Reflections in Cosmology 10: Time and Its Arrow

What, then, is time? If no one asks me, I know what it is. If I wish to explain what it is to him who asks me, I do not know. ~ Saint Ausgustine of Hippo

Newton avoided the issue entirely when formulating his laws of motion, writing: I do not define time, space, place and motion, as being well known to all.

A few centuries have passed since, and we who live in the post-Newtonian era of Einstein’s relativity claim to have a better grasp of the workings of time – yet our physical understanding of time is vastly different from our own experience of it.

In relativistic physics, time and space are different aspects of the same thing (space-time), both of which are warped in the presence of matter and energy

Science simplifies the time that we experience into a continuous one-dimensional space. Physics seizes time, strips away many of the characteristics ascribed to it in everyday life, and makes it akin to space. Our physical world has become a four-dimensional continuum that decomposes into a three-dimensional space and a one-dimensional time stretching from the past to the future. We must not be too surprised if physical time lacks some of the characteristics of the time that we experience. The neglected characteristics are usually regarded as psychological or metaphysical. ~ Edward Harrison, Cosmology: The Science of the Universe

We think we know what space is like: It is that thing all around us, stretching away, in which objects are visibly distributed. It is spanned by intervals of distance and measured in units such as meters with meter sticks that can be directly observed. Time is not so simple because we cannot objectively observe bodies distributed in it, and we cannot directly observe with the five senses intervals of time such as seconds. It seems that we experience intervals of time subjectively and cannot directly observe them objectively. The impression gained is that all our experiences are of two kinds, consisting of objective things (trees, clouds, and mountains) that are diversified in space, and subjective things (sensations, emotions, and ideas) that are diversified in time. Somehow these opposite kinds of experience come together to make up the phenomenal world in which we live and the physical world about which we theorize. ~ Edward Harrison, Cosmology: The Science of the Universe

I initially handwaved this last paragraph away as being rather silly, but further reflection made me realize its profundity. I can’t pinpoint what it is, but there’s something here. Is time something that is experienced only by the mind? Why do we experience transience? What is this ‘now’ that separates the future that we cannot perceive from the past that lives in our memory? And if this ‘now’ is moving forward in time, at what speed is it moving? Is there then a second ‘time’ through which it is moving in time? According to Edward Harrison, there are definitely deep biological and psychological aspects to our human experience of time.

When a man is racked with pain, or with expectation, he can hardly think of anything but his distress; and the more his mind is occupied by that sole object, the longer the time appears. On the other hand, when he is entertained with cheerful music, and lively conversation and brief sallies of wit, there seems to be the quickest succession of ideas but the time appears shortest. ~ Thomas Reid, Essays on the Intellectual Powers of Man

Many have dimissed these aspects of time as psychological illusions. Others talk about an ‘arrow of time’ – the fact that we observe time as flowing only in one direction. We expect eggs to be broken when dropped on the floor, but we do not expect to see broken pieces of an eggshell coming together to form a whole egg. This is an example of what is called the Second Law of Thermodynamics – in a closed system, disorder and randomness (entropy) tends to increase over time. yet, most other fundamental laws of physics are time-invariant. The laws that govern the individual particles within a closed system are time-reversible, meaning that they are applicable even if time is reversed. What makes it different in a larger system? Does this point us again to the possibility that the whole is more than the sum of its parts? Why can we remember the past but not the future? Is this experience related to entropy in any way? Is our observation of the Second Law of Thermodynamics a consequence of the way we experience time? Or do we perceive the arrow of time in our minds because of increasing entropy?

The great thing about time is that it goes on. But this is an aspect of it which the physicist seems inclined to neglect… I shall use the phrase ‘time’s arrow’ to express this one way property of time which has no analogue in space. It is a singularly interesting property from a philosophical standpoint. We must note that:

1. It is vividly recognized by consciousness.

2. It is equally insisted on by our reasoning faculty, which tells us that a reversal of the arrow would render the external world nonsensical.

3. It makes no appearance in physical science except in the study of the organization of a number of individuals. Here the arrow indicates the direction of progressive increase of the random element.

~ Arthur Eddington, The Nature of the Physical World