Re: The Spin Proviso to Relativity

From: Paul B. Andersen (paul.b.andersen_at_hia.no)
Date: 10/21/04 

Date: Thu, 21 Oct 2004 11:43:11 +0200

"sal" <pragmatist@nospam.org> skrev i melding news:pan.2004.10.20.19.52.25.700479@nospam.org...
> On Wed, 20 Oct 2004 21:06:20 +0200, Paul B. Andersen wrote:
>
> >
> > "Ben Bean" <kavs_delethis_@sysmatrix.net> skrev i melding
> > news:B8SdncZcW_z2v-ncRVn-oA@sysmatrix.net...
> >> I am eager to hear wisdoms in answer to the quandary below stated.
> >>
> >> SCENARIO: You stand on a planet just like Earth, but there's no
> >> atmosphere. You stand on the equator and hold your hands up to the air
> >> so that they are a meter apart. [Relax, this is NOT a study in relative
> >> simultaneity like the Barn/Pole thing.] As you stand there a huge
> >> spacecraft coasts by just overhead, just beyond your reach. The ship
> >> seems motionless to you, hovering, because it is going eastward at a
> >> speed to exactly match the planet's tangential rotational speed. As you
> >> reach up, your outstretched fingertips are just about touching the
> >> 842-meter mark and the 843-meter mark on the rule graduated on the
> >> enormous ship's straight exterior.
> >>
> >> Here's the quandary: the spaceship occupants can EMPHATICALLY assert
> >> that an all-way light beacon pulse emitted midway between their ship's
> >> 842 & 843-meter marks will hit the two nearby meter marks
> >> simultaneously, according to their native frame's clocks and such. Yet
> >> the guy on the planet cannot make the same claim?? When does an
> >> arbitrary local span become tantamount to an SR scenario. In spite of
> >> Sagnac, there must surely be some carry-over; I mean you're just about
> >> TOUCHING that other frame, comoving.
> >>
> >> -Ben
> >
> > Of course the guy on the planet will agree that the light will hit the two
> > metre marks simultaneously. That is, if he had one clock at each side of
> > himself, and he E-synched those clocks, they would show the same when hit
> > by the light.
> > However, if the two clocks were showing UTC, they would NOT show the same
> > when hit by the light.
> > Clocks on the surface of the Earth showing UTC are NOT synchronous in the
> > Earth fixed frame. They are synchronous in the non rotating ECI-frame.
>
> Paul, what do you mean by "Earth fixed frame"? Do you mean the
> inertial frame which is momentarily comoving with the surface at one
> particular point?

No, I mean the rotating frame fixed to the Earth and rotating along
with the Earth. A clock on the ground will be stationary in this frame.

What I meant to say above is that clocks on the Earth showing UTC
simultaneously (according to Einstein's definition) show the same in
the non rotating frame where the centre of the Earth is stationary
(the ECI-frame).
One way of saying this is that if you could imagine a flash of
light emitted from the centre of the (transparent) Earth, all the clocks
should show the same when hit by the light front.

If you imagine two such clock on the equator, say 1km from each
other, they will NOT simultaneously show the same in a local
inertial frame momentarily comoving with the surface.
If you measure the speed of light with those two clocks,
you will measure c+/-v (sign depending on the direction of the light),
where v is the peripheral velocity of the Earth in the ECI-frame.
This is usually called the "Sagnac effect".

The reason why UTC clocks are synched like this, is that it
is impossible to globally E-sync clocks to each other in
a rotating frame. If you could imagine a chain of clocks around
the equator, and tried to E-synch them one by one to the previous
clock all around the Earth, you would find that the last clock would
not be E-synched to the first.

Paul

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