On 1/18/2025 8:54 PM, Jesse Mazer wrote:
On Sat, Jan 18, 2025 at 8:58 PM Brent Meeker <meekerbr...@gmail.com>
wrote:
On 1/18/2025 4:56 PM, Alan Grayson wrote:
On Saturday, January 18, 2025 at 5:44:46 PM UTC-7 Brent Meeker wrote:
On 1/18/2025 4:32 PM, Alan Grayson wrote:
On Saturday, January 18, 2025 at 4:28:06 PM UTC-7 Brent
Meeker wrote:
On 1/18/2025 5:42 AM, Alan Grayson wrote:
On Saturday, January 18, 2025 at 6:13:27 AM UTC-7 John
Clark wrote:
On Fri, Jan 17, 2025 at 1:41 PM Alan Grayson
<agrays...@gmail.com> wrote:
/> IMO SR can handle curved spacetime. _All one
has to do_ is make the partitions very fine, so
we're approximating inertial motion along very
short paths. AG /
*All one has to do? Well yes but that's easier said
than done, it took Einstein 10 years of grueling
work to figure out exactly how to do it, and the
effort nearly killed him, he got sick, lost 50
pounds and figured he would die soon. Fortunately
he did not. One of the most difficult things he had
to figure out was how to measure distance in 4D
non-Euclidean spacetime that was curved in any
given way that was useful and never produced
self-contradictory results. Mathematicians insist
that distance must have the following properties:*
*1) Non-negativity: d(x,y) ≥ 0
2) Identity of indiscernibles: d(x,y) = 0 if and
only if x = y
3) Symmetry: d(x,y) = d(y,x)
4) Triangle inequality: d(x,z) ≤ d(x,y) + d(y,z)*
*
*
*After years of false starts and dead ends Einstein
eventually found a measuring stick that worked,
it's called the Metric Tensor.*
*
*
*John K Clark See what's on my new list at
Extropolis <https://groups.google.com/g/extropolis>*
Sorry to consume so much bandwidth here. I have one
question about the LT and one about the Metric Tensor
(MT) which will hopefully resolve most of my confusions.
I'll pose the LT question in the context of the TP. If
the stationary twin at rest on the Earth uses the LT to
calculate the clock reading at some time on the
traveling twin's clock, or its clock rate using two or
more time readings, what relationship, if any, does
this have on what the traveler twin's clock actually
reads,
Actually reads when?
and what he observes as his clock rate?
He observes his clock rate to be one second per second.
*
*
*IOW, using the LT, the stationary twin knows precisely what
the traveling twin will measure for his clock rate, but the
traveling twin detects nothing. You gotta luv it. AG*
*It's the same as length contraction, nobody ever measures
time dilation with their own clock.
Brent*
*So the claim that the LT yields what the target frame -- in this
case the frame of the traveling twin*
That doesn't even parse. Frames doesn't measure anything.
I assume you'd agree an inertial frame's coordinates are often defined
in intro textbooks in terms of local measurements on a system of
rulers with clocks attached to different markings, all mutually at
rest (and with the clocks synchronized in their rest frame using the
Einstein convention), as in the illustration at
http://www.upscale.utoronto.ca/GeneralInterest/Harrison/SpecRel/SpecRel.html#Exploring
-- even if such systems are not constructed in practice, this is a way
to conceive of an inertial frame's coordinates as physical
"measurements" which could be done in principle. And if we know the
coordinates assigned to events by the ruler/clock system corresponding
to some frame A, and want to know the coordinates that'd be assigned
to the same events by a ruler/clock system corresponding to some
different frame B, we can just apply the Lorentz transformation to the
coordinates in A to get the right answer for the coordinates in
B--Alan's confusion here (one of them, anyway) is that he thinks there
are situations where the Lorentz transformation would give the wrong
answer, and it seems like he misinterpreted your comment above as
supporting that.
When you said "nobody ever measures time dilation with their own
clock", did you mean that if there's a clock B in motion relative to
me, I can't measure its time dilation with a *single* clock A at rest
relative to me?
No I meant that one doesn't measure time dilation in their own frame.
It's always relative.
Personally I don't like to invoke ruler/clock systems. I think they
muddy explanations because they introduce simultaneity, /as measured in
the ruler/clock system/; while it's important to realize there is no
physical significance to "simultaneous" for spacelike events.
Brent
But to clarify for Alan, presumably you'd agree I could in principle
measure the time dilation of clock B in my frame with local
measurements on a system of multiple clocks of the kind I mentioned,
which are all at rest relative to me and pre-synchronized by the
Einstein convention?
Jesse
--
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 everything-list+unsubscr...@googlegroups.com.
To view this discussion visit
https://groups.google.com/d/msgid/everything-list/CAPCWU3JhKnYMTDjMn%2B44kBTuSnbDKXVJep8Tkxu4D4YOHwt_SQ%40mail.gmail.com
<https://groups.google.com/d/msgid/everything-list/CAPCWU3JhKnYMTDjMn%2B44kBTuSnbDKXVJep8Tkxu4D4YOHwt_SQ%40mail.gmail.com?utm_medium=email&utm_source=footer>.
--
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 everything-list+unsubscr...@googlegroups.com.
To view this discussion visit
https://groups.google.com/d/msgid/everything-list/a1730360-b733-4ba5-9268-e166876ba274%40gmail.com.
