On 10/1/2025 6:09 PM, Alan Grayson wrote:
The accelerations in my diagram are four equal changes in velocity. I split the turnaround into two burns for Red to make it clear that they were the same delta-v and for Blue's two, as shown at the left.On Wednesday, October 1, 2025 at 6:11:55 PM UTC-6 Brent Meeker wrote: On 10/1/2025 6:38 AM, Alan Grayson wrote:On Wednesday, October 1, 2025 at 7:20:13 AM UTC-6 John Clark wrote: On Wed, Oct 1, 2025 at 8:29 AM Alan Grayson <[email protected]> wrote: /> Have physicists in the last 120 years claimed that two paths of different lengths in spacetime which start and end at same events, have the same accelerations, except Brent in his diagram? AG/ *In a word, yes. Two worldlines between the same events in spacetime can have different lengths even if both involve acceleration. And proper time is the length of your world line. But of course if they have identical acceleration histories then they are in the same worldline, not a different one.* You're writing nonsense. Brent has two worldlines with different lengths, claiming they have identical accelerations. AGAnd he included diagrams showing the accelerations had the same amplitudes and durations. And that even was redundant. From the diagram it is clear that Red and Blue had the same velocity at the initiation of their accelerations and they turned their velocity thru the same angle in each period of acceleration...hence one can infer mathematically that their (acceleration*duration) products were the same. Brent * **That was your intention, and it appears so. But since the longer path goes further out, away from the shorter path, I don't think splitting the necessary accelerations into two parts implies the summed accelerations are the same as the acceleration for the shorter path. As I previously stated, the standard TP problem, with one twin spatially fixed and other traveling, is a limiting case of your diagram, and in that case the accelerations are not equal. AG*
You keep bringing up you "standard TP" problem, but by my examples I've shown that every proposed explanation (e.g. they experience different accelerations is you latest) is nullified by one or more example (like this one). If it can't be due to acceleration in this example, or in the gravitational slingshot example, or in the triplet example, why would you continue to suppose it could be due to acceleration in your "standard" example.
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