• Barbara Jesline

Do you know: What is Space-Time

The fabric of the Universe, spacetime, is a tricky concept to understand. Space and time form a system of such staggering complexity that it may defy our most ardent efforts to understand. Until the 20th century, it was assumed that the three-dimensional geometry of the universe (its spatial expression in terms of coordinates, distances, and directions) was independent of one-dimensional time. However, in 1905, Albert Einstein based work on special relativity on two postulates:

  • The laws of physics are invariant (i.e., identical) in all inertial systems (i.e., non-accelerating frames of reference)

  • The speed of light in a vacuum is the same for all observers, regardless of the motion of the light source.

The logical consequence of taking these postulates together is the inseparable joining together of the four dimensions—hitherto assumed as independent—of space and time. Many counterintuitive consequences emerge: in addition to being independent of the motion of the light source, the speed of light has the same speed regardless of the frame of reference in which it is measured; the distances and even temporal ordering of pairs of events change when measured in different inertial frames of reference (this is the relativity of simultaneity), and the linear additivity of velocities no longer holds true.

Conceptually, the metric tensor defines how spacetime itself is curved. Its curvature is dependent on the matter, energy and stresses present within it; the contents of your Universe define its spacetime curvature. By the same token, how your Universe is curved tells you how the matter and energy are going to move through it. We like to think that an object in motion will continue in motion: Newton's first law. We conceptualize that as a straight line, but what curved space tells us is that instead an object in motion continuing in motion follows a geodesic, which is a particularly-curved line that corresponds to unaccelerated motion. Ironically, it's a geodesic, not necessarily a straight line, that is the shortest distance between two points. This shows up even on cosmic scales, where the curved spacetime due to the presence of extraordinary masses can curve the background light from behind it, sometimes into multiple images.

Physically, there are a number of different pieces that contribute to the Metric Tensor in general relativity. We think of gravity as due to masses: the locations and magnitudes of different masses determine the gravitational force. In general relativity, this corresponds to the mass density and does contribute, but it's one of only 16 components of the Metric Tensor! There are also pressure components (such as radiation pressure, vacuum pressure or pressures created by fast-moving particles) that contribute, which are three additional contributors (one for each of the three spatial directions) to the Metric Tensor. And finally, there are six other components that tell us how volumes change and deform in the presence of masses and tidal forces, along with how the shape of a moving body is distorted by those forces. This applies to everything from a planet like Earth to a neutron star to a massless wave moving through space: gravitational radiation.

In ordinary space, a position is specified by three numbers, known as dimensions. In the Cartesian coordinate system, these are called x, y, and z. A position in spacetime is called an event, and requires four numbers to be specified: the three-dimensional location in space, plus the position in time (Fig. 1). Spacetime is thus four-dimensional. An event is something that happens instantaneously at a single point in spacetime, represented by a set of coordinates x, y, z and t.

The word "event" used in relativity should not be confused with the use of the word "event" in normal conversation, where it might refer to an "event" as something such as a concert, sporting event, or a battle. These are not mathematical "events" in the way the word is used in relativity, because they have finite durations and extents. Unlike the analogies used to explain events, such as firecrackers or lightning bolts, mathematical events have zero duration and represent a single point in spacetime.

The path of a particle through spacetime can be considered to be a succession of events. The series of events can be linked together to form a line which represents a particle's progress through spacetime. That line is called the particle's world line.

Mathematically, spacetime is a manifold, which is to say, it appears locally "flat" near each point in the same way that, at small enough scales, a globe appears flat. An extremely large scale factor, {\displaystyle c} (conventionally called the speed-of-light) relates distances measured in space with distances measured in time. The magnitude of this scale factor (nearly 300,000 kilometres or 190,000 miles in space is equivalent to one second in time), along with the fact that spacetime is a manifold, implies that at ordinary, non-relativistic speeds and at ordinary, human-scale distances, there is little that humans might observe which is noticeably different from what they might observe if the world were Euclidean. It was only with the advent of sensitive scientific measurements in the mid-1800s, such as the Fizeau experiment and the Michelson–Morley experiment, those puzzling discrepancies began to be noted between observation versus predictions based on the implicit assumption of Euclidean space.