Many thousands of years from now, any alien archaeologist discovering the traces of humans on Earth would likely conclude that we worship time. The face of a clock features on a wall in almost every public place, within every house, and on small votive devices on our wrists. We are lost without the clocks and phones that count the precious seconds, hours, days, and years by which we measure our lives. Time allows us to savour memories of the past and to form hopes for the future. It allows things to grow, move, age, and decay. We think of much of our science as describing how things evolve according to time’s order. Pre-Socratic philosopher Anaximander writes that ‘Things are transformed one into another according to necessity, and render justice to one another according to the order of time1’. Yet, the true nature of time remains perhaps the greatest mystery faced by philosophers and scientists alike. Why should time have an order? And for whom? And to what end? It is even questioned whether time exists at all, or whether it is merely an illusion.
It is first necessary to outline the characteristic features that we attribute to our ‘time’. Conventionally, time is considered an uncomplex and constant flow that moves from past to future, uniformly and independently from all other factors. Over time, the expansion of knowledge in the subject of physics has challenged these features, and, in turn, the notion of time that the majority of us so readily accept. Many physicists including Carlo Rovelli and Julian Barbour are proponents of the idea that time as we know it does not exist, and therefore there can be no time variable in the fundamental equations that describe the world. Perhaps they are correct. How far does our ignorance to the true nature of time stretch? How much does this naivety really matter?
In deconstructing our assumptions, the idea of a uniformly moving time disintegrates with ease. The evidence for this lies in the impact that distance from bodies of mass and speed of movement have on how fast time passes. If one high-precision atomic clock is placed on top of my head and another placed on my desk – a distance of about a foot – the clock on my head will age faster by approximately 90 billionths of a second over 79 years2. Furthermore, if the ion – normally completely motionless within the clock’s operation – of one clock is moved back and forth at speeds equivalent to several metres per second, this clock will tick at a minutely slower rate than the one in which the ion remains stationary. Closer to mass, and at a higher speed, time slows down. NIST’s ‘time dilation’ experiments produced the results described above, yet it was in 1907 when Einstein understood the slowing down of time – a century before clocks existed with enough precision to measure it. The fact prompts the question: If different clocks show different times, which tells the time correctly? Has the clock on the desk slowed relative to the real time recorded on top of my head, or has the clock on top of my head sped up relative to the real time recorded on my desk? The answer is neither. ‘Proper time’ refers to a time measured by a clock that has the same motion as the observer. A clock in a relative motion to the observer, or a different gravitational field, will not measure this ‘proper time’3. Einstein produced the equations that describe how these proper times develop relative to each other, allowing us to calculate the difference between two times. As a result, there is no correct and objective time to be defined, only proper times measured by particular observers and a how these relate to one another. And so, the unity within our idea of time does transpire to be an illusion. In practice, however, this seems of little practical consequence. The differences in speed of time are too small to be registered by anything other than the most precise clocks, and it would be futile to consider moving into an underground lair in an attempt to retain youthful looks.
Yet, what falls following a lack of uniformly flowing time is perhaps more significant to us. In the same way that there can be no single time for observers in different locations, nor can there be any objective duration of an event for a range of observers. The consequence of this is the loss of the present moment. Carlo Rovelli uses the analogy of a sibling making a trip to exoplanet Proxima b 4. If you enter your sister’s room before she leaves, to find out what she is doing ‘now’, the light from her location takes a tiny fraction of a second to reach your eyes – an insignificant period. When she travels to Proxima b, the extensive distance means that it takes approximately four years for the light to travel from her through a telescope and into your eyes. What you see her doing ‘now’ is what she was doing four years ago. Is ‘now’, then what she will be doing four years after you observe her through the telescope? As Rovelli points out, this cannot work. Four years after you observe her, in her time she might already have returned to Earth and be ten terrestrial years in the future. The non-uniformity of time makes it impossible to pin down when ‘now’ is. Since, as humans, our ability to distinguish fractions of seconds is greatly limited, we can refer to a general present moment applicable to our planet. We lack enough sensitivity to generalise the present to a ‘bubble’ around us, yet where this ends our own perspectives can no longer apply. One of the first to make this deduction was Kurt Gödel, asserting that ‘The notion of “now” is nothing more than a certain relation between a certain observer and the rest of the universe.’5.
It is difficult to come to terms with the fact that something as integral to human experience as the objective present moment is an illusion by the laws of pure physics. The knowledge brings a touch of irony to stereotypical phrases which tell us to forget the past and future in favour of ‘living in the present moment’, when in reality we have no real access to observing the real present, only the past. Yet perhaps the use of such phrases is not entirely hopeless. After all, only a small minority of people are concerned with events occurring so far away in the universe in their daily lives. Voyager 1 is the most distant man-made object in the universe, at over 23 billion kilometres away. Even at this distance, it takes only 20 hours for a radio message to travel to us on Earth. The vast majority have no reason to think outside the ‘bubbled’ present of our experience. Indeed, regardless of the acceptance of the theory of relativity, the idea of presentism flourishes in metaphysical debates. This is the view that only the present is real. While presentism faces many problems, including the significant one above, there are many who support it on account of being happy to settle for a completely subjective view of the present. Belief in the present as what appears now, for any particular observer, satisfies these people alongside the vast majority who do not necessarily even think to consider the question. Therefore, our insensitivity to minute fractions of time makes the lack of an objective ‘now’ largely unproblematic in practice.
