That's right -- the atmosphere stays attached to the Earth mostly thanks to gravity, and the Earth's gravity in GR is almost entirely the gradient in clock rate near the Earth.
Near Earth’s surface, clocks lower down tick very slightly slower than clocks higher up. The change in tick rate is on the order of 10^(-16) per meter. While extremely small, that's enough to generate the familiar 9.8 m/s^2 spatial acceleration we experience. Such a small gradient in clock rates generates macrosopically noticeable spatial accelerations because the "translation" factor is c^2, a tremendously large number.
Now, if I wanted to cover all my bases here, I'd need to point out that gravity does also bend space -- that is just not a relevant factor for "ordinary" gravity acting on relatively slow moving matter (like the Earth itself, or the Earth's atmosphere). For instance, for light itself, spatial bending is just as important (in fact, the gravitational deflection of light by a weak static gravitational field is controlled by a near 50/50 split between spatial and temporal effects). Near a massive black hole, it's not that simple and can't meaningfully be understood in terms of "time" and "space" effects being independently separated.
I’ve seen this described before in terms of how GPS is able to do what it does, so not surprising. But still haven’t explained why time would so dominate the space dimension.
Edit: The response below is dead for some reason, please vouch.
Everything we experience is far larger in time than space, so of course time effects dominate on scales we perceive.
But this just raises the question of what it means to be larger in time than space. You can look at it in terms of multiples of Planck distance or time, but I think there's a more enlightening way to look at it. If you express the speed of light in those Planck units, it's 1. But the speed of light is also the maximum speed of causality. Any causally-bound system must run long enough for chains of causation to propagate, usually far below the speed of light in practice. This means that basically anything that exists within the bounds of our manipulation must be happening at scales where there is far more time involved than space.
We all exist below the diagonal because the diagonal is the bound at which the ways chemistry and biology work no longer even are theoretically possible.
That's right -- the atmosphere stays attached to the Earth mostly thanks to gravity, and the Earth's gravity in GR is almost entirely the gradient in clock rate near the Earth.
Near Earth’s surface, clocks lower down tick very slightly slower than clocks higher up. The change in tick rate is on the order of 10^(-16) per meter. While extremely small, that's enough to generate the familiar 9.8 m/s^2 spatial acceleration we experience. Such a small gradient in clock rates generates macrosopically noticeable spatial accelerations because the "translation" factor is c^2, a tremendously large number.
Now, if I wanted to cover all my bases here, I'd need to point out that gravity does also bend space -- that is just not a relevant factor for "ordinary" gravity acting on relatively slow moving matter (like the Earth itself, or the Earth's atmosphere). For instance, for light itself, spatial bending is just as important (in fact, the gravitational deflection of light by a weak static gravitational field is controlled by a near 50/50 split between spatial and temporal effects). Near a massive black hole, it's not that simple and can't meaningfully be understood in terms of "time" and "space" effects being independently separated.
I’ve seen this described before in terms of how GPS is able to do what it does, so not surprising. But still haven’t explained why time would so dominate the space dimension.
Edit: The response below is dead for some reason, please vouch.
Everything we experience is far larger in time than space, so of course time effects dominate on scales we perceive.
But this just raises the question of what it means to be larger in time than space. You can look at it in terms of multiples of Planck distance or time, but I think there's a more enlightening way to look at it. If you express the speed of light in those Planck units, it's 1. But the speed of light is also the maximum speed of causality. Any causally-bound system must run long enough for chains of causation to propagate, usually far below the speed of light in practice. This means that basically anything that exists within the bounds of our manipulation must be happening at scales where there is far more time involved than space.
We all exist below the diagonal because the diagonal is the bound at which the ways chemistry and biology work no longer even are theoretically possible.
[dead]