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Given that the "old" version of time dilation has been tested and found to give the right answer, why would we want one that gave any different answer?

if an observer instantaneously changes his speed

The "old" version of the gravitational time dilation (GTD) equation, exponential {integral from 0 to L [ g(h) dh] },was tested only for a weak gravitational field.

Quote from: MikeFontenot on 27/01/2022 19:44:39 if an observer instantaneously changes his speedYou do realise that's impossible, don't you?

It was tested using the gravitational field of Sirius B which is pretty strong.How different would the calculations based on your idea be?

Did you notice how it's still impossible after you wrote all that?

Never mind; any progress on this bit?Quote from: Bored chemist on 27/01/2022 20:23:33It was tested using the gravitational field of Sirius B which is pretty strong.How different would the calculations based on your idea be?

In practice, there is usually a negligible difference between changing your velocity in absolutely zero time, and changing your velocity in a very small non-zero time.

Quote from: MikeFontenot on 28/01/2022 19:17:05In practice, there is usually a negligible difference between changing your velocity in absolutely zero time, and changing your velocity in a very small non-zero time. Except that one is possible and...

Quote from: Bored chemist It was tested using the gravitational field of Sirius B which is pretty strong.How different would the calculations based on your idea be?I'm not familiar with that experiment. Can you give me a link to it?

Quote from: MikeFontenot on 29/01/2022 00:26:37Quote from: Bored chemist It was tested using the gravitational field of Sirius B which is pretty strong.How different would the calculations based on your idea be?I'm not familiar with that experiment. Can you give me a link to it?It hardly matters.

Sirius B has about the same mass as our sun,

And I have given an equation which DOES fully agree with the twin paradox outcome.