Physical time

What is physical time?

The most intellectually challenging and potentially rewarding aspect of time^[1] has been the race between physicists to provide a satisfactory account of the physical reality of ‘physical time’.

The idealist philosophers focused their attention on what we now recognize as subjective aspects of time: our sense of its dynamic flow, even the changing speed of its passage according to our mood; our perception of the properties of past, present and future; our understanding of ‘now’; and our specifically human perspective on space and time in general. Not surprisingly many philosophers have concluded that time, when considered on these terms, is a product of the mind.

One of the most discussed idealist philosophers of the early twentieth century was Cambridge University’s McTaggart who wrote the philosophically highly influential paper ‘The Unreality of Time‘ in 1908. This was written at the same time that Einstein was working on his theories of relativity. Einstein’s work would produce a sea-change in attitude towards time as he demonstrated conclusively that although there may be subjective aspects to time, it was also part of the very physical fabric of the universe – it undoubtedly existed in reality ‘out there’. The precision of modern science can today be demonstrated by the elevation of one atomic clock 50 cm above another, relative to the surface of the earth, is sufficient for them to tell (predictable) different times.

The articles Time – Flow and Time – Now dealt with the psycho-biology of time, articles Time – Change and Time – Duration were concerned mainly with the philosophical logic of time. This article examines our evolving understanding of physical time in the discipline of physics.

When we say that one minute has passed, we know, roughly, what the passage of the interval of time we call a minute feels like. We regard this as an estimate because, as we have seen, psychological time is not precise. For a precise answer we use a watch which measures one minute exactly. In contrast to various subjective aspects of time, measured physical or public time, the time on clocks and watches, is accepted by everyone without question. We might ponder the ultimate nature of time but our behaviour in response to durations measured by clocks leaves no doubt that togther we acknowledge it as real. Time is part of the objective world investigated by science and is the most precisely measured physical parameter. Measurements of time in physics are critical to many of our basic physical concepts – rate, space-time, current, velocity, power, force and acceleration are all defined using with time as a critical parameter.

But what exactly is it that our watches are measuring? There is of course the movement of the hands on the clock, but isn’t there also the interval or duration between the hands being first at position 1 and then at position 2, whatever that duration is … ? Would time exist if there were no material objects in the universe? Does physical time exist independently of objects like clocks and revolving celestial bodies like the orbiting planets, or is it defined by them and their relations?

An examination of three influential views about time, referred to as Absolute, Relational and Relative time, will introduce historical arguments betwen physicists about the nature of time before we look more closely at the elements of physical time today.

Three theories of physical time

Absolute (realist) time

Most people feel intuitively that time is not a part of the physical universe but transcends it in some way – that it is independent of objects and events and exists in its own right (that it is absolute). It is as though time (and space) ‘contain’ events. So, if all activity in the universe were to cease completely, then we imagine that events would be frozen but time itself would march on regardless. If objects and events were removed from the universe then something would remain, and we could call what remained space and time.

The most comprehensive view of time in physics after the ancient Greeks was that of Isaac Newton (1642-1726) who maintained that time was absolute in the way just described.

A characteristic of absolute time is that it is eternal. It would not seem to make sense to ask when absolute time began or when it will end because we cannot imagine such a time. If we are told that time had a beginning then we inevitably ask ‘What was happening before that beginning?‘ Time, we feel, must always have been present everywhere.

The classical Newtonian view, therefore, was that absolute time was eternal, with an existence of its own independent of people, space, the universe and its events. It was treated as a kind of substance, container or substrate for events, so events happen in time. Sound waves require something, say, the atmosphere or water to push against: they cannot be propagated in a vacuum. Newton believed that space had a similar kind of atmosphere, which was called the ether, which was the substrate that light could push against.

For Newton, the passage of absolute time was the same for all people and objects in the universe (even though perception of it might vary). As a consequence, all observers with identical measuring devices would be in agreement about the sequence and timing of particular events.

Newton’s exact words were:

‘Absolute, true, and mathematical time, in and of itself, and from its own nature flows uniformly [equably] without reference to anything external. By another name it is called duration. Relative, apparent and common time is any sensible external measure of duration by means of motion. Such measures (for example, an hour, a day, a month, a year) are commonly used instead of true time.’

Our language reinforces the view of time as independent ‘stuff’. We speak of the ‘flow’ of time and an ‘instant’ or ‘moment’ of time and of events occurring in time, as though time is an object separate from events.

