"Einstein cast gravity not as a force but as the geometric bending of space and time. In a popular analogy, the fabric of space-time is like the flat expanse of a mattress, and a massive object like a star is like a bowling ball sitting on top. The weight of the bowling ball compresses the mattress, forming a dimple — matter tells space-time how to curve. In this analogy, a planet is like a smaller ball. If it rolls…
That’s very interesting, but the analogy is not wrong, because the mattress is analogous to space-time , not just space. Essentially it is a 2D analogy for a 3+1D reality.
If you view gravity as a mattress, you're stuck. There's nothing to do with it that you couldn't already do, because it's fundamentally wrong. Another way to say this is that it's actually an analogy for Newtonian gravity, not for GR, despite apparently including something curved.
If you view gravity as a field of local clocks that tick at different rates, you can make many correct predictions:
- Clocks at different heights will tick at different rates.
- GPS needs gravity corrections.
- Light climbing out of a gravitational field is redshifted.
- Radar signals passing near the Sun should be delayed (the Shapiro time delay).
- You can have no gravitational pull but still have time dilation (inside a perfectly spherical shell, Newtonian gravity seems to cancel out).
- From the outside, it appears to take an infinite amount of time for something to fall into a black hole's horizon.
- Aging can be path-dependent.
- Gravity affects every physical process: chemical reactions, radioactive decays, biological aging, atomic transitions, molecular vibrations, computer processors, pendulums, pulsars.
- A sufficiently precise clock can measure height.
- Objects in eccentric orbits should have periodic clock-rate changes.
- Quantum matter waves should accumulate gravitational phase shifts.
- Spectral lines from compact stars should reveal compactness.
- Thermal equilibrium in gravity should involve a temperature gradient.