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 Quote by Mike2 And if you continue and cancel out $$\rho$$, then this only says that the speed of light must be less than the square root of negative 3. What?
That just means that you can't cancel out $$\rho$$. $$\rho$$ is mass density and mass density can never be zero if there is pressure.

When you make an assumption which leads to something which is not physically meaningfull then that assumption is invalid