Relativity, theory, developed in the
early 20th century, which originally attempted to account for certain anomalies
in the concept of relative motion, but which in its ramifications has developed
into one of the most important basic concepts in physical science (see Physics).
The theory of relativity, developed primarily by German American physicist
Albert Einstein, is the basis for later demonstration by physicists of the
essential unity of matter and energy, of space and time, and of the forces of
gravity and acceleration (see Acceleration; Energy; Gravitation).
II

CLASSICAL PHYSICS

Physical laws generally accepted by
scientists before the development of the theory of relativity, now called
classical laws, were based on the principles of mechanics enunciated late in
the 17th century by the English mathematician and physicist Isaac Newton.
Newtonian mechanics and relativistic mechanics differ in fundamental
assumptions and mathematical development, but in most cases do not differ
appreciably in net results; the behavior of a billiard ball when struck by
another billiard ball, for example, may be predicted by mathematical
calculations based on either type of mechanics and produce approximately
identical results. Inasmuch as the classical mathematics is enormously simpler
than the relativistic, the former is the preferred basis for such a calculation.
In cases of high speeds, however, assuming that one of the billiard balls was
moving at a speed approaching that of light, the two theories would predict
entirely different types of behavior, and scientists today are quite certain
that the relativistic predictions would be verified and the classical
predictions would be proved incorrect.
In general, the difference between two
predictions on the behavior of any moving object involves a factor discovered
by the Dutch physicist Hendrik Antoon Lorentz, and the Irish physicist George
Francis FitzGerald late in the 19th century. This factor is generally
represented by the Greek letter β (beta) and is determined by the velocity of
the object in accordance with the following equation:

in which v is the velocity of the object and c
is the velocity of light (see Light). The beta factor does not differ
essentially from unity for any velocity that is ordinarily encountered; the
highest velocity encountered in ordinary ballistics, for example, is about 1.6
km/sec (about 1 mi/sec), the highest velocity obtainable by a rocket propelled
by ordinary chemicals is a few times that, and the velocity of the earth as it
moves around the sun is about 29 km/sec (about 18 mi/sec); at the lastnamed
speed, the value of beta differs from unity by only five billionths. Thus, for
ordinary terrestrial phenomena, the relativistic corrections are of little
importance. When velocities are very large, however, as is sometimes the case
in astronomical phenomena, relativistic corrections become significant.
Similarly, relativity is important in calculating very large distances or very
large aggregations of matter. As the quantum theory applies to the very small,
so the relativity theory applies to the very large.
Until 1887 no flaw had appeared in
the rapidly developing body of classical physics. In that year, the
MichelsonMorley experiment, named after the American physicist Albert
Michelson and the American chemist Edward Williams Morley, was performed. It
was an attempt to determine the rate of the motion of the earth through the
ether, a hypothetical substance that was thought to transmit electromagnetic
radiation, including light, and was assumed to permeate all space. If the sun
is at absolute rest in space, then the earth must have a constant velocity of
29 km/sec (18 mi/sec), caused by its revolution about the sun; if the sun and
the entire solar system are moving through space, however, the constantly
changing direction of the earth's orbital velocity will cause this value of the
earth's motion to be added to the velocity of the sun at certain times of the
year and subtracted from it at others. The result of the experiment was
entirely unexpected and inexplicable; the apparent velocity of the earth
through this hypothetical ether was zero at all times of the year.
What the MichelsonMorley experiment
actually measured was the velocity of light through space in two different
directions. If a ray of light is moving through space at 300,000 km/sec
(186,000 mi/sec), and an observer is moving in the same direction at 29 km/sec
(18 mi/sec), then the light should move past the observer at the rate of
299,971 km/sec (185,982 mi/sec); if the observer is moving in the opposite
direction, the light should move past the observer at 300,029 km/sec (186,018
mi/sec). It was this difference that the MichelsonMorley experiment failed to
detect. This failure could not be explained on the hypothesis that the passage
of light is not affected by the motion of the earth, because such an effect had
been observed in the phenomenon of the aberration of light; see Interference;
Interferometer; Wave Motion.
In the 1890s FitzGerald and Lorentz
advanced the hypothesis that when any object moves through space, its length in
the direction of its motion is altered by the factor beta. The negative result
of the MichelsonMorley experiment was explained by the assumption that the
light actually traversed a shorter distance in the same time (that is, moved
more slowly), but that this effect was masked because the distance was measured
of necessity by some mechanical device which also underwent the same
shortening, just as when an object 2 m long is measured with a 3m tape measure
which has shrunk to 2 m, the object will appear to be 3 m in length. Thus, in
the MichelsonMorley experiment, the distance which light traveled in 1 sec
appeared to be 300,000 km (186,000 mi) regardless of how fast the light
actually traveled. The LorentzFitzGerald contraction was considered by
scientists to be an unsatisfactory hypothesis because it could not be applied
to any problem in which measurements of absolute motion could be made.
III