We take it as intuitive and obvious that time flows in an eternal forward pointing arrow, from past to future. However, nineteenth and twentieth-century physicists realised that within the rules of physics in all areas but one, there is no such distinction between past and future. Newton’s laws of motion, Maxwell’s equations for electricity and magnetism, Einstein’s relativistic gravity, and the quantum mechanics of Heisenberg and Schrödinger all do not distinguish past from future. They are invariant under charge, parity, and time (CPT) reversal symmetry6. Only where there is heat is a future-pointing arrow of time required. For example, an object moving at a constant velocity is brought to a stop by friction, which produces heat. It would be implausible for this to be reversed, and for an object to begin to move from stationary on its own. In various ways, all physical processes which unfold forwards in time involve heat. Clausius’s entropy measures this irreversible progress of heat. It is defined as the measure of a system’s thermal energy per unit temperature that is unavailable for doing useful work7. Since work is achieved by ordered molecular motion, entropy is also a measure of the molecular disorder of a system. The equation below, where S indicates entropy, shows that the quantity never decreases but must either increase or stay the same.
This is the second principle of thermodynamics. The crux of entropy is that heat only passes from hot to cold bodies.
Boltzmann saw beneath entropy, recognising that heat is the microscopic agitation of molecules. It stimulates these molecules, setting off a chain of agitation to neighbouring still molecules. This is how heat is transferred. Boltzmann understood this thermal agitation and the growth of entropy as the natural increase of disorder – heat passing from hot to cold by the shuffling and disordering of molecules. What begins in a particular special configuration gradually becomes less and less ordered with the growth of entropy. Entropy drives our existence, as without low entropy, energy would dilute into uniform heat and the universe would fall into a state of thermal equilibrium without distinction between past and future, or events at all. This raises the question: What is it that gives the initial configurations a lower state of entropy to begin with? What makes any given state less or more of a particular and specially ordered configuration? Every configuration is equivalently particular when thought about carefully, as each always has something that characterises it as individual. This creates a problem for our increasing entropy, dependent on a particular previous state of less disorder. Particularity is perspectival. The notion of certain configurations being more particular than others only makes sense if we limit the number of characteristics by which we assess each configuration. We, as humans, have a macroscopic view of the universe, blind to all variables but those with which we physically interact. Our vision of the world is blurred by this exposure to a limited number of variables, allowing the concept of a previous lower entropy to exits. It is only from our perspective that any previous state billions of years ago had a particularly special configuration which could only be disordered, creating the increase in entropy that we rely on for our flow of time. This flow appears to be not intrinsic to the universe, but due to the particular perspective that we have from our corner of it. From this, it seems that the flow of time is ultimately the expression of our ignorance of the world. Yet it need not concern us, as our state of ignorance in this case is indeed bliss. We cannot escape the illusion and would not want to for loss of our flow of time. The blurring which we experience is not some mental construct within us, but instead depends on actual physical interactions.
Many of us tend to consider time in the same way as it was described by Newton: ‘Absolute, true, and mathematical time, of itself, and from its own nature, flows equably, without regard to anything external.’8. Newton’s time possesses a strong sense of independence – a ‘true’ time that passes even when nothing changes, and is only accessible indirectly, through calculation. Not even the time given by days qualifies for Newton’s ‘true’ time, because of their unequal natural lengths throughout the year. Equations using ‘t’ were written by Newton to indicate his ‘absolute, true and mathematical’ time, describing how things move within it – Newton’s laws of motion. Before Newton, Aristotle is the first scholar we know to have asked the question of what time is. Newton would go on to contradict Aristotle’s view, which described time simply as the measurement of change. For Aristotle, if nothing changed, time could not pass9. For him, time is not a type of change, but something dependent on change. Change could include that within the mind as well – an internal movement providing the change needed for time to exist as the registering of that change. Newton argues for an independent time, while Aristotle’s is entirely dependent on other events.
Einstein constructed an answer to combine arguments from both great thinkers. This was relativity. In Einstein’s theory of relativity, time is interlaced with the three dimensions of space to form a bendy four-dimensional space-time continuum. This block universe, visualised by his former professor Hermann Minowski, therefore encompasses all time that we have experienced, are experiencing and are yet to pass through. Satisfying Newton, this space-time exists regardless of matter. However, it is not independent as Newton thought, but subject to distortion because of the other fields that make up the fabric of the universe. It’s curvature results in gravity, and the dilation of time. In this way, time becomes interwoven with the geometry of space. Newton’s ‘true’ time does exist as a real entity but does not pass independently, unaffected by any other factors. Aristotle’s arguments are not completely lost – he contributes the idea that everything occurs in relation to something. The difference is that this something can simply include Einstein’s space-time entity itself. Space-time, therefore, eliminates the common assumption of a time flowing independently to all other factors. It also suggests a strict determinism, in which all moments of time exist as part of the four-dimensional block.
