tvb
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.
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 time-nuts mailing list is still very active, now in its 23rd year. More info at the group page:
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.
Ah, an example of the Butterfly Effect: then we'd have a billion references to FAABG on the web instead of FAANG.
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:
[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...
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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.
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.
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.
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).
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.
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.
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.
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".
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.
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...
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.
This was one of the atomic clocks I used for the time dilation / relativity experiment linked at the bottom of the page.
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
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