On 1/29/2020 7:21 PM, Alan Grayson wrote:
On Wednesday, January 29, 2020 at 12:18:40 PM UTC-7, Brent wrote:
The idea that some clocks run slower than others is a confusion.
Talk of clocks in general relativity always refers to ideal clocks
that, by definition, run at identical rates when compared at the
same place. "Running slow" really refers to taking a shorter path
(less elapsed proper time) thru spacetime, as reflected in the
metric. As AG noted the "running slow" relation is symmetric; so
it can't be invariant.
Using the CMB is an operational way to define a global time. It
is the same as co-moving coordinates in which matter is, on
average, stationary. But it is a good/useful coordinate system
because it makes the representation of an FLRW model simple.
There's an implicit assumption that the universe is homogenous and
isotropic, which implies that it satisfies an FLRW model. With
that assumption a measurement of curvature locally can be extended
to infer the whole spacetime. Space can be flat while spacetime
is curved, so as to be open or closed.
Brent
Can you answer the question? If we have two clocks at the distant
galaxy; some observer's clock which is running slower compared to a
local clock in this galaxy, and the CMBR clocks at every location in
the universe which are synchronized, what is the status of time
dilation? Do it exist or not? TIA, AG
If you're syncing clocks everywhere to the CMB then you've defined a
global time. You've also implicitly defined a space reference frame
that's stationary with respect to the CMB. There will still be
relativistic doppler shift between clocks because of the expansion rate
of the universe, i.e. if you look at a distant galaxy you will see
shifts in its spectral lines and you will be seeing the galaxy as it was
in the past. It's not though that clocks are running slower on that
galaxy; rather it's definition of the future direction is different (see
my popular lecture explanation of the twin's paradox).
Brent
On 1/29/2020 12:57 AM, Alan Grayson wrote:
Considering the distant galaxies, they're receding at near light
speed. So according to SR, their clocks should be ticking at a
much slower rates than, say, a local clock in our galaxy. OTOH,
there's a physical clock for the entire universe; namely, the
temperature of the CMBR. If we tell time by this clock, all clock
readings of all galaxies are identical. So which is it? Are
clocks in distant galaxies running slower than a local clock in
our galaxy, or are both clocks running at the same rate? TIA, 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] <javascript:>.
To view this discussion on the web visit
https://groups.google.com/d/msgid/everything-list/5c5aa450-761d-4784-9ba3-f25085991a83%40googlegroups.com
<https://groups.google.com/d/msgid/everything-list/5c5aa450-761d-4784-9ba3-f25085991a83%40googlegroups.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 [email protected]
<mailto:[email protected]>.
To view this discussion on the web visit
https://groups.google.com/d/msgid/everything-list/6752836c-a025-4a21-b1e5-0a690c1f6576%40googlegroups.com
<https://groups.google.com/d/msgid/everything-list/6752836c-a025-4a21-b1e5-0a690c1f6576%40googlegroups.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 [email protected].
To view this discussion on the web visit
https://groups.google.com/d/msgid/everything-list/f723aa98-3829-c8eb-99fd-eae3cb1e0e64%40verizon.net.
