Relativistic Time

Albert Einstein
The idea of relativistic time is a direct result of Albert Einstein’s Theory of Relativity

Since Albert Einstein published his Theory of Relativity (the Special Theory in 1905, and the General Theory in 1916), our understanding of time has changed dramatically, and the traditional Newtonian idea of absolute time and space has been superseded by the notion of time as one dimension of space-time in special relativity, and of dynamically curved space-time in general relativity.

It was Einstein’s genius to realize that the speed of light is absolute, invariable and cannot be exceeded (and indeed that the speed of light is actually more fundamental than either time or space). In relativity, time is certainly an integral part of the very fabric of the universe and cannot exist apart from the universe, but, if the speed of light is invariable and absolute, Einstein realized, both space and time must be flexible and relative to accommodate this.

Although much of Einstein’s work is often considered “difficult” or “counter-intuitive”, his theories have proved (both in laboratory experiments and in astronomical observations) to be a remarkably accurate model of reality, indeed much more accurate than Newtonian physics, and applicable in a much wider range of circumstances and conditions.


One aspect of Einstein’s Special Theory of Relativity is that we now understand that space and time are merged inextricably into four-dimensional space-time, rather than the three dimensions of space and a totally separate time dimension envisaged by Descartes in the 17th Century and taken for granted by all classical physicists after him. With this insight, time effectively becomes just part of a coordinate specifying an object’s position in space-time.

It was Hermann Minkowski, Einstein’s one-time teacher and colleague, who gave us the classic interpretation of Einstein’s Special Theory of Relativity. Minkowski introduced the relativity concept of proper time, the actual elapsed time between two events as measured by a clock that passes through both events. Proper time therefore depends not only on the events themselves but also on the motion of the clock between the events. By contrast, what Minkowski called coordinate time is the apparent time between two events as measured by a distant observer using that observer’s own method of assigning a time to an event.

An event is both a place and a time, and can be represented by a particular point in space-time, i.e. a point in space at a particular moment in time. Space-time as a whole can therefore be thought of as a collection of an infinite number of events. The complete history of a particular point in space is represented by a line in space-time (known as a world line), and the past, present and future accessible to a particular object at a particular time can be represented by a three dimensional light cone (or Minkowski space-time diagram), which is defined by the limiting value of the speed of light, which intersects at the here-and-now, and through which the object’s world line runs its course.

Modern physicists therefore do not regard time as “passing” or “flowing” in the old-fashioned sense, nor is time just a sequence of events which happen: both the past and the future are simply “there”, laid out as part of four-dimensional space-time, some of which we have already visited and some not yet. So, just as we are accustomed to thinking of all parts of space as existing even if we are not there to experience them, all of time (past, present and future) are also constantly in existence even if we are not able to witness them. Time does not “flow”, then, it just “is”. This view of time is consistent with the philosophical view of eternalism or the block universe theory of time (see the section on Modern Philosophy).

According to relativity, the perception of a “now”, and particularly of a “now” that moves along in time so that time appears to “flow”, therefore arises purely as a result of human consciousness and the way our brains are wired, perhaps as an evolutionary tool to help us deal with the world around us, even if it does not actually reflect the reality. As Einstein himself remarked, “People like us, who believe in physics, know that the distinction between past, present, and future is only a stubbornly persistent illusion”.

However, if time is a dimension, it does not appear to be the same kind of dimension as the three dimensions of space. For example, we can choose to move through space or not, but our movement through time is inevitable, and happens whether we like it or not. In fact, we do not really move though time at all, at least not in the same way as we move through space. Also, space does not have any fundamental directionality (i.e. there is no “arrow of space”, other than the downward pull of gravity, which is actually variable in absolute terms, depending on where on Earth we are located, or whether we are out in space with no gravitational effects at all), whereas time clearly does (see the section on The Arrow of Time).

With the General Theory of Relativity, the concept of space-time was further refined, when Einstein realized that perhaps gravity is not a field or force on top of space-time, but a feature of space-time itself. Thus, the space-time continuum is actually warped and curved by mass and energy, a warping that we think of as gravity, resulting in a dynamically curved space-time. In regions of very large masses, such as stars and black holes, space-time is bent or warped substantially by the extreme gravity of the masses, an idea often illustrated by the image of a rubber sheet distorted by the weight of a bowling ball.

Time Dilation
Time dilation is just one consequence of the Theory of Relativity and curved space-time

Also as a result of Einstein’s work and his Special Theory of Relativity, we now know that rates of time actually run differently depending on relative motion, so that time effectively passes at different rates for different observers travelling at different speeds, an effect known as time dilation. Thus, two synchronized clocks will not necessarily stay synchronized if they move relative to each other. There is a related effect in the spatial dimensions, known as length contraction, whereby moving bodies are actually foreshortened in the direction of their travel.

Time dilation (as well as the associated length contraction) is negligible and all but imperceptible at everyday speeds in the world around us, although it can be, and has been, measured with very sensitive instruments. However, it becomes much more pronounced as an object’s speed approaches the speed of light (known as relativistic speeds). If a spaceship could travel at, say, 99% of the speed of light, a hypothetical observer looking in would see the ship’s clock moving about twice as slow as normal (i.e. coordinate time is moving twice as slow as proper time), and the astronauts inside moving around apparently in slow-motion. At 99.5% of the speed of light, the observer would see the clock moving about 10 times slower than normal. At 99.9% of the speed of light, the factor becomes about 22 times, at 99.99% 224 times, and at 99.9999% 707 times, increasing exponentially. In the largest particle accelerators currently in use we can make time slow down by 100,000 times. At the speed of light itself, were it actually possible to achieve that, time would stop completely.

