An excellent analysis by Viktor T. Toth! Indeed, gravitational theory is a field theory like any other, which admits a very special geometrical interpretation. Unfortunately, it is as yet non-renormalizable...
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- The existence of a geometric interpretation does not mean that the theory cannot be quantized or that it does not have excitation quanta. From a quantum field theory perspective, gravity (represented by the metric tensor of spacetime in the geometric interpretation) is just a spin-2 tensor field that couples universally and minimally to all fields, including itself. Like other fields, this field can, in principle, be Fourier-transformed, its Fourier coefficients promoted to operators, leading to quantized field excitations, aka. gravitons. In practice, this approach fails because unlike other theories, like electromagnetism, gravity leads to infinities that are “unrenormalizable”, cannot be tamed using standard mathematical tools. So we don’t know how to quantize gravity.
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