The Arrow of Time

The arrow of time refers to the way we always see things progressing in a particular direction, e.g. eggs may break, but they never spontaneously reform
The arrow of time refers to the way we always see things progressing in a particular direction, e.g. eggs may break, but they never spontaneously reform

Time appears to have a direction, to be inherently directional: the past lies behind us and is fixed and immutable, and accessible by memory or written documentation; the future, on the other hand, lies ahead and is not necessarily fixed, and, although we can perhaps predict it to some extent, we have no firm evidence or proof of it. Most of the events we experience are irreversible: for example, it is easy for us to break an egg, and hard, if not impossible, to unbreak an already broken egg. It appears inconceivable to us that that this progression could go in any other direction. This one-way direction or asymmetry of time is often referred to as the arrow of time, and it is what gives us an impression of time passing, of our progressing through different moments. The arrow of time, then, is the uniform and unique direction associated with the apparent inevitable “flow of time” into the future.

The idea of an arrow of time was first explored and developed to any degree by the British astronomer and physicist Sir Arthur Eddington back in 1927, and the origin of the phrase is usually attributed to him. What interested Eddington is that exactly the same arrow of time would apply to an alien race on the other side of the universe as applies to us. It is therefore nothing to do with our biology or psychology, but with the way the universe is. The arrow of time is not the same thing as time itself, but a feature of the universe and its contents and the way it has evolved.

Is the Arrow of Time an Illusion?

As we have seen in the section on Relativistic Time, according to the Theory of Relativity, the reality of the universe can be described by four-dimensional space-time, so that time does not actually “flow”, it just “is”. The perception of an arrow of time that we have in our everyday life therefore appears to be nothing more than an illusion of consciousness in this model of the universe, an emergent quality that we happen to experience due to our particular kind of existence at this particular point in the evolution of the universe.

Perhaps even more interesting and puzzling is the fact that, although events and processes at the macroscopic level – the behaviour of bulk materials that we experience in everyday life – are quite clearly time-asymmetric (i.e. natural processes DO have a natural temporal order, and there is an obvious forward direction of time), physical processes and laws at the microscopic level, whether classical, relativistic or quantum, are either entirely or mostly time-symmetric. If a physical process is physically possible, then generally speaking so is the same process run backwards, so that, if you were to hypothetically watch a movie of a physical process, you would not be able to tell if it is being played forwards or backwards, as both would be equally plausible.

In theory, therefore, most of the laws of physics do not necessarily specify an arrow of time. There is, however, an important exception: the Second Law of Thermodynamics.

Thermodynamic Arrow of Time

Most of the observed temporal asymmetry at the macroscopic level – the reason we see time as having a forward direction – ultimately comes down to thermodynamics, the science of heat and its relation with mechanical energy or work, and more specifically to the Second Law of Thermodynamics. This law states that, as one goes forward in time, the net entropy (degree of disorder) of any isolated or closed system will always increase (or at least stay the same).

The concept of entropy and the decay of ordered systems was explored and clarified by the German physicist Ludwig Boltzmann in the 1870s, building on earlier ideas of Rudolf Clausius, but it remains a difficult and often misunderstood idea. Entropy can be thought of, in most cases, as meaning that things (matter, energy, etc) have a tendency to disperse. Thus, a hot object always dissipates heat to the atmosphere and cools down, and not vice versa; coffee and milk mix together, but do not then separate; a house left unattended will eventually crumble away, but a pile of bricks never spontaneously forms itself into a house; etc. However, as discussed below, it is not quite as simple as that, and a better way of thinking of it may be as a tendency towards randomness.

It should be noted that, in thermodynamic systems that are NOT closed, it is quite possible that entropy can decrease with time (e.g. the formation of certain crystals; many living systems, which may reduce local entropy at the expense of the surrounding environment, resulting in a net overall increase in entropy; the formation of isolated pockets of gas and dust into stars and planets, even though the entropy of the universe as a whole continues to increase; etc). Any localized or temporary instances of order within the universe are therefore in the nature of epiphenomena within the overall picture of a universe progressing inexorably towards disorder.

It is also perhaps counter-intuitive, but nevertheless true, that overall entropy actually increases even as large-scale structure forms in the universe (e.g. galaxies, clusters, filaments, etc), and that dense and compact black holes have incredibly high entropy, and actually account for the overwhelming majority of the entropy in today’s universe. Likewise, the relatively smooth configuration of the very early universe (see the section on Time and the Big Bang) is actually an indication of very low overall entropy (i.e. high entropy does not necessarily imply smoothness: random “lumpiness”, like in our current universe, is actually a characteristic of high entropy).

