[lutusp]

> FWIW, it's always been easier for me to think of it as 'moving' more quickly along the time axis - which would appear slowed down to someone farther away from the source of the gravity.

In reality, it's the other way around. At the bottom of a gravity well, time passes more slowly. An astronaut on the moon observing a laser beam from earth's surface would see it as red-shifted compared to a local reference, reflecting the fact that time passes more slowly at earth's surface than it does on the moon. The other equivalent interpretation under GR is that the light loses energy climbing out of the gravitational field and is therefore red-shifted. One of the beauties of Einstein's theory is that, if you do the math using either assumption (slower time or lost energy), the result comes out the same.

The classic confirmation of GR conducted in 1919 during a solar eclipse showed that the paths taken by starlight near the temporarily blocked sun were curved toward the sun. This is consistent with the idea that time passes more slowly near the sun. Consider that a light beam a bit closer to the sun would have a longer transit time (because of slower time passage) than one farther away, which would have the effect of curving the stellar light wavefront toward the sun.

This article has some graphics and deeper explanations to assist in understanding these ideas:

http://arachnoid.com/relativity

[deciplex]

It's not the other way around.

If you're deep in a gravity well, you observe physical processes happening outside that well to go along more quickly, not more slowly. And the reverse is true if you are outside a gravity well, observing something in it.

Take some observer, Alice, far away from a massive body, who sees some process occurring near it take one second to complete. A second observer, Bob, nearer to the massive body, will see the same process take 1 - ε seconds to complete (and Alice will say Bob's clock is slow). In effect, Bob has passed through one second of (Alice) time in only 1 - ε seconds of (local, to Bob) time.

That's what I mean when I say "pass through time / move along the time axis more quickly". To think of it another way, ask who ages faster, Alice or Bob?

[lutusp]

> It's not the other way around.

In your earlier post, you didn't clarify which observer was seeing which time pass more quickly, and where. In this post, you do -- sort of.

> Bob, nearer to the massive body, will see the same process take 1 - ε seconds to complete ...

If Bob and the process being observed are in the same frame of reference, Bob will see the process require a "normal" amount of time, i.e. a time consistent with classical physics. Alice will see Bob's process require more time on her clock, from her perspective. Bob, in the gravity well, will see Alice's time appear to be passing more quickly compared to his own.

> In effect, Bob has passed through one second of (Alice) time in only 1 - ε seconds of (local, to Bob) time.

This way of describing it is confusing. Here you are saying that Bob's experience of time is equal to Alice's time minus ε, when it's the reverse -- Bob sees Alice's time passing at 1 - ε, while his own time passes at a "normal" rate. It's a matter of how one describes it, because I suspect you understand how this works, the only problem is the prose.

> That's what I mean when I say "pass through time / move along the time axis more quickly".

Again, it's a matter of how one chooses to describe it, and it only proves the advantage of mathematics as a language. If we were discussing SR instead of GR, I would want to say, about the time experienced by (A)lice and (B)ob if (B)ob is moving at velocity v:

A = B / √(1-v^2/c^2)

B = A √(1-v^2/c^2)

In other words, Bob's time is slowed relative to Alice's time, as observed from Alice's frame of reference. The above two equations are only valid as written if Alice's time is compared to Bob's time after Bob completes his journey and brings his clock into Alice's frame of reference.