26 Feb 2015

Think About This For a Second

Deep Thoughts, Economics 25 Comments

We were talking about experiments concerning special relativity, and I said that an atomic clock was super accurate. My son asked what exactly that meant. This question befuddled me, because I realized I couldn’t come up with a non-arbitrary way of defining a “true” second. Wikipedia informs us:

The second (symbol: s) is the base unit of time in the International System of Units (SI)[1] and is also a unit of time in other systems of measurement (abbreviated s or sec[2]); it is the second division of the hour by sixty, the first division by 60 being the minute.[3] Between 1000 CE (when al-Biruni used seconds) and 1960 the second was defined as 1/86,400 of a mean solar day (that definition still applies in some astronomical and legal contexts).[4][5] Between 1960 and 1967, it was defined in terms of the period of the Earth’s orbit around the Sun in 1900,[6] but it is now defined more precisely in atomic terms. Seconds may be measured using mechanical, electric or atomic clocks.

Astronomical observations of the 19th and 20th centuries revealed that the mean solar day is slowly but measurably lengthening and the length of a tropical year is not entirely predictable either; thus the sun–earth motion is no longer considered a suitable basis for definition. With the advent of atomic clocks, it became feasible to define the second based on fundamental properties of nature. Since 1967, the second has been defined to be:

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.[1]

In 1997, the CIPM affirmed that the preceding definition “refers to a caesium atom at rest at a temperature of 0 K.”

I encourage you to really think through the philosophical implications of the above. Obviously, humans initially adopted units of time based on convenience and the regularity of planetary events. But you can see how humans refined the very definition of units of time, over the centuries. I’m having a hard time putting into words just how mind-blowing that is. It’s not analogous, say, to refining the measurement of the charge on an electron. But it’s also not analogous to deciding that “bad” can mean “good” if used by gang members.

Something like this happens in economics and libertarian political philosophy, where the original practitioners start out with a concept, and then over time it is refined to better get at the spirit of the original concept, even though it no longer directly corresponds to the original concept. For example, how indifference curves replaced cardinal utility in the work of Pareto (if I’m remembering my Hicks correctly).

25 Responses to “Think About This For a Second”

  1. S.C. says:

    That is generally how I view Supreme Court rulings.

  2. Joseph Fetz says:

    That took longer than a second, Bob.

  3. Rick Hull says:

    I hope this doesn’t come off as antagonistic, but I have a little essay about amazing things resulting from distributed cycles, and how time is at its core an accounting of cycles. I haven’t written the second part, which will delve into free market innovation also being due to massive distributed cycles iterating in parallel.


  4. Landa says:

    Maybe one should not say about atomic clocks that they were super accurate as in “accurate display of time” but rather that they are super regular, which in turn makes them suitable as norm for time measurements.
    I realize this does not quite solve the problem. Who said at first that atomic clocks are so regular? And how did he measure that? With some accurate clock … ?

    • Joseph Fetz says:

      How does the make of a ruler or yardstick know the length?

      • khodge says:

        A while back I was reading a post (I don’t remember whose) that said moving from English measurements to Metric really did not make much sense because we can easily get a feel for a foot, inch, &c but no one can instinctively know what a meter is (based on some multiple of a wavelength of light given off by some obscure mineral).

        When you divorce a second from its basis in nature you really are creating something without meaning.

        • Harold says:

          What is the basis of the second in nature? It is the second 60th division of an arbitrary division of the day into 24 equal parts.

  5. Harold says:

    A second is an arbitrary time division, so there is no way to define a “true” second in a non-arbitrary way. A day and a year have physical, non arbitrary meanings (although not unchanging). Landa has it right – the clocks do not measure a second accurately, but they are extremely regular and we can define our arbitrary measure of the second in terms of this regularity.

    The minute is the first small division of the hour (pars minuta prima), the second is the second division of the first (pars minuta secunda). Why we do not call minutes “prims” I don’t know. We have the Sumerians and Babylonians to thank for the use of 60 as the divisor. In France, decimal time was introduced at the time of the Revolution, where a day was divided into 10 hours. The hundredth part of an hour is the decimal minute, the hundredth part of the decimal minute is the decimal second. A standard day is 86,400 “normal” seconds long, but is 100,000 decimal seconds long. The decimal day has the advantages of all decimal systems – 3 hours is 300 minutes or 30000 seconds – much simpler for us to handle.

    I don’t find it too surprising that the definition of these divisions changes over time, since they are arbitrary anyway. The day and the year are different. The year is the orbital period of the Earth, which is not a stable period. In astronomy the Julian year is now defined as a stable time period – 86400 standard seconds. The calendar year is an approximation of the orbital year in a given calendar. It gets out of phase with the orbital year, so we correct it with leap years and leap seconds, so each calendar year in the same length.

