TimeLord,
I have conflicting ideas about this. First, it seems reasonable since relativity affects both mass and time simultaneously; also, mass determines how fast separate things go if they have equal energy & momentum. However, what about light? Light still has a speed, even if no mass, and speed is dependent on time. So I'm not really sure about this one.
If you look at a lightcone you see the areas where travel is timelike (sub-luminal velocity), spacelike (super-luminal velocity) and lightlike (the speed of light). Lightlike travel is along the edge at 45 degrees relative to either the space or time axis.
Normally you see space represented as a flat plane cutting across the cone. That's the plane of simultaniety where, if you ignore special relativity, all events on the surface of the plane occur at the same time. The plane is a representation of space.
But that isn't how it is actually presented in the expanded theory (Special Relativity). The plane is curved such that at the edges, where you are traveling at the speed of light, all of the planes converge and follow the lightlike 45 degree line along the edge of the cone. The translation of this is that photons can access all of space in zero time because they travel at the speed of light. Another way of looking at it is that spacetime, for photons, is a point, not a line.
And that's the crux. In the far distant future, 10^100 years from now, when all of the protons, neutrons, blackholes - all matter - has decayed to photons everything left in the universe travels at the speed of light. Everything is traveling along the lightlike edge of the lightcone. There is no clock because all of spacetime is instantly available to every photon.
Photons are very different from massive particles like protons and neutrons. Photons do not obey the Pauli Exclusion principle. Photons
like to simultaneously occupy the same quantum state. That's why we can have lasers. It's the definition of laser light.
Now, if everything left in the universe is a photon and if photons try to all occupy the same quantum state the picture that emerges is that no matter how much space has expanded if you look at the lightcone the photons are all simultaneously occupying the same state. And, of course, the entire energy of the universe is held by those photons...all of it.
If they all occupy the same state and if they hold all of the energy we have a name for this situation. We call it a singularity. We now have, in theory, the Cosmic Egg. The "old" universe doesn't disappear or expand forever but it is reborn in a flash of energy that we call The Big Bang. How long does it need for this to occur? Zero time - because that's the only time left in a totally photonic universe. It's a metastable situation that only needs some "twitch" to break the tenuous symmetry for the Big Bang to recur.