We are inescapably confronted with time on a daily basis. It assists us in organizing our lives, for the better or worse, and we have also grown comfortable with dividing our sense of time in three main blocks: a past, a present moment, and a future. Time is so intrinsically entangled with our everyday experiences that we take it for most of the time entirely for granted. But how sure should we be of its existence?

If we were asked to conjure up a definition of time, we would be quick on our feet to invoke clocks or other devices and phenomena that exhibit a steadily repeating motion. While these instruments are designed to measure time, i.e., the enterprise of timekeeping, they do not tell us what time actually is.

Even though we can wrap our head around the idea of a clock as an apparatus engaging in repetitive movements of some kind, it remains a bit puzzling as to on what grounds these recurrent physical changes — whether we think of the periodic energy transitions in atomic clocks, the vibrating quartz crystals in wristwatches, or the oscillations of a pendulum in a grandfather clock — link to the concept of time in the first place.

In fact, if time is so intimately related to clocks, does it still make sense to speak of time existing independently of clocks? If we answer in the negative, does that make time less universal? Do we effectively obliterate time when removing all clocks in the Universe? Did the Universe then not experience time before the existence of the first human-built clock? As the human species invented clocks, does that make time less real? If we argue that time is real, does it objectively exist within the Universe or is it somehow a consequence of the intricate workings of our brain trying to give meaning to the world around us?

By drawing upon insights from the field of physics, this article wishes to probe the following question: To what extent does time exist in its own right?

As the notion of time is closely affiliated with clocks, let us first delve into the definition of a clock. By and large, any device that possesses these three essential characteristics can be considered a clock: it features regular cyclic patterns of equal duration (a constant frequency), it is capable of measuring this periodic activity, and it subsequently reflects it onto an output display. Repetitive processes that can be used to design a clock include vibrations within a quartz crystal, the swings of a pendulum, bouncing springs, radioactive decay, and the recurrence of sunrises.

What counts as a clock according to this description extends — but not exclusively — to a wristwatch, a grandfather clock, a cell phone, a sundial, and an atomic clock. Excluded from this definition are timers, stopwatches, calendars, pendula, and circadian rhythms, i.e., biological and behavioural rhythms with a duration period of approximately 24 hours.

In the example of a quartz watch, a battery rushes electricity through a crystal making it oscillate 32,768 times per second — the cyclic pattern of equal duration. The circuitry of the watch — the measuring part — keeps count of the vibrations, producing one electric pulse every second. Upon receiving this pulse, an internal motor device instructs the watch’s hands to tick — the output display — which allows us to read the time.

The above example implies that the concept of a second must already be defined in order for the quartz watch to function properly — thus, a clock does not tell us what time is but measures it. As a matter of fact, the International System of Units (the SI system) defines the second as “the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the unperturbed ground state of the ¹³³Cs atom.”

To perform such accurate measurements, we need an atomic clock. This state-of-the-art timekeeping device basically consists of an interplay of six lasers cooling down a pack of caesium (Cs) atoms to a temperature of near absolute zero, whereby a microwave-emitting cavity then slightly changes the energy levels of the atoms — the atomic state with the lowest energy level is called the ground state.

When another laser is now directed onto the atoms, they emit light in the microwave region of the electromagnetic spectrum — if the energy difference between two atomic states matches the energy of incoming light, the atom will absorb and re-emit the light — as a consequence of the caesium atoms continually transitioning between two marginally distinct energy levels (called hyperfine levels) within their ground state.

This emitted light is detected and, given that light is made of oscillating electromagnetic waves, the property of light that is then used to define the second is the period, i.e., the time it takes the light wave to travel the distance between two consecutive peaks (or troughs) of the wave, which is called the wavelength. So, the second is defined as the total duration of 9,192,631,770 of these time intervals (periods) associated with the detected light — bear in mind that the above definition of a second is leaning on the concept of time but not explaining what time itself is.

The atomic clock.

Fig. 1. (1) The schematic structure of an atomic clock. (2) In a first instance, two lasers push the ball of caesium atoms upwards through the microwave cavity. (3) The lasers are then switched off and the atoms fall down. (4) When a probe laser is directed onto the descending atoms, those whose energy level was changed by the cavity will emit light, which is subsequently picked up by a detector. (Source: Adapted from NIST).