Most of the processes that appear to us to be irreversible in time are those that start out, for whatever reason, in some very special, highly-ordered state. For example, a new deck of cards are in number order, but as soon as we shuffle them they become disordered; an egg is a much more ordered state than a broken or scrambled egg; etc. There is nothing in the laws of physics that prevents the act of shuffling a deck of cards from producing a perfectly ordered set of cards – there is always a chance of that, it is just a vanishingly small chance. To give another example, there are many more possible disordered arrangements of a jigsaw than the one ordered arrangement that makes a complete picture. So, the apparent asymmetry of time is really just an asymmetry of chance – things evolve from order to disorder not because the reverse is impossible, but because it is highly unlikely. The Second Law of Thermodynamics is therefore more a statistical principle than a fundamental law (this was Boltzmann’s great insight). But the upshot is that, provided the initial condition of a system is one of relatively high order, then the tendency will almost always be towards disorder.

Thermodynamics, then, appears to be one of the only physical processes that is NOT time-symmetric, and so fundamental and ubiquitous is it in our universe that it may be single-handedly responsible for our perception of time as having a direction. Indeed, several of the other arrows of time noted below (arguably) ultimately come back to the asymmetry of thermodynamics. Indeed, so clear is this law that the measurement of entropy has been put forward a way of distinguishing the past from the future, and the thermodynamic arrow of time has even been put forward as the reason we can remember the past but not the future, due to the fact that the entropy or disorder was lower in the past than in the future.

Cosmological Arrow of Time

It has been argued that the arrow of time points in the direction of the universe’s expansion, as the universe continues to grow bigger and bigger since its beginning in the Big Bang (see the section on Time and the Big Bang). It became apparent towards the beginning of the 20th Century, thanks to the work of Edwin Hubble and others, that space is indeed expanding, and the galaxies are moving ever further apart. Logically, therefore, at a much earlier time, the universe was much smaller, and ultimately concentrated in a single point or singularity, which we call the Big Bang. Thus, the universe does seem to have some intrinsic (outward) directionality. In our everyday lives, however, we are not physically conscious of this movement, and it is difficult to see how we can perceive the expansion of the universe as an arrow of time.

The cosmological arrow of time may be linked to, or even dependent on, the thermodynamic arrow, given that, as the universe continues to expand and heads towards an ultimate “Heat Death” or “Big Chill”, it is also heading in a direction of increasing entropy, ultimately arriving at a position of maximum entropy, where the amount of usable energy becomes negligible or even zero. This accords with the Second Law of Thermodynamics in that the overall direction is from the current semi-ordered state, marked by outcroppings of order and structure, towards a completely disordered state of thermal equilibrium. What remains a major unknown in modern physics, though, is exactly why the universe had a very low entropy at its origin, the Big Bang.

It is also possible – although less likely according to the predictions of current physics – that the present expansion phase of the universe could eventually slow, stop, and then reverse itself under gravity. The universe would then contract back to a mirror image of the Big Bang known as  the “Big Crunch” (and possibly a subsequent “Big Bounce” in one of a series of cyclic repetitions). As the universe contracts and collapses, entropy will in theory start to reduce and, presumably, the arrow of time will reverse itself and time will effectively begin to run backwards. In this scenario, then, the arrow of time that we experience is merely a function of our current place in the evolution of the universe and, at some other time, it could conceivably change its direction. However, there are paradoxes associated with this view because, looked at from a suitably distant and long-term viewpoint, time will continue to progress “forwards” (in some respects at least), even if the universe happens to be in a contraction phase rather than an expansion phase. So, the cosmic asymmetry of time could still continue, even in a “closed” universe of this kind.

Radiative Arrow of Time

Radiating Waves
Waves always radiate away from a source

Waves, like light, radio waves, sound waves, water waves, etc, are always radiative and expand outwards from their sources. While theoretical equations do allow for the opposite (covergent) waves, this is apparently never seen in nature. This asymmetry is regarded by some as a reason for the asymmetry of time.

It is possible that the radiative arrow may also be linked to the thermodynamic arrow, because radiation suggests increased entropy while convergence suggests increased order. This becomes particularly clear when we consider radiation as having a particle aspect (i.e. as consisting of photons) as quantum mechanics suggests.

