On 9/17/2025 10:44 AM, Alan Grayson wrote:
On Tuesday, September 16, 2025 at 12:36:56 AM UTC-6 Alan Grayson wrote:
On Monday, September 15, 2025 at 5:31:57 PM UTC-6 Brent Meeker wrote:
On 9/15/2025 1:16 AM, Alan Grayson wrote:
*You've written that the TP cannot be solved using GR, so why
do you use GR in the turnaround scenario? Please don't ask me
to look it up. If you claim there is no acceleration in GR,
I'd like to know how acceleration is defined, and how it can
be calculated to be zero. I tried using the 2nd derivative of
dS, but it doesn't yield zero. AG*
*You have to take the covariant derivative. But it's easy to
see even from a Newtonian perspective. F=ma and F=0 and m>0
hence a=0. If you measured a with an accelerometer you'd get
zero.
See below.
Brent*
I've "solved" the TP a handful of different ways to make
clear what is happening. If it's not acceleration in the
Triplet case, then it's not caused by acceleration. If
it's not difference in acceleration in the equal
acceleration case then it's not due to acceleration
difference in any case. If it's not due to stresses on
the clocks in the slingshot case then it's not due to
stress on the clocks in any case. The point is to
eliminate every possible cause of the difference in ages
in order to point to the essential cause.
Brent
*The Newtonian perspective doesn't help since in free fall a test
object can still change direction, and this is acceleration. *
You keep saying that as if it's a mantra. What's a change in direction
if it not deviation from a straight path?
*If acceleration in GR is redefined and related to the covariant
derivative, what is the argument or variable must I take the
derivative of? AG *
*Your primary argument is that the TP is resolved not by an appeal to
Newtonian acceleration, but to different path lengths in spacetime,
with the result that the longer path length has less proper time
elapsed than the stationary twin. But ignoring the Triplet scenario,
which deviates from the TP, in that a third clock is postulated (so
no turnaround), ISTM that it is Newtonian acceleration which is
responsible for, and causes the differering spacetime paths. AG *
An acceleration that can't be detected by an accelerometer.
Brent
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