Category Archives: Time

My Turf

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Built onFacts: Time and Navigation

Matt gives a brief summary of time and navigation. There’s one point that he glosses over, and it’s something that a lot of GPS summaries gloss over, to the point that they are misleading.

All a GPS satellite does is eternally broadcast two continuously updated pieces of information: its position and the time on its atomic clock. Knowing that light travels at about 1 foot per nanosecond, we can calculate how far we are from the satellite to the foot, as long as the GPS clock is accurate to the nanosecond and we have a receiver that can handle such a precise signal.

Actually you can’t do this unless you have a synchronized clock, and unless you’ve done this already, in order to synchronize the clocks properly you have to know … [wait for it] … the distance to the satellite. Many of the explanations of GPS completely miss this little tidbit. If you haven’t got a synchronized clock, and all you have are the GPS signals, you need four satellites to find your position. In practice four may not be necessary, because if you know your approximate position on the earth and have a topographic map, you can get the elevation from that, in which case three satellites is sufficient to get your position, to some level of uncertainty.

Time In

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Start the clock

A modest proposal for improving football: the ‘time-in’

If you’ve ever noticed that football games slow to a predictable crawl at the end of each half, the time-in is the rule for you. The idea is simple: When the clock is stopped, for whatever reason, a coach could call a “time-in,” and force the clock to start up again. Think of it as the antimatter version of the timeout.

The time-in is so powerful that I recommend it be strictly rationed: each team would get only one time-in per season. The possibility of a sudden time-in would loom large in every coach’s mind at the most tense points in the game, introducing just enough concern and uncertainty to make the game different. Timeworn clock-management strategies would no longer be a given. And yet, for the average viewer on a Sunday, the game on the field would still be your father’s football.

…

Of course, this assumes that the time-in is used that game. If it hasn’t been used yet, it affects the game in a different, but more subtle way: the opposing team will simply have to assume that it might be used. Coaches would enter the realm of game theory: how do we calculate when it’s the best game to use it? And what if the other team is expecting us to think this way?

TIME on Time

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Why Can’t My Clocks Keep Time Accurately?

A short article, directed mostly at the problem of synchronization, as applied to everyday life: your electronic devices display different times. Why? Because you always have to synchronize your clocks, no matter how good they are. The question remains, how often do you need to do this?

From the article:

Most computers carry an on-board clock powered by a separate battery. As the battery drains over time, the computer’s timekeeping becomes less accurate.

This is true, but the clocks aren’t super-accurate to begin with. The battery draining isn’t the whole problem.

Who Watches the Watch, Man?

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Who Watches the Watchman?

Let’s say you own a big building full of valuable stuff. How do you make sure that the night watchman patrolling your factory floor or museum galleries after closing time actually makes his rounds? How do you know he’s inspecting every hallway, floor, and stairwell in the facility? How do you know he (or she) is not just spending every night sleeping at his desk?

If you’re a technology designer, you might suggest using surveillance cameras or even GPS to track his location each night, right? But let’s make this interesting. Let’s go a century back in time to, say, around 1900. What could you possibly do in 1900 to be absolutely sure a night watchman was making his full patrol?

It's About Time, Part II

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Super clocks: More accurate than time itself

An article discussing the progression of atomic clock technology, and also relating to something I posted earlier, a discussion of what happens when the next generation of atomic clocks is deployed: the clocks won’t be the limiting factor in determining the time.

To tell the time consistently, all clocks need to be at a known height relative to Earth’s “geoid”, an imaginary surface that links points at which the gravitational field has the same strength. But the height of this geoid varies over time at any given place by up to 20 centimetres, because of effects such as tectonic movements, glacial melting and changes in ocean levels, and varying atmospheric pressure. Changes of that magnitude could wreak havoc with any attempt to establish a global time standard at an accuracy of 1 part in 1018 or better

One of the things that always glossed over in these discussions is that almost everything that is called a clock is actually a frequency standard, which is part of a clock. Clocks run continuously, because you are measuring a phase, and frequency standards don’t. Now, there’s a caveat here in “running continuously,” because even commercially-available clocks will skip measurement cycles to do self-diagnostics. During those skips in measurement, as with the time between measurements, the frequency is maintained with some oscillator. Usually this is a quartz crystal, which typically has excellent short-term stability. The important point becomes how long the clock is running on the “flywheel” oscillator and what kind of degradation that introduces. The latest generation of frequency standards run for several hours, but then are shut down for extended periods of time, which is not surprising for a cutting-edge kind of experiment. But while the frequency standard is not running, the clock’s performance approaches whatever the flywheel performance is, whether that’s cesium beam clocks or hydrogen masers, etc., or some ensemble made up of several clocks.

