On 11/6/2025 2:49 PM, Alan Grayson wrote:
"Adjusting its rate" would imply that there was some absolute motion that would tell it how to adjust. Judging how /some other clock/, that's moving relative to you, keeps time can depend on relative motion and doesn't imply any absolute.On Tuesday, November 4, 2025 at 11:38:20 AM UTC-7 Alan Grayson wrote: On Tuesday, November 4, 2025 at 1:35:06 AM UTC-7 Brent Meeker wrote: On 11/3/2025 9:20 AM, Alan Grayson wrote:On Saturday, November 1, 2025 at 9:07:12 PM UTC-6 Alan Grayson wrote: On Saturday, November 1, 2025 at 5:15:36 PM UTC-6 Brent Meeker wrote: On 10/31/2025 10:36 PM, Alan Grayson wrote:On Friday, October 31, 2025 at 4:15:29 PM UTC-6 Brent Meeker wrote: On 10/31/2025 6:17 AM, Alan Grayson wrote:On Friday, October 31, 2025 at 2:40:07 AM UTC-6 Alan Grayson wrote: 1) For a body at rest, we multiply clock time, aka proper time, and/or coordinate time by some velocity, so its units become spatial. But why multiply by c? Is this procedure really a *definition* to get a velocity of c in spacetime? 2) Proper time and coordinate time are notequal along some arbitrary path in spacetime.*Note that for a body at rest, coordinate and proper time are identical. Hence, d(tau)/dt = 1, where t is coordinate time and tau is proper time. But this is not true for a body not at rest. How does a physical clock "know" is it moving, making that derivative non-zero. AG *You're muddling things. For a clock moving inertially in flat spacetime, the coordinate times are arbitrary up to a linear transformation. So d(tau)/dt=const. not necessarily 1. And the constant depends on the speed (time dilation). So the coordinate speed depends on the choice of coordinate time, i.e. relativity of motion. Brent *In the video toward the end, he claims d(tau)/dt=1, so every 1 sec increment in coordinate time is set to 1 sec increment in proper time. *I don't understand that. *It's pretty straightforward. If you're at rest in some frame in spacetime, you're moving along the time axis only. Along that axis are coordinate labels, but since you've multiplied these lables by c, you're left with distances (as on spatial axis), and the distance separation of two adjacent coordinate unit times, has a distance which light traverses in one second of proper time. IOW, along the time axis, proper and coordinate time are identical. Thus, d(tau)/dt=1. *OK, you've used proper (clock) time to mark the intervals of coordinate time.*I didn't do it. The community of physicists did it. How can a test particle at rest move at light speed? Makes no sense AFAICT. AG **When motion is not strictly along time axis, that is, when you're not at rest, coordinate and proper time no longer coincide, no longer have equal values. The non trivial existential question is why a clock which measures only proper time, "knows" to adjust its rate when moving along some arbitrary path in spacetime? AG*It doesn't "adjust its rate". The clock continues to measure proper time along the new spacetime direction. But because the new direction is not parallel to the old one the intervals don't match the intervals of the clock that remained on the stationary worldline. Motion is only relative. So each clock sees the other as running slow because they judge the other clock to not be going in the futureward direction. Brent *I don't see any daylight between "adjusting its rate" and "judging" how another clock is moving. That aside, you seem to be affirming the TP. AG*
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