A frozen universe?

Philosopher of Physics Craig Callender discusses the arguments for considering that time is an illusion in the June edition of Scientific American. Particularly striking is the following analogy Callender draws between time and money:

We might describe the variation in the location of a satellite around Earth in terms of the ticks of a clock in my kitchen, or vice versa. What we are doing is describing the correlations between two physical objects, minus any global time as intermediary...Instead of saying a baseball accelerates at 20 meters per second per second, we can describe it in terms of the change of a glacier...Time becomes redundant. Change can be described without it.

This vast network of correlations is neatly organized, so that we can define something called "time" and relate everything to it, relieving ourselves of the burden of keeping track of all those direct relations...Money, too, makes life easier than negotiating a barter transaction every time you want to buy coffee. But it is an invented placeholder for the things we value, not something we value in and of itself. Similarly, time allows us to relate physical systems to one another without trying to figure out how a glacier relates to a baseball. But it, too, is a convenient fiction that no more exists fundamentally in the natural world than money does.

In terms of direct relations between physical objects, one could say that x generations of bacteria reproduce in one's intestine for every rotation of the Earth, and one could exchange y cups of coffee for an iPod. In terms of more abstract concepts, in the first case one could say how many seconds it takes for one rotation of the Earth, and how many seconds it takes for the bacteria in one's intestine to reproduce, and in the second case one could express the value of a cup of coffee in pounds, and the value of an iPod in pounds.

However, whilst it might well be possible to describe change without time, a static universe is a universe without time or change, hence the eliminability of time does not entail that the universe is static. Consider again the economic analogy. Money is a common means of expressing the relative values of different goods and services. If we refer to goods and services as economic objects, then money can be said to be an abstraction from the network of direct relative values of all the various pairs of economic objects. Time, by analogy, is a common means of expressing the relative change of different pairs of physical objects.

If time is to physical objects as money is to economic objects, then it must be an abstraction from a network of direct relations between pairs of physical objects. And what is that direct relation, if it isn't the relative amount of change? Conversely, relative change is to time as relative value is to money. The notion of money makes no sense without the concept of value, and the notion of time makes no sense without the concept of change.

As Callender asserts, [relative] change can be described without time, just as one can imagine an economy which operates without money. However, an economy without money is clearly not an economy in which economic objects have no value, and a timeless universe is not necessarily a universe without change. To eliminate change, and to reduce it to mere correlations between variables, an independent argument is required.

Here, Callender turns to canonical quantum gravity, in which the wave-function of the universe is represented by an apparently time-independent solution to the Wheeler-DeWitt equation. It is this fact which has been the primary spur behind the modern arguments for a static universe. To reconcile the time-independence of the wave-function of the universe with our perception of change, the concept of intrinsic time has been proposed.

The wave function Ψ in quantum theory is considered to be a function of various degrees of freedom: Ψ(x₁,...,x_j,...x_n). (In quantum cosmology, there are an infinite number of such degrees of freedom, but to keep things simple, let us suppose that there are only a finite number). The idea of intrinsic time is to identify at least one degree of freedom x_j, which behaves like a clock, and can be used as a surrogate time variable. Thence, one can denote x_j as t, and treat the wave-function as a time-dependent function Ψ_t(x₁,...,x_j-1,x_j+1,...x_n) of the remaining degrees of freedom.

On this view, time is an internal, approximate, emergent property of certain physical systems.