The End of Time: The Next Revolution in Physics

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.

CHAPTER 7

Paths in Platonia

NATURE AND EXPLORATION

The two-and-a-bit puzzle is the statement that two snapshots of a dynamical system are nearly but not quite sufficient to predict its entire history. We need to know not only two snapshots, but also their separation in time and their relative orientation in absolute space. These are exactly the things that determine the energy and angular momentum of any system, both of which, as we have seen, have a profound influence on its behaviour.

There are two different ways to approach this problem. Either we assume the known laws of nature are correct and simply ask how they can be verified, or we take a more ambitious stance and ask if they arise from some deeper level that we have not yet comprehended. The latter is the approach of this chapter. We shall forget absolute space and time and take Platonia for real. I have likened it to a country; countries are there to be explored. In exploring a country, one follows a path through it. Any continuous curve through Platonia is such a path. A natural question is whether some paths are distinguished compared with others. It leads directly to the idea of optimization.