I wish I could take the credit for being evil here, but no.
What the natural consequence is that every atomic clock of this type
should have a gravitational sensor that compensates for gravitational
shift, as it now has become a frequency shift component. The first
degree compensation should not be too shabby.
Cheers,
Magnus
On 11/04/2014 08:27 PM, Bob Bownes wrote:
You people are evil. Now you have me wondering where I can get a microgram
level accurate scale. Simply tracking the weight of a 'constant' (anyone
got a silicon sphere with exactly 1 mole of Si atoms in it? :)) over time
would be an interesting experiment.
As a geologist, I also have to say, that while we know the geoid to ~1cm,
it is ~1cm at the time it was measured, which is constantly changing. The
obvious tidal effects, as well as internal heating effects (and I suspect
external heating effects), continental drift (both long term events and
short term events like earthquakes), currents in the molten layers,
probably magnetic effects all are going to contribute to geoid uncertainty.
I really do need to spin the seismograph back up.
On Tue, Nov 4, 2014 at 2:04 PM, Peter Monta <[email protected]> wrote:
Hi Tom,
Based on mass and radius, a clock here on Earth ticks about 6.969e-10
slower than it would at infinity. The correction drops roughly as 1/R
below
sea level and 1/R² above sea level. For practical and historical reasons
we
define the SI second at sea level.
Yes, the change in clock rate at sea level is about 1e-18 per centimeter,
and the geoid is known only to about 1 centimeter uncertainty at best.
The non-local gravity perturbations you speak of are 2nd or 3rd order and
so you probably don't need to worry about them. Then again, if you want
to
get picky, it's easy to compute how much the earth recoils when you stand
up vs. sit down. So it's best to avoid the notion of "arbitrary"
precision;
that's for mathematicians. For normal people, including scientists, we
know
that precision and accuracy have practical limits.
Let me rephrase what I'm after. The geoidal uncertainty sets a hard limit
on clock comparison performance on the Earth's surface (for widely-spaced
clocks). At some point, as Chris Albertson noted, the clocks will measure
the potential and not the other way around. (It should be possible to
express this geoidal uncertainty as an Allan variance and include it in
graphs with the legend "Earth surface performance limit".)
What I'm curious about is this: what are the limits on clocks in more
benign environments? How predictable is the potential in LEO, GEO,
Earth-Sun L2, solar orbit at 1.5 AU, solar orbit at 100 AU, etc.? I
imagine the latter few are probably very, very good, because the tidal
terms get extremely small, but how good?
Suppose a clock dropped into our laps with 1e-21 performance, just to pick
a number. Where would we put it to fully realize its quality (and permit
comparisons with its friends)? And is the current IAU framework adequate
to define things at this level (or any other arbitrarily-picked level)?
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