On 10/1/2025 7:13 PM, 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. *
What the hell does "solves you intention" mean. The velocities are the
same and the angle thru which they turn is the same...those are
hypotheticals of the story. It follows that the (acceleration*duration)
are the same.
*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. *
NO, IT IS THE SAME CASE. In my diagram it is clear that Blue is
stationary for the duration of Red's trip. Are you going to claim that
it matters whether Blue was stationary some other time??
*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*
Which only shows how ignorant or unserious you are.
Brent
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