Time and Again

It is within my mind, then, that I measure time. I must not allow my mind to insist that time is something objective. When I measure time, I am measuring something in the present of my mind. Either this is time or I don’t know what time is.

St Augustine, Book Xl of the Confessions.


I have always been fascinated by time and the part it plays in the explanation of the physical universe. I have written a number of essays previously about time. Stephen Hawking’s passing has given me pause to revisit the subject. Hawking’s first popular book, published in 1988, was A Brief History of Time. Some have disparagingly said it was a popular book, appearing on many bookshelves, but was largely unread! Well I read it, but I must confess that it was not as influential on my thinking as many other science books have been.

It was perhaps Aristotle who provided us with the first major insight into time. Aristotle believed that time was inexorably linked to change. It was his contention that if nothing changes, nothing moves, time does not pass. Time, according to Aristotle, is our way of relating ourselves to the change in the universe within and around us. It seems as though Aristotle did not only relate time to physical change in the universe but also to the workings of the mind. In his Physics he wrote:

When some change is happening within the mind, we immediately suppose that some time has passed as well.

But that 18th century scientific genius, Isaac Newton, differed with Aristotle. In the Principia Newton maintains:

I do not define Time, Space, Place and Motion, as being well known to all. Only I must observe, that the vulgar conceive these quantities under no other notions but from the relation they bear to sensible objects. And thence arise certain prejudices, for the removing of which, it will be convenient to distinguish them into Absolute and Relative, True and Apparent, Mathematical and Common. (Capitalisation in the original.)

Thus Newton believed that an Absolute Time existed. He denigrated the time of Aristotle as relative and apparent. For Newton time was independent of other physical variables. It could not be perceived directly but must be deduced or measured indirectly. Clocks for example enabled us to apprehend this uniform flow of absolute time.

These beliefs were widely accepted for two centuries. Newton’s model, based on the assumption that time was independent of all else in the Universe, produced standard modern physics that worked incredibly well.

Most of us have learned to look at time in a similar way. We believe in a time that is uniform, independent of things and their movement. And for most purposes this is a sufficient description.

(It is interesting that Gottfried Wilhelm Leibniz, the famous French Mathematician, who preceded Newton, had argued that there is no such thing as autonomous time. Similarly to Aristotle he believed that time was merely the ordering of events. So without things “happening”, i.e. change, there was no time. Leibniz, of course, is famous for his discovery of differential and integral calculus independent of Newton who is generally accredited with the discovery of this important field of mathematics.)

In preparation for later discussion it is worth contrasting Aristotle’s and Newton’s concept of space.

Aristotle gave thought to the notion of “place”. The place that a thing occupies is described by the other things that surround that particular thing. If I asked you the simple question, “Where are you now?” You might reply, “I’m in Brisbane by the river at Southbank.” So you describe the place you are at by relating it to other things. So Aristotle’s space is circumscribed by other things.

Newton, on the other hand, was unimpressed by such a description because such space was reliant on its definition being dependent on other things. Newton believed that there was “absolute, true and mathematical” space which existed in itself, independent of its surroundings. Such space could exist even where there was nothing.

Thus Newton believed that both space and time were autonomous entities, independent of anything else.

It was up to Einstein in the early twentieth century to reconcile the differences between Aristotle and Newton. Einstein proved, as Newton had suggested, that time and space could exist beyond tangible matter. But contrary to Newton’s belief, Einstein demonstrated that there is no absolute time and space. They are not independent of what happens in the Universe around them. They are in fact relative phenomena.

Returning to time, Einstein proved that time was effected by both:

  • Gravitation, and
  • Relative velocity.

In this regard, for example, on earth, time passes faster in the mountains than it does at sea level. We could just as legitimately argue that objects are attracted to those places where time moves slowest as to say they move to where the gravitational field is strongest.

It can be argued that spacetime is largely a manifestation of the gravitational field.  Whilst, as Newton intuited, the gravitational field is something that exists by itself, it is not unique in this regards but exists with other fields, the interactions between which give rise to the Universe as we know it.

Newton’s beliefs would have been more accurate if the gravitational field was always smooth and uniform. These are the assumptions of Euclidian geometry. But the gravitational field isn’t smooth and uniform and, as a result Newtonian physics and Euclidian geometry are usually, but occasionally not, good approximations of perceived “reality”.

For human beings a fundamental function which seems to arise from our notion of time is memory.

Our notion of memory reflects our normal concept of time. We don’t have a memory of the future because indeed we haven’t been there. I don’t have any memories of Paris either, because I have never been there. But I could if I wished travel to Paris in the next few days, and then I would have a memory of Paris. I haven’t been to 2020 yet either. But what stops me from deciding to go there tomorrow?

Another apparent quandary relating to memory is that we apparently acquire our memories in a serial fashion. As we age we lay down additional memories related to that particular period of time. But when I access memory I don’t have to replay the tape of my life, reeling back to a specific point of interest. My memories are all available to me at once. In fact if anything some of my remoter memories that I have revisited many times are probably more vivid than the memory of what I had for breakfast this morning.

