On Monday, September 29, 2025 at 4:21:29 PM UTC-6 Brent Meeker wrote:



On 9/29/2025 10:39 AM, 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.


*Aren't you assuming that the integrated S over both paths is the same? 
This is the issue I previously flagged. How do we know that both paths when 
integrated, have identical lengths, S? AG *

Certainly not.  *The whole point is that they have different length!*  The 
proper time S is what a clock (or age) measures. 

Brent


*If they have different S lengths, how can you conclude the proper time on 
stationary twin's clock records more time than the traveling twin's clock? 
Only if the S lengths are identical (which I didn't believe when I posted 
my question) can you reach that conclusion. AG *


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