SPECIAL THEORY OF
RELATIVITY

In 1905, Einstein published the first
of two important papers on the theory of relativity, in which he dismissed the
problem of absolute motion by denying its existence. According to Einstein, no
particular object in the universe is suitable as an absolute frame of reference
that is at rest with respect to space. Any object (such as the center of the
solar system) is a suitable frame of reference, and the motion of any object
can be referred to that frame. Thus, it is equally correct to say that a train
moves past the station, or that the station moves past the train. This example
is not as unreasonable as it seems at first sight, for the station is also
moving, due to the motion of the earth on its axis and its revolution around
the sun. All motion is relative, according to Einstein. None of Einstein's
basic assumptions was revolutionary; Newton had previously stated “absolute
rest cannot be determined from the position of bodies in our regions.” Einstein
stated the relative rate of motion between any observer and any ray of light is
always the same, 300,000 km/sec (186,000 mi/sec), and thus two observers,
moving relative to one another even at a speed of 160,000 km/sec (100,000
mi/sec), each measuring the velocity of the same ray of light, would both find it
to be moving at 300,000 km/sec (186,000 mi/sec), and this apparently anomalous
result was proved by the MichelsonMorley experiment. According to classical
physics, one of the two observers was at rest, and the other made an error in
measurement because of the LorentzFitzGerald contraction of his apparatus;
according to Einstein, both observers had an equal right to consider themselves
at rest, and neither had made any error in measurement. Each observer used a
system of coordinates as the frame of reference for measurements, and these
coordinates could be transformed one into the other by a mathematical
manipulation. The equations for this transformation, known as the Lorentz
transformation equations, were adopted by Einstein, but he gave them an entirely
new interpretation. The speed of light is invariant in any such transformation.
According to the relativistic
transformation, not only would lengths in the line of a moving object be
altered but also time and mass. A clock in motion relative to an observer would
seem to be slowed down, and any material object would seem to increase in mass,
both by the beta factor. The electron, which had just been discovered, provided
a means of testing the last assumption. Electrons emitted from radioactive
substances have speeds close to the speed of light, so that the value of beta,
for example, might be as large as 0.5, and the mass of the electron doubled.
The mass of a rapidly moving electron could be easily determined by measuring
the curvature produced in its path by a magnetic field; the heavier the
electron, the greater its inertia and the less the curvature produced by a
given strength of field (see Magnetism). Experimentation dramatically
confirmed Einstein's prediction; the electron increased in mass by exactly the
amount he predicted. Thus, the kinetic energy of the accelerated electron had
been converted into mass in accordance with the formula E=mc^{2}
(see Atom; Nuclear Energy). Einstein's theory was also verified by
experiments on the velocity of light in moving water and on magnetic forces in
moving substances.
The fundamental hypothesis on which
Einstein's theory was based was the nonexistence of absolute rest in the
universe. Einstein postulated that two observers moving relative to one another
at a constant velocity would observe identically the phenomena of nature. One
of these observers, however, might record two events on distant stars as having
occurred simultaneously, while the other observer would find that one had
occurred before the other; this disparity is not a real objection to the theory
of relativity, because according to that theory simultaneity does not exist for
distant events. In other words, it is not possible to specify uniquely the time
when an event happens without reference to the place where it happens. Every
particle or object in the universe is described by a socalled world line that
describes its position in time and space. If two or more world lines intersect,
an event or occurrence takes place; if the world line of a particle does not
intersect any other world line, nothing has happened to it, and it is neither
important nor meaningful to determine the location of the particle at any given
instant. The “distance” or “interval” between any two events can be accurately
described by means of a combination of space and time, but not by either of
these separately. The spacetime of four dimensions (three for space and one
for time) in which all events in the universe occur is called the spacetime
continuum.
All of the above statements are
consequences of special relativity, the name given to the theory developed by
Einstein in 1905 as a result of his consideration of objects moving relative to
one another with constant velocity.
IV

