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Quote from: imatfaalSorry Pete but can you run that again? How can you produce a gravitational field by a coordinate transform - you can show that acceleration is indistinguishable (tidal aside) but after that I am flummoxed; it is the "elevator car" that is either in a gravitational field or accelerating - you cannot just transform that away. First let’s look at where I got that notion from just so that the world can be sure that it’s not pmb who has been creating wild fantasies in his mind.From The Foundations of the General Theory of Relativity by A. Einstein, Annalen der Physik, 49, 1916.QuoteIt will be seen from these reflexions that in pursuing the general theory of relativity we shall be led to a theory of gravitation, since we are able to “produce” a gravitational field merely by changing the system of co-ordinates.If you were to invoke a spacetime coordinate transformation that is changes from an inertial frame of reference S in flat spacetime to a uniformly accelerating frame S’ then observers in S’ will observe that there is a uniform gravitational field in their frame of reference.If you were in a frame of reference in which there was a gravitational field of the Earth’s gravitational field then you can only transform the gravitational field away locally (i.e. in a small region of spacetime). Please explain what your objection is and what the talk about the elevator has to do with it? I.e. please explain why it can’t be transformed away? You do understand, don’t you, that when the spacetime is curved then you can only transform the field away locally? What local means has to do with the precision of the instruments that you’re using to detect the tidal forces.

Sorry Pete but can you run that again? How can you produce a gravitational field by a coordinate transform - you can show that acceleration is indistinguishable (tidal aside) but after that I am flummoxed; it is the "elevator car" that is either in a gravitational field or accelerating - you cannot just transform that away.

It will be seen from these reflexions that in pursuing the general theory of relativity we shall be led to a theory of gravitation, since we are able to “produce” a gravitational field merely by changing the system of co-ordinates.

But Pete that section is dealing with an object at rest with respect to an accelerated non-inertial reference frame - that is indistinguishable from a uniform gravitational field - and as AE states a co-ordinate change will create the gravitational field BUT only in a frame that could otherwise be thought of as a non-inertial accelerating frame (K') .

I still do not understand how you could create a grav field with is identical locally to a non-inertial frame (with pseudoforces etc) from an inertial frame via coordinate transformations.

imatfaal - You have me curious. What is it you think Einstein meant when he saidQuoteIt will be seen from these reflexions that in pursuing the general theory of relativity we shall be led to a theory of gravitation, since we are able to “produce” a gravitational field merely by changing the system of co-ordinates.?