HN user
http://www.LeapSecond.com
Many pendulum clocks are capable of well under 1 ppm accuracy, which is better than many quartz oscillators. Here is a tour of clock precision by orders of magnitude:
Here is a world record setting pendulum clock from a few years ago:
http://leapsecond.com/pend/clockb/
Precision pendulum clocks are a very deep rabbit hole.
That's correct. On NT/Alpha context switching was done in ntos\ke\alpha\ctxsw.s, which was regular kernel mode assembler code. A PAL call was made but it simply set the new Teb and Pdr; two or three lines of code. I've never seen the PALcode for VMS or OSF/Tru64 but the NT PAL for swpctx was designed so that alpha assembler code in NT looked as much like the mips code that davec wrote. It made the port easier that way.
Interesting Raymond continues to mention NT/Alpha now and then. If you run into him mention I have a collection of NT/Alpha artifacts and anecdotes he might be interested in.
The original volt-nuts mailing list pretty much faded away as the members use the eevblog forum now. See the Metrology section.
The time-nuts mailing list is still very active, now in its 23rd year. More info at the group page:
That's the price -- when new. But most "time nuts" buy their atomic clocks well used on eBay or local surplus sales at a massive discount. For example the most recent H-maser on the hobbyist market went for just a few thousand. Granted it was in need of repair, but that journey is part of the fun of an atomic timekeeping at home hobby.
Author of the web site (leapsecond.com) here if you have any questions. I don't know how the title of the HN post was chosen. The actual title of the web page is "GPS, UTC, and TAI Clocks".
The page is a javascript animation of "GPS system time", UTC, and TAI showing how they all tick together but are offset from each other by an integer number of seconds. It's a fixed integer in the case of TAI and GPS and a variable integer in the case of UTC.
Blockbuster had a chance to buy Netflix in the early 2000's for $50,000,000.
Ah, an example of the Butterfly Effect: then we'd have a billion references to FAABG on the web instead of FAANG.
Previously (and posted 64000/89 days ago):
TAI and UTC are based on the SI second. The SI second is specifically defined in terms of cesium atoms at no temperature, no velocity, and no elevation (aka, on the geoid). Consequently TAI and UTC are immune from relativistic effects, by definition.
On the other hand, the physical clocks in the laboratory are not immune and that's why they have to be corrected for a dozen factors, the largest of which is usually gravitational redshift. To appreciate the complexity and precision of this correction see this NIST paper:
The original pi/spigot work was done by Rabinowitz & Wagon [1]. See also the very readable works by Jeremy Gibbons [2] [3].
[1] https://en.wikipedia.org/wiki/Spigot_algorithm
[2] https://www.cs.ox.ac.uk/people/jeremy.gibbons/publications/s...
[3] https://seminar-materials.iijlab.net/iijlab-seminar/iijlab-s...
You can grep the web for Dik's original version. The 3-line homage version I linked contains both his full name and the name of the algorithm used: "spigot" (as in spew, faucet), which itself contains the letters PI. In addition, this version outputs exactly 31416 digits of pi. So it's triple self-referential. Happy 2022.03.14 pi day to all.
With a nod to fellow pi-hound Dik T Winter, three equal lines of C give 32k digits of pi:
LF is line feed, thus new line.
LF is line feed, thus next line.
The CR
is to
readjust the write head
back to the
starting position.
Only a positive leap second is “over in a second”. A negative leap second is essentially “over before it starts”. This asymmetry is an opportunity for code to implement UTC incorrectly.
Another issue is that a positive leap second cannot be represented using time_t-like representations. But at least every time_t value maps to a UTC time.
By contrast a negative leap second, should one occur, will cause a permanent illegal time_t value that has no existence in UTC. Checking for that illegal value in every piece of code that uses time_t values will not be fun.
DCF77 has a leap second warning bit. PTB says it is up to the user to know if it positive or negative. If a clock blindly assumes it is a positive leap that’s an error in the design of the clock. This is not ideal.
Likewise WWVB has a leap second warning bit. But it includes a UT1 sign bit so the user can know if the leap will be positive or negative. This design is fine and any WWVB clock or software can properly handle positive or negative leap seconds.
This is true for both the amplitude and the phase modulation formats.
