1. What Is Essential to Being a clock?

Clocks record numerical information about time. They measure the quantity of time, the duration. Every clock has two functions. One function is to generate a sequence of events of hopefully the same durations. Periodic processes provide these events. In a wall clock, the events are pairs of successive ticks. In a pendulum clock, the events are swings (that is, oscillations) of the pendulum. The second function is to count these events, thereby providing a measurement of their durations in seconds and minutes and hours and years. This counting can be especially difficult if the ticks are occurring a trillion times a second. However, it is an arbitrary convention that we design clocks to count up to higher numbers rather than down to lower numbers as time goes on.

One principal goal in clock-building is to make the clock’s basic durations be congruent. That is, the duration between any two adjacent ticks should be the same. When this goal is achieved, the clock is said to be uniform or regular.

A second goal is for the time measurements of the clock to agree with those of the standard clock. When this happens, the clock is said to be properly calibrated or accurate or synchronized with the standard clock. To calibrate a clock, that is, to synchronize it with the standard clock, we want our clock to show that it is time t just when the standard clock shows that it is time t, for all t.

A clock isn’t really measuring the time in a reference frame other than one fixed to the clock. In other words, a clock primarily measures the elapsed proper time between events that occur along its own worldline. Technically, a clock is a device that measures the spacetime interval along its own worldline. If the clock is at rest in an inertial frame, then it measures the “coordinate time.” If the spacetime has no inertial frame then it can’t have a coordinate time. Because clocks are intended to be used to measure events external to themselves, a third goal in clock building is to ensure there is no difficulty in telling which clock tick is simultaneous with which events occuring away from the clock. For example, we might want to determine when the sun comes up in the morning at some particular place where we and our clock are located. For some clocks, the sound made by the ticking helps us make this determination. For other clocks, the determination is made by our seeing the sun rise just when we see the digital clock face show a specific time of day. More accuracy in the determination requires less reliance on human judgment.

In our discussion so far, we have assumed that the clock is very small, that it can count any part of a second and that it can count high enough to be a calendar. This isn’t always a good assumption with a real clock. Despite the practical problems, there is the problem of there being a physical limit to the shortest duration measurable by a given clock because no clock can measure time more accurately than the time it takes light to travel between the components of that clock, the components in the part that generates the sequence of regular ticks.

  1. What Is Our Standard Clock?

By current convention [in 1964 by ratification by the General Conference of Weights and Measures for the International System of Units, which replaced what was called the “metric system”], the standard clock is the clock we agree to use for defining the standard second. The current standard second is defined to be the duration of 9,192,631,770 periods (cycles, oscillations, vibrations) of a certain kind of microwave radiation in the standard clock. More specifically, the second is defined to be the duration of 9,192,631,770 periods of the microwave radiation required to produce the maximum fluorescence of cesium 133 atoms (that is, their radiating a specific color of light) as the atoms make a transition between two specific hyperfine energy levels of the ground state of the atoms.  This is the internationally agreed upon unit for atomic time [the T.A.I. system].  The old astronomical system [Universal Time 1] defined a second to be 1/86,400 of an Earth day.

For atomic time, the atoms of cesium with a uniform energy are sent through a chamber that is being irradiated with these microwaves. The frequency of these microwaves is tuned until the maximum number of cesium atoms flip from one energy to the other, showing that the microwave radiation frequency is now precisely tuned to be 9,192,631,770 vibrations per second. Because this frequency for maximum fluorescence is so stable from one experiment to the next, the vibration number is accurate to so many significant digits. The National Institute of Standards and Technology’s F-1 atomic fountain clock, which was adopted in late 1999 as the primary time standard of the United States, is so accurate that it drifts by less than one second every 20 million years.  We know there is this drift because it is implied by the laws of physics, not because we have a better clock from which to make the judgment.

The standard clock is used to fix the units of all lengths. The unit of length depends on the unit of time. The meter depends on the second. It does not follow from this, though, that time is more basic than space. All that follows is that time measurement is more basic than space measurement. And this has to do with convention and with the fact that current science is capable of measuring time more precisely than space.

Thanks to the regularity of light propagation in a vacuum, the meter is defined in terms of the second.  The meter is defined in terms of the pre-defined second as being the distance light travels in exactly 0.000000003335640952 seconds or 1/299,792,458 seconds. That number is picked so that the new meter will be nearly the same distance as the old meter, which was the distance between two marks on a platinum bar that was kept in the Paris Observatory.  Why is the meter defined in terms of the second, instead of having the second defined in terms of the meter as, say, how long it takes light to travel a certain distance?  The answer is that distance can’t be measured as accurately as time.  Time can be more accurately measured than distance, voltage, temperature, mass, or anything else.