We can summarize Newtonian Absolute Time as follows:

• The duration of an event is independent of observers (frames of reference)
• Simultaneity of events is independent of frames of reference
• Duration is the same regardless of motion and gravity
• The metric of time is intrinsic to the temporal interval. That is, the units of time are the same everywhere (it flows “equably”)
• Time is a substrate or medium in which physical events occur (it is independent from other items in the universe)
• Time is infinite as it is totally independent of an existent or non-existent physical universe

It should be noted that in his statement Newton distinguished two kinds of time – Absolute (true and mathematical), and Relative (apparent and common) or, as we should now say, relational time. Absolute time was, presumably, metaphysical because relational time, he said, was founded on sense perceptions.

It is often implied that his absolute time was an empirical aberration with more to do with his theism that his science – but this is not necessarily so (see later).

Relational (reductionist) time

Liebnitz (1646-1716) was a mathematician, philosopher and contemporary of Newton’s who did not share Newton’s views on Absolute Time. The two crossed paths on several issues. It is still uncertain, for example, whether we should thank Newton or Liebniz for the calculus.

For Liebnitz time did not have an existence of its own but was defined by events within the universe. This contrasted strongly with Newton’s idea of time as ultimately something unchanging (in the sense that it is transcendent, even though for Newtin it ‘flowed’). In other words Liebnitz believed that at its most basic, time could be reduced to change.

Liebnitz’s view was similar to that of many ancient philosophers who equated time with change. Plato (427-327 B.C.) maintained that time did not exist in its own right but was a characteristic or property of the universe. Aristotle (384-322 B.C.) considered time and events mutually dependent. We measure ‘movement by time and time by movement‘ he had stated, ‘so they define one-another, time being like a sequential numbering process with a ‘before’ or past and ‘after’ or future‘.

For Liebnitz time was simply the fact that we experience ideas and events one after another – in succession. In Liebnitz’ words, time was ‘the order of succession of phenomena’ or ‘the successive order of things’ – the overall ordering of non-simultaneous events. This has undergone revision and restatement until nowadays relationalism is taken to mean that, essentially, there is nothing to space and time over and above spatial and temporal relationships. All talk about temporal items such as moments and instants can be reduced to talk about events and their relationships. Change and motion exist but time does not: the concept of time exists in order to make sense of change. The physical or metaphysical referents for time concepts are either incoherent, unverifiable or superfluous. We should not talk and think of time and space but of times and places.

We define and understand time through events. We measure time because it is related to something that is happening. To obtain useful regular intervals we use regular motions (isochronous intervals) – the hands on a clock have moved, a pendulum has swung, or the Earth has rotated on its axis: it is relational. Similarly spatial relationalism argues that the intervals between objects fully describe their position without reference to any underlying non-material absolute space. Relations, like properties, are not something in addition to what has them, but an aspect of the thing that has them.

Time is no longer like a separate substance or container, an image that can be regarded as the source of much confusion. Events do not occur in time but time is, as it were, “created” by a sequence of events. Thus simultaneous events do not occur at the same moment in time (Absolute Time view) but simply occur together (Relational Time view). And events are sequential, not because they occur in different instants of time, but because they occur in a definite order. For Relational Time it is simpler and more realistic to say that events happen one minute apart, than to say that they are separated in time by one minute.

On the Relationist view Absolute Time becomes, at best, an unnecessary hypothesis. The question of infinite time would depend on whether ‘events’ had a beginning and whether they will have an end. Without a physical universe there could be no Relational Time. The prevailing current view would be that time began with the Big Bang but will continue indefinitely as we do not envisage a complete end to the universe.

In spite of their differences, Liebnitz would have agreed with Newton that identical measuring devices would give the same readings of the sequence and timing of particular events in the universe.

Relational Time has great appeal because it removes the transcendental, mysterious component of Absolute time and equates time with tangible events in the physical universe. If time is no more than a sequence of events then Absolute time becomes a simple misunderstanding – it has no independent existence of its own and its mystery dissolves. It also allows us to clear away some muddy language.

Relational time is thus a simple and practical solution to questions about time. It has appeal to science because it removes an unnecessary metaphysical object; it is Occam’s razor in action.

It may be claimed that succession (or change) creates the idea of time in our minds. Liebnitz, however, maintained that the succession of events in the world was time.

Objections
• Relativism does not appear to deal effectively with the durational aspect of time – the important interval between events is not explained satisfactorily. Time has ‘betweenness’; everything does not happen at once. It is not possible to conceive of succession without duration. And it seems impossible to think of duration without succession (at least in our minds).