    The day is a unit of time equal to 86400 seconds, but it is also one revolution of the Earth wrt the sun (solar day) or wrt distant stars(stellar day). Because the Earth makes about 366 rotations as it goes round the sun. The orbit reduces by one the number of transitions the sun makes across the sky in a sidereal year. So the stellar day is 3m:56s shorter than the solar day. We have to specify what we mean by “day” and “year” if there is any chance of confusion. However, each definition retains its original meaning.

    I am not sure this corresponds with indifference curves and cardinal utility in economics. For the time period of the second, the definition is arbitrary anyway, and for the year and day the original meanings are retained in some contexts. The development of indifference curves form cardinal utility seems to be much more of real development of ideas.

    • Harold says:

      Correction in astronomy, a Julian year (a) is 365.25 days of 86400 standard seconds.

    • Gene Callahan says:

      “but they are extremely regular…”

      But the trick is, by what means are we measuring *their* regularity? There is a definite chicken-and-egg problem here. It is similar to the problem of developing the thermometer: we need a substance that exhibits very regular changes as the temperature changes to act as a measuring device… but how do we know what changes regularly with temperature *before* we have the accurate measuring device for measuring temperature?

      • Keshav Srinivasan says:

        Gene, we have a wide variety of processes we believe are regular, and they agree with each other. Wouldn’t it be a massively unlikely coincidence if they were all irregular in precisely the same way?

      • Tel says:

        The fundamental belief is that an ideal reference:

        [A] should not be effected by spacial location (e.g. multiple teams around the world can construct the reference device and get the same result);

        [B] should not be effected by temporal translation (you can do the same experiment next year and get the same result).

        We select a reference by checking these properties, and of course price, and simplicity of description. NOTE: I say “belief” because we don’t really know that the universe itself is invariant to spacial or temporal shifts, for example caesium atom’s may slowly be evolving into something different, but the basis of science is that you can repeat an experiment and it’s worked out OK so far.

        • Keshav Srinivasan says:

          Actually we do know, to a high degree of certainty, that the Universe is invariant with respect to spatial and temporal shifts, because Noether’s theorem says that spatial invariance is equivalent to conservation of momentum, and temporal invariance is equivalent to conservation of energy. (That result doesn’t depend on any specific assumptions about the laws of physics, it drops right out of the principle of least action.) So if spatial and temporal shifts mattered, we would observe violations of these conservation laws.

      • Major.Freedom says:

        Gene, Keshav and Tel:

        You, each of you, are the ultimate ground for measurement.

        There is no chicken and egg problem (note: evolutionary biologists do not consider it a problem. The way DNA evolves leads to the solution that the egg came first, as the animal that the egg is to become is not exactly like its mother).

        It is not a coincidence that a link among all various processes, you, would be in agreement with yourself, and hence all the various processes to that extent would agree with themselves.

        You infer that a true regular process must be invariant across space and over time, because there is something about you that is invariant across space and over time, and you are the true measurement.

        • Tel says:

          No, I need something that works for other people as well.

          In the simplest case, if we are going to meet for lunch we have to be able to agree on the date and time, this requires we both have compatible standards, else we never meet. In many ways the choice of standard is arbitrary (look at our crazy calendar system, don’t even get me started on Daylight Saving evil) but that’s still workable, providing the other guy uses the same standard.

          In more complex cases, building something large requires teamwork, and this is only achievable with good standardization of measurement (also interfaces, connectors, specifications, etc). Hence why large numbers of standards bodies have popped up over the centuries… because they are useful.

          The classic case was this one:


          NASA has been metric for a long time, while most US aerospace industries are running the US version of imperial units. With modules being subcontracted they ended up with something that appeared compatible, but when running in practice there was a unit conversion issue. These unit conversions have caused a number of other mishaps which is why most of the world decided to use metric and be done with it (except metric time, and that’s never going to happen).

          • Major.Freedom says:


            I’ll agree with everything you said, with the exception of the first word in your reply.

            Yes, in order for two people to coordinate, there would be a need to find an agreement in measurements.

            Yet this is a separate problem.

            What I am saying is that whatever measurement you decide on, the ground for that measurement is you.

            Imagine being stranded alone on a deserted island. You would still be able to measure, because you would still be you. You would be the ground of all measurement. You might even use your “foot” to measure distances.

            Now do not misunderstand me as saying that the ground of measurement being each of you, Gene and Keshav, that this ipso facto implies incompatible groundings, with no chance of agreement and mutual understanding. I think they are compatible. You can choose your standard of measure, but the range of your choices would be necessarily constrained to whatever is grounded on you as an individual person.