However, space-time does maintain the notion of causality. The fact that there is a constant speed of light is very significant to space and time in special relativity and is expressed geometrically in space-time geometry through ‘light cone’ structures10. By imagining light confined to a two-dimensional plane, the light from an event spreads out in a circle after the event has occurred. If this growing circle is graphed with a third, vertical, dimension of time, a cone shape is formed. In reality there are three spatial dimensions, and so the light cone would be a four-dimensional version of a cone with cross-sections of three-dimensional spheres, but a cone in two spatial dimensions is easier to visualise. The set of events in the past send light signals to an event, creating a ‘past’ light cone, and this event passes light signals to a further set of events in the future, creating a ‘future’ light cone. This means that any occurrence outside the past or future light cones cannot influence, nor be causally influenced by, the event.
(Fig.1: The light cone structure illustrated in two spatial dimensions. Source: https://www.conncoll.edu/news/cc-magazine/past-issues/2019-issues/fall-2019/the-flash-of-light/)
However, the space-time theory faces some problems. Amongst these is that fact that if time is to be equated with space as a physical entity, it, too, must be subject to the effects of quantum mechanics. The field of research that attempts to explain the gravitational physics of relativity in terms of quantum mechanics is quantum gravity. There is no theory that has been accepted generally by the scientific community as of yet, and the problem is one that many theoretical physicists are currently pre-occupied with finding a possible solution to – in the form of work on string theory and loop quantum gravity, for example. When the quantum properties of space and of time are considered, the ideas of temporal structure which general relativity and space-time have left us with collapse. Like space, time should be subject to the key features of quanta: granularity, quantum indeterminacy and relational aspects of physical variables11.
Quantum mechanics takes its name from the feature of granularity, in which ‘quanta’ are the elementary grains making up the universe. In quantum theory, a minimum scale for all phenomena exists. For time, this is called ‘Planck time’ and is calculated 5.39 × 10-44 s
12. This quantisation has severe consequences for our idea of time. We are forced to confront a time which is granular and discontinuous, progressing in leaps of a minimum interval rather than flowing. Below this minimum interval of time, the notion of time does not even exist.
On this scale, quantum indeterminacy manifests itself. Before measured, an electron passing through a slit towards a screen has no precise position – instead a probabilistic superposition of possible positions. As a physical object, space-time must experience the same effect. This means that the four-dimensional block of space-time should become blurred with the superposition of different space-times, due to its granularity. The distinction between time passed and time ahead and the order in which time is experienced could itself fluctuate on this fundamental level.
An interaction resolves the indeterminacy of a quantity, collapsing the superposed possibilities to a concrete outcome. Yet, the superposition is only resolved in relation to whatever it has interacted with. From the perspective of everything else, there is still simply indeterminacy. The image we are left with, of a fluctuating spacetime materialising discretely at certain times only with respect to particular objects, is a far reach from the concept of time that we started with.
Must the contrast between this image and the time of our experience mean that our time is a complete illusion? It is now obvious that time does not exist in the way that we intuitively think it does, yet the absence of this time does not mean that everything is frozen and unmoving. It does mean that there is no ordering of the world along a strict timeline like Newton’s ‘t’. Instead, we find a network of events where the variables in play obey probabilistic rules. Our ignorance of the complexity of this time is excusable due to our make-up. Our interaction with the world is partial, which is why we see it in a blurred way. Quantum indeterminacy adds to this blurring. What follows from this is increasing entropy in relation to us. This gives us a perceived order which is real but perspectival, with the growth of entropy distinguishing past and future. This is the time of our experience.
Despite our illusion of time, we have enough information to have written equations that successfully describe how variables tend to evolve with respect to each another in the way that we observe them. At our scale, we do not perceive quantum fluctuations, so it is possible to think of spacetime as determined. In daily life on Earth, we move at low speeds in relation to the speed of light and so do not perceive the minute differences between different times of clocks, and differences in the speed at which time passes. The non-relativistic classical mechanics that uses Newton’s common time works well for describing the everyday phenomena of most people’s experience. For some of us this is sufficient, and our illusion is practically acceptable. Yet, our illusion does not allow us to understand the world in its many layers and incomprehensible size. Neither does it satisfy our inherent curiosity. Humans have always been fascinated by the mystery of time and will continue to grapple with it for the rest of time – or, the rest of our illusion of it.
Carlo Rovelli, ‘The Order of Time’
Kurt Gödel, ‘An Example of a New Type of Cosmological Solutions of Einstein’s Field Equations of Gravitation’. Reviews of Modern Physics
Rynasiewicz, Robert, “Newton’s Views on Space, Time, and Motion”, The Stanford Encyclopedia of Philosophy
Coope, Ursula. Time for Aristotle: Physics IV.