So when these stories appear touting the great performance of cutting-edge clocks, there’s an unwritten implication that we will be getting an improvement in the flywheel operation as well, to be able to leverage this improved frequency-standard performance.

How Atomic Clocks Don't Work

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I was listening to a podcast recently that delved into timekeeping and atomic clocks, and was surprised that they got a couple of details wrong. I haven’t done a post explaining how atomic clocks work, because that’s something easily found on the intertubes, and so I’m not particularly motivated to recreate Wikipedia or HowStuffWorks.

But someone was wrong on the internet, and the basis of that “wrongness” has some physics behind it. The claim was made in explaining clocks that when electrons absorb energy they jump up a level, and then radiate it when they jump back down. And while that’s true, it’s not the basis for a Cesium or Rubidium clock. The thing is that you don’t want the atom to radiate on its own if you are going to make a clock out of it. Transitions between atomic states are not infinitely narrow, i.e. there is an uncertainty in the energy of the emitted photon. This is known as the linewidth of the transition, and for a good clock you want a really narrow transition so that you know what the frequency is. While there are several factors that can increase that linewidth, the fundamental width is due to the Heisenberg Uncertainty relation between energy (or frequency) and time.

The uncertainty of the frequency and the lifetime of the transition are inversely related, and \(Delta omega Delta t = 1 \) (that should be greater than or equals, but latex is choking on that for some reason)

In order to get a narrow transition, you want a long-lived state. So you don’t want something that radiates readily on its own, and atomic clocks don’t. Cesium and Rubidium devices are passive: you shine radiation on them, and then read out whether or not your radiation was on resonance by looking at which state the atoms are in. Active masers do radiate, but as the acronym tells us, the radiation is stimulated, rather than being spontaneous. (Left on its own, the lifetime of the Hydrogen atom state is about 10 million years) The search for long-lived states becomes even more important for optical clocks, since the larger energy differences tend to lead to shorter lifetimes. What is generally done is to search for so-called forbidden transitions, in which the strong coupling of electric dipole transitions aren’t present, and you are left with other types of transitions or ones that must couple through other states and end up taking much longer.

And I Say, It's Alright

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Here comes the sun, or at least its shadow, at Dot Physics: When is the Sun directly overhead?

There’s a nice little video that accompanies the post which also demonstrates some of the foibles of doing experiments

What I want to do is change the question a little bit. Rhett points out that one of the common answers is “Everyday at noon,” which can never be correct if you are outside of the tropics. But let’s change this to “When is the sun on the N-S line that goes directly overhead?” The answer still isn’t “everyday at noon.”

Why? Because the earth’s orbit isn’t a circle, and we orbit the sun fastest when we are near perihelion (in January) and slowest near aphelion (in July), with the difference being about a kilometer per second. If we define our time in terms of the sun being on that overhead line — i.e. we use a sundial — then the length of the day will vary, and this is why we generally don’t use solar time (when we’re using solar time) without modifying it. What we do is apply the equation of time, which gives rise to the figure-eight-ish analemma (found on globes as well as sundials). This takes into account both the inclination of the sun and the eccentricity, to give a correction to solar time and correct the reading. While this makes our day 24 hours again, it also means that the sun will be on that overhead line as much as 15 minutes or so before or after actual noon, as kept by our clocks.

Time to Answer the Wrong Question

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What Do Timekeepers Do?

On New Year’s Eve at 6:59:59 p.m. ET, an “international consortium of timekeepers” will add one second to the world’s clock. How do you get to be an official timekeeper?

Earn a Ph.D. in astronomy and move to France. Tweaks to the official clock are announced by the Earth Orientation Center, a Paris-based subunit of the International Earth Rotation and Reference Systems Service.

Well, no. That’s how you get to make the decision of when to add a leap second. But the IERS is not the official timekeeper, that’s the BIPM, who calculate the atomic time scale TAI and the coordinated universal time scale UTC. Countries that contribute to the international standard realize their own versions of these time scales.

In the US, there aren’t a lot of places where you can learn to be a timekeeper. Contrary to the article’s suggestion, your best bet is probably a degree in atomic physics or math, depending on whether you want to work on hardware or on the timescale algorithms, and then apply for a job at USNO or NIST.