            There is a harmony in all things self-centered. You and I can get along, agree, co-exist, etc, while each of us is out to improve ourselves individually. The same thing is the case for measurements.

            Even if we devise standards of measure separately, you devising your own and me deviding my own, provided they are consistent and capable of being communicated, then there will always be a system of conversion between the two. For example, populations in imperial based societies can coordinate with populations in metric based societies rather handily, and they don’t even need to agree to actually use the other’s system of measure! The same principle applies to individual standards of measure that are not utilized by anyone else.

            You want to meet in my devised standard based 10 snagglets of time? We can meet on time if we convert it to minutes. The conversion is 10 minutes per snagglet. So we meet in 100 minutes. The reason why such conversion is possible is because there is something in you and something in me, which grounds our respective standard, and understanding of, and ability to measure, and they just so happen to be similar.

            If a more advanced race of intelligent beings were to have a standard of measurement, then it is quite possible for their standard to to be unintelligible to we humans. That would mean humans and that race of beings don’t agree on a standard. But does that mean we can’t each understand how to measure? Of course not! That is my point. Your ability to measure, the ground for all of your measurement, is YOU. The ground for any being’s standard of measure, is that being.

            • Tel says:

              Even if we devise standards of measure separately, you devising your own and me deviding my own, provided they are consistent and capable of being communicated, then there will always be a system of conversion between the two. For example, populations in imperial based societies can coordinate with populations in metric based societies rather handily, and they don’t even need to agree to actually use the other’s system of measure!

              That’s the way to go about burning up your Mars probe… which is why I linked to the example.

              Works in theory, but the added complexity tends to get it messed up in on the shop floor. Calculation efficiency cannot be ignored, it is part of the overall utility. Metric won the battle.

              • Major.Freedom says:

                It works in practice as well. Come on Tel, it’s like you’re saying we’ll burn up ourselves in rocket explosions continually if we don’t all speak English.

                Imperial is just as capable of being utilized as is metric. Whether one is easier to use in the sense of internal logic, I’ll give you that, but that point is superfluous to mine, which is the actual grounding of standards of measure. We can’t even agree to a standard unless that standard is grounded in who you are and who I am.

                I am only replying to the claim that there is no way we can confirm any standard of measure due to the alleged fact that every standard of measure requires another standard of measure in an infinite regress.

                It is just a translation.

                We don’t all need to use the same standard of measure in the practical sense because it is all the same standard springing forth from each of us actors. If mistakes are made, it is not because the standards are not grounded on who you are after all. It just means you erred in understanding that which derives from who you are.

        • Harold says:

          I agree about the chicken and the egg – we can view the egg as a baby chicken. Which came first, the baby or the adult? Or perhaps that should be babies or adults? That does put us back where we started.

          As for the rest, I really have no idea what you mean. “because there is something about you that is invariant across space and over time, and you are the true measurement.” Sounds a bit new-agey to me, but doesn’t seem to mean anything.

          Our units of measurement have to be understandable to our senses and our intellects, but the choice, once made, exists as a physical reality. The kg is the only SI unit that still resists definition in terms of more fundamental properties – it is still the mass of a lump of metal. The mass of that lump is the kilogram. Unfortunately, if that mass changes, the kg changes. If all humans died out, aliens could determine the mass of that lump and they would know what we meant by a kg. I don’t see how the kg ” derives from who you are” in a meaningful way.

          • Major.Freedom says:


            “Our units of measurement have to be understandable to our senses and our intellects”

            Your units of choice do not have to be immediately understandable to my units of choice.

            Measurement in your understanding need not my sanction.

  6. Andrew_FL says:

    We also refined units of distance as an extension. The meter, for example, is now the distance light travels in 9192631770/299792458 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom at rest at a temperature of 0 K.

    In other words the unit of distance is defined in terms of the speed of light and the second.

    • Andrew_FL says:

      Sorry, travels in a vacuum.

  7. Mogan Schmidt says:

    The current time is based on the half life of the caesium atom at or near a mass of 5.97219e24 kg (Earth). If we were to change the point of measurement to a larger mass i.e. a different planet would necessarily change the rate of decay and a delta or difference would need to be calculated. We have to remember that time is relative.

    • Yancey Ward says:

      Mogan beat me to it- time is always relative to where you are measuring it. For purposes of measuring stuff on and from the Earth, we have defined a second based on the behavior on the Earth. My understanding (not sure I right!) of relativity is that the decay of Cesium 133 will be slower in a deeper gravity well if the decay observed from the Earth; but if observed from within the new gravity well will appear to be the same as it was on Earth.

      • Harold says:

        I believe you are right. As long as you are in the same conditions as the Caesium it will go at the same rate. It will appear to go at a different rate if you are in a different condition of gravity or acceleration.

Leave a Reply