4D spacetime Light cone Twins paradox

[jcsd]

Unfortunately, a lot of what I say is just parroting what I read. I have no deep understanding of it. I'll guess that using the MCRF never gives the same answer as the full GR treatment unless there is no curvature. The reason I make this guess is that if it were not true, then there would be no need for GR. The amount of difference between the MCRF calculated result and the GR result is probably related to the amount of spacetime curvature. When that curvature is small, the difference is below the threshold of what can be measured. When the curvature is larger than some threshold value, the difference becomes measureable.
So, to answer your question, if GR gives a value that conforms with measurement, and using MCRF gives a measurably different result, that is when MCRF gets a wrong answer.

There are some situations which cannot be decribed by SR, this is when there is curvature but as I said accelartaion in itself does not imply curvature. The use of the MCIFs (I prefer momentarily comoving inertial frame) gives the correct results (i.e. the ones that conform with GR) within it's limit of appplicabilty. There are of course difficulties (I use the word loosely as I'm ceratinly not implying that there are flaws) that you encounter in non-ienrtial frames in SR that you don't encounter in non-inertial frames (if you read the link in my last post one of these is very briefly mentoned - the difficulty of defining simulatneity), but these are the same general difficulties that occur in GR.

In GR you can always apply SR locally due to the tangent space to an event in spacetime, this means that when considering a vanishingly small region of spacetime GR reduces to SR.

I am currently reading "A First Course in GR" by Schutz. I note that in many equations terms that are quadratic or higher in small quantities are ignored. I realize that in some cases this is justified because the small quantity is a differential which will tend to zero, however not all small quantities treated this way are differentials. This is of course the only practical way to get pretty compact equations. However, nature is not concerned with this particular aspect of beauty and practicality and retains those terms. Are you comparing the results of using MCRF to the results of using this smoothed out version of GR? It reminds me that Newton's equations of motion are correct. When there is no motion that is.

GR reduces to SR in flat spacetime.