Category Archives: Time

You Twist and Turn Like a Twisty-Turny Thing

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Bad Weather Makes for a Long Day

Changes in mass distribution affect the earth’s rotation rate. A little.

The National Institute of Standards and Technology in Boulder, Colo., occasionally adds a “leap second” to the atomic clocks used to standardize time. The last such update took place on January 1, 2006.

Arrg. And so do all of the timing labs around the world. The determination of whether or not to add (or possibly subtract) a leap second is the responsibility of the the International Earth Rotation and Reference Systems Service.

Trivia Time, part II

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In Einstein’s 1905 paper in which he describes special relativity (“On the Electrodynamics of Moving Bodies”), there is a mention of what would happen to a clock on the equator vs. a clock at one of the poles. The clock at the equator is moving, and so should run slower. It turns out this is wrong, and I was surprised to find that there is some discussion, especially involving those who are convinced relativity is wrong anyway, about how this could be. (OK, not really surprised, considering that crowd) It would be correct if the earth were a rigid sphere, but it’s not — the earth is oblate because it is rotating. And surely, the arguments go, Einstein was aware of this. Well, it doesn’t really matter (and don’t call me Shirley). The reason has to do with general relativity, and in 1905, Einstein hadn’t yet formulated the theory!

The earth’s geoid (basically, the surface at sea level, without disruptions like currents and tides) is an equipotential surface. The gravitational potential (gh) and the kinetic potential (1/2 v^2/c^2) are exactly the terms that go into the dilation calculations, and if you spin up a deformable planet, you will get an exact balance between the change in gravitational potential with the kinetic potential. The dilation terms have opposite signs, and cancel. So clocks anywhere on the geoid always tick at the same basic rate — no correction for your latitude is necessary, though the elevation above the geoid must still be taken into account.

Forward, Sproing!

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Spring forward tomorrow (or tonight just before bed). Daylight Saving Time begins in the US.

Three things:

– It’s saving, not savings.

– “Don’t blame me, blame the dee-oh-tee.” DST is the purview of the Department of Transportation. Universal time is unchanged — from a timekeeping standpoint this is a non-event. Displays get changed for devices that read out in local time, but atomic clocks that have displays read out in UTC.

– It apparently doesn’t save energy, at least in Indiana. But the story (not surprisingly) gets it wrong.

For decades, conventional wisdom has held that daylight-saving time, which begins March 9, reduces energy use. But a unique situation in Indiana provides evidence challenging that view: Springing forward may actually waste energy.

But later,

They conclude that the reduced cost of lighting in afternoons during daylight-saving time is more than offset by the higher air-conditioning costs on hot afternoons and increased heating costs on cool mornings.

So the decades-old “conventional wisdom” is only wrong if there has been widespread use of air conditioning during that time. If, however, the use of air conditioning has increased in that time, the conclusion is wrong. What you can conclude is that that right now, in Indiana, DST uses extra energy. Because they are selfish bastards who like air conditioners way too much.

Crazy Eights

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My memory was just jogged, bringing this to the fore. A series of cool analemma pictures taken in Greece, showing ruins in the foreground, with the additional feature of some being multiple exposures on a single frame of film.

The analemma — which you can often see on a globe — describes the variation in the position of the sun over the course of the year. Besides the pretty obvious vertical motion you get from the axial tilt of the earth, there is also the effect from the noncircular nature of the earth’s orbit. This causes the earth’s speed to change over the course of the year, so we do not sweep out exactly the same angle from day to day, if you were to assume that noon is when the sun reaches some position in the sky (like straight overhead, or on the vertical line that includes that point). In other words, the time you would read on a sundial will not agree with the time kept by a very good clock. The variation over the course of the year is on order of ± 15 minutes, or almost 4º of arc in each direction. The math that describes this is known as the equation of time.

More detail here or here or many other places on the web.

Leap Day

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Phil Plait runs down the numbers about leap days, and why the Gregorian calendar has them every 4 years but skip every 100, except when we unskip every 400.

And if you find that confusing, you’re still probably not as confused as we Swedes are. The old Julian calendar didn’t have the rules about skipping (or not) years divisible by 100 or 400, so that’s why it got off track and countries started changing to the Gregorian. And while most countries just bit the bullet and dropped the 10 or 11 days (depending on when the change was made), Sweden tried to think different … and screwed it up. Miserably.