True, but note the GPS data transmission rate is only 50 bps; yes, just 50 bits per second. The signal is so week and so slow that after headers and error correction you get less than 4 bytes of data per second.
When comparing satellite reception it's not so much if you can receive data or not, but at what bandwidth. By contrast, data rates for Starlink are roughly 50 to 100 megabits per second; a million times greater than GPS.
So that's why the Starlink dish and electronics are orders of magnitude larger than a phone. Or to put it another way, that's why mobile phones can handle GPS data but not Starlink data.
Don't worry. This happened once before in 2003 [1].
UTC has provisions for positive or negative leap seconds; that works fine. GPS runs without the hassle of leap seconds; that works fine too. GPS users often want to know UTC, so GPS also broadcasts the difference between GPS time and UTC; this works fine.
All of this is in the GPS spec; almost all GPS receiver firmware gets it right. But there is a weird edge case that is hard to test. Specifically if there has been no leap second for 256 weeks (1792 days, ~5 years) inadequately tested GPS receiver firmware could mess up. It happened to one make/model GPS receiver in 2003. [1] It could happen again later this year, in 2021.
The math is fun. The most recent leap second was 2016-12-31 (MJD 57753). 8 bits or 256 weeks later(1792 days, not to be confused with Ramanujan's taxi number 1729) will be 2021-11-27 (MJD 59545). So shortly before, or on, or after that date it is possible a faulty GPS receiver will misrepresent a leap second or miscalculate UTC. GPS positioning and navigation is likely completely unaffected (because it avoids leap seconds entirely).
As a patient hobbyist collector I try to buy one of each. My goal was to learn the history and theory of each one, explore the magnificent design, measure the actual timing accuracy, read as many old books or articles about them, and in some cases meet the designers of the clocks. Atomic timekeeping, like computing, is a new enough field that a few of the old timers are still around.
For the valley-mountain gravitational time dilation experiments that I've done I use 5071A cesium clocks. Even though 25+ years old, no commercial clock works better for this portable application. That is to say, rubidium clocks and older model cesium clocks are not quite good enough to detect these tiny relativistic effects with confidence.
Others here have mentioned prices. Surplus rubidium atomic clocks can be found for as low as $100 on eBay. Surplus cesium clocks range from $1k to $10k, depending on model and condition. Factory new 5071A are close to $100k so no one I knows is crazy enough to do that. If you are very patient and lucky on eBay you will find 5071A for as low at $2k to $5k once every couple of years.
Yes, 500 pounds of gear sounds about right. I was aware that the car was slightly heavier than usual and drove accordingly. There was no hurry; it was not a race, just a leisurely weekend trip, about 2.5 hours in the car, with an average speed of maybe 35 mph.
With 3 expensive clocks, 3 priceless kids, not to mention hot coffee in hand, I accelerated and decelerated modestly. The drive from Bellevue to Paradise Lodge up on Mt Rainier is mostly rural and then follows a long slow winding mountain road to 5000 ft elevation.
Look for any vintage caesium clock made by National, Varian, Hewlett-Packard / Agilent / Symmetricom / Microsemi / Microchip, FEI, FTS / Austron / DATUM, Oscilloquartz, and maybe others. None of them are a restricted item because of a "radio-isotope". Again, cesium 133 is not a radioactive isotope. Atomic timekeeping is based on ultra-precise quantum mechanics, not random nuclear radioactive delay.
Just take your time. Some of us look for months and even years before we find one worth the eBay risk.
There is one fact to consider. I have heard that the 5071A clock is still ITAR classified. It's not because of "atomic" or "cesium", but because the internal design is so advanced that the US decided it was essentially like a military weapon.
If in doubt look for vintage models like 5060, 5061, 5062, or 4050, 4060, 4065 instead of the still current model 5071.
I anticipated that, so I had relativity books and physics magazines with pictures of Einstein on the front seat just in case we got stopped and the officer wanted a quick lesson in the fun of measuring time dilation. It was 2005, the 50th anniversary of the first cesium clock, the 100th anniversary of the theory of relativity, so it was also a current news topic.
