Subject: RE: [TICTOC] Draft BOF description

From: "Sasha Vainshtein" <[email-masked]>
Date: Tue, 16 Jan 2007 08:57:59 +0200

Marshall and all,
A couple of questions stemming from you last message to the list:

1. Do I understand correctly that the relativistic effects you have
mentioned affect
   synchronization but not syntonization (at least if we restrict
ourselves to
   the objects that stay in the same place on the surface of Earth)?

2. Do I further understand correctly that verifiable quality of
synchronization
    depends on the distance between the server and the client while the
    verifiable quality of syntonization does not depend on that (at
least in theory)?

Regards,
                   Sasha

-----Original Message-----
From: Marshall Eubanks [mailto:[email-masked]] 
Sent: Monday, January 15, 2007 7:24 PM
To: Stewart Bryant
Cc: [email-masked]
Subject: Re: [TICTOC] Draft BOF description

Dear Stewart;

On Jan 15, 2007, at 11:20 AM, Stewart Bryant wrote:

> Marshall Eubanks wrote:
>
>> Hello;
>> I will ask again the questions I asked in San Diego :
>> What are the accuracy goals of this work, for both synchronization  
>> and syntonization ?
>> What is the expected integration time ?
>> What is the expected geographical area over which these goals are   
>> likely to be met ?
>> Is this effort designed to replicate or instantiate ITU G.8261 ?  
>> To  support TDMoIP ? Some other standard ?
>> In my experience, timing does not lend itself to a "let's make it as

>> good as possible" mode of
>> development, as the most important question is generally, what   
>> complications can I leave out and still meet my goals ?
>
> Sure you have to know what you can acheive in a particular network 
> environment - i.e. is this network and this technique good enough and 
> reliable enough to serve this need ... but... there is a very large 
> range of applications that need time and the result is a range of 
> requirements that range from NTP style 10ms to rather better than we 
> can expect to do ns. From a rough survey of the applications it looks 
> like we need to get from 10ms class to 1us class to satisfy the 
> majority of the demand. However unlike the original assumptions make 
> in the NTP design, I think that we can make requirements on the 
> network to achieve high end performance.
>

Global relativistic synchronization effects start coming at 4 . 10^-7
sec, assuming that your network is restricted to be on the surface of
the Earth, so they shouldn't be ignored even at the microsecond level,
if you want the domain of your synchronization to be global.  
Things are worse if parts of your network are on an airplane, or in LEO;
note also that time dilation effects for LEO are order 6 * 10^-10 s/s,
and 10^-8 in deep space.

> (I derived the initial IERS standards for VLBI differential

>
> I am not familiar with either of those FLAs

Here is the paper referred to

http://www.iers.org/documents/publications/tn/tn32/tn32_109.pdf

Regards
Marshall

>
>> In order to be specific, I assume that one purpose here is meeting  
>> the TDMoIP accuracy discussed in the ITU SG15, which is roughly 10^-6

>> sec and 10^-8 s/s. Does that mesh with other people's expectations ?
>
> Support for Circuit Emulation and Mobile Phone base stations are the 
> two primary drivers for frequency. I think that PDV measurement is the

> poster child for time, but as I mentioned in my earlier message today 
> there are end user applications that also need time in the 1us class.
>
>> I would be willing to participate in but not take the lead on writing

>> the requirements document.
>
> Thanks
>
> Stewart

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---

From: Marshall Eubanks <[email-masked]>
Date: Tue, 16 Jan 2007 12:55:47 -0500

>    the objects that stay in the same place on the surface of Earth)?

Relativistic effects start with the Lorentz transformations of  
Special Relativity (SR).
The synchronization effects start to show up with magnitudes roughly  
of the order 2 PI L * v, where
L is the radius of a loop and v is a characteristic velocity. These  
are simultaneity effects - they
don't really matter for 2 points, just 3 or more.
We used to call this "clock closure effects" (sync clock 1 with 2, 2  
with 3, then
there is an offset between 3 and 1). Acceleration (and we live in an  
accelerated frame of reference) will cause
syntonization closure effects from the same source. This is called  
the Sagnac effect if you are on a rotating (and thus accelerated)  
frame of reference, but the same happens from any source of  
acceleration.

Time dilation effects do effect syntonization, but do not to first  
order cause syntonization not to close, and come in as order v^2 (the  
general relativistic time dilation is the same order of magnitude but
opposed in sign  to the special relativistic one for an orbiting  
body, so there is partial cancelation).
For bodies at "rest" on the Earth's the special relativistic  
dilatation is smaller than the general relativistic contribution. (To  
be clear - these do not cause syntonization closure failure above the  
level of v^3, which is pretty small, so could be ignored.)

TAI is defined as the time at the gravitational potential at sea  
level. (I.e., it is time for the surface of the Earth.) It take into  
account the equatorial bulge, but I believe still ignores elevation  
about sea level - it can just do this as still meet their accuracy  
goals.

GPS time is adjusted so that the signals coming down are on TAI  
(i.e., the clocks do not keep TAI rate  on the satellites).

For scaling (I will resolutely ignore factors of 2, 2/3, etc., this  
is for order of magnitude).

Earth's rotational velocity ~ 1.5 x 10^-6 x cos(latitude) so ~ 10^-6  
for most clocks
LEO velocity ~ 2.7 x 10^-5
One Earth radii is 0.02 seconds

The Sagnac effect is some 100's of nanoseconds. This is of order 2 PI  
x L x v or  2 x 10^-7 sec on the equator in vacuum. For clocks on  
board an airplane, this could easily be doubled (or even zero'ed  
out). For a network of clocks in LEO, it would be order 3 micro seconds.

Acceleration on the Earth's surface due to rotation is 10^-10 cos 
(lat) sec^-1, so syntonization closure for clocks on the surface of  
the Earth will be of order 2 PI x L x a, or order 10^-11

Since acceleration in LEO is 3 x 10^-8 sec^-1, syntonization closure  
will be of order 2 PI x L x a, or order 4 x 10^-9 for LEO networks.  
Clocks on airplanes accelerating at 1 g would have similar  
syntonization closure errors.

The time dilation on the surface is order 10^-12 (for rotation, from  
SR) and 0.7 x 10^-9 (for gravity, from GR)
However, the biggest "mountain" (the equatorial bulge) is only 21 km,  
and so the actual dilation difference
(between a polar clock and an equatorial one) is only of order 0.7 x  
10^-9 x (21/6371) or 2 x 10^-12. Since most clocks are at mid- 
latitudes, including the ones defining TAI, the typical error is  
less, less than 10^12 on average IIRC. Mountain ranges are less than  
10 km in altitude, So in TAI, clocks are all treated as if they were  
at sea level, and the smaller than 10^-12 error is ignored. (This is  
in the system, of course individual clock comparisons can correct for  
these things if they feel the need.)

All of these effects become bigger if your network extends into deep  
space.

>     verifiable quality of syntonization does not depend on that (at

I hope I made this a little bit clearer above. Upon reflection, I  
would suggest that we ignore scalar effects (time dilation) but at  
least potentially take into account simultaneity effects.

Regards
Marshall