Experiments are carried out to further upgrade the accuracy of the atomic clock, such as those based on strontium, ytterbium, or aluminum atoms. These so-called optical atomic clocks of the next generation rely on the higher frequencies of optical light — the frequency refers to the number of oscillations or periods per second, expressed as Hertz (Hz) — as opposed to caesium-driven atomic clocks, which fall back on microwave radiation at lower frequencies. For example, an ytterbium atomic clock exhibits a frequency of 518,295,836,590,863.6 Hz, while one running on caesium atoms ticks slower at 9,192,631,770 Hz.

The SI definition of the second forms the bedrock for the organization of societies across our planet. In a first instance, a weighted average is taken of the measurements from around 420 atomic clocks around the world, of which the large majority are caesium-based, and designated the International Atomic Time (TAI). The TAI time is subsequently corrected for variations in the Earth’s rotational speed, resulting in the Coordinated Universal Time (UTC), which is our common time standard and the time indicated at zero degrees longitude.

All the above still leaves us in the dark when it comes to understanding the notion of time. Why do we relate cyclical patterns to time or to the evolution of time? Does time exist outside our wristwatches and clocks? In other words, is time an existing physical quantity, such as mass and temperature, or are we imagining it out of practical or existential purposes?

The next section explores to what extent the field of physics can shed light on the nature of time.

Even though some theoretical physicists regard time as an illusion, such as Paul Wesson, who argues that “time is a subjective ordering device, invented by the human mind to make sense of its perceived world”, most of them acknowledge that time exists. Yet, when trying to find a clear definition of time in the physics literature, we seem to come back empty-handed more often than not.

One point of contention that prohibits the formulation of a consistent definition is the way in which time is treated in two of the most successful theories in physics of the past century, i.e., quantum mechanics and Albert Einstein’s theory of relativity.

In the latter theory, time is not regarded as absolute or universal in at least two ways: According to special relativity, time is relative to an observer since the rate of its flow depends on how fast one is moving through space — from the perspective of a stationary observer, time ticks slower on the clock of someone who is traveling at greater speeds — and as per general relativity, time slows down in the vicinity of very massive objects, such as planets, stars, and black holes, relative to an observer farther away — this is why time is perceived (and has been measured) to run faster at the top of a building compared to the bottom floor and why GPS satellites must take this effect into account to function adequately.

The theory of relativity thus teaches us that time as well as space must be considered dynamical constructs. What is more, they are related concepts — unlike Newtonian mechanics, where time and space exist independently of each other — and the combined entity is called spacetime, i.e., a four-dimensional mathematical object whereby time, along the three dimensions of space, makes up the fourth dimension, geometrically represented by a line in space. General relativity states that large masses and high energies curve spacetime, and it is this curvature that explains the notion of gravity.

In contrast, time in quantum mechanics is not relative or dynamical. This theory describes the behaviour of atomic and subatomic particles, such as quantum entanglement (the instantaneous correlation between quantum objects regardless of the distance between them) and superposition (the ability to exist in two different physical states simultaneously). To study the evolution of such quantum systems, time takes up the role of an a priori fixed parameter, an external variable unaffected by the relative position or velocity of observers, much like the absolute notion of time in classical Newtonian mechanics.

The problem with time manifests itself more distinctly at extremely small distances since quantum mechanics tells us that at these scales the corresponding energies grow large enough for the curvature of spacetime — described by the theory of general relativity — to become significant. This means that, even though we are dwelling in the realms of quantum mechanics where time is considered absolute, time should simultaneously be regarded as relative, in line with the theory of relativity. Which one is it, then?

To better grasp the concept of time, physicists are working towards a draft of the theory of quantum gravity, which aims to consistently marry quantum mechanics with the theory of relativity across all energy scales. In this way, the final theory would, supposedly, be able to explain what happened at the moment of the creation of the Universe and also what is going on inside black holes, two situations where both quantum mechanical effects and gravity hold sway.

