The Watchmaker: my fav argument

[polymath257]

The final nail was Newton's discovery of his laws of motion and his law of universal gravity.

Out of curiosity, since I'm reaching far beyond my comfort zone, what role does Einstein play in this battle? If Newton put the final nail, but Einstein is often described as somewhat replacing Newton, what does Einstein's theory do to these models? Relativity seems to make use of "frames of reference" and "observers," which at first glance is the main difference between the geocentric and heliocentric model.

The simple answer is 'it's complicated'.

Special relativity has no distinguished inertial observers. In other words, motion at a uniform velocity cannot be distinguished from being at rest in SR.

BUT acceleration is a different story, even in SR. There is NOT a symmetry between observers in accelerated frames of reference. That is part of the resolution of the twin paradox: the twin that experiences the acceleration is the one that ages less.

In general relativity, things get stranger. gravity is considered to be a curvature of spacetime and different locations do have different curvature. That means that two observers with different spacetime geometry are NOT equivalent. Things like proper time (what is measured by clocks) depends on the path through spacetime taken.

In particular, a rotating observer will experience corriolis forces because of their peculiar frame of reference. They can see themselves as being at rest, but to do so drastically limits their usable coordinate system. In particular, distances that 'look' like they would be moving at faster than the speed of light can be present. An observer that is not rotating will not have those same limitations. In any case, all local motion will appear to be less than the speed of light.

So, in reference to the current discussion, the Ptolemaic system cannot be fit into GR. A *very limited* version of Tycho's system is at least consistent with GR, but there are severe restrictions on the coordinate system used by the observer on a 'fixed Earth' that are not present for an observer that is closer to being inertial.

This actually shows up in cosmology, by the way. In cosmology there *is* a preferred reference frame for any observer: the one in which universal expansion does not depend on direction. The Earth is NOT in that frame of reference: we are moving with respect to it. That motion shows up as a 'dipole' component to the cosmic background radiation.