On Wednesday, October 1, 2025 at 8:13:27 PM UTC-6 Alan Grayson wrote:
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. AG
And 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, but since the clock moving along the longer path,
needs a greater turn if done in one acceleration, I don't think splitting
the accelerations into two components solves your intention to make the
accelerations of both paths equal. Recall that in the usual interpretation
of the TP, where one twin is stationary and the other traveling, this
situation is a limiting case of what you're doing in the diagram. It tends
to confirm that the accelerations are not identical in your more general
case. The only real proof of your claim is mathematically. The fact that
your diagram affirms your claim is, IMO, insufficient. AG*
*The other limiting case is when both paths coincide, in which case their
accelerations are identical. So, between these limiting cases, where the
shorter path has zero acceleration (the original TP), and where the paths
coincide to produce identical accelerations, there is your general case,
between the two mentioned. This isn't a conclusive proof, but suggests that
in the intermediate situation, the one you've diagramed, there is a
difference in accelerations. AG*
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