One of the consequences of this conundrum about time is that a debate is taking place in the field of physics on the question of whether time really exists on the most fundamental scale of reality or whether time somehow at some point emerges higher up on that scale — this discussion is addressed in more detail further below in the subsection “How Deep Does Time Run Through the Fundaments of Reality?”.

Another reason why it is hard to define time is because physicists do not currently agree on whether time is finite or infinite. This discussion is related to questions asked in the field of cosmology about the origin and fate of our Universe, whose various answers are subject to speculation.

If you assume that the Universe sprang forth from a speck of nothingness — see, for instance, the No-Boundary Proposal developed by Stephen Hawking and James Hartle — then you must be content with the idea that time had a beginning.

Yet, if you subscribe instead to cosmological models that include a multiverse — for example, the Chaotic Eternal Inflation theory — or to cyclic models whereby the Universe continually expands (a Big Bang) and contracts (a Big Crunch) — as suggested by the Cyclic Model devised by Paul Steinhardt and Neil Turok — then you may come to terms with the thought that time knows no beginning nor end.

Having said that, some cosmologists, such as Audrey Mithani and Alexander Vilenkin, disagree with the claim that the Universe extends infinitely into the past under the inflation and cyclic models, for the reason that certain energy conditions are violated.

Moreover, physicist Paul Davies argues that an infinite Universe cannot exist because otherwise we would have already reached a state of thermodynamic equilibrium whereby nothing (including life) happens anymore in the Universe, due to the fact that any differences in temperature are smoothened out — this fatal scenario is the so-called heat death of the Universe.

Cosmological Models of the Universe

Fig. 2. Three cosmological models. (Sources: KITP (No-Boundary proposal), Paper Andrei Linde (Eternal Inflation), and adapted from G. Venkataraman (Cyclic Model)).

As it remains excruciatingly difficult to empirically test such theories, any progress on formulating a definition of time coming from the field of cosmology is most likely to advance at a rather sluggish pace.

Be that as it may, perhaps the closest we can come to a crude definition is saying that time is a quantitative entity of which we can only know and measure its effects or properties through clocks — time under this operational definition is referred to as clock time. This says nothing about what time actually is, and, as such, it might be possible that the nature of time remains indefinitely concealed from us.

This stance could explain why some physicists point to a particular characteristic of time as the smoking gun for its existence. That is, it is the direction in which time flows, the so-called arrow of time, that asserts time is real, because it effectively distinguishes the past from the future — in a more technical jargon, it is said that time is asymmetrical.

In fact, a plethora of different arrows of time have been identified. One of them is believed to be implied by the much-cited second law of thermodynamics, which dictates that a closed system always evolves from a more ordered state (lower entropy) to a less ordered one (higher entropy) — generally, entropy refers to the number of ways in which the microscopic constituents of a macroscopic system can be arranged, whereby each time the state of the macroscopic system is left unaltered.

It is this fixed directedness of the disorder within a closed system that gives rises to the thermodynamic arrow of time. For instance, mixing together two miscible liquids do not spontaneously separate again; gas always dissipates until it is equally dispersed across the volume of the container in which it is held; the ashes of a burnt book do not convert back into the original book; and a crumpled piece of paper does not naturally uncrumple.

A second arrow of time is the cosmological arrow of time, which arises from the fact that there is a direction in which the Universe is evolving: it is expanding. According to the standard model of cosmology, the Universe started out from an infinitesimally small point — called a singularity — and subsequently went through a period of cosmic inflation, during which it expanded at an unimaginably high rate in just a fraction of a second. The Universe has been expanding in size ever since and the current data strongly suggest that its expansion is accelerating.

In step with the second law of thermodynamics, the cosmological arrow of time seems furthermore to indicate that the Universe started out in a state of low entropy, a scenario dubbed the Past Hypothesis and not without its controversies.

Two more arrows of time can be found in waves and radiation. Sound and water waves always originate from a source and move spherically away from it; the waves do not come together and converge into the source — this is referred to as the radiative arrow of time. Regarding electromagnetic waves (radiation), there is a retardation effect since they travel at a fixed speed, i.e., the speed of light, so that the world that we see through the light hitting our eyes or measurement instruments always reflects a view onto the past — this is called the electromagnetic arrow of time.

