| Relativity Essay, Research Paper
Relativity
Albert Einstein’s theory of relativity has caused major revolutions in
physics and astronomy during the 20th century. It introduced to science
the concept of “relativity”–the notion that there is no absolute motion
in the universe, only relative motion–thus superseding the 200-year-old
theory of mechanics of Isaac Newton. Einstein showed that we reside not
in the flat, Euclidean space and uniform, absolute time of everyday
experience, but in another environment: curved space-time. The theory
played a role in advances in physics that led to the nuclear era, with
its potential for benefit as well as for destruction, and that made
possible an understanding of the microworld of elementary particles and
their interactions. It has also revolutionized our view of COSMOLOGY,
with its predictions of apparently bizarre astronomical phenomena such
as the big bang, NEUTRON STARS, BLACK HOLES, and GRAVITATIONAL WAVES.
SCOPE OF RELATIVITY
The theory of relativity is a single, all-encompassing theory of
space-time, gravitation, and mechanics. It is popularly viewed,
however, as having two separate, independent theoretical parts–special
relativity and general relativity. One reason for this division is that
Einstein presented special relativity in 1905, while general relativity
was not published in its final form until 1916. Another reason is the
very different realms of applicability of the two parts of the theory:
special relativity in the world of microscopic physics, general
relativity in the world of astrophysics and cosmology. A third reason is
that physicists accepted and understood special relativity by the early
1920s. It quickly became a working tool for theorists and
experimentalists in the then-burgeoning fields of atomic and nuclear
physics and quantum mechanics. This rapid acceptance was not, however,
the case for general relativity. The theory did not appear to have as
much direct connection with experiment as the special theory; most of
its applications were on astronomical scales, and it was apparently
limited to adding minuscule corrections to the predictions of Newtonian
gravitation theory; its cosmological impact would not be felt for
another decade. In addition, the mathematics of the theory were thought
to be extraordinarily difficult to comprehend. The British astronomer
Sir Arthur Eddington, one of the first to fully understand the theory in
detail, was once asked if it were true that only three people in the
world understood general relativity. He is said to have replied, “Who
is the third?” This situation persisted for almost 40 years. General
relativity was considered a respectable subject not for physicists, but
for pure mathematicians and philosophers. Around 1960, however, a
remarkable resurgence of interest in general relativity began that has
made it an important and serious branch of physics and astronomy. (By
1977, Eddington’s remark was recalled at a conference on general
relativity attended by more than 800 researchers in the subject.) This
growth has its roots, first, beginning around 1960, in the application
of new mathematical techniques to the study of general relativity that
significantly streamlined calculations and that allowed the physically
significant concepts to be isolated from the mathematical complexity,
and second, in the discovery of exotic astronomical phenomena in which
general relativity could play an important role, including quasars
(1963), the 3-kelvin microwave background radiation (1965), pulsars
(1967), and the possible discovery of black holes (1971). In addition,
the rapid technological advances of the 1960s and ’70s gave
experimenters new high-precision tools to test whether general
relativity was the correct theory of gravitation. The distinction
between special relativity and the curved space-time of general
relativity is largely a matter of degree. Special relativity is actually
an approximation to curved space-time that is valid in sufficiently
small regions of space-time, much as the overall surface of an apple is
curved even though a small region of the surface is approximately flat.
Special relativity thus may be used whenever the scale of the phenomena
being studied is small compared to the scale on which space-time
curvature (gravitation) begins to be noticed. For most applications in
atomic or nuclear physics, this approximation is so accurate that
relativity can be assumed to be exact; in other words, gravity is
assumed to be completely absent. From this point of view, special
relativity and all its consequences may be “derived” from a single
simple postulate. In the presence of gravity, however, the approximate
nature of special relativity may manifest itself, so the principle of
equivalence is invoked to determine how matter responds to curved
space-time. Finally, to learn the extent that space-time is curved by
the presence of matter, general relativity is applied.
