The result is worthless.  This is 6x10^-14 which is within the drift of two
cesium clocks.  There are no mountains in New Hampshire that are equal to
the task.  Mt Rainier in Washington state barely works.

On Tuesday, January 31, 2023, Joseph B. Fitzgerald via time-nuts <
time-nuts@lists.febo.com> wrote:

On 1/31/23 7:01 AM, Tom Van Baak via time-nuts wrote:

TAI please, not UTC with ickyness like leapseconds. And, yes, there are
people who use GMT (although they're really using UTC, they just call it
GMT).

Relativistic effects have been in the navigation models for decades.
Navigation, for the most part, depends on precision ranging from Earth
based stations to measure the round trip time to/from the spacecraft,
but there's also one-way ranging. The latter depends  having a good
clock (Hg ion trap is the most likely going forward) on the spacecraft.

The ability to accurately measure time (and position) and, even more, to
carry that forward through a time gap (when you're not measuring) is
what enables a lot of future missions, particularly ones where you are
expecting cooperative behavior between spacecraft or close in relative
proximity operations (consider bistatic radar, or multistatic sensing). 
My SunRISE mission is a baby step - we use GPS (from above GEO, so we're
looking at the "other side of the Earth") to measure time and position
for collecting the RF signals from the sun, among six space vehicles
spread over ~10 km. For SunRISE, on board, we only need to know time to
1 microsecond, but in post processing on the ground, we're at the 1 ns
level (well, 1 ns in time, 1 m in position).  Future missions, though,
will need more precise time knowledge, over wider distances, without a
handy GPS constellation. Relativistic effects will be important.

The typical incremental ADEV from the spacecraft in the turnaround is
<1E-15 (tau= 1000 or 10,000 sec) after taking into account calibrated
temperature effects.  1E-15 on a 1E12 meter path (e.g. distance to
Jupiter 8e9 km or Saturn 1.6E9 km) is 1mm. When making the overall
measurement they also take into account distortion of the DSN antennas,
etc. It's even trickier when the station that transmits is different
than the station receiving.

And they're getting more attention these days because folks really want
to do what's called "one-way ranging", which relies on having a good
clock (Hg ion trap is the most likely going forward) on the spacecraft
so you can compare phase of a received signal at time t1 to phase of a
received signal at time t2, on board.  But you get to remove the
uncertainties in one direction.

There's quite a bit of interest in navigation in cislunar space, too,
and there's countless papers and proposed systems. There's a lot of
folks who don't appreciate the scale and complexity of modern GNSS
constellations, which also take into account relativistic effects. It's
not just a matter of putting up a few 6U cubesats with a CSAC in a NRHO,
that's for sure.  The Moon is kind of a problem, because the gravity
isn't smooth (neither is Earth's, but we have a lot more knowledge of
that), and if you want position accuracy of centimeters, then those
effects might be important.

Hi Marek,

It seems this effect is below the noise floor of the current clocks. See this paper:

https://link.springer.com/content/pdf/10.12942/lrr-2003-1.pdf

Here's the relevant text:

​
Maybe future GNSS with optical clocks (or advanced Cs clocks) could get to this level.

Cheers,
Peter

There's an excellent book called Gravity From The Ground Up by Bernard Schutz:

https://www.amazon.co.uk/Gravity-Ground-Up-Introductory-Relativity/dp/0521455065/ref=sr_1_1?crid=253QEUS0PJDXU https://www.amazon.co.uk/Gravity-Ground-Up-Introductory-Relativity/dp/0521455065/ref=sr_1_1?crid=253QEUS0PJDXU&keywords=gravity+from+the+ground+up&qid=1675248211&s=books&sprefix=gravity+from%2Cstripbooks%2C82&sr=1-1 &keywords=gravity+from+the+ground+up&qid=1675248211&s=books&sprefix=gravity+from%2Cstripbooks%2C82&sr=1-1

…which gives a fairly straightforward derivation of the small-field approximation to GR including gravitational time dilation – actually the latter comes just from a very simple thought experiment with observers and falling clocks, and once you have that the small field approximation follows quite easily.  That is a/k/a Newtonian Mechanics…  The book is quite expensive but there’s a lot of good reading to keep one busy.

John.

-----Original Message-----
From: alan bain via time-nuts time-nuts@lists.febo.com
Sent: 31 January 2023 13:40
To: Discussion of precise time and frequency measurement time-nuts@lists.febo.com
Cc: alan bain alan.bain@gmail.com
Subject: [time-nuts] Re: gravity fields affect time keeping?

It's a consequence of general relativity.

The simplest way I can think to answer this question is to think of a point mass in a spherically symmetric situation  (as one would expect around a point mass in a vacuum) and solve Einstein's equation which in this case (point mass is handy) is just

G_{\mu\nu}=0

After some boring algebra with tensors in spherical co-ordinates which some examiners seem to think it is interesting to see if you can reproduce, you arrive at a metric

ds^2 = - (1-r_s/r) c^2 dt + dr^2/ (1-r_s/r) + r^2 (dtheta^2 + sin^2 theta dphi^2)

r,theta,phi are usual spherical co-ordinates, c is the speed of light in vacuum and the Schwartzchild radious r_s = 2 G M /c^2 (which is found by comparing with Newtonian Gravitation, G is Newtonian coefficient, M is mass of point mass). So if we stay in the same place and compare time

ds^2 = - (1-r_s/r) c^2 dt

And ds^2 = -c^2 d (tau)  where tau is time measured at a stationary point arbitrarily far from the mass.

So

\delta t_{on planet} = \delta t_{clock infinitely far away} sqrt ( 1-r_s/r).

