On 2010-02-28, Danny Mayer <[email protected]> wrote: > Kevin Oberman wrote: >>> Date: Sat, 27 Feb 2010 23:05:30 -0500 >>> From: Danny Mayer <[email protected]> >>> Sender: [email protected] >>> >>> unruh wrote: >>>> On 2010-02-10, David J Taylor >>>> <david-tay...@blueyonder.delete-this-bit.and-this-part.co.uk.invalid> >>>> wrote: >>>>> "David Woolley" <[email protected]> wrote in message >>>>> news:[email protected]... >>>>>> David J Taylor wrote: >>>>>> >>>>>>> I remember the flying of caesium or other atomic clocks round the >>>>>>> world, and that folks had to invoke relativistic corrections. Were >>>>>>> these better than microseconds as well? >>>>>> That's called Navstar (GPS) and GPS position solutions do have to >>>>>> include a general relativity correction to the satellite clocks. >>>>> Not today's GPS, but some forty or more years ago: >>>>> >>>>> http://www.hp.com/hpinfo/abouthp/histnfacts/timeline/hist_60s.html >>>>> >>>>> 1964: >>>>> >>>>> "The highly accurate HP 5060A cesium-beam atomic clocks gain worldwide >>>>> recognition as the "flying clocks" when they are flown from Palo Alto to >>>>> Switzerland to compare time as maintained by the U.S. Naval Observatory >>>>> in >>>>> Washington, D.C. to time at the Swiss Observatory in Neuchatel. The >>>>> atomic >>>>> clock was designed to maintain accuracy for 3000 years with only one >>>>> second of error. The cesium-beam standard becomes the standard for >>>>> international time." >>>>> >>>>> I had wondered what accuracy was obtained - i.e. how far was each nation >>>>> out - and whether relativistic corrections had been needed for these >>>>> "flying clock" tests. >>>> 1 sec/3000years is 1 part in 10^-11. The gravitational redshift is >>>> gh/c^2 (g is gravity acceln on earth, h the height of the flight, and c >>>> vel of light) which is 10^-12 -- ie below ( but not by much) the >>>> accuracy of the clock. The velocity correction is 1/2 v^2/c^2 which is >>>> again about 1 part in 10^12. Ie, both corrections are smaller (but not >>>> much) than the uncertainty in the clock rate. If the plane flew at Mach >>>> 2, rather than well below Mach 1, you could get that velocity correction >>>> up the accuracy and one would have to take special relativity into >>>> account. >>>> >>>> >>>> Since the flight probably lasted say 10 hr, which is 100000 sec, th >>>> eclocks would have been out by about 1usec. Assuming that the clocks >>>> could then have been synchronized, that would mean that US and >>>> Switzerland time have been out by about 1usec. (Why they would fly from >>>> Palo Alto when the time standard is in Washington DC I have no idea). >>> Actually the Time Standards lab for NIST are half-way up a mountain in >>> Colorado. As a result they have to make corrections to the time to >>> account for the difference between where they are and sea level. It's >>> not USNO. >> >> A slight exaggeration, I believe. While the elevation of the clock must >> be taken into account to deal with general relativity, it is hardly >> "halfway up a mountain". >> >> It is located in Boulder, Colorado, USA. While I failed to find the >> exact elevation of the clock, Boulder is at 5430 ft. (1655 m.) above sea >> level. While this ay sound like it is halfway up a mountain, it is at >> nearly the same elevation as Denver (5280 ft.) and is actually at the >> base of the Rocky Mountains. >> > > Yes, that was something of an exaggeration but it's not at sea level. > >> The clock should remain accurate to within a second for about 20 million >> years (assuming no adjustment is made). When the clock was moved down a >> floor a year or two ago, the difference in elevation and the strength of >> the gravitational field had to be adjusted for. Even if it was at the >> USNO, elevation would need to be taken into account. > > The reason that they have to apply general relativistic corrections is > that their clocks are far more precise than anything that even a cesium > clock will give you. Their current uncertainty is about 5 x 10-16 with > the NIST-F1 clock. There's a discussion here: > http://tf.nist.gov/cesium/fountain.htm about their current clock though > for some reason I don't see any discussion about the relativistic > corrections for not being at sea level. That memory may have been from a > discussion I had with Judah.
The relativistic correction is approx 10^-16/m (or 10^-10PPM/m) If the clock has an accuracy of 5 10^-16, a 5 m change in height will be larger than that the uncertainty (or course it depends on what 5 10^-16 uncertainty means). Certainly the 1600m above sea level will make a very very noticeable difference. > > Danny _______________________________________________ questions mailing list [email protected] http://lists.ntp.org/listinfo/questions