GENERAL THEORY OF
RELATIVITY

In 1915 Einstein developed the general
theory of relativity in which he considered objects accelerated with respect to
one another. He developed this theory to explain apparent conflicts between the
laws of relativity and the law of gravity. To resolve these conflicts he
developed an entirely new approach to the concept of gravity, based on the
principle of equivalence.
The principle of equivalence holds that
forces produced by gravity are in every way equivalent to forces produced by
acceleration, so that it is theoretically impossible to distinguish between
gravitational and accelerational forces by experiment. In the theory of special
relativity, Einstein had stated that a person in a closed car rolling on an
absolutely smooth railroad track could not determine by any conceivable
experiment whether he was at rest or in uniform motion. In general relativity
he stated that if the car were speeded up or slowed down or driven around a
curve, the occupant could not tell whether the forces so produced were due to
gravitation or whether they were acceleration forces brought into play by
pressure on the accelerator or on the brake or by turning the car sharply to
the right or left.
Acceleration is defined as the rate of
change of velocity. Consider an astronaut standing in a stationary rocket.
Because of gravity his or her feet are pressed against the floor of the rocket
with a force equal to the person's weight, w. If the same rocket is in
outer space, far from any other object and not influenced by gravity, the astronaut
is again being pressed against the floor if the rocket is accelerating, and if
the acceleration is 9.8 m/sec^{2} (32 ft/sec^{2}) (the
acceleration of gravity at the surface of the earth), the force with which the
astronaut is pressed against the floor is again equal to w. Without
looking out of the window, the astronaut would have no way of telling whether
the rocket was at rest on the earth or accelerating in outer space. The force
due to acceleration is in no way distinguishable from the force due to gravity.
According to Einstein's theory, Newton's law of gravitation is an unnecessary
hypothesis; Einstein attributes all forces, both gravitational and those
associated with acceleration, to the effects of acceleration. Thus, when the
rocket is standing still on the surface of the earth, it is attracted toward
the center of the earth. Einstein states that this phenomenon of attraction is
attributable to an acceleration of the rocket. In threedimensional space, the
rocket is stationary and therefore is not accelerated; but in fourdimensional
spacetime, the rocket is in motion along its world line. According to
Einstein, the world line is curved, because of the curvature of the continuum
in the neighborhood of the earth.
Thus, Newton's hypothesis that every object
attracts every other object in direct proportion to its mass is replaced by the
relativistic hypothesis that the continuum is curved in the neighborhood of
massive objects. Einstein's law of gravity states simply that the world line of
every object is a geodesic in the continuum. A geodesic is the shortest
distance between two points, but in curved space it is not generally a straight
line. In the same way, geodesics on the surface of the earth are great circles,
which are not straight lines on any ordinary map. See Geometry;
Navigation.
V

