Re: Redshift of Light Near a Black Hole

From: The Ghost In The Machine (ewill_at_sirius.athghost7038suus.net)
Date: 03/14/05 

Date: Mon, 14 Mar 2005 18:00:11 GMT

In sci.physics, Nick
<macromitch@yahoo.com>
 wrote
on 13 Mar 2005 23:07:43 -0800
<1110784063.196002.80210@o13g2000cwo.googlegroups.com>:
> I know what the theory predicts.
> And you can't demostrate otherwise Sam.
>

Fine. Give us a prediction. Something along these lines, for
example, might work.

Two rockets launch from Earth. One lands on the Moon and
sets up a transceiver unit with a known delay. The other
keeps going, accelerating as much as it can until its fuel
runs dry, then starts broadcasting regular signals both
to Earth and to the Moon, which relays them.

Assuming that the rocket is now moving away from Earth at
30 km/s = 10^-4 c, and that the Earth and the Moon are in
line (or as nearly in line as one can manage), what delay
would one expect between the signals, once the known delay
of the transceiver and the difference in length between
signal paths is compensated for?

SR: Zero.
GR: Zero.
Newton: The rocket signal lags by 10 milliseconds.

Will this delay increase or decrease as the rocket continues to move
away, assuming the rocket is no longer accelerating using fuel?

SR: No.
GR: No.
Newton: The delay might decrease as the rocket climbs out of the
        Sun's gravitational potential well and thereby slows down.
        However, that delay may be compensated for because the
        light "balls" now get to "roll" down this potential.

Also, what frequency and/or wavelength shifts might be expected
between the signals, assuming the rocket transmits at 1 GHz?

SR: 5 Hz decrease, with a wavelength increase of about 150 nm.
GR: Around 5 Hz decrease, when the moon's gravity is factored in,
    depending on exactly where the rocket is. The wavelength shift
    is also about 150 nm, and similarly vary. The effect is
    not much: one might get a variance of 0.1 Hz if not even less.
Newton: The wavelength (nominally 30 cm) will
        increase by about 30 microns. The frequency will
        decrease by about 100 kHz.

Not that this is that useful an experiment; we've already learned the
physical workings of most of this by bouncing radar waves off
Venus, by observing pulsars, and by conducting Earthside stuff,
which is lots cheaper. :-) Neutron stars make very good clocks.

A far more esoteric result will (may?) be obtained from
Gravity Probe B, which tests one of GR's predictions that
the Earth's rotation twists the very fabric of spacetime,
by throwing a gyro-stabilized unit off a guide star.

(Disclaimer: I've not checked these calculations in detail
so they may be off.) 

-- 
#191, ewill3@earthlink.net
It's still legal to go .sigless.

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