NOT ONLY "SPACE" BUT, "SPACETIME"
NOT ONLY "SPACE" BUT, "SPACETIME"
In physics, spacetime is any mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams can be used to visualize relativistic effects such as why different observers perceive where and when events occur.
Until the turn of the 20th century, the assumption had been 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 his seminal work on special relativity on two postulates: (1) The laws of physics are invariant (i.e., identical) in all inertial systems (i.e., non-accelerating frames of reference); (2) 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.
Einstein framed his theory in terms of kinematics (the study of moving bodies). His theory was a breakthrough advance over Lorentz's 1904 theory of electromagnetic phenomena and Poincaré's electrodynamic theory. Although these theories included equations identical to those that Einstein introduced (i.e. the Lorentz transformation), they were essentially ad hoc models proposed to explain the results of various experiments—including the famous Michelson–Morley interferometer experiment—that were extremely difficult to fit into existing paradigms.
In 1908, Hermann Minkowski—once one of the math professors of a young Einstein in Zürich—presented a geometric interpretation of special relativity that fused time and the three spatial dimensions of space into a single four-dimensional continuum now known as Minkowski space. A key feature of this interpretation is the formal definition of the spacetime interval. Although measurements of distance and time between events differ for measurements made in different reference frames, the spacetime interval is independent of the inertial frame of reference in which they are recorded.
Minkowski's geometric interpretation of relativity was to prove vital to Einstein's development of his 1915 general theory of relativity, wherein he showed how mass and energy curve this flat spacetime to a Pseudo Riemannian manifold.
Non-relativistic classical mechanics treats time as a universal quantity of measurement which is uniform throughout space and which is separate from space. Classical mechanics assumes that time has a constant rate of passage that is independent of the state of motion of an observer, or indeed of anything external. Furthermore, it assumes that space is Euclidean, which is to say, it assumes that space follows the geometry of common sense.
In the context of special relativity, time cannot be separated from the three dimensions of space, because the observed rate at which time passes for an object depends on the object's velocity relative to the observer. General relativity, in addition, provides an explanation of how gravitational fields can slow the passage of time for an object as seen by an observer outside the field.
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, (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 being 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, that puzzling discrepancies began to be noted between observation versus predictions based on the implicit assumption of Euclidean space.
In special relativity, an observer will, in most cases, mean a frame of reference from which a set of objects or events are being measured. This usage differs significantly from the ordinary English meaning of the term. Reference frames are inherently nonlocal constructs, and according to this usage of the term, it does not make sense to speak of an observer as having a location. In Fig. 1‑1, imagine that the frame under consideration is equipped with a dense lattice of clocks, synchronized within this reference frame, that extends indefinitely throughout the three dimensions of space. Any specific location within the lattice is not important. The latticework of clocks is used to determine the time and position of events taking place within the whole frame. The term observerrefers to the entire ensemble of clocks associated with one inertial frame of reference. In this idealized case, every point in space has a clock associated with it, and thus the clocks register each event instantly, with no time delay between an event and its recording. A real observer, however, will see a delay between the emission of a signal and its detection due to the speed of light. To synchronize the clocks, in the data reduction following an experiment, the time when a signal is received will be corrected to reflect its actual time were it to have been recorded by an idealized lattice of clocks.
In many books on special relativity, especially older ones, the word "observer" is used in the more ordinary sense of the word. It is usually clear from context which meaning has been adopted.
Physicists distinguish between what one measures or observes (after one has factored out signal propagation delays), versus what one visually sees without such corrections. Failure to understand the difference between what one measures/observes versus what one sees is the source of much error among beginning students of relativity.
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