On Mon, Nov 3, 2014 at 1:18 PM, Mike Feher mfeher@eozinc.com wrote:

This may not be a very satisfactory explanation, but in a nutshell
it's not the atomic transition time that changes with gravitational
potential, but time itself.  And remember, it's a relative effect

• you can only measure it when you compare two clocks at different
  heights, never just by looking at one by itself, no matter how good it
  is.

Weighing scales do not work by measuring the gravitational attraction
between the scale and the object to be measured.  They measure the
attraction between the earth and the object to be measured. When you
go up a hill, you move the apparatus and the object, but not the
earth.

Henry

On 11/3/2014 3:54 PM, Tom Van Baak wrote:

According to the BIPM: "At its 1997 meeting the CIPM affirmed that:
"This definition refers to a caesium atom at rest at a temperature of 0
K." - http://www.bipm.org/en/publications/si-brochure/second.html

Isn't weight equivalent to acceleration, and it's therefore not "at
rest" when sitting on a table at sea level?

I don't see anything in the BIPM definition of the second regarding sea
level.

Hi Peter,

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.

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.

The most obvious gravitational perturbation is that of the Moon. You can predict, and even measure, that g changes in the 7th decimal place as the moon orbits the earth. This is so minor it cannot as yet be measured by the best atomic clocks, but it has been measured by the best pendulum clocks (because pendulum clock make better gravimeters than atomic clocks). For details, see:
http://leapsecond.com/hsn2006/

Your "fuzzy" question is good. When error or noise is constant one can simply use standard deviation or rms to quantify the amount of fuzz. But when the perturbations are not simple and fixed in time you want a statistic that incorporates not just accuracy, but stability. For this you need something like ADEV and its log-log plots of stability as a function of tau. As an example, here is the ADEV of Earth:
http://leapsecond.com/museum/earth/

/tvb

Hi Mike,

The usual wording for the definition of the SI second also includes the word "unperturbed". That little word covers a host of physics and engineering effects and can keep graduate students busy for years. You either have to eliminate them from your clock or your lab, or extra carefully measure then and back-out their effects on your clock's operating frequency.

For a really good example of the sort of corrections that are made inside a cesium clock see: http://tf.nist.gov/general/pdf/1497.pdf

By the time you read to page 30, you'll see table 3 and 4 which summarize the perturbing corrections.

/tvb

Not to put too fine a point on it, but my practical understanding is that
any two or more clocks generally do not agree (that is - yield identical
phase/frequency information) ever, anyway. So atomic horology - and beyond

• means that we continue to ?adjust? ?compensate? clocks of whatever
  stability and accuracy to the current, agreed upon "ideal" - even as the
  ideal may move or evolve.

On Mon, Nov 3, 2014 at 4:27 PM, Tom Van Baak tvb@leapsecond.com wrote:

Hi Ken,

That's correct. No two clocks ever agree. If they look like they do, you are not looking close enough or not waiting long enough.

That's also why UTC is based on the combined stability of hundreds of clocks. The weighted average of many cesium clocks is known to be better than any one cesium clock. So a big part of the UTC infrastructure is the inter-comparison of clocks all around the world. Another part is then slowly adjusting local standards to follow the more accurate global mean.

You'll notice too, that many postings to this list are not just about clocks, but also precise time measurement, and about disciplining. Whether UTC at a national lab or a GPSDO at home, there is clock, measurement, and gradual adjustment.

/tvb
----- Original Message -----
From: ken hartman
To: Tom Van Baak ; Discussion of precise time and frequency measurement
Sent: Monday, November 03, 2014 2:52 PM
Subject: Re: [time-nuts] NPR Story I heard this morning

Not to put too fine a point on it, but my practical understanding is that any two or more clocks generally do not agree (that is - yield identical phase/frequency information) ever, anyway. So atomic horology - and beyond - means that we continue to ?adjust? ?compensate? clocks of whatever stability and accuracy to the current, agreed upon "ideal" - even as the ideal may move or evolve.

On Mon, Nov 3, 2014 at 4:27 PM, Tom Van Baak tvb@leapsecond.com wrote:

Hi Mike,

The usual wording for the definition of the SI second also includes the word "unperturbed". That little word covers a host of physics and engineering effects and can keep graduate students busy for years. You either have to eliminate them from your clock or your lab, or extra carefully measure then and back-out their effects on your clock's operating frequency.

For a really good example of the sort of corrections that are made inside a cesium clock see: http://tf.nist.gov/general/pdf/1497.pdf

By the time you read to page 30, you'll see table 3 and 4 which summarize the perturbing corrections.

/tvb

Because for optical clocks Strontium is better suited than Caesium.
Caesium was at one time judged as the best suited for atomic beam
designs, but is not considered the best for fountain clocks, since
caesium has larger cross-section than rubidium, so the effect of
collisions becomes larger. For optical clocks strontium and aluminium is
among several possible choices.

There is nothing magic about caesium, it was just the chosen reference
at one time. There where actually a better choice from certain aspects,
but for several reasons judged as harder to design a clock from.

Cheers,
Magnus

On 11/03/2014 07:16 PM, xaos wrote:

On 11/3/14, 1:50 PM, Tom Van Baak wrote:

Sun and Moon are of about the same gravity magnitude, and, of course,
you get approx one cycle/day for both.

Wikipedia says about 2E-6 m/sec^2  (e.g. 7th digit, as Tom said)

Wikipedia also provides some math models for variation with latitude, etc.

Interestingly, they say that the variation among different cities
amounts to about 0.5% (Anchorage high, Kandy low)

for height..
g(h) = g(0) * (Re/(Re+h))^2

Change of 0.08% for 0 to 9000 meters

Since the period of a pendulum goes as Sqrt(1/g), the sun/moon effect is
about 1E-7.. Set up a 10 meter long pendulum, which will have a period a
bit longer than 6 seconds.    Set it swinging, and time it for 200
swings (about 20 minutes) (I think it will run that long if you've got a
nice heavy bob, etc.) Accurately(!) time that 1200 second interval with
100 microsecond precision and you might just be able to see the effect.

I started down this measurement path in the 70s in high school, but
encountered several logistics problems.
-> big pendulums are subject to environmental effects.  You might do
better with a shorter pendulum in a vacuum, which would eliminate air
drag and reduce temperature effects.
-> this kind of timing implies that you've got a counter stable to 1E-8
over the measurement period (notionally 12 hrs)

And at this precision, there's all kinds of other effects one should
take into account (for instance, the period is only approximately =
2pisqrt(L/g).. that depends on the sin(theta)=theta small angle
approximation.

However, i've always wanted to set up a rig where there's one of those
big Foucault pendulums and see if you can do it.  I suspect the drive
system on the big ones would perturb the system, but maybe you could do
an off hours experiment and let it just swing down to zero.

->

Hi Tom,

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.

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)?

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 pmonta@gmail.com wrote: