On 9/9/2025 1:19 PM, Alan Grayson wrote:
On Saturday, September 6, 2025 at 5:56:36 PM UTC-6 Brent Meeker wrote:
No. You're over complicating the problem. It's as simple as the
fact that two different thru spacetime are different lengths.
Because the spatial coordinate distance, X, appears with a minus
sign relative to the coordinate time, T, the proper time, S (which
is what a clock measures). So the rocket, which takes the longer
spatial path, experiences less proper time lapse.
*If the spacetime distance between two points in invariant, how can
you say one path has a different length than another? *
That's like saying there's a fixed distance between L.A. and NYC so how
can there be different path lengths between them.
*BTW, considering acceleration does NOT necessarily mean invoking GR,
and the invariance is a result of SR. AG *
This result has nothing to do with accelerations experience by the
traveler.
*
*
*I disagree since it is what indicates lack of symmetry, which causes
the paradox. *
See (1) my triplet example in which nobody accelerates and (2) my
example in which Red and Blue accelerate exactly the same.
Brent
*Moreover, referring to acceleration does not necessarily invoke GR. AG*
This a common specious "explanation" trying to connect it to
general relativity. This is most easily seen by the triplet
version of the paradox. In this version the one triplet stays
home, one travelers away from Earth, and one who has been far away
returns to Earth. When the outbound triplet passes the inbound
triplet he hands off the time to the inbound one, so together they
measure the same path as the turnaround twin.
Notice that I have also avoided any acceleration at the beginning
and end, so no triplet ever accelerates.
Brent
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