In summary, Relational Time is a function of the universe, being a sequence of events or relations between things, rather than having an independent existence of its own. Time is not like a vast invisible container in which things happen (Absolute Time) but a relationship between events. No events: no time. (Relational time).

For Newton the universe had a clock, the movement of the planets. For Liebnitz the universe was a clock. Leibniz, like Newton, presumed that the “rate of passage” of time was the same throughout the universe so that the sequence, timing and simultaneity of events would be the same for any observer. Newton and Liebnitz agreed on many aspects of time, differing only on the critical nature of its existence. This was a very important difference though. With a relational view of space and time questions such as “Where in space did the universe emerge?” or “Was time ticking away before the Big Bang?” are no longer necessary.

We can summarize Liebniz’s Relational theory of time as follows:

• The duration of an event is independent of observers (frames of reference)
• Simultaneity of events is independent of observers
• Duration is the same regardless of motion and gravity
• The metric of time is intrinsic to the temporal interval. That is, the units of time are the same everywhere (it flows “equably”)
• Time is not a substrate or medium in which physical events occur but it coexists with (is relational to) things in the universe
• Whether time is infinite or not depends on the existence or non-existence of events (a physical universe)

Relative time

Although the competing Relational and Absolute views of time presented conflicting outlooks on the true nature of time, they agreed on the sequence in which events occurred and the association of particular times with particular events.

Einstein (1879-1987) radically changed our understanding of time measurement. The Theory of Relativity was a total re-examination and replacement of the Newtonian physical laws of motion. Basic to this theory of motion was the realization that there is no object in the universe that can serve as a stationary reference point acting as a standard for measurement. All measurements of motion are made relative to other objects – hence the theory of relativity.

According to Relativity, time is an aspect of the universe (in agreement with the relational view of time) but it is possible for measurements of time to differ between observers. We now have the introduction of an observer into our understanding of time – because it is the observer that gives us our frame of reference for measurement. This marked a major change in thinking.

Space-time (time at a distance)
Newton regarded space and time as independent entities and assumed that time would be the same for every person and object in the universe. For Einstein all events in the universe were defined in four dimensions (three of space and one of time). This is not counter to common sense because we generally define an event by when and where it took place. Since space and time are measured together (distances in space being defined in terms of time and the speed of light as light-years) scientists now speak of space-time, or the space-time continuum (which describes the geometry of the universe – sometimes called the 4-D manifold, which is mathematician Riemann’s term for space). A point in space is also a point in time, called a world-point. Matter then traces out world-lines. If world lines intersect then objects have collided. A point in space is an event in space-time. It is important to note that under this theory time and space are interwoven physically, not just metaphorically: space shrinks as time expands.

No matter how strongly our common sense tells us time and space are separate, the objective world of physics recognizes only a 4-dimensional continuum that is neither time nor space. Different observers may not agree on particular measurements of space and time but they can agree on suitable combinations of the two.

It is not possible to take equal-moment slices through space-time in an absolute and universal way. Each individual will have a different slicing (see Block Universe). We might note in passing that space, time and space-time do not have an intrinsic metric. That is, the units we use for space and time are purely of convenience and convention. We should therefore beware of equating geometry and chronology.

Light is at the very core of the theory of Relativity because it is the signal used to measure space and time across the universe.

Two important properties of light are critical for Relativity. Firstly, its speed is finite and calculable. Secondly, it is absolute (the same regardless of the relative velocity of any observer).

Historically, it would seem that as light emerged as a physical absolute, time became relative and Einstein convincingly wove time into the very fabric of the universe.

Philosophically it in important to note that what is independently real is what does not vary from one reference frame to another and that can only be achieved through space-time. Space-time interval measurements between events provide the scientifically invariant fact independent of one’s own state of motion.

The speed of light

The speed of light was first determined in 1675 by the Danish astronomer A. Roemer from observations he made of the eclipses of the moons of Jupiter. The discovery that the speed of light was finite (not instantaneous or infinite as Newton believed) was of profound importance because we use light to take many measurements, notably those of outer space.

In 1887 Americans Albert Michelson and Edward Morley carried out experiments comparing the speed of light while varying the speeds of the points of observation. To their surprise it was found that the speed of light was always the same, being constant at 300,000 km/s. Contrary to intuition, the speed of light is not relative to the speeds of observer and source but is the same for all observers whatever their relative motion. As a result of these experiments the speed of light is now recognized as a universal constant – a physical absolute.