Then there is the singularity arrow of time whereby one initial singularity, which according to general relativity corresponds to the birth of our Universe, precedes many so-called final singularities at the centre of black holes. Due to the deterministic characteristic of general relativity, no new initial singularities can crop up — if they do, however, they should be hidden behind the event horizon of black holes, as per Hawking’s cosmic censorship principle — otherwise the Universe would no longer be described by the theory.

A final arrow of time that we will discuss here is the quantum arrow of time, which is part of an ongoing debate, as a recent paper by James Hartle demonstrates. According to the textbook interpretation of quantum mechanics called the Copenhagen interpretation, the act of performing a measurement on a quantum system collapses the wave function — this function is a mathematical expression that contains information about the state of a particular quantum system. As a result, the system irreversibly evolves from a superposition of quantum states towards a final, single measured state, whereby no information about the superposed quantum states can be retrieved from the final collapsed state.

Nonetheless, the arrow of time within the field of physics remains controversial. One of the major issues can be traced to the fact that the fundamental laws of physics do not reflect this time asymmetry. That is to say, they are reversible in time and do not distinguish between the past, the present, and the future.

As a case in point, all the events across spacetime in relativity theory share an equal status — this is known as the Block Universe idea — meaning that an event in the present moment is no less special than some event that occurred twenty years ago or some other event that will take place in the next century. This means that, although events occur at certain points along the time dimension, the spacetime block itself is not evolving in time. In other words, if there is no physical distinction between the past, the presence, and the future, the Universe represented by spacetime can be described as static since it lacks any direction of time.

For example, in a simplified Newtonian system consisting of the Sun and the Earth, the elliptical orbit of the Earth around the Sun under the force of gravity in the forward direction of time would be exactly the same if we let the time parameter of the equations run backwards. So, how then do we explain the existence of an arrow of time?

Keep in mind, however, that although the weak interactions, which are one of the four fundamental forces in nature and responsible for decay processes of subatomic particles, do violate time-reversal symmetries, they have no bearing on the macrophysics of our everyday life and can therefore not serve as an explanatory, physical basis for our perceived arrow of time.

The absence of time asymmetry in the natural laws of physics, despite our perceived flow of time in the macroscopic world from the past towards the future, further obfuscates the concept of time, rendering the drawing up of a clear definition an even more confounding task. This leads many physicists to the conclusion that the flow of time — not time itself — is an illusion.

Yet not all physicists agree with this view, including George Ellis and Joan Vaccaro, who incorporate an arrow of time within the Block Universe by taking into account time-irreversible macro-physical behaviour and emergent complex systems and by relying on time-symmetry violations of the weak interactions, respectively. The model developed by Ellis is referred to as the Evolving Block Universe, which is a block universe that is no longer static but is able to expand in the future direction.

The Block Universe versus the Evolving Block Universe

Fig. 3. In the Block Universe (left), everything is static, whereas in the Evolving Block Universe (right), the future boundary keeps moving upwards along the time dimension, effectively making the Block Universe expand in size. (Source: Adapted from George Ellis).

Another solution to this enigma at the heart of physics is the contemplation of the existence of a multiverse, whereby our Universe along with countless others arose from a vast empty space. In this way, the notion of time symmetry and the arrow of time are no longer mutually exclusive since time is able to run forward in some universes — like ours — and backwards in others while the multiverse as a whole remains time symmetric, given that all the arrows of time would statistically cancel out.

It seems as if we are only collecting more questions about the concept of time instead of solidifying a definition. As a matter of fact, one can ask at this point the following questions: Does the arrow of time truly suggest the existence of time or only imply a particular order in which certain events occur and which may or may not be underpinned by causation? If the flow of time is not about time, does that allow us to assert that time is an illusion? Furthermore, how certain can we be that the arrow of time that we allegedly perceive is part of the fundamental structure of reality?

These questions about the nature of time lie at the heart of another debate in physics in which it is generally assumed that time itself is real, but physicists disagree on whether time is fundamental or emergent.

