The End of Time: The Next Revolution in Physics

Imagine that two philosophers meet on a walk. Each believes in a present that sweeps through instants of time. But that implies a unique succession of instants, or Nows. Which Nows are they? If the two philosophers are to make such claims, they should be able to ‘produce’ the Nows through which time flows. Unfortunately, they face the problem of the relativity of simultaneity. Each can define simultaneity relative to themselves, but, since they are walking towards each other, their Nows are different, and that puts paid to any idea that there is a unique flow of time. There is no natural way in which time can flow in Minkowski’s space-time. At least within classical physics, space-time is a block – it simply is. This is known as the block universe view of time. Everything – past, present and future – is there at once. Some authors claim that nothing in relativity corresponds to the experienced Now: there are just point-like events in space-time and no extended Nows. At the psychological level, Einstein himself felt quite disturbed about this. Reporting a discussion, the philosopher Rudolf Carnap wrote:

Einstein said the the problem of the Now worried him seriously. He explained that the experience of the Now means something special for man, something essentially different from the past and the future, but that this important difference does not and cannot occur within physics. That this experience cannot be grasped by science seemed to him a matter of painful but inevitable resignation. So he concluded ‘that there is something essential about the Now which is just outside the realm of science’.

The block universe picture is in fact close to my own, but the idea that Nows have no role at all to play in physics, and must be replaced by point-like events, would destroy my programme. However, it is only absolute simultaneity that Einstein denied. Relative simultaneity was not overthrown.

We are all familiar with flat surfaces (two-dimensional planes) in three-dimensional space. Such planes have one dimension fewer than the space in which they are embedded, and are flat. Hyperplanes are to any four-dimensional space what planes are to space. In Newtonian physics, space at one instant of time is a three-dimensional hyperplane in four-dimensional Newtonian space-time. It is a simultaneity hyperplane: all points in it are at the same time. Such hyperplanes also exist in Minkowski space-time, but they no longer form a unique family. Each splitting of space-time into space and time gives a different sequence of them.

Now, what is Minkowski space-time made of? The standard answer is events, the points of four-dimensional space-time. But there is an alternative possibility in which three-dimensional configurations of extended matter are identified as the building blocks of space-time. The point is that the three-dimensional hyperplanes of relative simultaneity are vitally important structural features of Minkowski space-time. It is an important truth that special relativity is about the existence of distinguished frames of reference. And an essential fact about them is that they are ‘painted’ onto simultaneity hyperplanes. As a consequence, simultaneity hyperplanes, which are Nows as I define them, are the very basis of the theory. They are distinguished features. You cannot begin to talk about special relativity without first introducing them. At this point, the way both Einstein and Minkowski created special relativity becomes significant.

The question is this: how is a four-dimensional structure built up from three-dimensional elements? To make this easier to visualize, consider the analogous problem of building up a three-dimensional structure from cards with marks on them representing the distribution of matter. From one set of cards with given marks, many different structures can be built simply by sliding the cards horizontally relative to one another and changing their vertical spacings. Tait’s problem shows that in general the markings in a structure built without special care will not satisfy the laws of motion. What is more, to find the correct positionings we have to use the complete extended matter distributions. These are what I have identified as instants of time. You simply cannot make the space-time structure without using them.