You might think that this is all far removed from practical considerations. It is true that scientists have learned to make extremely accurate clocks using atomic phenomena. But this is a comparatively recent development. Before then, astronomers faced a tricky situation, which is worth recounting.
For millennia, the Earth’s rotation provided a clock sufficiently reliable and accurate for all astronomical purposes. It was unique – the astronomers had access to no other comparable clock. However, about a hundred years ago, astronomical observations had become so accurate that deficiencies in it began to show up. Tidal forces of the Moon acting on the Earth sometimes give rise to unpredictable changes of the mass distribution in its interior. As my accident in Oxford demonstrated, such changes in a rotating body must change its rotation rate. The clock was beginning to fail the astronomers’ growing needs for greater accuracy. Such crises highlight fundamental facts. What could the astronomers do?
They managed to find a natural clock more accurate than the Earth: the solar system. To make this into a clock, they assumed that Newton’s laws governed it. (After the discovery of general relativity, small corrections had to be made to them, but this did not change the basic idea.) However, the astronomers had no direct access to any measure of time. Instead, they had to assume the existence of a time measure for which the laws were true. Making this assumption and using the laws, they could then deduce how all the dynamically significant bodies in the solar system should behave. Although they had no access to it, they then knew where the various bodies should be at different instants of the assumed time. Monitoring one body – the Moon, in fact – they could check when it reached positions predicted in the assumed time and verify that the other bodies in the solar system reached the positions predicted for them at the corresponding times. The astronomers were thus forced into the exercise just described, and they used the Moon as the hand of a clock formed by the solar system.
They originally called the time defined in this manner Newtonian time. It is now called ephemeris time. (An ephemeris is a publication which gives positions of celestial objects at given times.) For a decade or more it was actually the official time standard for civil and astronomical purposes. More recently, atomic time, which relies on quantum effects, has been adopted. There are several important things about ephemeris time. First, it is unthinkable without the laws that govern the solar system. Second, it is a property of the complete solar system (because all its bodies interact, all co-determine one another’s positions). Third, it exists only because the solar system is well isolated as a dynamical system from the rest of the universe.
Ephemeris time may be called the unique simplifier. This is an important idea. If, as Mach argued, only configurations exist and there is no invisible substance of time, what is it that we call time? When we hold the configurations apart in time and put a duration between them, this something we put there is a kind of imagined space, a fourth dimension. The spacing is chosen so that the happenings of the world unfold in accordance with simple laws (Newton’s or Einstein’s). This is a consequence of the desire to represent things in space and time, and our inability hitherto to find laws of a simple form in any other framework.
Ephemeris time is the only standard we can use if clocks are to march in step. If we could not construct such clocks, we could never keep appointments and clocks would be useless. To see that there is only one sensible definition of duration, imagine that two teams of astronomers were sent to two similar but nevertheless different isolated three-body stellar systems. All they can do is observe their motions. From them they must generate time signals. Each team works separately, but the signals they generate must march in step – one clock may run faster than the other, but the relative rate must stay constant. There is only one measure of duration they can choose. In general, no motion in one system marches in step with any motion in the other. Only ephemeris time, deduced from the system as a whole, does the trick. A clock is any mechanical device constructed so that it marches in step with ephemeris time, the unique simplifier.
We can now see that there is only one ultimate clock: the universe. Although it would not be practicable, if we wanted to obtain time of ultra-high accuracy from the solar system, we would, sooner or later, have to take into account the disturbances exerted by bodies farther away. Since there are no perfectly isolated systems within the universe, this process can only stop, if ever, when the entire universe has been made into a clock. The universe is its own clock.
In the light of this, let us think again about Galileo’s ball rolling across the table in Padua. Snapshots of the ball alone were not sufficient to tell what would happen when it rolled over the edge. It seemed inconceivable that the ball’s path could be determined by the little bit of water flowing from a tank used to tell the time. For such reasons as this, Newton rejected speed relative to any one motion as a fundamental concept and invoked instead speed relative to an abstract time. However, if we conceive the universe as a single dynamical entity, the abstract time becomes redundant. The speed of Galileo’s ball that determines which parabola it will trace is its speed as measured by the totality of motions in the universe. This explains why some motions are distinguished from others for timekeeping. They are those that march in step with the cosmic clock, the unique true measure of time. This time is the distillation of all change. High noon is a configuration of the universe.
But the two-and-a-bit puzzle persists. We still have no simple direct way to measure time in Platonia, we always have to go through the intermediary of absolute space. This reflects the hybrid nature of energy. Kinetic energy is defined in absolute space, whereas potential energy is determined by instantaneous configurations and is thus independent of Newton’s invisible framework. We shall be able to claim that Platonia is the arena of the world only if we can dispense with absolute space in the definition of kinetic energy. That is the next topic.
The Inertial Clock (p. 99) Tait’s work, which I feel is very important, passed almost completely unnoticed. This is probably because two years later the young German Ludwig Lange introduced an alternative construction for finding inertial frames of reference, coining the expression ‘inertial system’. Lange deserves great credit for bringing to the fore the issue of the determination of such systems from purely relative data, but Tait’s construction is far more illuminating. Lange’s work is discussed in detail in Barbour (1989) and Tait’s in Barbour (forthcoming).
The Second Great Clock (p. 107) A very nice account of the history of the introduction of ephemeris time was given by the American astronomer Gerald Clemence (1957).
CHAPTER 7
Paths in Platonia