Classical physics owes its definitive formulation to the British scientist Sir Isaac Newton. According to Newton, when one physical body influences another body, this influence results in a change of that body's state of motion, its velocity; that is to say, the force exerted by one particle on another results in the latter's changing the direction of its motion, the magnitude of its speed, or both. Conversely, in the absence of such external influences, a particle will continue to move in one unchanging direction and at a constant rate of speed. This statement, Newton's first law of motion, is known as the law of inertia.

As motion of a particle can be described only in relation to some agreed frame of reference, Newton's law of inertia may also be stated as the assertion that there exist frames of reference (so-called inertial frames of reference) with respect to which particles not subject to external forces move at constant speed in an unvarying direction. Ordinarily, all laws of classical mechanics are understood to hold with respect to such inertial frames of reference. Each frame of reference may be thought of as realized by a grid of surveyor's rods permitting the spatial fixation of any event, along with a clock describing the time of its occurrence.

According to Newton, any two inertial frames of reference are related to each other in that the two respective grids of rods move relative to each other only linearly and uniformly (with constant direction and speed) and without rotation, whereas the respective clocks differ from each other at most by a constant amount (as do the clocks adjusted to two different time zones on Earth) but go at the same rate. Except for the arbitrary choice of such a constant time difference, the time appropriate to various inertial frames of reference then is the same: If a certain physical process takes, say, one hour as determined in one inertial frame of reference, it will take precisely one hour with respect to any other inertial frame; and if two events are observed to take place simultaneously by an observer attached to one inertial frame, they will appear simultaneous to all other inertial observers. This universality of time and time determinations is usually referred to as the absolute character of time. The idea that a universal time can be used indiscriminately by all, irrespective of their varying states of motion--that is, by a person at rest at his home, by the driver of an automobile, and by the passenger aboard an airplane--is so deeply ingrained in most people that they do not even conceive of alternatives. It was only at the turn of the 20th century that the absolute character of time was called into question as the result of a number of ingenious experiments described below.

As long as the building blocks of the physical universe were thought to be particles and systems of particles that interacted with each other across empty space in accordance with the principles enunciated by Newton, there was no reason to doubt the validity of the space-time notions just sketched. This view of nature was first placed in doubt in the 19th century by the discoveries of a Danish physicist, Hans Christian Ørsted, the English scientist Michael Faraday, and the theoretical work of the Scottish-born physicist James Clerk Maxwell, all concerned with electric and magnetic phenomena. Electrically charged bodies and magnets do not affect each other directly over large distances, but they do affect one another by way of the so-called electromagnetic field, a state of tension spreading throughout space at a high but finite rate, which amounts to a speed of propagation of approximately 186,000 miles (300,000 kilometres) per second. As this value is the same as the known speed of light in empty space, Maxwell hypothesized that light itself is a species of electromagnetic disturbance; his guess has been confirmed experimentally, first by the production of lightlike waves by entirely electric and magnetic means in the laboratory by a German physicist, Heinrich Hertz, in the late 19th century.

Both Maxwell and Hertz were puzzled and profoundly disturbed by the question of what might be the carrier of the electric and magnetic fields in regions free of any known matter. Up to their time, the only fields and waves known to spread at a finite rate had been elastic waves, which appear to the senses as sound and which occur at low frequencies as the shocks of earthquakes, and surface waves, such as water waves on lakes and seas. Maxwell called the mysterious carrier of electromagnetic waves the ether, thereby reviving notions going back to antiquity. He attempted to endow his ether with properties that would account for the known properties of electromagnetic waves, but he was never entirely successful. The ether hypothesis, however, led two U.S. scientists, Albert Abraham Michelson and Edward Williams Morley, to conceive of an experiment (1887) intended to measure the motion of the ether on the surface of the Earth in their laboratory. On the reasonable hypothesis that the Earth is not the pivot of the whole universe, they argued that the motion of the Earth relative to the ether should result in slight variations in the observed speed of light (relative to the Earth and to the instruments of a laboratory) travelling in different directions. The measurement of the speed of light requires but one clock, if, by use of a mirror, a pencil of light is made to travel back and forth so that its speed is measured by clocking the total time elapsed in a round trip at one site; such an arrangement obviates the need for synchronizing two clocks at the ends of a one-way trip. Finally, if one is concerned with variations in the speed of light, rather than with an absolute determination of that speed itself, then it suffices to compare with each other round-trip-travel times along two tracks at right angles to each other, and that is essentially what Michelson and Morley did. To avoid the use of a clock altogether, they compared travel times in terms of the numbers of wavelengths travelled, by making the beams travelling on the two distinct tracks interfere optically with each other. (If the waves meet at a point when both are in the same phase--e.g., both at their peak--the result is visible as the sum of the two in amplitude; if the peak of one coincides with the trough of the other, they cancel each other and no light is visible. Since the wavelengths are known, the relative positions of the peaks give an exact measure of how far one wave has advanced with respect to the other.) This highly precise experiment, repeated many times with ever-improved instrumental techniques, has consistently led to the result that the speed of light relative to the laboratory is the same in all directions, regardless of the time of the day, the time of the year, and the elevation of the laboratory above sea level.