So the closer one gets to the point mass the slower time goes.

I don't really know any maths-free explanation of this (unlike for say special relativity when there are good no-maths explanations). Would like to know one if someone does...

Alan

On Tue, 31 Jan 2023 at 13:00, Kevin Rowett via time-nuts < mailto:time-nuts@lists.febo.com time-nuts@lists.febo.com> wrote:

time-nuts mailing list --  mailto:time-nuts@lists.febo.com time-nuts@lists.febo.com To unsubscribe send an email to  mailto:time-nuts-leave@lists.febo.com time-nuts-leave@lists.febo.com

On 1/31/23 9:19 AM, Bob Camp via time-nuts wrote:

Now that I  think about it, that might special relativity - due to the
velocity of the satellite, not the gravity field.

Don,

Well, that depends. In cases like this you must consider exactly what
kind of clock(s) are used. The performance of an old 5061A cesium clock
may be different than a later model 5061B and both very different from a
5071A, the model still in use by timing laboratories around the world.
Plus there's the high-performance option with even better performance,
having a noise floor around 5e-15. That's what I tend to use for my
relativity experiments.

In the short video Joe Fitzgerald posted, we see that the team used Mt
Sunapee in New Hampshire which is about 2700 ft (0.8 km). True, that's
not very tall and the predicted blueshift from sea level is just 9e-14.
I can tell you that a 5061 or equivalent vintage cesium clock would not
be adequate for that experiment.

But they didn't use a pair of surplus cesium clocks. The video makes it
clear they used a 5071A [1] for the portable clock, and likely they used
a H-maser [2] for the base clock (the Einstein doll is sitting on top of
a MHM 2010 maser).

It appears the clock comparison scene was filmed at Microsemi (was
Symmetricom, now Microchip), the company that manufacturers the 5071A
and the maser. What you see behind the glass is their main clock room
[3]. In other words, this was not some cheap backyard experiment from
eBay. See also the original discussion about the video on time-nuts [4].

There's not quite enough information in the video to calculate the error
bars, so I'll not stick my neck out too far on that point. But from what
I can tell, the results are totally plausible, in spite of the mountain
not being very tall. Thus I'm curious what assumptions or calculations
you used to reach the opposite conclusion.

/tvb

[1]
https://www.microchip.com/en-us/products/clock-and-timing/components/atomic-clocks/atomic-system-clocks/cesium-time/5071a

[2]
https://www.microsemi.com/product-directory/active-hydrogen-maser/4123-mhm-2010-active-hydrogen-maser

[3] National labs and clock companies often have a special clock room,
aka "house standard". The one you see in the video has roots (hp 5060 ->
hp 5061 -> hp 5071) back this clock room 50 years ago:

http://www.leapsecond.com/history/Benchmark.htm

[4]
https://febo.com/pipermail/time-nuts_lists.febo.com/2015-November/subject.html#start

On 1/31/2023 10:09 AM, Donald E. Pauly wrote:

Hi

One of the most basic issues with manufacturing any accurate standard / clock is that you
need “something better” for your reference. If you manufacture things like active masers
and 5071’s that makes this a significant challenge. For the MHM-2010 you might want to
demonstrate <1x10^-15 sort of ADEV numbers at 10,000 seconds before they ship.

One way to go for an ADEV target is to run a reference that is 5X better than the device
you are testing. This makes for less math and far fewer hours spent explaining this and
that to customers. <2x10^-16 at 10,000 sec puts you into the land of experimental standards.
There aren’t any off the shelf answers.

If you want to look at the long term spec on the MHM-2010, you are after 2x10^-16 per day
test results. You are off into the parts in 10^-17 world for a reference. Same basic answer,
not much off the shelf

One answer is an ensemble of devices. You then might hope that performance improves
by sqt(N). That’s why you see people go to rooms full of fancy standards. Common mode
issues (temperature ….) then become a big challenge. Still, that’s the “why?” when you
see that room full of standards.

It’s a pretty good bet that whatever the comparison was made to, it is in the parts in 10^-16
per day sort of range and it is monitored in a fashion that can back that claim up pretty
well. Can they back up a 1x10^-16 / day number? You’d have to give them a call and ask.

Bob

On Tue 2023-01-31T10:20:13-0800 Lux, Jim via time-nuts hath writ:

But UTC is the primary.  UTC is the tail that wags the dog.
TAI has no legal existence.  UTC is the legal time scale most places.
Only BIPM can make TAI, no national laboratory can make TAI.
Most national labs are required by statue to make UTC, and from
those BIPM constructs TAI.

--
Steve Allen                    sla@ucolick.org              WGS-84 (GPS)
UCO/Lick Observatory--ISB 260  Natural Sciences II, Room 165  Lat  +36.99855
1156 High Street              Voice: +1 831 459 3046        Lng -122.06015
Santa Cruz, CA 95064          https://www.ucolick.org/~sla/  Hgt +250 m

On 2/1/23 9:19 AM, Steve Allen via time-nuts wrote:

But in a space application you want no leapseconds - In practice
everyone runs a local clock, and then goes through gyrations to convert
that into some recognized frame and epoch.

There have been papers published about why there is no noon/midnight effect, and some dispute by the theorists about the proper explanation for the lack of it.

I can point you to N. Ashby and M. Weiss, 2013, “Why there is no noon-midnight shift in the GPS”, http://arXiv [gr-qc]:1307.6525,https://arxiv.org/abs/1307.6525  These authors, as brilliant as the ones they disagree with, state that past arguments appealing to the second-order doppler shift being cancelled by the gravitational gradient miss the fundamental ideas behind the principle of simultaneity.