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[OngBonga]

Also, the force between charges would diminish at a greater rate than the 1/r^2 relationship we observe.

But how accurately can we actually measure things like this? Our observations might be within the parameters that allow such a negligable mass to go unnoticed.

I can't get my head around the idea of gravity just disappearing.

[MadMojoMonkey]

But how accurately can we actually measure things like this? Our observations might be within the parameters that allow such a negligable mass to go unnoticed.

I can't get my head around the idea of gravity just disappearing.

You're asking a great question.

An accepted upper bound for the mass of a photon is 10^-18 eV/c^2 which is ~2*10^-54 kg.

eV/c^2 are units of mass that are commonly used in particle physics.
If E = mc^2, then E/c^2 = m

eV means electron Volt. It is the amount of kinetic energy an electron gains having traversed a potential difference of 1 V. Interestingly, the amount of space and time required to do so is not relevant.
1 eV = 1.6*10^-19 J

1 eV/c^2 = 1.6*10^-19 J / (3*10^8 m/s)^2 ~= 1.8*10^-36 kg


The simple fact is that even if photons have a mass as large as 10^-18 eV/c^2, it's nowhere near enough to account for the mass annihilated in, say an electron positron collision.

mass of electron + positron prior to collision: ~10^6 eV/c^2
mass of 2 photons moving in opposite directions after annihilation: ~2*10^-18 eV/c^2

That's 24 orders of magnitude in difference between the starting mass and the ending mass. This process (electron / positron annihilation) is well known and studied.

While the energy is conserved, mass is not conserved. While the total energy of the resulting photons is equal to the total energy of the initial particles, it is no longer expressed in terms of mass. If no mass, no gravity.