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.