To avoid the havoc of just obliterating the large chunk of days, the Swedes decided to do it this way: just say no to leap days for 40 years, and then their calendar would be in synch with the Gregorian calendar. The problem of not lining up with either calendar didn’t dissuade them from this plan. It started out well enough — they began this in 1700, which was a leap year for the Julian but not the Gregorian calendar, so there would have been no Feb 29 with either method of adoption. But something went terribly wrong: somebody (no doubt addled by overconsumption of herring) forgot the master plan, so 1704 and 1708 both had a leap days. Rather than just go ahead with the Gregorian adoption, it was decided to go back to the Julian calendar, but an extra day would be needed, since one had been dropped in 1700. Solution? A leap day! It was added in 1712, and since 1712 was already a leap year, that meant there was a Feb. 30.

The Swedes went ahead with the Gregorian calendar in 1753, adding in the 11 days all at once.

Trivia Time, part I

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Trivia about time, to be precise. Prior to my current job, my knowledge of timekeeping was pretty much knowing how to read and adjust a clock, and because I’m a physicist, Einstein synchronization (basically accounting for propagation delay of light) and the effects of general and special relativity. All of the physics-related exercises with time conjure up a perfect clock, so you don’t have to worry about all the little details that arise when dealing with real-world hardware. Now, I don’t actually do time measurements, I “just” work on building clocks, but there are some things I’ve picked up.

A clock will have an oscillator in it, and some way of counting the oscillations. Time is the phase of these oscillations — one “tick” represents one cycle or some number of cycles. The derivative is the frequency, and if you take another derivative you get the rate of change of the frequency, which is the drift. Which sounds just like kinematics — the basic equation that describes all of this looks just like basic kinematics, as long as the rate of change of your frequency is a constant. And that brings up a point commonly fumbled by the popular press: leap seconds are often described as being added because the earth’s rotation is slowing. And while it’s true that over long times, the rate is slowing, that term could be zero and you’d still have to add leap seconds. The frequency represented by an earth that has slowed (but is no longer slowing) is different than that of atomic time, and so one will accumulate a phase difference (i.e. one will run slow compared to the other). That the rotation rate is slowing means that we will add leap seconds more often, assuming other effects on the rotation rate don’t mask this.

The above assumes “perfect” clocks. However, in all real processes that we measure, there is noise. Different kinds of noise, too, depending on the systems being measured. The best you can hope for is random, (i.e. white) noise, which gets averaged down as you take more measurements, and varies with the inverse square root of the number of data points (in this case, time). There are noise processes that average down faster, but eventually white frequency noise will dominate, and then the best case is that there are no other noise processes that dominate at longer times (like flicker or drift).

You integrate white frequency noise to get the effect on the phase, or time. The integral of this white noise gives you a random walk. That is, for any two real clocks, with exactly the same frequency, the best you can do is have them random-walk with respect to each other. They will never stay synchronized.

The Relativistic Van

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Who cares about gas mileage? This sucker warps time!

When relativity is discussed in popular literature it’s often couched in terms of affecting objects moving at a significant fraction of the speed of light, and that’s a true statement: kinematic time dilation cannot generally be ignored in that situation. But the implication that the opposite is true — that you can ignore these effects under other circumstances — doesn’t hold. At least, it doesn’t hold if you have some expensive toys at your disposal.

Let’s say you were going to drive across the US and back, and you had the aforementioned expensive toys. Maybe you wanted to calibrate clocks and check on the reliability of a satellite time-transfer system, and you have a mobile system that would do time transfer at the source and at the target site, allowing you to check on that calibration. Or something like that.

The time dilation in question gives a fractional frequency shift that goes with the square of the speed, as compared to the square of speed of light. That’s normally very small, and has to be under this approximation (c is big, v/c is small, (v/c) squared is reeaaally small), so you can usually ignore it, right? Not everyone can. The famous Hafele-Keating experiment that used airplanes and around–the–world travel was able to measure kinematic dilations. A trip across the US is ~2700 miles, and at 600 mph you’d get a frequency shift of 4 parts in 10^13 and a dilation of about 13 nanoseconds on your round-trip due to traveling at that speed. (one thing to note is that I’m using a different coordinate system than is used in the H-K writeup, in case you want to play along at home. The answer will be the same, but the east vs west contributions are accounted for differently, and I’m not showing that detail)

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