Sure, John.
"Clock rates slow as gravity contracts space/time. Correct/not?"
Incorrect. A clock is any regular process (e.g., oscillation of an atom under constant conditions; or the pendulum of a grandfather clock) by which we measure the passing rate of time in a given local inertial frame, by counting beats. If we remove an identical atom, or clock, further from the influence of the gravity field where we first synchronized the beats, and then bring the clocks back together, we will find that the clock that traveled outside the local frame has recorded fewer beats than the one that stayed at home. Why?
Newton showed (by the calculus he invented), from Galileo's results, that free falling bodies accelerate in a gravity field independent of their inertial mass, according to the rate of change squared. This applies whether the bodies fall in a straight line toward the center of the Earth, or in a curved trajectory -- so we can consider the local gravity source as a flat plane in which gravity accelerates bodies vertical to the plane, never horizontally.
Einstein found that because this vertical acceleration is indistinguishable in principle between some force pushing bodies upward and another force pulling bodies downward -- there is equivalence between inertial mass and gravitational mass, and therefore between gravity and acceleration.
This being true, then, a clock at rest in a gravity field, keeping time at a constant rate, when moving in the opposite direction of gravitational acceleration *must* record a slower rate the further it moves from the field -- because the increased rate caused by gravitational acceleration (rate of change squared) is in a sense "undone" by motion against the gravity field.
One might ask reasonably -- as perhaps you are -- why the moving clock doesn't simply return to its prior state of timekeeping when it rejoins the stay at home clock, so that we could never tell that the time changed at all? The answer is -- it does return to its prior state of local timekeeping. We know the moving clock has become "younger" than the Earthbound clock, however, because its *record* of beats is out of sync with the other. By accelerating against the gravity field, it gained time compared to the stay at home clock.
This relative gain/loss of measured elapsed time values tells us that time is not absolute. Gravity doesn't contract spacetime; gravity affects the trajectory of particles in spacetime.
"So if space expands, how/where do clock rates increase/expand?"
Only locally. "All physics is local," as Einstein said. If an observer were watching time pass on the face of the traveling clock, she would see that her own rate of time in that inertial frame is consistent with the clock time. An observer watching the Earthbound clock would see that his own time is consistent with his clock. Because all motion is relative, though, the Earthbound observer can say that the moving clock is slow compared to his own -- no, says the traveling clockwatcher, it's *your* clock that is slow there on Earth. And both are right.
Not until the clocks are brought back into the same inertial frame can we know that true time dilation has occurred -- the traveling clock really moved slower than the one that stayed at home. So long as the two clockwatchers were in relative uniform motion, their clocks were perfectly synchronized even though they each claimed the other's clock was fast or slow. Why?
Here, finally, is where space, speed of light constant, and the FRW metric come in.
Time dilation cannot be separated from length contraction when we speak of real measurement parameters. The contraction of time and space is covariant but not symmetric -- "We measure time with clocks," said Einstein, "We measure space with rods." You can do the calculation, and find that at about 85% of the speed of light, a body is contracted to about one-half its length at rest.
This is why special relativity as a bedrock physical principle finds that physical influences among bodies cannot exceed the speed of light in a vacuum. Colloquially speaking, there is more space in the universe than time, and always will be; space can expand indefinitely, and bodies will never exchange physical influences faster than the speed of light. And because there are no isolated inertial systems, locality is preserved as complementary to special relativity everywhere in the universe.
General relativity extends and generalizes special relativity because it recognizes that there are no actually rigid rods. So when we speak of a metric, whether FRW or any metric measure, we need to simplify the measure to a flat space that accommodates the measure. Study 4.5 of the attachment, and you should understand why. To get a little technical, briefly:
One thing that even experienced teachers of general relativity often get wrong, is in describing the shape of the Riemannian manifold as curved space. Einstein's choice of the four dimensional Riemannian geometry, however, actually characterizes the space as a pseudo-Riemannian manifold of Lorentzian metric properties -- this is very important, because it tells us that the flat plane metric of Euclidean space applies all the way to the cosmological limit. (It also opens the door to more sophisticated topology, such as Joy Christian's, which we'll save for another time and another thread.)
All best,
Tom
