Science > Physics > [GR] Where do clocks run faster: on equator or on poles?
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Science > Physics |
| User: |
"sasha semenov" |
| Date: |
24 Apr 2007 10:34:14 AM |
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[GR] Where do clocks run faster: on equator or on poles? |
Sea level, cesium etalons.
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| User: "Karmine" |
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| Title: Re: [GR] Where do clocks run faster: on equator or on poles? |
24 Apr 2007 01:00:59 PM |
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"sasha semenov" <cemca@yahoo.com> wrote in message
news:1177428854.430213.113860@n15g2000prd.googlegroups.com...
Sea level, cesium etalons.
in relation to the universe, on the poles.
Question for you, by how much ?
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| User: "Jim Black" |
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| Title: Re: Where do clocks run faster: on equator or on poles? |
26 Apr 2007 12:47:21 AM |
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On Apr 24, 1:00 pm, "Karmine" <nos...@nospam.com> wrote:
"sasha semenov" <c...@yahoo.com> wrote in message
news:1177428854.430213.113860@n15g2000prd.googlegroups.com...
Sea level, cesium etalons.
in relation to the universe, on the poles.
That would be the answer you'd get from special relativity alone. But
you need to take gravitational effects into account as well.
--
Jim E. Black
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| User: "Androcles" |
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| Title: Re: Where do clocks run faster: on equator or on poles? |
26 Apr 2007 06:51:59 AM |
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"Jim Black" <tramspap@yahoo.com> wrote in message =
news:1177566441.248562.257790@t38g2000prd.googlegroups.com...
On Apr 24, 1:00 pm, "Karmine" <nos...@nospam.com> wrote:
"sasha semenov" <c...@yahoo.com> wrote in message
news:1177428854.430213.113860@n15g2000prd.googlegroups.com...
Sea level, cesium etalons.
in relation to the universe, on the poles.
=20
That would be the answer you'd get from special relativity alone. But
you need to take gravitational effects into account as well.
Funny how one exactly balances the other. ***** meets cowshit and
annihilates.
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| User: "Jim Black" |
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| Title: Re: Where do clocks run faster: on equator or on poles? |
26 Apr 2007 12:45:37 AM |
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On Apr 24, 10:34 am, sasha semenov <c...@yahoo.com> wrote:
Sea level, cesium etalons.
Neither. They run at the same rate.
(Assumptions here are a static gravitational field, and that objects
dropped at sea level fall perpendicular to sea level.)
Consider a coordinate system which rotates with the earth:
x^0 = a time coordinate, defined so that
transformations x^0 -> x^0 + k leave the metric unchanged
x^1 = height above sea level
x^2 = a north-south coordinate, defined so that
x^2 = k planes are perpendicular to sea level,
according to an observer fixed w.r.t. the earth's surface.
x^3 = an east-west coordinate, defined so that
x^3 = k planes are perpendicular to sea level
and to the x^2 planes, in the same frame.
The acceleration of objects dropped at sea level, as seen by observers
fixed with respect to the earth, is perpendicular to sea level. The 4-
velocity u^i = d(x^i)/ds of such an object started out with only u^0
nonzero. At least initially, the acceleration causes a change only in
the u^1 component. The covariant derivative of the 4-velocity is
zero, and the parial derivative of the u^2 component is zero:
(Semicolons = covariant derivatives, commas = ordinary partial
derivatives)
u^2_;0 = u^2_,0 + C^2_0i u^i
0 = 0 + C^2_0i u^i
0 = C^2_00 u^0
This means the connection component C^2_00 has to be zero. We can
plug this into the formula for the connection components based on the
metric:
0 = C^2_00 = (1/2) g^u2 ( g_u0,0 + g_0u,0 - g_00,u )
Derivatives with respect to x^0 are zero, so we can eliminate these
terms:
- (1/2) g^u2 g_00,u = 0
g^u2 g_00,u = 0
Since the x^1, x^2, and x^3 planes were defined to be orthogonal in a
local frame of reference fixed with respect to the earth's surface,
the 4-vectors orthogonal to them will be perpendicular to each other
and to the worldline of an observer on the earth's surface. This
gives us g^12 = 0 and g^32 = 0.
g^02 g_00,0 + g^22 g_00,2 = 0
g^22 g_00,2 = 0
g_00,2 = 0
For a clock fixed with respect to the earth's surface, the only
nonzero component of its four-velocity is the u^0 component. Thus,
the clock rate depends only on g_00. We have just shown that g_00
does not depend on how far north or south you are, as long as you are
at sea level. An almost identical argument shows that g_00 does not
depend on how far east or west you are. Provided you are at sea
level, the clock rate is the same anywhere.
