After graduation Einstein was unable to obtain a regular position
for two years and did occasional tutoring and substitute teaching,
until he was appointed an examiner in the Swiss Patent Office at
Berne. The seven years Einstein spent at this job, with only evenings
and Sundays free for his own scientific work, were years in which
he laid the foundations of large parts of twentiethcentury physics.
They were probably also the happiest years of his life. He liked
the fact that his job was quite separate from his thoughts about
physics, so that he could pursue these freely and independently,
and he often recommended such an arrangement to others later on.
In 1903 Einstein married Mileva Maric, a Serbian girl who had been
a fellow student in Zurich. Their two sons were born in Switzerland.
Einstein received his doctorate in 1905 from the
University of Zurich for a dissertation entitled, “Eine neue
Bestimmung der Moleküldimensionen” (“A New Determination
of Molecular Dimensions”), a work closely related to his studies
of Brownian motion. It took only a few years until he received academic
recognition for his work, and then he had a wide choice of positions.
His first appointment, in 1909, was as associate professor (extraordinarius)
of physics at the University of Zurich. This was followed quickly
by professorships at the German University in Prague, in 1911, and
at the Polytechnic in Zurich, in 1912. Then, in the spring of 1914,
Einstein moved to Berlin as a member of the Prussian Academy of
Sciences and director of the Kaiser Wilhelm Institute for Physics,
free to lecture at the university or not as he chose. As it turned
out, he found the scientific atmosphere in Berlin very stimulating,
and he greatly enjoyed having colleagues like Max Planck, Walther
Nernst, and, later, Erwin Schödinger and Max von Laue. During
World War 1, Einstein’s scientific work reached a culmination
in the general theory.of’relativity, but in most other ways
his life did not go well.
Mileva Einstein and their two sons spent the war
years in Switzerland and the Einsteins were divorced soon after
the end of the war. Einstein then married his cousin Elsa, a widow
with two daughters. Einstein’s health suffered, too. One of
his few consolations was his continued correspondence and occasional
visits with his friends in the NetherlandsPaul Ehrenfest and H.
A. Lorentz, especially the latter, whom Einstein described as having
“meant more to me personally than anybody else I have met
in my lifetime” and as “the greatest and noblest man
of our times.”
Einstein became suddenly famous to the world at
large when the deviation of light passing near the sun, as predicted
by his general theory of relativity, was observed during the solar
eclipse of 1919. His name and the term relativity became household
words. The publicity, even notoriety, that ensued changed the pattern
of Einstein’s life.
In 1933 Einstein was considering an arrangement
that would have allowed him to divide his time between Berlin and
the new Institute for Advanced Study at Princeton. But when Hitler
came to power in Germany, he promptly resigned his position at the
Prussian Academy and joined the Institute. Princeton became his
home for the remaining twentytwo years of his life. He became an
American citizen in 1940.
During the 1930’s Einstein was convinced that the menace to
civilization embodied in Hitler’s regime could be put down
only by force. In 1939, at the request of Leo Szilard, Edward Teller,
and Eugene Wigner, he wrote a letter to President Franklin D. Roosevelt
pointing out the dangerous military potentialities offered by nuclear
fission and warning him of the possibility that Germany might be
developing nuclear weapons. This letter helped to initiate the American
efforts that eventually produced the nuclear reactor and the fission
bomb, but Einstein neither participated in nor knew anything about
these efforts.
Einstein received a variety of honours in his
lifetime – from the 1921 Nobel Prize in physics to an offer
(which he did not accept) of the presidency of Israel after Chaim
Weizmann’s death in 1952.
One of Einstein’s last acts was his signing
of a plea, initiated by Bertrand Russell, for the renunciation of
nuclear weapons and the abolition of war. He was drafting a speech
on the current tensions between Israel and Egypt when he suffered
an attack due to an aortic aneurysm; he died a few days later. But
despite his concern with world problems and his willingness to do
whatever he could to alleviate them, his ultimate loyalty was to
his science. As he said once with a sigh to an assistant during
a discussion of political activities: “Yes, time has to be
divided this way, between politics and our equations. But our equations
are much more important to me, because politics is for the present,
but an equation like that is something for eternity.”
Einstein’s early interests lay in statistical
mechanics and intermolecular forces. However, his predominant concern
throughout the career was the search for a unified foundation for
all of physics. The disparity between the discrete particles of
matter and the continuously distributed electromagnetic field came
out most clearly in Lorentz’ (18531928) electron theory,
where matter and field were sharply separated for the first time.