Examples of emergent phenomena include the hardness and temperature of an object. At the microscopic (fundamental) level, the atoms and molecules are neither solid (or soft) nor hot (or cold), but when zooming out, it appears that at a certain scale the properties of hardness and temperature manifest themselves by emerging from the collectiveness of the individual components.

In the same vein, physicists who subscribe to the idea of emergence of time proclaim that the notion of time is not present at the deep roots of reality but arises only at a higher level of description, out of the interactions among some more fundamental entities.

In the context of quantum gravity, Daniele Oriti, for one, makes the case that time is emergent, as it progressively disappears when zeroing in on the more fundamental levels of reality. Stated in the words of Claus Kiefer: “the world is fundamentally timeless”. With respect to one specific theory of quantum gravity, i.e., loop quantum gravity, Suddhasattwa Brahma presents a similar argument.

In fact, such views about the emergence of time are gaining an overall stronger foothold in the research field of quantum gravity. As Sean Carroll points out: “If the quantum state of the universe obeys the Wheeler-DeWitt equation (which is plausible, but far from certain), time has to be emergent rather than fundamental” — the Wheeler-DeWitt equation brings together quantum mechanics and general relativity and lacks any reference to the notion of time.

Enrico Prati also envisages a timeless foundation of nature and presents a framework that connects such fundamental physics devoid of time to the macroscopic measurement of time. To further bolster the idea of emergence, Ekaterina Moreva et al. take a practical approach and show experimentally how light can be used to demonstrate how time emerges from quantum entanglement — for a more theoretical discussion on this topic, see for instance the paper by Tommasso Favalli and Augusto Smerzi.

At the other, more controversial end of the debate, we find physicists arguing that time is intimately woven into the deepest layers of the fabric of reality. One such voice is Lee Smolin who proposes that the existence of time at the most basic description of the natural world helps to explain why there is structure and complexity in the Universe, why the future is not entirely predictable, and why natural laws evolve.

What is more, Matej Pavšič devised a new theoretical approach to quantum gravity in which the fundamental Wheeler-DeWitt equation now contains a time parameter, doing away with the need to let time emerge from the timeless foundations of physics. Albeit through a different route, i.e., by relying on Bohmian quantum mechanics instead of orthodox quantum mechanics, Nelson Pinto-Neto and Ward Struyve also manage to introduce the evolution of time at the heart of quantum gravity.

Another theoretical framework that retains the flow of time at its fundamental description of nature is causal set theory, one of the candidates for a final theory of quantum gravity. This theory stipulates that spacetime is discrete whereby its basic building blocks are mathematical elements interpreted as events and placed in a certain partially ordered set. New events continuously pop up into existence, and it is the particular sequence in which adjacent elements are arranged that creates the notion of time.

As we have pointed out in the previous subsection, claiming that time is emergent does not per se imply the statement that time is not real. However, some physicists do indeed go as far as eliminating time completely from their description of nature.

Julian Barbour is among one of them. Based on his views, space is the more fundamental entity — more accurately, it is the concept of shape that takes a central role in his theory — and the illusory idea of time emerges from the changes that we observe all around us.

Another physicist is Carlo Rovelli, who argues that neither the perceived flow of time nor the concept of space has a place at the deepest level of physical reality. According to Rovelli, the most fundamental thing is a causal web of interactions among events written in the language of quantum mechanics and thermodynamics, from which everything else emerges.

These intricate dynamical connections equally produce our perception of a temporal order, but at the end of the day, the notion of time for Rovelli is more of an apparent construct conjured up by the combination of neural activity and human emotions than a physical entity in its own right grounded in the fundamentals of reality.

If Rovelli is right and time is personal to each and one of us, does that conclusively eliminate the possibility of an external, objective concept of time? Perhaps not, as we could, for instance, interpret subjective, psychological time as objective time being registered by our mind and physical time as objective time being measured by clocks.

Finding a universal definition of time, if any, may well require collaboration with other fields of science, such as biology, neuroscience, psychology, and philosophy, as cross-disciplinary research could potentially lead to inspiring insights with regard to our quest for a greater understanding of time.

Whether time turns out to be a mere illusion or an undeniable physical fact of our Universe, only time will tell.

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