--
Jim E. Black
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| User: "Androcles" |
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| Title: Re: Where do clocks run faster: on equator or on poles? |
26 Apr 2007 06:51:59 AM |
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"Jim Black" <tramspap@yahoo.com> wrote in message =
news:1177566337.786635.283110@r3g2000prh.googlegroups.com...
On Apr 24, 10:34 am, sasha semenov <c...@yahoo.com> wrote:
Sea level, cesium etalons.
=20
Neither. They run at the same rate.
=20
(Assumptions here are a static gravitational field, and that objects
dropped at sea level fall perpendicular to sea level.)
Neither. They run at the same rate.
No assumption necessary, the observation is empirical and first made by
Sir Isaac Newton.
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| User: "Rock Brentwood" |
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| Title: Re: Where do clocks run faster: on equator or on poles? |
29 Apr 2007 05:30:13 PM |
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On Apr 24, 10:34 am, sasha semenov <c...@yahoo.com> wrote:
Sea level, cesium etalons.
Wherever you weigh less is where the clocks will run faster. The poles
are flattened, and the equator bulges, so you're further out from the
Earth's center on the equator. I'm not sure if that's counteracted by
the larger mass underneath you under the bulge, but I think the
gravity is less on the equator than on the poles. Then, on top of
that, you have the centrifugal effects of your inertia coming from the
Earth's rotation which reduce your effective weight. So the ones on
the equator should run slower.
What that means (and this is something that can actually be tested,
provided you have high enough precision clocks), is that if you set up
a clock in Greenland (or in Antarctica), and another in Quito; let
them go for a long enough time, and then bring them together; the one
from Quito should have registered more nanoseconds and the one from
Greenland or Antarctica.
A similar effect also takes place between the clocks on two different
stories of a skyscraper or other multi-story building. The ones higher
up feel less gravity due to being further out from the Earth's center.
Consequently, they will run faster.
The actual difference can be computed, and the comparison actually
run. It actually has been, and the effect is confirmed with the
difference matching what the theory predicts.
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| User: "Uncle Al" |
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| Title: Re: Where do clocks run faster: on equator or on poles? |
30 Apr 2007 09:33:03 AM |
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Rock Brentwood wrote:
On Apr 24, 10:34 am, sasha semenov <c...@yahoo.com> wrote:
Sea level, cesium etalons.
Wherever you weigh less is where the clocks will run faster. The poles
are flattened, and the equator bulges, so you're further out from the
Earth's center on the equator. I'm not sure if that's counteracted by
the larger mass underneath you under the bulge, but I think the
gravity is less on the equator than on the poles. Then, on top of
that, you have the centrifugal effects of your inertia coming from the
Earth's rotation which reduce your effective weight. So the ones on
the equator should run slower.
[snip]
Proper time is identical at the geoid at the equator and poles.
Everything exactly cancels, Special and General Relativity. Look up
the "Physics Today" article in the past five years or so. That is one
reason why gravitation (GR) is not gravity. Gravity on a spinning
planet is always normal to its surface though said surface is
centripetally deformed out of sphericity.
--
Uncle Al
http://www.mazepath.com/uncleal/
(Toxic URL! Unsafe for children and most mammals)
http://www.mazepath.com/uncleal/lajos.htm#a2
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| User: "Androcles" |
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| Title: Re: Where do clocks run faster: on equator or on poles? |
30 Apr 2007 03:10:33 PM |
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"Uncle Al" <UncleAl0@hate.spam.net> wrote in message =
news:4635FE1F.BA4DAEAB@hate.spam.net...
[snip wet fart]
Proper time is identical at the geoid at the equator and poles.=20
Everything exactly cancels, Special and General Relativity.
[snip diarrhoea]
How fucking convenient, a theory that cannot be checked.
What a *****...
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| User: "H. Wabnig .... .-- .- -... -. .. --. @ .- --- -. DOT .- -" |
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| Title: Re: Where do clocks run faster: on equator or on poles? |
01 May 2007 12:25:08 AM |
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On Mon, 30 Apr 2007 20:10:33 GMT, "Androcles"
<Engineer@hogwarts.physics.co.uk> wrote:
"Uncle Al" <UncleAl0@hate.spam.net> wrote in message news:4635FE1F.BA4DAEAB@hate.spam.net...
[snip wet fart]
Proper time is identical at the geoid at the equator and poles.
Everything exactly cancels, Special and General Relativity.
[snip diarrhoea]
How fucking convenient, a theory that cannot be checked.
What a *****...
Of course, we can, Andro.
We divide by Zero at the North Pole, and then at the Equator.
Compare the results.
I do the one at 40° C in the shadow, you go to the cold.
Ready?
w.
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