Seeing as the higher-ups see

So much for speed — what about gravity?

It’s not just speed that affects records of time – closer to a mass, clocks tick more slowly; durations are longer. This difference is not symmetric, and you should not expect it to be: Bob and Charlie are closer to a big mass.

Free-falling past Bob and Charlie

Alice is free-falling past a Bob, and then Charlie. Alice passes Bob more slowly than Charlie – that’s free-fall towards a mass. Alice will notice Bob‘s clock ticking more slowly than Charlie’s clock, and both ticking more slowly than her clock(moving clocks tick more slowly). As everyone in free-fall will agree with Alice about the difference in the rate of ticking for Bob‘s clock and Charlie‘s clock, this is something about what’s there — something about the ticking of clocks near a large mass. Bob and Charlie do both notice Alice‘s clock running slow compared to their own as she whizzes past, but everyone who free-falls past Bob and Charlie will find the same difference in the ticking of their two clocks. A difference that depends on where they are and not how fast they’re moving.

One way to show that time is running at different rates is to use Bob‘s now-line and Charlie‘s now-line to orientate their cones. These two cones show the local environment for the local witness. Not what Alice notices, but what she figures Bob and Charlie will notice.

Represent this variation in the space-time geometry with appropriately tilted light cones, remembering that the light cones are those for a local witness. You’re getting closer to being able to draw representations of space-time.