*Re 2) 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 * 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. 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/495ee107-26d6-4f03-86a1-777b4e2939b1n%40googlegroups.com.