These standard definitions of the second and the meter amount to defining or fixing the speed of light in a vacuum in all inertial frames. The speed is exactly one meter per 0.000000003335640952 seconds or 299,792,458 meters per second, or approximately 186,282 miles per second or about a foot per nanosecond. There can no longer be any direct measurement to see if that is how fast light REALLY moves in an inertial frame; it is simply defined to be moving that fast. Any measurement that produced a different value for the speed of light would be presumed initially to have an error in, say, its measurements of lengths and durations, or in its assumptions about the influence of gravitation and acceleration, or in its assumption that the light was moving in a vacuum. This initial presumption comes from a deep reliance by scientists on Einstein’s theory of relativity. However, if it were eventually decided by the community of scientists that the theory of relativity is incorrect and that the speed of light shouldn’t have been fixed as it was, then the scientists would call for a new world convention to re-define the second. Some physicists believe that a better system of units would first define the speed of light, then define the second, and then make the meter be a computed consequence of these.

Although a microwave atomic clock is currently used for our standard unit of time, it is expected that in the first quarter of the 21st century, physicists will agree to use an optical atomic clock, and then the definition of the second will be changed to refer to an optical frequency, rather than to a microwave frequency.

  1. Why Are Some Standard Clocks Better Than Others?

We choose as our standard clock our best clock, the one with the least drift, the one with the most regularity in its period. Other clocks ideally are calibrated by being synchronized to this standard clock.

In about 1700, scientists discovered that their best watches and clocks showed that the time from one day to the next, as determined by sunrises, varied throughout the year.  Therefore, they preferred to define durations in terms of the mean or average day throughout the year.  Before the 1950s, the standard clock was defined astronomically in terms of the mean rotation of the earth upon its axis [solar time].  For a short period in the 1950s and 1960s, it was defined in terms of the revolution of the earth about the Sun [ephemeris time]. The second was defined to be 1/86,400 of the mean solar day, the average throughout the year of the rotational period of the earth with respect to the Sun. Now we’ve found a better standard clock, a certain kind of atomic clock [atomic time]. All atomic clocks measure time in terms of the natural resonant frequencies of various atoms and molecules. The periodic behavior of a super-cooled cesium atomic clock is the best practical standard clock we have so far discovered.  [The dates of adoption of the standards was left vague in the previous sentences because different international organizations adopted different standards in different years.]

The principal theoretical goal in selecting a standard clock is to find a periodic (cyclic) process that, if adopted as our standard, makes the resulting system of physical laws simpler and more useful.   Choosing the atomic clock as standard is much better for this purpose than choosing the periodic dripping of water from our goat skin bag or the period of a special pendulum or even the periodic revolution of the earth about the Sun.

When we choose a standard clock we are making a choice about how to compare two durations in order to decide whether they are of equal duration. Is this choice somehow forced upon us? To what extent is this choice conventional? Philosophers dispute the extent to which the choice of metric is conventional rather than forced by nature. Taking the conventional side, Adolf Grünbaum argues that time is metrically amorphous. It has no intrinsic metric in the sense of its structure determining the measure of durations. Instead, we analysts establish durations between instants by the way we assign coordinates to instants. If we were to say the instant at which Jesus was born and the instant at which Abraham Lincoln was assassinated occurred only 24 seconds apart, whereas the duration between Lincoln’s assassination and his burial is 24 billion seconds, then we can’t be mistaken. It’s up to us to say what is correct when we first create our conventions about measuring duration. We can consistently assign any numerical time coordinates we wish, subject only to the condition that the assignment properly reflect the betweenness relations of the events that occur at those instants. That is, if event J (birth of Jesus) occurs before event L (Lincoln’s assassination) and this in turn occurs before event B (burial of Lincoln), then the time assigned to J must be numerically less than the time assigned to L, and both must be less than the time assigned to B. t(J) < t(L) < t(B). A simple requirement. It is other requirements that lead us to reject the above convention about 24 seconds and 24 billion seconds as unhelpful. What requirements? We’ve found that, for doing science, certain processes are more “regular” than others. Pendulum swings are more regular than repeated barks of a dog. Periodic appearances of the sun overhead are more regular than rainstorms. Why are they? It’s because there are many periodic processes in nature that have a special relationship to each other; their periods are very nearly constant multiples of each other, and this constant stays the same over a long time. For example, the period of the rotation of the Earth is a fairly constant multiple of the period of the revolution of the Earth around the Sun, and both these periods are a constant multiple of the periods of swinging pendulums. The class of these periodic processes is very large, so the world will be easier to describe if we choose our standard clock from one of these periodic processes. If we were to choose the standard to be the period of our own pulse, then we’d find that all those other processes would speed up when we are excited and slow down when we are not, and we’d find that it would be more difficult to find simple laws of nature. A good convention for what is regular will make it easier for scientists to find simple laws of nature and to explain what causes other events to be irregular. It is the search for regularity and simplicity that leads us to adopt the conventions for numerical time coordinate assignments that we do. No, says the objectivist, the success of the atomic clock over these other clocks we might have chosen as our standard clock shows that we picked the correct clock. An objectivist believes that whether two intervals of time are really equivalent is an intrinsic feature of nature, and choosing an atomic clock instead of the earth’s revolutions about the sun as the standard clock isn’t any more conventional than is choosing to say the Earth is round rather than flat.