The special theory of relativity resulted from the acceptance of this experimental finding. If an Earth-bound observer could not detect the motion of the Earth through the ether, then, it was felt, probably any observer, regardless of his state of motion, would find the speed of light the same in all directions.

An Irish and a Dutch physicist, George Francis FitzGerald and Hendrik Antoon Lorentz, independently showed that the negative outcome of Michelson's and Morley's experiment could be reconciled with the notion that the Earth is travelling through the ether, if one hypothesizes that any body travelling through the ether is foreshortened in the direction of travel (though its dimensions at right angles to the motion remain undisturbed) by a ratio that increases with increasing speed. If v denotes the speed of the body relative to the ether, and c is the speed of light, that ratio equals the quantity (1 - v²/c²)^1/2. At ordinary speeds, c is so much greater than v that the fraction, practically speaking, is zero, and the ratio becomes 1, which is 1; i.e., the foreshortening is nil; as v approaches c, however, the fraction becomes significant. The travelling body would be flattened completely if its speed through the ether should ever reach that of light.

Suppose, now, that the variations in the speed of light were to be determined not by interference but by means of an exceedingly accurate clock and assume further that in such a modified experiment (whose actual performance is precluded at present, because even the best atomic clocks available do not possess the requisite accuracy) the motion through the ether were still imperceptible, then, Lorentz showed, one would have to conclude that all clocks moving through the ether are slowed down compared to clocks at rest in the ether, again by the factor (1 - v²/c²)^1/2. Thus, all rods and all clocks would be modified systematically, regardless of materials and construction design, whenever they were moving relative to the ether. Accordingly, for theoretical analysis, one would have to distinguish between "apparent" and "true" space and time measurements, with the further proviso that "true" dimensions and "true" times could never be determined by any experimental procedure.

Conceptually, this was an unsatisfactory situation, which was resolved by Albert Einstein in 1905. Einstein realized that the key concept, on which all comparisons between differently moving observers and frames of reference depended, is the notion of universal, or absolute, simultaneity; that is to say, the proposition that two events that appear simultaneous to any one observer will also be judged to take place at the same time by all other observers. This appears to be a straightforward proposition, provided that knowledge of distant events can be obtained practically instantaneously. Actually, however, there is no known method of signalling faster than by means of light or radio waves or any other electromagnetic radiation, all of which travel at the same rate, c.

Suppose, now, that someone on Earth observes two events, say two supernovae (suddenly erupting very bright stars) appearing in different parts of the sky. Nothing can be said about whether these two supernovae emerged simultaneously or not from merely noting their appearance in the sky; it is necessary to know also their respective distances from the observer, which typically may amount to several hundred or several thousand light-years (one light-year, the distance light moves in one year, equals approximately 5.88 x10¹² miles, or 9.46 x10¹² kilometres). By the time one sees the eruption of a supernova, it has in actuality faded back into invisibility hundreds of years ago. Applying this simple idea to the observations and measurements made by different observers of the same events, Einstein demonstrated that if each observer applied the same method of analysis to his own data, then events that appeared simultaneous to one would appear to have taken place at different times to observers in different states of motion. Thus, it is necessary to speak of relativity of simultaneity.

Once this theoretical deduction is accepted, the findings of FitzGerald and Lorentz lend themselves to a new interpretation. Whenever two observers are associated with two distinct inertial frames of inference in relative motion to each other, their determinations of time intervals and of distances between events will disagree systematically, without one being "right" and the other "wrong." Nor can it be established that one of them is at rest relative to the ether, the other in motion. In fact, if they compare their respective clocks, each will find that his own clock will be faster than the other; if they compare their respective measuring rods (in the direction of mutual motion), each will find the other's rod foreshortened. The speed of light will be found to equal the same value, c = 186,000 miles per second, relative to every inertial frame of reference and in all directions. The status of Maxwell's ether is thereby cast in doubt, as its state of motion cannot be ascertained by any conceivable experiment. Consequently, the whole notion of an ether as the carrier of electromagnetic phenomena has been eliminated in contemporary physics.

The mathematical equations that relate space and time measurements of one observer to those of another, moving observer are known as Lorentz transformations. If the relative motion is measured along the x-axis and if its magnitude is v, these expressions are: