The “present of the universe” is meaningless.
TEMPORAL STRUCTURE WITHOUT THE PRESENT
Gorgo is the woman who saved Greece by realizing that a wax-covered tablet sent there from Persia carried a secret message concealed beneath the wax: a message that forewarned the Greeks of a Persian attack. Gorgo had a son called Pleistarchus, fathered by the king of Sparta, the hero of Thermopylae: Leonidas. Leonidas was Gorgo’s uncle, the brother of her father, Cleomenes. Who belongs to the “same generation” as Leonidas? Gorgo, who is the mother of his son—or Cleomenes, who is the son of the same father? Here is a diagram for those who, like me, have difficulties with genealogy:
There is an analogy between generations and the temporal structure of the world as revealed by relativity. It makes no sense to ask if it is Cleomenes or Gorgo who is “of the same generation” as Leonidas, because there is no single concept30 of “same generation.” If we say that Leonidas and his brother are “of the same generation” because they have the same father, and that Leonidas and his wife are “of the same generation” because they have a son together, we must therefore say that this “same generation” includes Gorgo and her own father! The filial relationship establishes an order between human beings (Leonidas, Gorgo, and Cleomenes come after Anaxandridas and before Pleistarchus), but not between any humans: Leonidas and Gorgo are neither before nor after in respect to each other.
Mathematicians have a term for the order established by filiation: “partial order.” A partial order establishes a relation of before and after between certain elements, but not between any two of them. Human beings form a “partially ordered” set (not a “completely ordered” set) through filiation. Filiation establishes an order (before the descendants, after the forebears), but not between everyone. To see how this order works, we need only think of a family tree, like this one for Gorgo:
There is a cone-shaped “past” made up of her forebears, and a “future” cone comprising her descendants. Those who are neither ancestors nor descendants remain outside of the cones.
Every human being has their own past cone of ancestors and future cone of descendants. Those of Leonidas are shown below, alongside Gorgo’s:
The temporal structure of the universe is very similar to this one. It is also made of cones. The relation of “temporal precedence” is a partial order made of cones.31 Special relativity is the discovery that the temporal structure of the universe is like the one established by filiation: it defines an order between the events of the universe that is partial, not complete. The expanded present is the set of events that are neither past nor future: it exists, just as there are human beings who are neither our descendants nor our forebears.
If we want to represent all the events in the universe and their temporal relations, we can no longer do so with a single, universal distinction between past, present, and future, like this:
We must do so instead by placing above and below every event the cones of its future and past events:
(Physicists have the habit in such diagrams, I don’t know why, of placing the future above and the past below—the opposite of how it is done in genealogical trees.)
Every event has its past, its future, and a part of the universe that is neither past nor future, just as every person has forebears, descendants, and others who are neither forebears nor descendants.
Light travels along the oblique lines that delimit these cones. This is why we call them “light cones.” It is customary, as in the previous diagram, to draw these lines at an angle of forty-five degrees, but it would be more realistic to make them more horizontal, like this:
The reason for this is that, at the scale to which we are accustomed, the expanded present separating our past from our future is extremely brief (a matter of nanoseconds) and almost imperceptible, as a result of which it is “squashed” into a thin horizontal band we usually call “the present,” without any qualification.
In short, a common present does not exist: the temporal structure of spacetime is not a stratification of times such as this:
It is, rather, a structure made up entirely of light cones:
This is the structure of spacetime that Einstein understood when he was twenty-five years old.
Ten years later, he comes to understand that the speed at which time flows changes from place to place. It follows that spacetime does not really have the order outlined above but can be distorted. It now looks rather more like this:
When a gravitational wave passes, for example, the small light cones oscillate together from right to left, like ears of wheat blown by the wind.
The structure of the cones can even be such that, advancing always toward the future, one can return to the same point in spacetime, like this:
In this way, a continuous trajectory toward the future returns to the originating event, to where it began.*32 The first to realize this was Kurt Gödel, the great twentieth-century logician who was Einstein’s last friend, accompanying him on walks along the streets of Princeton.
Near to a black hole, the lines converge toward it, like this:33
This is because the mass of the black hole slows time to such a degree that, at its border (called the “horizon”), time stands still. If you look closely, you will see that the surface of the black hole is parallel to the edges of the cones. So, in order to exit from a black hole, you would need to move (like the trajectory marked in dark gray in the following diagram) toward the present rather than toward the future!
This is impossible. Objects can only move toward the future, as in the trajectories outlined in the diagram in white. This is what constitutes a black hole: an inclination of the light cones toward the interior, marking a horizon, closing off a region of space in the future from everything that surrounds it. It is nothing other than this. It is the curious local structure of the present that produces black holes.
More than a hundred years have passed since we learned that the “present of the universe” does not exist. And yet this continues to confound us and still seems difficult to conceptualize. Every so often a physicist mutinies and tries to show that it isn’t true.34 Philosophers continue to discuss the disappearance of the present. Today, there are often conferences devoted to the subject.
If the present has no meaning, then what “exists” in the universe? Is not what “exists” precisely what is here “in the present”? The whole idea that the universe exists now in a certain configuration and changes together with the passage of time simply doesn’t stack up anymore.
4 LOSS OF INDEPENDENCE
And on that wave
we will all have to navigate,
all who are nourished
by the fruits of the Earth. (II, 14)
WHAT HAPPENS WHEN NOTHING HAPPENS?