I'm not a particle physicists by any means, but doesn't any theory of gravity have to deal with 'real' infinities at high energies from the physics we already know?
We have some idea that black holes are a type of singularity (something that could possibly called an infinity). With E=MC2 we have an idea that if you apply enough energy to a particle it can become massive enough that it becomes a singularity itself.
We have some idea that black holes are a type of singularity (something that could possibly called an infinity). With E=MC2 we have an idea that if you apply enough energy to a particle it can become massive enough that it becomes a singularity itself.