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- Summary
- In QM frequencies scale linearly with energy, but in GR they scale exponentially. These can't both be true.

The exact formula for gravitational time dilation is [tex]T_d = exp(m\phi / mc^2)[/tex]. (We usually cancel out the

*m*s, but I want to show this as a ratio of energies.) Since [tex]m\phi[/tex] is the potential energy, this says that the rates or frequencies of things in GR depend*exponentially*on their energy. On the other hand, [tex]E = h\nu[/tex] implies that the frequencies of things in QM are*linearly proportional to*their energy. It's quite obvious that these things cannot both be universally true. So, which one is wrong, and when?