A practical goal in selecting a standard clock is to find a clock that is relatively insulated from environmental impact such as comet impacts, stray electric fields or the presence of dust.  If not insulation, then compensation.  That is, if there is some theoretically predictable effect upon the standard clock, then the clock can be regularly adjusted to take account of the effect.  Sensors, such as a thermometer or whatever, will sense the local conditions that affect the clock, and their readings can be used to apply a suitable correction in order to compensate for the effect of those conditions.

Why is choosing the cesium atomic clock as our standard better than choosing an astronomical process such as the mean yearly motion of the earth around the Sun? The brief answer is that the earth’s rate of spin varies.  The ocean’s tides, the sloshing of earth’s molten core, and other things, are affecting the rotation of the earth, but not affecting the atomic clock.  If we said that by definition the earth doesn’t slow down, then scientists would have to say that the frequency of light emitted from cesium atoms is gradually increasing for seemingly no apparent reason.  That is, by sticking to the earth-sun clock, we have trouble accounting for accelerations and retardations of the orbital motions of the other planets compared with earth’s rotational period, and we have trouble accounting for the simultaneous accelerations and retardations of atomic motions such as those in cesium-133 atoms compared again with earth’s rotational period. Our atomic theory says that these atomic processes should behave uniformly as time goes on, so sticking with the earth-sun clock forces us accept awkward changes in our atomic theory and in the rotations of the other planets. On the other hand, by switching to the cesium atomic standard, these alterations are unnecessary, the mysteries vanish, and we can readily explain the non-uniform wobbling of the earth’s yearly revolutions by reference to the tides on the earth, the movement of the liquid metal at the center of earth, the gravitational pull of other planets, dust between planets, and collisions with comets. These influences affecting a solar clock do not affect the cycles of the cesium atom.

There are two principal advantages of the cesium clock: (1) it provides a standard that is reproducible anywhere in the universe where there is cesium, and, more importantly, (2) the behavior of the cesium atom is relatively insulated or isolated from other processes, especially from a comet’s bombarding the earth.

In order to keep our atomic-based calendar in synchrony with the rotations and revolutions of the earth, say, to keep atomic-noons occurring on astronomical-noons and ultimately to prevent Northern hemisphere winters from occurring in some future July, we systematically add leap years and leap seconds and leap microseconds in the counting process. These changes don’t affect the duration of a second, but they do affect the duration of a year because, with leap years, not all years last the same number of seconds.

Our universe has a large number of different processes that bear consistent time relations, or frequency of occurrence relations, to each other. For example, the frequency of a fixed-length pendulum is a constant multiple of the half life of a specific radioactive uranium isotope; the relationship doesn’t change as time goes by (at least not much and not for a long time). The existence of these sorts of relationships makes our system of physical laws much simpler than it otherwise would be, and it makes us more confident that there is something objective we are referring to with the time-variable in those laws.

  1. What Does It Mean For a Clock To Be Accurate?

It’s important to distinguish accuracy from precision. If you use a bow to shoot arrows at a target, then the shooting is precise if all the arrows cluster near a point, even if that point is off-target. For your shooting to be accurate you need to hit the bull’s-eye.  The standard clock’s ticking is our bulls-eye. An ordinary wristwatch is considered to be accurate if it ticks in synchrony (that is, in step) with our standard clock.

What it means for the standard clock to be accurate depends somewhat on your philosophy of time. If you are a conventionalist, then once you pick the convention, the standard clock can’t fail to be accurate. There may be more or less useful standards (you would do better choosing the ticks of an atomic clock rather than the barks of your neighbor’s dog as the standard periodic process), but usefulness isn’t a sign of truth. The absolute theory of time, on the other hand, implies time is marching on independent of all events, and an accurate standard clock will be in sync with this “march.” If it is out of sync, then our standard clock won’t be telling the true time. But since our civilization doesn’t know how to establish this synchrony, we take a very different route to accuracy by saying the best choice for a standard clock is one that is the most regular, and we find out which is the most regular by finding the clock that is best at meeting the following three goals:

  1. The most accurate clock will use a process that is not affected very much by environmental conditions such as temperature, time of day, where it’s located, the presence of dust and comets. [The standard atomic clock meets goal (a) better than the standard astronomical clock does.]
  2. Exact reproductions of the clock should stay in synchrony with each other when environmental conditions are the same. To use the technical expression, the reproductions should remain sufficiently congruent, i.e., more congruent than competing clocks using a different standard.
  3. The standard clock’s readings should be consistent with the Newton’s first and second laws of motion (assuming we are in a situation where these laws should hold so that we don’t need to deal with Einstein’s revisions of Newton’s laws). If we run a test of those laws, and if we find that Newton’s laws are violated, then the problem isn’t with the laws but with the clock used in our test, and we say the clock is inaccurate, provided there are no other mistakes in the experiment. The first person to notice requirement (c) on accuracy of clocks was Leonhard Euler [1707-1783], a Swiss mathematician and physicist.

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