The second is defined as “the duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom”.
OK, great. So I’ve got a caesium atom, and I want to calibrate my stopwatch. Now what? How would I go about counting my nearly 9.2 billion periods of radiation?
Oh, and apparently the atom needs to be at zero kelvin, too. Given that you can’t actually ever attain 0K, how is this definition actually useful?
It’s a modern standard, based on atomic physics. It’s certainly an esoteric definition, but since it’s based on an objective and precise physical property of the cesium atom, it’s extremely useful if you want amazingly precise clocks (with several decimal places) for any number of practical and research related applications (GPS comes to mind).
You can’t actually measure it, but you can get close. It’s useful because the standard is based on an objectively quantifiable feature of the universe which will never change.
Previous definitions of the second were less precise. It used to be sufficient to say that seconds are 1/60 of a minute. How long is a minute? 1/60 of an hour. OK, how long is that? There are 24 of them in a day. What’s a day? One rotation of the earth.
But some rotations of the earth are longer than others. The earth wobbles a little. So then the second was redefined as being 1/31,556,925.9747 of a year. But not just any year - a particular year - because the Earth is, after all, slowly hurtling towards the sun.
But it’s hard to measure the duration of a year in the past. So if you want a really accurate clock, the best you could do is measure the number of seconds in the year right now and try and adjust for changes in the Earth’s orbit.
But a cesium atom at absolute zero will never, ever change it’s physical properties. OK, so it can’t be measured precisely, but having a definition that you can approach and which will always be the same duration for the rest of the life of the universe has some merit. You can always be sure that a clock calibrated to such a standard will be as good or better than all other clocks.
But how do you calibrate it if you can’t actually get to 0 K? Wouldn’t it have been more useful to use an attainable standard like 4 K?
Wikipedia mentions that the best atomic clocks are precise in measuring its frequency up to 1 part in 10[sup]15[/sup].
That means it would only be off by about 1 second over 300 million years!
An atom at 0K behaves more predictably than one at 4K. 0K is of course an impossible standard, but you can get really, really close. Close enough that it’s good enough for all conceivable measurement purposes in the real world. And at any time if they need a more precise clock than that, they’ll probably have sufficiently advanced technology to get even closer to 0K.
(1) You build yourself a microwave oscillator and feed the output into a cavity filled with your cesium atoms. You tune the oscillator until the cesium starts sucking power out of it. You tape the knobs down and label them “9.192631770 Ghz (exactly).” If you want a lower frequency signal to calibrate your stopwatch, you build a lot of frequency divider circuits, so the RF signal turns (for example) into a 1 Hz heartbeat. The details of the circuit design, and considerations of stability, are left as an exercise for the student.
(2) A 9 GHz microwave photon corresponds to a temperature of about 0.5 K. As long as the surroundings are substantially (e.g. 1/10 to 1/100) cooler, there will be no way your atoms can be perturbed by them, thanks to the quantization of energy. That is, quantization of the energy means cesium atoms at 0.05K will behave almost indistinguishably from the same atoms at 0K. (I refer only to one-body properties, nothing collective.)
There’s a useful principle they are using here.
Could you use (6-2x)/(3-x), for x=3, as a standard for a number? Obviously this expression is going to equal 2 for values of x other than 3. But right at 3 it is undefined. Still, you could get as close as you wanted. Never mind that this example is kind of pointless. What’s important here is that an unreachable idealization can be very useful.
They want this standard to appear perfect and unchangeable for as long into the future as possible, so they are making educated guesses about strategies for realizing a frequency, such that the strategies are likely to not introduce their own inaccuracies even as science and technology march along in unknowable ways.
It’s a lot more accurate than saying “One Mississippi”.
Thanks - that’s what I was looking for, a technical description of how one would actually use this definition to get “a second”, if you wanted to.
I wouldn’t be surprised to learn that there are scientific studies where the exact definition of the unit of time is crucial for understanding the science and comparing results of different experiments.
I wouldn’t be too surprised to learn that GPS wouldn’t work as well as it does without a very carefully defined unit of time. (It’d be amusing to know what kinds of errors it can tolerate. We already know that it’s compensated for relativistic effects.)
Yes, I am not disputing why it’s useful to have an exact definition. Perhaps I phrased my question poorly.
What I really mean is: is it actually physically possible (rather than theoretically possible) to count “9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom” and use it to calibrate something? Or is it something that is used as a theoretical standard but you would actually use something else to calibrate your timing device?
In other words, is the kind of set-up that Carl Pham describes something that people would actually do in the real world?
You cracked me up!
But… can he use that timing standard to calibrate his stopwatch?
Aren’t we?
I mean, the atomic clocks being kept and maintained at all the national standard institutions, labs, universities (et al) across the globe are physically reading the transitional EM frequencies from these atoms to keep time.
The Internet even, pings these very clocks to keep everything on time and in tune.
The second is defined that way because that’s exactly how an atomic clock works. Or the most common type of atomic clock, at least.
By my calculations, the best atomic clocks are precise to one part in 10 to the 16th, in order to make them equivalent to them being off by no more than a second in 300,000,000 years. A second is defined as 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom. This must mean that it’s possible to set the atomic clock so that somewhere between 9,192,631,770.999999 and 9,192,631,770.000001 periods pass for each second that it measures.
For more time keeping fun, how 'bout the Quantum Logic Clock (using aluminum ions) developed by the NIST.
The one built in 2010 is capable of not gaining or losing a second in 3.7 billion years. Almost as long as the earth has been around.
As a LORAN ground stations systems technician and instructor in the Coast Guard, I had personal experience with the operation, care, and feeding of both rubidium and cesium frequency standards. The Cesium was a “Primary Passive” standard and the Rubidium was a “Secondary Passive” standard. At the heart of them was a 5MHZ quartz voltage controlled oscillator in an oven. The 5MHZ output was split, or maybe duplicated if you prefer. One output was lead through frequency multipliers to about 128Mhz. Then it was split again. One output went to a phase comparitor circuit and the other got frequency multiplied some more until it reached enough to cause the sealed cesium (or rubidium) cell to go into resonance. The output of the cesium cell went through frequency dividers until it was 128MHZ and fed into the other side of the above mentioned phase comparitor. Think of putting one sine wave into channel a of an o’scope and another into channel b and then pressing the “add and invert” button. The output was a control voltage that went to the input of the quartz VCO. I believe in other uses, that sort of circuit is called a “phase locked loop”. The other 5MHZ output went through frequency dividers to provide 1MHZ and 200KHZ outputs. And if you wanted to pay for the option, you could get a “One Pulse Per Second” output too. That’s the one you’d want if you want to calibrate a wristwatch or a wall clock.
The cesiums gave +/- 1 femtosecond or so precision. The rubidiums gave +/- 10 fsec or so.
Thanks!
Not that it makes any difference to your point or this discussion, but where did you get the idea that the Earth is “slowly hurtling towards the Sun”? Last report I heard was that the Earth’s orbit was increasing by some 15 cm/year.