The received view in physics is that the direction of time is provided by the second law of thermodynamics, according to which the passage of time is measured by ever-increasing disorder in the universe. This view, Julian Barbour argues, is wrong. If we reject Newton’s faulty assumptions about the existence of absolute space and time, Newtonian dynamics can be shown to provide a very different arrow of time. Its direction, according to this theory, is given by the increase in the complexity and order of a system of particles, exactly the opposite of what the received view about time suggests.

Two of the most established beliefs of contemporary cosmology are that the universe is expanding and that the direction of the arrow of time in the universe is defined by ever-increasing disorder (entropy), as described by the second law of thermodynamics. But both of these beliefs rest on shaky ground. In saying that the universe is expanding, physicists implicitly assume its size is measured by a rod that exists outside the universe, providing an absolute scale. It's the last vestige of Newton's absolute space and should have no place in modern cosmology. And in claiming that entropy is what gives time its arrow, physicists uncritically apply the laws of thermodynamics, originally discovered through the study of steam engines, to the universe as a whole. That too needs to be questioned.

SUGGESTED READING Einstein and why the block universe is a mistake By Dean Buonomano In the absence of an absolute space and external measuring rods, size is always relative - relative to a measure of distance internal to the system. Starting from the simplest case, a triangle, what we find is that the internal measure of size produces a ratio which also happens to be related to a mathematical measure of complexity that intriguingly plays the central role in Newtonian universal gravitation. Applying these findings to the universe as a whole, we find that Newton’s theory of gravity, contrary to what physicists believe, contains within it an intrinsic arrow of time. This provides a strong hint that the direction of time is not defined by an increase in entropy, but by an increase in structure and complexity.

Part I. The Relativity of Size and the Expansion of the Universe

In Science and Method published in 1908, the great French mathematician Henri Poincaré said. "Suppose that in one night all the dimensions of the universe became a thousand times larger. The world will remain similar to itself ... Only what was a metre long will now measure a kilometre, and what was a millimetre long will become a metre. The bed in which I went to sleep and my body itself will have grown in the same proportion. When I wake in the morning what will be my feeling in face of such an astonishing transformation? Well, I shall not notice anything at all ... In reality, the change only exists for those who argue as if space were absolute."

In the light of Poincaré’s comments, how are we to understand the supposed expansion of the universe? As beings like Poincare in his bed, it would seem we should not be able to tell that the universe is expanding.

How the changing shape of the universe mimics expansion
 
The way that many authors explain the expansion of the universe is by likening it to a balloon that is being blown up. Its surface is covered with dots which represent galaxies getting ever farther from each other. The problem is, a dot has no size. If you are watching a balloon with dots being blown up in a room, the background gives you a scale with respect to which the separations are visibly changing. For you the relative change is objective because you can see both the balloon and the room. However, as far as the dots on the surface of the balloon are concerned no ratios are changing: the distance between dots 1 and 2 divided by the distance between dots 3 and 4 does not change. This is the point Poincare was making when he asks his readers to imagine that one night every distance in the universe became 1000 times larger. Unless we assume a Newtonian absolute space, a ruler outside of the universe - an idea that’s clearly nonsense - this model doesn’t explain how the universe could be expanding.