[jerf]

To put it another way, with aether, the zeroth derivative of position may be relative ("above me" may be "below you"), but the first derivative (in principle) had a universally agreeable absolute value as the velocity of something against the universal aether.

In current physics, it is only the second derivative that is absolute. We can universally agree how much acceleration something is undergoing, but neither position nor velocity have a method for absolutely measuring them.

This can be a difficult distinction to express in English but with this math terminology it should be clear how very significant the difference is.

[whatshisface]

>We can universally agree how much acceleration something is undergoing,

You can't tell the difference between acceleration and gravitation. That's the principle of equivalence from general relativity. [0]

[0] https://www.physicsoftheuniverse.com/topics_relativity_gravi...

[raattgift]

Pretty sure you know this, but for the benefit of other readers, extracting from the SEP we might more properly put this as, "no-one can tell the difference between uniform acceleration and being at rest while immersed in a uniform gravitational field".

A uniform gravitational field is not a feature of our universe, and especially not around our planet. More concretely, a necessary condition for a spacetime equipped with a uniform gravitational field is a constant https://en.wikipedia.org/wiki/Scalar_curvature .

In sufficiently small (compared to galaxy clusters) patches of our universe we can get an excellent (corrections in less than parts per billion) local approximation of the SEP, however, as tested by human-built space probes like MESSENGER ( https://pgda.gsfc.nasa.gov/products/66 ) and observations of natural systems like Archibald et al.'s work on the PSR J0337+1715 triple ( https://astrobites.org/2019/03/25/testing-einsteins-equivale... and to save clicks, here are the linked-to the pre-referreed version https://arxiv.org/abs/1807.02059 and the pretty animation at https://vimeo.com/83397123 ).

Additionally, in our universe one can only accelerate uniformly for a finite time, whereas in a universe equipped with a uniform gravitational field, one can be at rest eternally.

The SEP (strong equivalence principle) imposes deep requirements on the mathematical structure of any general (as in insensitive to initial conditions) theory of gravitation that is compatible with it to such high precision and on the mechanisms that generate stress-energy (that is, the non-gravitational behaviour of matter).