic of its fundamental frequency.
This defines how and why the field properties of space time can evolve to create a quantized increase in the energy density and therefore gravity in a space-time environment.
This suggests the quantization of gravity is not a fundamental property of space but a dynamic one of continuous property of space-time.
As was mentioned earlier Einstein defined gravity and the shape or geometry of space in terms of its energy density. However as was shown above its value would be independent of the value of the various fields within it and the coordinate system in which it is formed because its geometry is only related to the number and quantum properties of particles in a volume of space.
However, some feel that this would contradict the fact that gravity waves cause acceleration when they interact with objects which they feel suggests they are background dependent because they change geometry of space as they move through it.
The reason this is not true is because the energy density associated with a mass is static or unchanging with respect to the geometry of space, it can be defined by the background independent equation of Special Relativity.
However, because Einstein defined the propagation of energy including gravitational in terms of waves moving through space at the speed of light means the energy associated with a collision of two gravitating masses would result in that energy being radiated through space at the speed of light in the form of gravity waves. This suggests they would obey the same laws that govern the relativistic properties of space and time associated with background. independent properties of electromagnetic energy in Special Relativity.
This is how Einstein could have defined a background independent quantum gravity in terms of the relativistic properties of space time as defined by him.
Einstein’s Explanation of the Unexplainable
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