Quantum Arrow of Time

The whole mechanism of quantum mechanics (or at least the conventional Copenhagen interpretation of it) is based on Schrödinger’s Equation and the collapse of wave functions (see the section on Quantum Time), and this appears to be a time-asymmetric phenomenon. For example, the location of a particle is described by a wave function, which essentially gives various probabilities that the particle is in many different possible positions (or superpositions), and the wave function only collapses when the particle is actually observed. At that point, the particle can finally be said to be in one particular position, and all the information from the wave function is then lost and cannot be recreated. In this respect, the process is time-irreversible, and an arrow of time is created.

Some physicists, including the team of Aharonov, Bergmann and Lebowitz in the 1960s, have questioned this finding, though. Their experiments concluded that we only get time-asymmetric answers in quantum mechanics when we ask time-asymmetric questions, and that questions and experiments can be framed in such a way that the results are time-symmetric. Thus, quantum mechanics does not impose time asymmetry on the world; rather, the world imposes time asymmetry on quantum mechanics.

It is not clear how the quantum arrow of time, if indeed it exists at all, is related to the other arrows, but it is possible that it is linked to the thermodynamic arrow, in that nature shows a bias for collapsing wave functions into higher entropy states versus lower ones.

Weak Nuclear Force Arrow of Time

Of the four fundamental forces in physics (gravity, electromagnetism, the strong nuclear force and the weak nuclear force), the weak nuclear force is the only one that does not always manifest complete time symmetry. To some limited extent, therefore, there is a weak force arrow of time, and this is the only arrow of time which appears to be completely unrelated to the thermodynamic arrow.

The weak nuclear force is a very weak interaction in the nucleus of an atom, and is responsible for, among other things, radioactive beta decay and the production of neutrinos. It is perhaps the least understood and strangest of the fundamental forces. In some situations the weak force is time-reversible, e.g. a proton and an electron can smash together to produce a neutron and a neutrino, and a neutron and a neutrino smashed together CAN also produce a proton and an electron (even if the chances of this happening in practice are very small). However, there are examples of the weak interaction that are time-irreversible, for example the case of the oscillation and decay of neutral kaon and anti-kaon particles. Under certain conditions, it has been shown experimentally that kaons and anti-kaons actually decay at different rates, indicating that the weak force is not in fact time-reversible, thereby establishing a kind of arrow of time.

It should be noted, though, that this is not such a strong or fundamental arrow of time as the thermodynamic arrow (the difference is between a process that could go either way but in a slightly different way or at a different rate, and a truly irreversible process – like entropy – that just cannot possibly go both ways). Indeed, it is such a rare occurrence, so small and barely perceivable in its effect, and so divorced from any of the other arrows, that it is usually characterized as an inexplicable anomaly.

Causal Arrow of Time

Although not directly related to physics, causality appears to be intimately bound up with time’s arrow. By definition, a cause precedes its effect. Although it is surprisingly difficulty to satisfactorily define cause and effect, the concept is readily apparent in the events of our everyday lives. If we drop a wineglass on a hard floor, it will subsequently shatter, whereas shattered glass on the floor is very unlikely to subsequently result in an unbroken held wine glass. By causing something to happen, we are to some extent controlling the future, whereas whatever might do we cannot change or control the past.

Once again, though, the underlying principle may well come back to the thermodynamic arrow: while disordered shattered glass can easily be made out of a well-ordered wineglass, the reverse is much more difficult and unlikely.

Psychological Arrow of Time

A variant of the causal arrow is sometimes referred to as the psychological or perceptual arrow of time. We appear to have an innate sense that our perception runs from the known past to the unknown future. We anticipate the unknown, and automatically move forward towards it, and, while we are able to remember the past, we do not normally waste time in trying to change the already known and fixed past.

Stephen Hawking has argued that even the psychological arrow of time is ultimately dependent on the thermodynamic arrow, and that we can only remember past things because they form a relatively small set compared to the potentially infinite number of possible disordered future sets.

Anthropic Principle

Some thinkers, including Stephen Hawking again, have pinned the direction of the arrow of time on what is sometimes called the weak anthropic principle, the idea that the laws of physics are as they are solely because those are the laws that allow the development of sentient, questioning beings like ourselves. It is not that the universe is in some way “designed” to allow human beings, merely that we only find ourselves in such a universe because it is as it is, even though the universe could easily have developed in a quite different way with quite different laws.

Thus, Hawking argues, a strong thermodynamic arrow of time is a necessary condition for intelligent life as we know it to develop. For example, beings like us need to consume food (a relatively ordered form of energy) and convert it into heat (a relatively disordered form of energy), for which a thermodynamic arrow like the one we see around us is necessary. If the universe were any other way, we would not be here to observe it.

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