This discovery also had other far-reaching and counter-intuitive implications that emerged when Einstein showed in his Theory of Relativity that, relative to an observer, objects nearing the speed of light approach infinite mass, their length shrinks towards zero, and time expands towards infinity. It should be noted, however, that the effects (time dilation, size diminution, and mass increase) only become noticeable at speeds approaching the speed of light; for everyday situations the mathematics of Newton’s laws of motion are perfectly adequate.

Since we observe events through the medium of light and light has a finite speed it is immediately evident that we do not observe events instantaneously. Someone close to an event will see that event before someone who is further away. The light from the Moon takes a half second to reach Earth, and from the Sun it takes 8.3 minutes. The time scale of a particular observer is generally referred to as proper time, defined as the time that would be given by a clock at rest with respect to a particular observer. This is often compared with coordinate time which is the time which an observer assigns to a distant event, knowing its distance away, the speed of the signal (usually light), and the proper time at which it was observed.

Wave structure of light

Paradoxically light displays the characters of both particles and waves.

Although the speed of light is constant regardless of the motion of the observer, its wave structure varies according to the relative velocities of the observer and object.

Wave frequencies increase with increase in the speed at which objects approach each other, and decrease with decreasing relative speeds. A longer wavelength produces a reddening or red shift, and a shortening wavelength produces a bluing or blue shift of light. This is the Doppler Effect – where the number of wave crests per second arriving from a receding source is fewer than those actually emitted from the source (this also occurs with sound waves, which lower in pitch as an object moves away). Only particles with zero mass at rest can travel at the speed of light and the photon can only travel at the speed of light. As the energy of a photon decreases, its wavelength increases. For example, light loses energy in a gravitational field producing a red shift.

A colour shift is a natural clock, being the interval between successive crests of a light wave. In 1929 the American astronomer Hubble observed a red shift in the universe that indicated clearly that it was undergoing rapid expansion in all directions. The background galaxies of the universe are receding from one-another at a rate that is proportional to their distances from one-another as measured by the red shift and the most distant galaxies appear to be moving away from us at close to the speed of light.

This was compelling evidence for the origin of the universe in a Big Bang.

The Special Theory of Relativity

Einstein’s Special Theory of Relativity (STR) of 1905 dealt with unaccelerated frames – those under uniform motion – referred to as an inertial frame of reference.

As we have seen, the time interval measured in a reference frame in which a clock is at rest is called the proper time. Einstein showed mathematically that if two observers are moving at constant velocity relative to each other, it appears to each that the time on the other’s clock would be slowed down, a phenomenon known as time dilation. This is so because there is no preferred frame of reference. The first direct test of time dilation occurred in 1941, 36 years after Einstein’s theory, and it confirmed his theory. Though Relativity runs counter to common sense its conclusions are now backed up by abundant experimental evidence.
[M – But what produces this effect? Is it actual or apparent due to the fact that light takes time to travel distances? Because of the peculiar behaviour of light waves and also because light has a finite speed and therefore takes time to travel large distances.]

One obvious outcome of the STR is that there is a multiplicity of time frames in the universe associated with different observers.

It is important to remember that the STR deals with uniform motion.

Imagine that an astronaut, A, left Earth travelling close to the speed of light, returning in several years to meet his twin, B, who remained on Earth. Under STR it would appear to both that the time of the other person would be slowed down. Each would think that they would be the younger when they eventually meet – which is not possible in reality. This situation is referred to as the “twins paradox”. In fact, astronaut A would be the younger. While the Earthling B may be considered in an inertial frame, the astronaut A has undergone acceleration and deceleration and is therefore to be treated under General Relativity (see below). The two frames of reference are not equivalent.

The General Theory of Relativity

The General Theory of Relativity (GTR) of 1916 dealt with accelerated observers – those experiencing gravitation (which produces the same effects as acceleration and deceleration). The faster an object moves, the slower time passes for someone observing that object. At the speed of light it would appear to an observer that the object had frozen still.

Einstein found that gravity also has an effect on time which passes more slowly on larger masses. One second on Earth is equal to 1.0000025 s on the Sun, equivalent to a difference of 1 second in 6 days.

The GTR demonstrated the way light rays are deflected by gravitational masses. Einstein came to realize that it was incorrect to think of gravitation as causing a distortion or warping of time – it was a warping of time or, more accurately space-time. The geometry of space-time is often represented as a trampoline-like grid with the gravity of solid objects puckering its surface, the bends in the lines being the bending of light towards sources of gravity. Space-time does not therefore operate in straight lines (Euclidian geometry) but exhibits curvature where mass exerts a gravitational pull on light (Riemannian geometry). Gravity is not a field of force but a curvature in the geometry of space-time, an effect known as gravitational lensing. Physicists now prefer to say that bodies do not “feel” gravitational forces but respond to the curvature of space-time in their vicinity. It should be pointed out that STR has had wider recognition and experimental verification than GTR.