SPECIAL RELATIVITY
The two basic concepts of special relativity are the inertial frame and
the principle of relativity. An inertial frame of reference is any
region, such as a freely falling laboratory, in which all objects move
in straight lines with uniform velocity. This region is free from
gravitation and is called a Galilean system. The principle of
relativity postulates that the result of any physical experiment
performed inside a laboratory in an inertial frame is independent of the
uniform velocity of the frame. In other words, the laws of physics must
have the same form in every inertial frame. A corollary is that the
speed of light must be the same in any inertial frame (because a
speed-of-light measurement is a physical experiment) regardless of the
speed of its source or that of the observer. Essentially all the laws
and consequences of special relativity can be derived from these
concepts. The first important consequence is the relativity of
simultaneity. Because any operational definition of simultaneous events
at different locations involves the sending of light signals between
them, then two events that are simultaneous in one inertial frame may
not be simultaneous when viewed from a frame moving relative to the
first. This conclusion helped abolish the Newtonian concept of an
absolute, universal time. In some ways the most important consequences
and confirmations of special relativity arise when it is merged with
quantum mechanics, leading to many predictions in agreement with
experiments, such as elementary particle spin, atomic fine structure,
antimatter, and so on. The mathematical foundations of special
relativity were explored in 1908 by the German mathematician Hermann
Minkowski, who developed the concept of a “four-dimensional space-time
continuum,” in which time is treated the same as the three spatial
dimensions–the fourth dimension of Minkowski space-time.
THE PRINCIPLE OF EQUIVALENCE AND SPACE-TIME CURVATURE
The exact Minkowski space-time of special relativity is incompatible
with the existence of gravity. A frame chosen to be inertial for a
particle far from the Earth where the gravitational field is negligible
will not be inertial for a particle near the Earth. An approximate
compatibility between the two, however, can be achieved through a
remarkable property of gravitation called the weak equivalence principle
(WEP): all modest-sized bodies fall in a given external gravitational
field with the same acceleration regardless of their mass, composition,
or structure. The principle’s validity has been checked experimentally
by Galileo, Newton, and Friedrich Bessel, and in the early 20th century
by Baron Roland von Eotvos (after whom such experiments are named). If
an observer were to ride in an elevator falling freely in a
gravitational field, then all bodies inside the elevator, because they
are falling at the same rate, would consequently move uniformly in
straight lines as if gravity had vanished. Conversely, in an
accelerated elevator in free space, bodies would fall with the same
acceleration (because of their inertia), just as if there were a
gravitational field. Einstein’s great insight was to postulate that this
“vanishing” of gravity in free-fall applied not only to mechanical
motion but to all the laws of physics, such as electromagnetism. In any
freely falling frame, therefore, the laws of physics should (at least
locally) take on their special relativistic forms. This postulate is
called the Einstein equivalence principle (EEP). One consequence is the
gravitational red shift, a shift in frequency f for a light ray that
climbs through a height h in a gravitational field, given by (delta f)/f
= gh/c(2) where g is the gravitational acceleration. (If the light ray
descends, it is blueshifted.) Equivalently, this effect can be viewed as
a relative shift in the rates of identical clocks at two heights. A
second consequence of EEP is that space-time must be curved. Although
this is a highly technical issue, consider the example of two frames
falling freely, but on opposite sides of the Earth. According to EEP,
Minkowski space-time is valid locally in each frame; however, because
the frames are accelerating toward each other, the two Minkowski
space-times cannot be extended until they meet in an attempt to mesh
them into one. In the presence of gravity, space-time is flat only
locally but must be curved globally. Any theory of gravity that fulfills
EEP is called a “metric” theory (from the geometrical, curved-space-time
view of gravity). Because the equivalence principle is a crucial
foundation for this view, it has been well tested. Versions of the
Eotvos experiment performed in Princeton in 1964 and in Moscow in 1971
verified EEP to 1 part in 10(12). Gravitational red shift measurements
using gamma rays climbing a tower on the Harvard University campus
(1965), using light emitted from the surface of the Sun (1965), and
using atomic clocks flown in aircraft and rockets (1976) have verified
that effect to precisions of better than 1 percent.
