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
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
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