Find Einstein's GR Papers: Read His Own Words

[aashay]

We start with Newton's laws in an inertial frame. When we transform to a noninertial frame, we pick up "Christoffel symbols". If instead of defining "same form" without Christoffel symbols, we define it as including the Christoffel symbols, then Newton's laws are valid in any frame.

It is the same with special relativity, which is capable of handling accelerated frames (eg. Rindler coordinates).

I like http://arxiv.org/abs/gr-qc/0603087 .

But the moment you bring Christoffel symbols into the picture, don't you march away from Newtonian Physics to General Relativity by taking into account the effects of curvature? And all this has been done quite recently after GR was developed and not at the time of Newton.vCorrect me if I am wrong as I am quite new to General Relativity.

 

[atyy]

But the moment you bring Christoffel symbols into the picture, don't you march away from Newtonian Physics to General Relativity by taking into account the effects of curvature? And all this has been done quite recently after GR was developed and not at the time of Newton.vCorrect me if I am wrong as I am quite new to General Relativity.

http://www.mth.uct.ac.za/omei/gr/chap6/node4.html

You can have Christoffel symbols in flat space, eg. when you use polar coordinates.

The essential idea is that the Christoffel symbols are first derivatives of the metric, where the Riemann curvature tensor which indicates the difference between flatness and curvedness is made of second derivatives of the metric.

In GR, fake gravity (from acceleration) makes first derivatives of the metric, whereas true gravity (more properly, tidal gravity) is due to curvature. (I'm sure bcrowell is going to disagree with my terminology here!)