GENERAL RELATIVITY
The principle of equivalence and its experimental confirmation reveal
that space-time is curved by the presence of matter, but they do not
indicate how much space-time curvature matter actually produces. To
determine this curvature requires a specific metric theory of gravity,
such as general relativity, which provides a set of equations that allow
computation of the space-time curvature from a given distribution of
matter. These are called field equations. Einstein’s aim was to find the
simplest field equations that could be constructed in terms of the
space-time curvature and that would have the matter distribution as
source. The result was a set of 10 equations. This is not, however, the
only possible metric theory. In 1960, C. H. Brans and Robert Dicke
developed a metric theory that proposed, in addition to field equations
for curvature, equations for an additional gravitational field whose
role was to mediate and augment the way in which matter generated
curvature. Between 1960 and 1976 it became a serious competitor to
general relativity. Many other metric theories have also been invented
since 1916. An important issue, therefore, is whether general relativity
is indeed the correct theory of gravity. The only way to answer this
question is by means of experiment. In the past scientists customarily
spoke of the three classical tests proposed by Einstein: gravitational
red shift, light deflection, and the perihelion shift of Mercury. The
red shift, however, is a test of the equivalence principle, not of
general relativity itself, and two new important tests have been
discovered since Einstein’s time: the time-delay by I. I. Shapiro in
1964, and the Nordtvedt effect by K. Nordtvedt, Jr., in 1968. The
confirmation of the deflection of starlight by the Sun by the solar
eclipse expedition of 1919 was one of the triumphant moments for general
relativity and brought Einstein worldwide fame. According to the
theory, a ray of light propagating through the curved space-time near
the Sun should be deflected in direction by 1.75 seconds of arc if it
grazes the solar surface. Unfortunately, measurements of the deflection
of optical starlight are difficult (in part because of need for a solar
eclipse to obscure the light of the Sun), and repeated measurements
between 1919 and 1973 yielded inaccurate results. This method has been
supplanted by measurements of the deflection of radio waves from distant
quasars using radio-telescope interferometers, which can operate in
broad daylight. Between 1969 and 1975, 12 such measurements ultimately
yielded agreement, to 1 percent, with the predicted deflection of
general relativity. The time-delay effect is a small delay in the return
of a light signal sent through the curved space-time near the Sun to a
planet or spacecraft on the far side of the Sun and back to Earth. For
a ray that grazes the solar surface, the delay amounts to 200 millionths
of a second. Since 1964, a systematic program of radar ranging to the
planets Mercury and Venus, to the spacecraft Mariners 6, 7, and 9, and
to the Viking orbiters and landers on Mars has been able to confirm this
prediction to better than half of 1 percent. Another of the early
successes of general relativity was its ability to account for the
puzzle of Mercury’s orbit. After the perturbing effects of the other
planets on Mercury’s orbit were taken into account, an unexplained shift
remained in the direction of its perihelion (point of closest approach
to the Sun) of 43 seconds of arc per century; the shift had confounded
astronomers of the late 19th century. General relativity explained it
as a natural effect of the motion of Mercury in the curved space-time
around the Sun. Recent radar measurements of Mercury’s motion have
confirmed this agreement to about half of 1 percent. The Nordtvedt
effect is one that does not occur in general relativity but is predicted
by many alternative metric theories of gravity, including the
Brans-Dicke theory. It is a possible violation of the equality of
acceleration of massive bodies that are bound by gravitation, such as
planets or stars. The existence of such an effect would not violate the
weak equivalence principle that was used as a foundation for curved
space-time, as that principle applies only to modest-sized objects whose
internal gravitational binding is negligible. One of the remarkable
properties of general relativity is that it satisfies EEP for all types
of bodies. If the Nordtvedt effect were to occur, then the Earth and
Moon would be attracted by the Sun with slightly different
accelerations, resulting in a small perturbation in the lunar orbit that
could be detected by lunar laser ranging, a technique of measuring the
distance to the Moon using laser pulses reflected from arrays of mirrors
deposited there by Apollo astronauts. In data taken between 1969 and
1976, no such perturbation was detected, down to a precision of 30 cm (1
ft), in complete agreement with the zero prediction of general
relativity and in disagreement with the prediction of the Brans-Dicke
theory. A number of secondary tests of more subtle gravitational effects
have also been performed during the last decade. General relativity has
passed every one, while many of its competitors have failed. Tests of
gravitational radiation and inertial frame-dragging are now being
devised. One experiment would involve placing spinning objects in Earth
orbit and measuring expected relativistic effects.