A corollary to Einstein’s findings that there is no absolute time is that there can be no universal present. As the ancient sages told us, the only thing we can ever experience is the eternal present. The memories I have of my past are a reconstruction in the present. My future aspirations again can only be experienced as a construct in the “now”. But my “now” is a uniquely personal “now” which cannot be shared with anyone else. And if there is no absolute time it is nonsense to talk about the “present” in any inclusive way. My “present” will never be shared by the rest of the universe. Even though they may be minutely different, each of us and indeed every point in the universe occupies a unique place in the spacetime continuum.

But research to enhance our basic understanding of time didn’t stop with Einstein. The development of quantum mechanics offered other insights.

Carlo Rovelli is an Italian theoretical physicist whose research focus is quantum gravity. Rovelli asserts that the three fundamental discoveries of quantum mechanics are these:

  • Granularity,
  • Indeterminacy, and
  • The relational aspects of physical variables.

I will try to summarise how these discoveries impact on our notion of time.

Quantum mechanics is built from the supposition that physical phenomena can be reduced to the reaction between fundamental “bits” in statistical relationships. Quantum mechanics shows that time does not “flow” in a continuous way as humans normally perceive it. Time, just like all other physical phenomena, proceeds in discrete pulses. These pulses of time are so small that it is beyond our human capacity to detect them. This minimum time is called Planck time and its minute duration is 10-44seconds. But this is sufficient to have us realise that time does not flow continuously. Time can take only certain discrete, special values. Time is therefore not continuous, but granular.

The issue of determinacy is one we have encountered before. For instance when we attempt to measure exactly where an electron is before the act of observation the electron has no precise position. It is the intervention of the observer that collapses the probability function that locks the electron’s position in to a discrete location. Between any such observations, the electron has no precise position. Where it is located can only be described in terms of probability. In the jargon of physics it is said to be in a “superposition” of positions. If such determinacy is reflected in time as well, which seems to all intents and purposes to reflect the same quantum characteristics, it is likely that an event should have the same determinacy such that time might fluctuate. In such a world, at least at the quantum level, there might be no certainty that past, present and future should be indistinguishable before the intervention of an observer. (And indeed we know in theoretical physics of subatomic particles, the arrow of time does not exist and the most fundamental equations have no reference to time and as such physical events can just as easily occur forward or backwards!)

[Einstein writing about the death of his lifelong friend Michele Besso in 1955 ( and less than a month before his own death) said, “And now he has departed from this strange world a little ahead of me. That signifies nothing. For us believing physicists the distinction between past, present and future is only a stubbornly persistent illusion.”]

Now as for Rovelli’s third point, as I understand it, he is making the case that as a result of indeterminacy, concrete physical outcomes only emerge when something interacts with something else.  When you think of this, it reverses our normal take on the universe. We normally think of the universe as an agglomeration of physical things. If Rovelli is right, a more apt description of the universe might be that it is a series of events! The physical aspects of the universe only manifest themselves after such interactions. In such a universe time, again, is not continuous but dependent on, as Aristotle had asserted, change.  And of course the essential difference between events and things is that whilst events are of limited duration, things persist.

Acknowledging the spacetime continuum, the basic units by which we comprehend the world are not only located in some specific point in space but also at some specific time in space. Our understanding requires not only a “where” but a “when”. In this respect what we identify as “things” are just long events. There are no “things” that endure forever. The hardest rocks will eventually be eroded away and disperse. So it is more enlightening to think of the world as a network of events, even though some events might be perceived as of extremely long duration.

The insightful Greek philosopher, Anaximander, who lived around 600BC, and had already deduced that the earth was a body in space, had something to say about time. Only one small fragment of his writing has survived. In it he proclaimed:

Things are transformed one into another according to necessity, and render justice to one another according to the order of time.

Perhaps I read this wrongly, but I suspect that Anaximander was hinting that the mind needed to use time as an ordering process. In a universe that it seems is largely built on events rather than things, human understanding seems to be enhanced by such ordering.

We know that at the quantum level nothing can be concrete without the impact of an observer (an event). Each observation is in itself a unique event. Between such events quantum phenomena can only be described in terms of probabilities. It is tempting to assume that the intervention of mind in creating time is in fact creating the universe.

That might seem a wildly improbable conjecture. So let me leave you with another thought from Carlo Rovelli who is far more well-informed than I am.

What is entirely credible, in any case, is the general fact that the temporal structure of the world is different from the naïve image that we have of it. This naïve image is suitable for our daily life, but it is not suitable for understanding the world in its minutest folds, or in its vastness. In all likelihood, it is not even sufficient for understanding our own nature, because the mystery of time intersects with the mystery of our personal identity, with the mystery of consciousness.

It would seem quite appropriate then that the French philosopher, Gaston Bachelard said that “meditating on time is the first step towards metaphysics”.