STR established space and time as the inextricably linked space-time. GTR demonstrated space-time acting on and being acted on by matter.

Earth is responsible for 2 time warps, which tend to cancel one-another – one due to the Earth’s rotation, the other to its gravity. The higher up you go, the faster time runs relative to clocks lower down.

It is sobering to know that from a pulsar, which has a “gravitational field” a billion times stronger than the Earth, time is slowed by 20% relative to the Earth – so the Earth would appear only 3.5 (not 5) billion years old.

Both Newton and Einstein regarded the universe as being in more or less the same state throughout its history.

In contrast to both Absolute Time and Relational Time we can list the features of Relative time as follows:

• The duration of an event is dependent on the observer (frame of reference)
• Simultaneity of events is dependent on the observer (frame of reference)
• Duration will vary with relative motion and gravity
• The metric of time is intrinsic to the temporal interval. That is, the units of time are the same everywhere (it flows “equably”) Time passes at different relative rates
• Whether time is infinite or not depends on the existence or non-existence of events (a physical universe)

SubstantivilismBSTANTIVALISM (SUBSTANTIALISM) VS RELATIONALISM

During the 18th and 19th centuries the Absolute view of time held sway, to be taken over in the 20th century by Relationalism. With the advent of Relativity in the 20th century the old Absolute vs Relational controversy changed to accommodate modern physics. Since time over vast distances could only be measured using space, the distinct concepts of time and space became superceded by the notion of space-time.

Spacetime as substance
Continuous physical fields are now recognized as physical entities; they are distributed throughout space so there are no unoccupied locations – there is no empty space. Space-time is a field that not only acts upon material objects but is also acted upon by them. The new interpretation of space-time was that it is substance-like, or substantival, acting like a container in which events occur. It is a system of space-time points in which events are located and, like a container, it exists distinctly from its contents. This is Minkowskian space-time in the case of STR which acts like a container. Riemannian space-time of GTR posits that the curvature of space-time as determined by the matter present, and it, in turn, determines how bodies will move. Here the substantivalist can no longer claim that the “container” is independent of what it contains. It is significant that although space-time interacts with the matter in the universe, it is nevertheless distinct from it: in this sense it may be said to be Absolute and the old Absolute-Relational distinction dissolves away.

It should be noted that the word “relativity” refers to the covariance of spatial and temporal intervals; it does not imply that it is the relations of material objects that are physically significant.

If it is argued that only material objects truly exist then the debate remains relevant and unresolved.

The problem of inertia
Newton’s Law of Inertia states that a body remains at rest or continues in uniform motion in a straight line (or “right” line as he called it) unless acted upon by an external force. Such a statement begs the question of motion in relation to what? This cannot be answered by referring to local bodies such as the Earth’s spinning surface (objects themselves generally in non-uniform motion) – his answer was absolute space and time. This is distinct from an absolute state of rest which Newton acknowledged was a matter of convention. [The inertial centre of gravity is the centre of the universe…]

• The problem is acceleration in general and rotation in particular. It is expressed most dramatically through a series of real situations and thought experiments:
• Is the bulge at the centre of the Earth due to its rotation relative to anything? Would it be there if the universe rotated around the Earth and the Earth was still (if that makes sense)? Would the bulge steadily decrease if matter were gradually removed from the universe?
• Imagine two balls in space attached to one another by a piece of string, then rotate them about their axis. The string will be taught but they will not be rotating relative to one-another. If the balls are like ballooons filled with water and one is rotated about its axis will the centre bulge? If so is this due to its rotation relative to the rest of the universe. If the matter in the universe were gradualy removed would the bulge decrease?
• Are the centrifugal, centripetal and coriolus forces intrinsic or extrinsic (or neither or both)?

Thus Newton postulated immovable space (as he called it) as the centre of the system of the universe. This did not change for Einstein who stated himself that space-time is endowed with physical qualities that enable it to establish the local inertial frames, but “the idea of motion may not be applied to it”.

For the purposes of dynamical analysis, motion must be referred to an absolute background metric of rectilinear inertial coordinates rather than to relations between (local) material bodies, or even classical fields. We cannot infer everything important about an object’s state of motion simply from its distances from nearby objects. In this sense both Newtonian and relativistic physics find it necessary to invoke absolute space. It seems that position and velocity are relative, but accelerations have absolute significance independent of the relations between material bodies (at least locally).