Perhaps the easiest way to think of this difficult concept is that, when an object or person moves in space-time, its movement “shares” some of its spatial movement with movement in time, in the same way as some northward movement is shared with westward movement when we travel northwest. What forces this sharing of dimensions is the invariant nature of the speed of light (slightly less than 300,000km/s), which is a fundamental constant of the universe that can never be exceeded. Thus, the slowing of time at relativistic speeds occurs, in a sense, to “protect” the inviolable cosmic speed limit (the speed of light).

It should be noted that, although a spaceship travelling at close to the speed of light would take 100,000 years to reach a distant star 100,000 light years away as judged by clocks on Earth, the astronaut in the spaceship might hardly age at all as he travels across the galaxy. This characteristic of relativistic time has therefore spawned much discussion of the possibility of time travel (see the separate section on Time Travel).

According to Einstein, then, time is relative to the observer, and more specifically to the motion of that observer. This is not to say that time is in some way capricious or random in nature – it is still governed by the laws of physics and entirely predictable in its manifestations, it is just not absolute and universal as Newton thought (see the section on Absolute Time), and things are not quite as simple and straightforward as he had believed. Some commentators, like the Christian philosopher William Lane Craig, have suggested that there may be a need to distinguish between the reality of time and our measurement of time: according to this line of thinking (which, it should be mentioned, is not a mainstream position in physics), time itself MAY be absolute, but the way we measure it must be relativistic.

One casualty of the Theory of Relativity is the notion of simultaneity, the property of two events happening at the same time in a particular frame of reference. According to relativistic physics, simultaneity is NOT an absolute property between events, as had always been taken for granted up to that point. Thus, what is simultaneous in one frame of reference will not necessarily be simultaneous in another. For objects moving at normal everyday speeds, the effect is small and can generally be ignored (so that simultaneity CAN normally be treated as an absolute property); but when objects approach relativistic speeds (close to the speed of light) with respect to one another, such intuitive relationships can no longer be assumed.

Gravitational Time Dilation

When Einstein extended his Special Theory of Relativity to his General Theory, it became apparent that a similar time dilation effect would also occur in the presence of intense gravity, an effect usually referred to as gravitational time dilation. It is almost as if gravity is somehow pulling or dragging on time, slowing its passage. The closer an object is to another object, the stronger the pull of gravity between them (according to an inverse-square law first identified by Sir Isaac Newton), and thus the more the time drag.

Again, these effects are negligible at the kinds of gravitational differences experienced in everyday life: even though, technically, a person living in a ground floor apartment ages slower than their twin who lives in a top floor apartment of the same building (due to the difference in gravity they experience), the effect might amount to maybe a microsecond over a full lifetime. There is, however, one aspect of modern everyday life where we do experience the effects of gravitational time dilation: it has a noticeable impact on the Global Positioning System (GPS), which many of us now rely on for navigation. The orbiting satellites used by the GPS system experience significantly less gravity than the Earth’s surface, and are also moving very fast, so that the time distortion effects of about 38 microseconds a day have to be specifically factored in or GPS would very quickly begin to accumulate errors.

But, just as with a spaceship travelling at near the speed of light, in the extreme gravity at the edges of a black hole, for example, substantial time differences can become apparent. A black hole spins at close to the speed of light, dragging anything in the vicinity around with it, and the huge gravitational pull of a black hole can bend and warp space-time to a substantial degree. Over the “event horizon” of a black hole – the gravitational point of no return – a hypothetical clock on a spaceship (and indeed the progress of the spaceship itself) would appear from the outside to stop completely due to the infinite time dilation effect. At the gravitational singularity at the centre of a black hole, gravity and density is infinite, and all the normal rules of physics just break down. Time effectively stops, just as there is no time beyond the singularity of the Big Bang (see the section on Time and the Big Bang).

Twins Paradox

The dilation of time also gives rise to the so-called “twins paradox” or “clock paradox”, whereby a hypothetical astronaut returns from a near-light speed voyage in space to find his stay-at-home twin many years older than him (as travelling at relativistic high speeds has allowed the astronaut to experience only, say, one year of time, while ten years have elapsed on Earth). Because of the time dilation effect, a clock in the spaceship literally registers a shorter duration for the journey than the clock in mission control on Earth.

The real paradox, though, as Einstein explained it, arises from the fact that (because there is no “preferred” frame of reference in relativity) we could just as easily consider the traveller in the spaceship as the one remaining at rest, while the Earth shoots off and back at close to the speed of light. In that scenario, Einstein argued, one would expect the astronaut to age much more than the inhabitants of the Earth. In fact the “paradox” is explained by Mach’s Principle: the spaceship is accelerating away at near-light speed from the bulk of the universe, whereas the Earth is not. Hence, it is the spaceship (and its astronaut) that experiences the relativistic time dilation, not the Earth.

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