Time marches on, but in which direction?

Kate Bryan

Rhodes University

Two theoretical physicists walk into an airport. The first complains that gravity is a real problem at the microscopic level, where things are too small to see. The second responds that there is no problem: “Here is an equation for the whole Universe and all we must give up is time.” And so, having eliminated the ticking of the clock, they spend eternity in the airport regretting their decision.

The two physicists were John Wheeler and Bryce DeWitt. They did make it out the airport, and their equation became well known throughout the physics community as the Wheeler-DeWitt equation. It united gravity and quantum mechanics, the theory of the tiny, but had the side effect of taking time out of the equation. The concept of time has always challenged human understanding. The Greeks found it important enough to personify as the god Kronos. Sir Isaac Newton interpreted time as a real and absolute part of the Universe and which would exist without us. Others, such as German savant Gottfried Leibniz, saw time as something we construct in order to relate events but which would not exist without objects.

Despite the previous debates throughout history, we do not really understand what drives the ticking clock of the Universe and most of time’s characteristics. But using the Wheeler-DeWitt equation, we may be able to shed some light on this elusive subject. The equation’s unusual nature provides a window into interpreting the role of time in the Universe.

At first glance, it may not seem that difficult to define time: it is the change from past to present, a feature of reality which allows a small acorn to sprout into an oak tree. This gives the impression that time is an immutable backdrop to reality and whether the acorn exists to grow into a tree or not, time will continue to march on regardless. But there is still no conclusive description or explanation for the cogs and wheels that keep the clock of the Universe ticking towards the future.

The issue gets more confusing when we include fundamental physicists’ ideas of time. For most theories in physics, the description of a pile of glass shards spontaneously forming an unbroken window is not a problem. From past to future or future to past, there is nothing to say either is special. Only one theory forces a forward direction of time on us: thermodynamics. This is the theory of all things hot and cold and how to make engines more effective. Thermodynamics uses four laws and it is the second of these which rules out being able to turn an oak tree into an acorn. But it is the only place where such a restriction exists in physics.

This “arrow of time”, which places the future after the past and is dictated by the second law of thermodynamics, applies only to what we as humans can see and experience. It omits the microscopic world, which we cannot see and which is described by quantum mechanics. Quantum mechanics, developed at the beginning of the last century, provides mathematical rules for the smallest things we know about in the Universe and it often contradicts what we consider to be “normal”. It has no such “arrow” to tell us which direction in time the future lies when we discuss the tiniest particles.

And so it is only the second law of thermodynamics and our own experience which tells us the acorn becomes the oak tree and not the other way around. All other theories in physics, whether we are talking big or small, would be happy reversing that picture. This possibility of a reversal of time opens up the door to time travel theories, which is a tale all of it own. However, even if physical laws allowed the possibility of time travel, attempting to apply it would probably lead to troubling situations plagued by paradoxes as science fiction writers often discover.

The problems of time only continue from there. Indeed, Albert Einstein wrestled with the problems of time himself and the result was the concept of space-time, which combines the concepts of space and time.
This merger makes up the fabric of reality in which you and I and all matter exist. This idea suggests that thinking of where you are must always go hand in hand with the question of when you are.

Does this imply that the space you exist in needs time to work? Or can time only exist if there is space for it to exist in? Could we imagine ourselves existing without time passing at all? A person sitting in stagnant traffic might argue that the answer is yes.
Theoretical physics and philosophy open up these avenues of thought about time. Unfortunately, the answers are not always forthcoming. While it may be simple to ask the questions, the answers always take more work to find.

This is why we need maths. Finding answers to these tricky questions is easier once they are translated into the language of mathematics, which lets us test our guesses against logic and may even lead to answers we hadn’t considered.

This is where the Wheeler-DeWitt equation comes in. Its unique interpretation of the role of time delivered a provocative option that is still under debate today. The controversy lies in the fact that time is booted out of the fundamental picture, essentially freezing the clock until time is manually inserted. Some argue that this supports German scientist Leibniz’s argument that time is not a fundamentally real thing but only a construct. Others suggest that this is the equation’s flaw: we can’t use an equation which implies that the Universe’s clock never moves forward.

Regardless of which camp the physicists, mathematicians and philosophers pitch their tent in, the Wheeler-DeWitt equation’s special view of time (or lack thereof) lends itself to a discussion about the real nature of time.

If the picture this equation paints of the Universe can be accurately matched to what we experience in the real world, it would advance our understanding of the Universe’s use of time. It may even settle the debate over the nature of time for good.

My own work involves looking for such a connection between this equation and the real world. Using the equation, we aim to describe a natural clock which may open up a pathway to experimental testing in the future. The regular rhythm of particles being emitted from a decaying atom could serve our purpose because it provides the tick we need in a natural clock.
Even if we managed to devise an experimental model to test the nature of time, we do not know how it will influence the society. Unlike with the search for a specific new technology to improve the lives of those around us, theoretical physics often cannot predict how it will change the world. Today we rely on GPS systems and these use Einstein’s theories to operate. But had you asked a contemporary of Einstein, or the man himself, how the theory would influence technology, they could not have predicted our current dependence on it.

As we gain further understanding of all aspects of the Universe, we gain knowledge that is vital not only for the development of new technologies but we also aid ourselves in learning how to put current technologies to better use.

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