COSMOLOGY
One of the first astronomical applications of general relativity was in
the area of cosmology. The theory predicts that the universe could be
expanding from an initially condensed state, a process known as the big
bang. For a number of years the big bang theory was contested by an
alternative known as the steady state theory, based on the concept of
the continuous creation of matter throughout the universe. Later
knowledge gained about the universe, however, has strongly supported the
big bang theory as against its competitors. Such findings either were
predicted by or did not conflict with relativity theory, thus also
further supporting the theory. Perhaps the most critical piece of
evidence was the discovery, in 1965, of what is called BACKGROUND
RADIATION. This “sea” of electromagnetic radiation fills the universe
at a temperature of about 2.7K (2.7 degrees C above absolute zero).
Background radiation had been proposed by general relativity as the
remaining trace of an early, hot phase of the universe following the big
bang. The observed cosmic abundance of helium (20 to 30 percent by
weight) is also a required result of the big-bang conditions predicted
by relativity theory. In addition, general relativity has suggested
various kinds of celestial phenomena that could exist, including neutron
stars, black holes, gravitational lenses, and gravitational waves.
According to relativistic theory, neutron stars would be small but
extremely dense stellar bodies. A neutron star with a mass equal to
that of the Sun, for example, would have a radius of only 10 km (6 mi).
Stars of this nature have been so compressed by gravitational forces
that their density is comparable to densities within the nuclei of
atoms, and they are composed primarily of neutrons. Such stars are
thought to occur as a by-product of violent celestial events such as
supernovae and other gravitational implosions of stars. Since neutron
stars were first proposed in the 1930s, numerous celestial objects that
exhibit characteristics of this sort have been identified. In 1967 the
first of many objects now called pulsars was also detected. These
stars, which emit rapid regular pulses of radiation, are now taken to be
rapidly spinning neutron stars, with the pulse period represent the
period of rotation. Black holes are among the most exotic of the
predictions of general relativity, although the concept itself dates
from long before the 20th century. These theorized objects are
celestial bodies with so strong a gravitational field that no particles
or radiation can escape from them, not even light–hence the name. Black
holes most likely would be produced by the implosions of extremely
massive stars, and they could continue to grow as other material entered
their field of attraction. Some theorists have speculated that
supermassive black holes may exist at the centers of some clusters of
stars and of some galaxies, including our own. While the existence of
such black holes has not been proven beyond all doubt, evidence for
their presence at a number of known sites is very strong. In theory,
even a relatively small mass could become a black hole. The mass would
have to be compressed to higher and higher densities until it diminished
to a certain critical radius, the so-called “event horizon,” named the
SCHWARZSCHILD RADIUS because it was first calculated in 1916 by German
astronomer Karl Schwarzschild. (His calculations apply to a nonrotating
object. The figures for a rotating object were developed in 1963 by New
Zealand mathematician Roy Kerr.) For an object having the mass of the
Sun the event horizon would be approximately 3 km (2 mi). Scientists
such as the English theoretical physicist Stephen HAWKING have
speculated that tiny black holes may indeed exist. The concept of
gravitational lenses is based on the already discussed and proven
relativistic prediction that when light from a celestial object passes
near a massive body such as a star, its path is deflected. The amount
of deflection depends on the massiveness of the intervening body. From
this came the notion that very massive celestial objects such as
galaxies could act as the equivalent of crude optical lenses for light
coming from still more distant objects beyond them. An actual
gravitational lens was first identified in 1979. One phenomenon
predicted by general relativity has not yet been substantially verified,
however: the existence of gravitational waves. Gravitational waves
would be produced by changes in gravitational fields. They would travel
at the speed of light, transport energy, and induce relative motion
between pairs of particles in their path (or produce strains in more
massive objects). Astrophysicists think that gravitational waves should
be emitted by dynamic sources such as supernovae, massive binary (or
multiple-star) systems, and black holes or collisions between black
holes. Various attempts, unsuccessful thus far, have been made to
observe such waves. A more fundamental matter confronting general
relativity is that of the attempt being made by physicists to unite
gravitation with QUANTUM MECHANICS, the other paradigm of modern
physics. This search for some UNIFIED FIELD THEORY is the major task of
workers in QUANTUM COSMOLOGY.
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