Actually, a three letter agency did ask me what was going on: NPS, the National Park Service! But they kindly allowed us to park in front of the Lodge for the weekend. The advice I was given by old timers was to refer to the electronics simply as accurate clocks instead of atomic clocks or cesium clocks because many people false trigger on words like cesium or atomic. You'll notice that the official name on the front panel of a 5071A is "Primary Frequency Standard".
If you have experience with analog and digital electronics it's not very hard. Atomic clocks were part of Hewlett-Packard's glory days and in that era the user got full documentation, schematics, theory, trouble-shooting guides, etc. The manuals are all still available online or on eBay.
There is also the time-nuts mailing list where hundreds of us share questions and experiences with repairing and running old atomic clocks. The archive is 20 years deep so there's lots of good info on bringing dead cesium and rubidium clocks back to life:
http://leapsecond.com/time-nuts.htm
The one problem is if the old cesium clock you buy has "run out of gas". The quantum mechanics physics experiment encapsulated inside the tube is a one-way street so once the tube runs out of cesium one has to replace it. The typical solution is to buy a few cesium clocks over time on eBay and mix parts until you have one that works well.
Cesium atomic clocks are not radioactive, nor are they based on radioactive decay. The isotope used for cesium beam atomic clocks is natural and stable Cs-133. The clock is based on an ultra-precise energy transition near 9.192 GHz.
You may be thinking of the nasty radioactive isotope Cs-137, which is unnatural and often a byproduct of nuclear tests or accidents.
It's not unlike Carbon or Potassium; Carbon 12 is the safe stuff, the rarer Carbon 14 is radioactive. Potassium 39 is the safe one and rare Potassium 40 is radioactive. Which is why bananas are slightly radioactive:
https://en.wikipedia.org/wiki/Banana_equivalent_dose
You can make a cesium clock radioactive by placing a banana on top of it. See page 1, 36, 37 of:
http://leapsecond.com/ptti2020/2020-PTTI-tvb-Atomic-Timekeep...
Yes, the original Mt Rainier experiment in 2005 caught the attention of Stephen Hawking and I was asked to repeat the experiment for his PBS/BBC TV series in 2016. It was mid-winter up here in PNW so we used Mt Lemmon in Arizona instead:
http://www.leapsecond.com/great2016a/
And in 2018 I was asked to be part of a "time travel" episode on a History channel show. We used Palomar Mountain in California:
http://www.leapsecond.com/great2018a/
Each experiment was a little different; different combination of clocks, different audience, different mountain, different elevations, different latitude, etc.
Thanks, DanG. Author here. I happen to be reading HN right now if anyone has questions about cesium clocks or using them to demonstrate relativistic effects. This is just a DIY hobby of mine.
About 70 lbs (30 kg), so not difficult to lift or carry with two hands. But it took a real man (my brother-in-law, construction worker) to hold it outstretched like you see in the photo.
Cesium beam atomic clocks are available on the surplus market, though not nearly as common or as cheap as Rubidium. The clock in the photo is model hp 5071A and I got it on eBay 20 years ago. The tube will last on the order of 7 to 20 years with continuous use, depending on which type of tube is installed.
This was one of the atomic clocks I used for the time dilation / relativity experiment linked at the bottom of the page.
One degree is 40,000 km / 360 = 111 km at the equator. But Greenwich is at 51 degrees latitude so you apply a cos (51.5°) = 0.622 factor. That's why 1 degree of longitude at latitude 51 is 69 km. Does that help clear it up?
Note also if you're walking in a circle 57 meters from the monument at the South pole, then each 1 m step you take crosses one degree of longitude. Google for: south pole ceremonial sphere
Makes a good C interview question:
char c;
short h;
int i;
char *s;
1 = sizeof (char)
2 = sizeof (short)
4 = sizeof (int)
4 = sizeof (float)
8 = sizeof (double)
1 = sizeof (c)
2 = sizeof (h)
4 = sizeof (i)
4 = sizeof (s)
4 = sizeof &c
1 = sizeof c
2 = sizeof h
4 = sizeof i
4 = sizeof s
1 = sizeof *s
4 = sizeof &main
4 = sizeof (sizeof (i))
4 = sizeof (sizeof i)
4 = sizeof sizeof i
4 = sizeof sizeof sizeof i