CONFIRMATION AND
MODIFICATION

As in the cases mentioned above,
classical and relativistic predictions are generally virtually identical, but
relativistic mathematics is more complex. The famous apocryphal statement that
only ten people in the world understood Einstein's theory referred to the
complex tensor algebra and Riemannian geometry of general relativity; by
comparison, special relativity can be understood by any college student who has
studied elementary calculus.
General relativity theory has been confirmed
in a number of ways since it was introduced. For example, it predicts that the
world line of a ray of light will be curved in the immediate vicinity of a
massive object such as the sun. To verify this prediction, scientists first
chose to observe a star appearing very close to the edge of the sun. Such
observations cannot normally be made, because the brightness of the sun
obscures a nearby star. During a total eclipse, however, stars can be observed
and their positions accurately measured even when they appear quite close to
the edge of the sun. Expeditions were sent out to observe the eclipses of 1919
and 1922 and made such observations. The apparent positions of the stars were
then compared with their apparent positions some months later, when they
appeared at night far from the sun. Einstein predicted an apparent shift in
position of 1.745 seconds of arc for a star at the very edge of the sun, with
progressively smaller shifts for more distant stars. The expeditions that were
sent to study the eclipses verified these predictions. In recent years,
comparable tests were made of radiowave deflections from distant quasars,
using radiotelescope interferometers (see Radio Astronomy). The tests
yielded results that agreed, to within 1 percent, with the values predicted by
general relativity.
Another confirmation of general relativity
involves the perihelion of the planet Mercury. For many years it had been known
that the perihelion (the point at which Mercury passes closest to the sun)
revolves about the sun at the rate of once in 3 million years, and that part of
this perihelion motion is completely inexplicable by classical theories. The
theory of relativity, however, does predict this part of the motion, and recent
radar measurements of Mercury's orbit have confirmed this agreement to within
about 0.5 percent.
Yet another phenomenon predicted by general
relativity is the timedelay effect, in which signals sent past the sun to a
planet or spacecraft on the far side of the sun experience a small delay, when
relayed back, compared to the time of return as indicated by classical theory.
Although the time intervals involved are very small, various tests made by
means of planetary probes have provided values quite close to those predicted
by general relativity (see Radar Astronomy). Numerous other tests of the
theory could also be described, and thus far they have served to confirm it.
The general theory of relativity
predicts that a massive rotating body will drag space and time around with it
as it moves. This effect, called frame dragging, is more noticeable if the
object is very massive and very dense. In 1997 a group of Italian astronomers
announced that they had detected frame dragging around very dense, rapidly
spinning astronomical objects called neutron stars. The astronomers found
evidence of frame dragging by examining radiation emitted when the
gravitational pull of a dense neutron star sucks matter onto its surface. This
radiation showed slight differences from the radiation that was predicted by
classical physics.
In 1998 another group of astronomers
from the United States and Europe announced that the orbits of some artificial
satellites around the earth showed the effects of frame dragging. The earth is
much lighter and less dense than a neutron star, so the effects of the earth’s
frame dragging are much more subtle than those of the neutron star’s frame
dragging. The astronomers found that the orbits of two Italian satellites seem
to shift about 2 m (about 7 ft) in the direction of the earth’s rotation every
year. The launch of the U.S. spacecraft Gravity Probe B in 2000 should provide
even more evidence of frame dragging around the earth and other bodies.
VI

LATER OBSERVATIONS

Since 1915 the theory of relativity has
undergone much development and expansion by Einstein and by the British
astronomers James Hopwood Jeans, Arthur Stanley Eddington, and Edward Arthur Milne,
the Dutch astronomer Willem de Sitter, and the German American mathematician
Hermann Weyl. Much of their work has been devoted to an effort to extend the
theory of relativity to include electromagnetic phenomena (see Unified
Field Theory). Although some progress has been made in this area, these efforts
have been marked thus far by less success. No complete development of this
application of the theory has yet been generally accepted. See Elementary
Particles.
The astronomers mentioned above also devoted
much effort to developing the cosmological consequences of the theory of
relativity. Within the framework of the axioms laid down by Einstein, many
lines of development are possible. Space, for example, is curved, and its exact
degree of curvature in the neighborhood of heavy bodies is known, but its
curvature in empty space is not certain. Moreover, scientists disagree on
whether it is a closed curve (such as a sphere) or an open curve (such as a
cylinder or a bowl with sides of infinite height). The theory of relativity
leads to the possibility that the universe is expanding; this is the most
likely theoretical explanation of the experimentally observed fact that the
spectral lines of all distant nebulae are shifted to the red; on the other hand
the expandinguniverse theory also supplies other possible explanations. The
latter theory makes it reasonable to assume that the past history of the
universe is finite, but it also leads to alternative possibilities. See Cosmology.
Much of the later work on relativity
was devoted to creating a workable relativistic quantum mechanics. A
relativistic electron theory was developed in 1928 by the British mathematician
and physicist Paul Dirac, and subsequently a satisfactory quantized field
theory, called quantum electrodynamics, was evolved, unifying the concepts of
relativity and quantum theory in relation of the interaction between electrons,
positrons, and electromagnetic radiation. In recent years, the work of the
British physicist Stephen Hawking has been devoted to an attempted full
integration of quantum mechanics with relativity theory.
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