In developing his GTR Einstein hoped that the field equations represented true relationalism but he was to find out, to his dismay, from Schwartzchild that there is a preferred coordinate system. GTR correlates the relations between objects (including fields) and the absolute background metric. This metric is affected by, but not determined by, the distribution of objects. So space-time is itself an absolute entity exerting influence on fields and material bodies.

The prevailing ethos of the time was relationalist and proponents like Mach anticipated that space-time, like Absolute space, could be eliminated by denying that it has any physical significance. Mach believed that the average state of motion of matter in the universe counted as the basic inertial field – what he called the distant stars. However, it is now acknowledged that this basic inertial field cannot be attributed to the distribution of matter and energy in space (the distant stars), we simply have to assume a plausible absolute inertial background field.

A dense mass will cause a depression of space-time, (rotational) motion drags space-time in the direction of rotation. This is called frame-dragging (Lense-Thirring effect, gravitomagnetism).

Absolute and Relative time each have major arguments to confront:

If time is the relation between things how do we account for the reality of the “moving” now with its imprint on, not only the limited lives of biological organisms, but also the evolution and ageing of the entire physical universe. The argument that now is a peculiarity of human perception or in some way illusory is difficult to sustain. In other words now is not a special relation between human beings and the world – now is a real and objective aspect of the universe: it would exist in the universe whether humans were present or not. [is this what R claims???] There is also the problem of duration – events have duration that seems real.

For Absolute time there is the problem that we can have no Absolute measure of time itself. If the Earth were to suddenly rotate at twice the speed (this being our natural clock), apart from a whole range of physical effects there would be obvious discrepancies in relation to our biological and other clocks. If atomic clocks sped up or slowed down, for whatever reason, we would be aware of the problem in relation to other measuring devices. All our measurement of time is in relation to something else. But if Absolute time exists independently of these clocks (which are only measuring time in relation to one-another), then we are entitled to ask what it would be like for the universe and/or our clocks, and/or ourselves, if Absolute Time itself were to speed up or slow down. Could we measure its speed in any way? If we answer that there would be no noticeable difference then the question of the relevance and, indeed, the existence of Absolute Time arises again. Can we know if time of the past, relative to time of today passed more quickly or more slowly? Since we know that time passes more slowly in a dense place such as the Sun relative to us, then it seems safe to assume that time passed at differing rates as the universe evolved.

Could physical time be unreal? Many philosophers through the ages have thought so.

There are other philosophers who claim just the opposite. Physical, measured time, lies firmly in the objective world (see also objectivity of time). Newton’s time was precisely measurable. Einstein’s time was precisely measurable but had to take into account relative motion and gravity. Einstein placed time strongly within the physical world and, it seems, completely removed any transcendental associations. Time was not “just there”, or necessarily linked to “events” but part of the very physical fabric of the universe. Time is now the most accurately measured physical parameter.

It should be emphasized that in speaking of the relativity of time, it really is the time that is relative, not our experience of it, nor the operations of the measuring devices we use.
Space-time is a measurable physical parameter, present in the universe even, we assume, in the absence of humans. In this sense it exists as an objective reality.
The paradoxes of time (see, for example, McTaggart’s paradox) and intangible nature of time has persuaded many philosophers that it is not real. This is certainly contrary to common sense and our scientific theories, many of which have time at their core.

For physical time we can simply accept time as the latest accepted definition of t given by physicists.] However, this leaves ample room for debate about the nature of its existence. We can hardly doubt that it exists, how it exists is another matter.

Relative time

The Relative view of time presented by Einstein introduced a new factor, the frame of reference which was used for measurement. Thus a particular event might be associated with different times depending on the frame of reference and this was a development not anticipated by either Relational or Absolute time.

The ‘equable’ time of Newton, although a measurable aspect of the physical world, had a now that was the same time throughout the universe. With Relativity there was, on a universal scale, no longer the time but my time and your time depending on relative motion and the effects of gravity. The time dilation of STR involved speed, and that of GTR accelerations or gravity (regarded by Einstein as equivalent).

Time, we now know, “passes” at different rates in one part of the universe relative to another, and in a mathematically predictable way.

Commentary

Absolute time (A) as articulated by Newton, views time as existing independently of space, things and events. It is treated as a substance or container in which other things exist and events happen. “Moments” of time are thus separate from objects and events. This position finds modern proponents in a modification called substantivalism.

