Re: Does gravity do work on the freely falling body?

pmb wrote:
As far as coordinates being “human choice” as Tom claims, that’s
mostly nonsense.

Then you should be able to display cases where nature or some non-human entity selects coordinates. Please do so.

Coordinates in modern physics are just like they are in differential geometry: a diffeomorphism of a region of the N-dimensional manifold to a region of R^N. Note that any diffeomorphism will do, and the choice of which to use is an arbitrary choice of the human analyst.

Of course in practice most people will select a
diffeomorphism that results in coordinates that respect
a symmetry of the manifold, or that make the desired
computations simpler in some way.

Note there is no requirement to select coordinates in any particular way -- just look at the many different coordinate systems applied to the various regions of Schwarzschild spacetime. Selecting among them makes different aspects of the geometry and physics simpler to discuss; this choice is INHERENTLY HUMAN (it depends on what one wants to discuss).


Observers are more general than that. An observer can
be many things like a light detector or a light emitter.

Sure. This has nothing whatsoever to do with coordinates, in general. Sure, detectors and measuring instruments can be used to construct coordinates, but there is no requirement to do so.

Also: observer != coordinate system.


Tom has a
bizarre attitude towards coordinates. Use caution where he mentions
them.

My attitude "towards coordinates" is mainstream physics. You need to study GR to learn this. As I said, you have not made the necessary leap of understanding.


Tom Roberts

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