On Friday, October 31, 2025 at 11:36:14 PM UTC-6 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 not equal 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. With c multiplied by coordinate time along time axis for a particle spatially at rest, isn't this tantamount to a definition with the intended result that spacetime velocity is c? You refer to time dilation, but this definition seems unrelated to that concept. The key question is how a physical clock measures something other than coordinate time when moving along some arbitrary path? AG * *Since c is multiplied by coordinate time, the distance between coordinate time units is the distance light travels in a vaccum during one second. >From this, we get that bodies at rest in spacetime are traveling at light speed, even though relativity assumes material bodies cannot travel at light speed. If this makes sense, I'd like to know how. TY, AG* How does a clock "know" it isn't reading coordinate time, but something else called proper time? Alternatively, what principle can we apply to put proper time on a logically necessary footing? 3) When moving along some arbitrary path in spacetime, the Pythagorean theorem holds; that is, (ds)^2 = (ct)^2 + (dx)^2. So how do we get a negative sign preceding the spatial differentials? Here I'm referring to a YouTube video whose link I will post later. 4) If (ds)^2 is an *invariant *under SR, does this hold only for the LT, but is it true for any linear transformation, as well as non-linear transformations? AG -- 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/b1fdfe5a-63c6-4daa-8712-2b00e5e5caf4n%40googlegroups.com.