Relational time (R) as originally articulated by Liebnitz maintains that time does not have a separate, independent existence but coexists with objects and events. Relativity emphasizes the significance of the relationship between observers and events. Relational time expresses the prevailing view of modern science.Isaac Newton’s view of time corresponded to our everyday intuition that there is a sort-of universal cosmic clock proceeding at a universal rate. Space and time are discrete. ‘Now’ is exactly the same across the universe. Space was like a container or environment within which the events of the universe happen.

Einstein showed that physical time, the time that we see marked by the movement of hands on clocks, can proceed at different rates under the influence of relative motion and gravitation. And ‘now’ (whatever temporal interval is selected) will depend on the spatiotemporal circumstances at one part of the universe compared to those at another. There is an intimate and roughly reciprocal connection between motion ‘through’ space and the passage of time: the more speed, the less time. From your location in time and space the watch, and all movement, on someone moving towards you is moving slower than if they were standing still. This is because part of their motion in time is being diverted into motion in space. Two locations that are not in relative motion would show identical time.

Clarke-Maxwell had shown that the speed of light was constant; it was fixed regardless of the motion of its observers. Einstein realized that if speed is a measure of space (distance) and time (duration) then, depending on the circumstances (motion and gravity) space and time must vary if the speed of light is to remain fixed. Space can shrink and time can expand (dilate) depending on how you are moving. Theoretically watching someone moving close to the speedof light means that they would appear to live much longer than the usual life span. Motion through space affects passage through time.

In a sense Einstein had realised that the two discrete scientific categories space and time were so closely interconnected that they were better regarded as a single physical entity, spacetime, in much the same way that a biologist might decide that two organisms once given different names were in fact the same species and therefore better understood under one name. ‘Spacetime’ was a linguistic marker of a physical reality.

Taking Einstein’s theory seriously challenges our sense of past, present, and future. We can think of time’s lapsing as either continuous (becoming) or as myriad discrete moments like the refreshing images on a TV or the individual frames of a celluloid movie that we do not notice. Indeed, we can envisage the entire history of the universe laid out as a spacetimescape, as a ‘block’ of spacetime with spacetime coordinates marking out everything.

During one cosmic time-slice of this block which we might call ‘now’ (lasting, say, 1.5 seconds for humans) we can imagine events happening across the universe in this now-slice. We might also think that wherever you were in the now-slice there would be agreement about what was going on elsewhere across the universe during that now-slice. But Einstein showed that if we take motion into account the now-slices will be different and depend on the location where the ‘now’ slice is cut. Someone in the Andromeda galaxy not moving relative to you on earth will agree with you on the contents of their now-slice. But if there is relative motion then watches would disagree and the now-slices would be different. Moving away from you would give a now-slice terminating in your past and moving towards you would give a now-slice terminating in your future. And over vast distances these discrepancies in time can be 100s of years, even millennia. So there would be disagreement about what was past, present and future. Relative motion leads to watches moving out of synchronisation.

Einstein’s physics demonstrated that since no perspective is privileged then we must take past, present and future as equally real. Each individual has a distinct past, present and future but this may not agree with that of other people (locations) in the universe. There is a sense in which time just is, it is static, eternal and timeless. On this view we must think of time spatially, so that, just as all space is out there in the universe, so too is all of time too – it is not confined to a now-slice. The equations of physics do not pick out one now as special from another. Moments are: they just exist: the Platonic world of Being.

One way in which Absolute and R time can be contrasted is in developing a model of the history of our universe. In a universe of Absolute time and Absolute space matter would be visualized as expanding outward into empty space through the void (ether). In a relational universe our whole universe is expanding so there is a combined motion outwards of space, time and matter.

Be careful of Absolute and R. – Newton was possibly correct: duration is Absolute (we sense it); R is the measure of Absolute by motion. If the question what is time is the same as the question what is duration then this could well be a matter for physics.

