- #126

- 8,919

- 2,905

To illustrate how confused it is to think that GR is needed to use coordinates in which an accelerated observer is at rest, take a look at Rindler coordinates. It's a coordinate transformation from

[itex](x,t) \Rightarrow (X,T)[/itex]

where [itex]T = tanh^{-1}(\frac{ct}{x})[/itex] and [itex]X = \sqrt{x^2 - c^2 t^2}[/itex]

In terms of the coordinates [itex](X,T)[/itex], you find that

There is no need for a "principle of equivalence" to allow us to use these coordinates, any more than there is a need for a principle of equivalence to use Newtonian physics in polar coordinates.

[itex](x,t) \Rightarrow (X,T)[/itex]

where [itex]T = tanh^{-1}(\frac{ct}{x})[/itex] and [itex]X = \sqrt{x^2 - c^2 t^2}[/itex]

In terms of the coordinates [itex](X,T)[/itex], you find that

- Clocks at "rest" (that is, [itex]X[/itex] is constant) run faster the higher up they sit (larger values of [itex]X[/itex])
- Light rays bend downwards (toward negative values of [itex]X[/itex]).
- An object dropped from "rest" will accelerate downward (decreasing [itex]X[/itex])

There is no need for a "principle of equivalence" to allow us to use these coordinates, any more than there is a need for a principle of equivalence to use Newtonian physics in polar coordinates.

Last edited: