On Wednesday, September 17, 2025 at 7:12:17 PM UTC-6 Brent Meeker wrote:
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? *In your neutron star example of turnaround, the motion starts as a straight line but continues turning for awhile. More important is your claim the GR cannot be used to solve the TP, yet here you are using it. AG * *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. *In the formula for (ds)^2, the increase in spatial length is what produces a shortening of proper time compared with some other shorter path with the same endpoint events. Isn't this Newtonian acceleration and what causes differential clock readings which the twins measure when juxtaposed, or when passing each other without stopping? AG * Brent -- You received this message because you are subscribed to the Google Groups "Everything List" group. To unsubscribe from this group and stop receiving emails from it, send an email to [email protected]. To view this discussion visit https://groups.google.com/d/msgid/everything-list/c2a1cef6-1d17-405f-ad6e-9f8080e7f0a1n%40googlegroups.com.