Although we speak of time as separate from space in everyday language, technically we are, for the most part, speaking of space as well. In this way the concept of space-time has relevance in day-to-day life as well as science. It would seem that the scientific description of space-time as having time-like and space-like dimensions has echoes in our day-to-day understanding of space and time through the following questions:

• Whether time is Absolute (moments) or R (a relation between things and/or events) it is manifest as events (change)
• An event proceeds by a succession or temporal ordering (temporal relations) of two kinds: before and after (B series), or past, present and future (A series). The A series is sometimes treated as a human construct
• Events have an asymmetry (irreversible direction – they are anisotropic – see Arrow of time)
• Events have (and are sometimes separated by) duration (a temporal interval) which is measured in units of convenience and convention
• The measured duration of events (the intervals between events), may differ according to the relations between their frames of reference. That is, events succeed each other at a particular rate that is determined by relative motion and gravity (curvature of space-time)
• Temporal length and temporal motion are qualitatively different from spatial length and spatial motion
• Everything exists in time and therefore ages as “now” extends the time frame of the universe as a process of temporal becoming (flow of time), often construed as a human construct that has no meaning in the objective world

A pi-meson exists for 10-16 seconds.
It is noteworthy that, in spite of the incredible precision of modern timekeeping, no time scale can be proved to be uniform by measurement, as measurement is always a relative activity – although this is of no consequence to everyday affairs. We therefore have no way of knowing whether time at one historical epoch passed at a different rate relative to the time of another historical epoch.

Time, space, matter (mass-energy) and motion are inextricably interlinked? What is separate and what inextricable – how and why?

Does time have properties? Is an hour an event (things endure, durations do not) – therefore time does not exist any more than events!? Existence of changes and events.

Although we measure time, we are also physically aware of it.

Continuity mathematically is termed denseness which is infinite divisibilty. The modern notion of continuity is different.

In what sense does time (space-time) exist?

Is time a thing (individual), a property or a relation? Or something else?

Absolute Time (A) and Relational Time (R) represent the two major views about the nature of existence of time, and we have already examined these in some detail.

We can now state these two major positions simply and clearly.

For R, if there are no events (or things) standing in temporal relations to each other, then time would not exist. In fact, time is the temporal relations between events or things. For R, time co-exists with the universe rather than being separate from it. For A, time could exist even if there were no events (no change). Absolute space-time could exist, even if there was no matter in the universe. In contrast R maintains that space-time is nothing but material objects, their events, and the spatio-temporal relationships between them.

Science emphasizes time as R in character because we measure it in relation to objects and events such as the movement of hands or numbers on a clock. This is all that is needed for the practical purposes of science, so Absolute can be denied or treated as an unnecessary hypothesis.
Although it is perfectly clear that time cannot be measured without change or events, the important point at issue here is whether time can exist without change.

Our everyday language and assumptions treat time as something separate that is content-independent. Most people feel intuitively that empty space and eventless time are a possibility.

Absolute treats time as a substance, solid or thing-in-itself, a kind of container within which the events of the universe happen. Philosophically time in this form is referred to as an individual. Giving something the character of a substance is called hypostasis.

According to Absolute there are temporal individuals such as moments: for R there are only temporal relations.

Historically Liebnitz and the early Einstein maintained that R was the only view consistent with science. It is possible to postulate an absolute space-time that could exist, even if there was no matter in the universe. Likewise a relational theory would maintain that space-time is nothing but material objects, their events, and the spatio-temporal relationships between them.

But in recent times absolute theories have gained ground so that there is now no convergence of opinion on this central issue. Nowadays absolute theories are called “substantival” or “substantial” if space-time is treated as a kind of substance, an “antecedent arena for events”, “substrata for properties” or somesuch. Einstein maintained a loose Absolute in his later days although it must be pointed out that the container metaphor might work for STR but GTR requires curvature of space-time be affected by the distribution of matter, so it does not seem plausible here.

In the early 21st century the A-R distinction has blurred. Time appears to be real and absolute in the sense that space-time is like a substance (albeit extremely “thin”) or container that occupies the whole of the universe – there is no empty space. It is relational in the sense that we assume that space-time originated with the Big Bang and is not an independent ‘stuff’ but interacting with (co-existing with) the matter of the universe.
Time is a physical product of the universe that co-exists with it. It is not independent of the universe but can be treated as a real substance (it is substantival). It is best understood through the notion of duration. We measure duration in relation to the regular behaviour of objects within the universe.
[Distinguish between times mode of existence, origin and nature. How is time separate from events and objects – explore the new approach]

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First published on the internet – 1 March 2019

Artists impression of Gravity Probe B orbiting the Earth to measure space-time, a four-dimensional description of the universe including height, width, length, and time using differential geometry.
Differential geometry is the language in which Einstein’s general theory of relativity is expressed as a smooth manifold that describes the curvature of space-time. Understanding this curvature allows us to position satellites in orbit around the earth. Differential geometry is used to study gravitational lensing and black holes.
Courtesy Wikimedia Commons image sourced from NASA at http://www.nasa.gov/mission_pages/gpb/gpb_012.html