This theory strongly influenced Einstein. The problems generated
by the incompatibility between mechanics and electromagnetic theory
at several crucial points claimed his attention. His strengths with
these problems led to his most important early work – the
special theory of relativity and the theory of quanta in 1905.
The discovery of Xrays, radioactivity, the electron
and the quantum theory brought about a sea change in our ideas and
understanding of phenomena at the atomic level. The world of Physics
was, however, changing in far reaching ways  with ramifications
for our understanding of the very shape of time, space and the universe.
This part of the revolution was brought about Albert Einstein, a
brilliant and creative theorist and the only thinker ever to be
ranked in the same class as Newton. To understand this part of the
revolution, we shall need to go back to James Clerk Maxwell (18311879)
and his ideas about light.
Ether – Unbroken from star to star
Maxwell had introduced a revolutionary set of equations that predicted
the existence of electromagnetic fields and established that magnetism,
electricity and light were a part of the same spectrum: the electromagnetic
spectrum. Light, he maintained, was a wave, not a particle, and
he thought that it travelled through an invisible medium he called
“the ether”, which filled all space. But physicists
began to see a problem, not with Maxwell’s electromagnetic
field equations, but with his ideas about the ether.
Maxwell wasn’t the first to come up with
this idea that some invisible medium called the ether must fill
the vastness of space, extending “unbroken from star to star”.
It dated back to the time of ancient Greeks. “There can be
no doubt,” Maxwell said in a lecture in 1873, “that
the interplanetary and interstellar spaces are not empty but are
occupied by a material substance or body, which is certainly the
largest, and probably the most uniform, body of which we have any
knowledge”. The idea of the ether seemed necessary because,
if light was a wave, it seemed obvious that it had to be a wave
travelling in some medium. But accepting what “seems obvious”
is not the way to do good science; if the ether existed, it should
be possible to find some proof of its existence.
The most famous “failed” experiment
Albert Michelson (18521931), an American Physicist,
had an idea . If the ether that filled the universe were stationary,
then the planet Earth would meet resistance as it moved through
the ether, creating a current, a sort of “wind”, in
the ether. So it followed that a light beam moving with the current
ought to be carried along by it, whereas a light beam travelling
against the current should be slowed. While studying with Hermann
von Helmholtz (18211894) in Germany, in 1881 Michelson built an
instrument called an interferometer, which could split a beam of
light, running the two halves perpendicular to each other, and then
rejoin the split beam in a way that made it possible to measure
differences in the speeds with great precision.
Michelson ran his experiment, but he was puzzled
by his results. They showed no differences in light velocity for
the two halves of the light beam. He concluded, “The result
of the hypothesis of a stationary ether is …. shown to be
incorrect, and the necessary conclusion follows that the hypothesis
is erroneous”.
But may be his results were wrong. He tried his
experiment again and again, each time trying to correct for any
possible error. Finally, in 1887, joined by Edward Morley, Michelson
tried a test in Cleveland, Ohio. Using improved equipment, and taking
every imaginable precaution against inaccuracy, this time surely
they would succeed in detecting the ether. But the experiment failed
again. Let us briefly describe the salient features of this momentous
experiment.
The Experiment
If there is an ether pervading space, we move through it with at
least the 3x104 m/sec speed of the earth’s orbital motion
about the sun; if the sun is also in motion, our speed through the
ether is even greater (Motions of the Earth through a hypothetical
ether). From the point of view of an observer on the earth,
the ether is moving past the earth. To detect this motion, we can
use the pair of light beams formed by a half silvered mirror (The
Michelson  Morley experiment). One of these light beams
is directed to a mirror along a path perpendicular to the ether
current, while the other goes to a mirror along a path parallel
to the ether current. The optical arrangement is such that both
beams return to the same viewing screen. The purpose of the clear
glass plate is to ensure that both beams pass through the same thickness
of air and glass.
If the path lengths of the two beams are exactly
the same, they will arrive at the screen in phase and will interfere
constructively to yield a bright field of view. The presence of
an ether current in the direction shown, however, would cause the
beams to have different transit times in going from the half silvered
mirror to the screen, so that they would no longer arrive at the
screen in phase but would interfere destructively. In essence this
is the famous experiment performed in 1887 by Michelson and Morley.
In the actual experiment the two mirrors are not
perfectly perpendicular, with the result that the viewing screen
appears crossed with a series of bright and dark interference fringes
due to differences in path length between adjacent light waves (Fringe
Pattern observed in Michelson  Morley experiment). If
either of the optical paths in the apparatus is varied in length,
the fringes appear to move across the screen as reinforcement and
cancellation of the waves succeed one another at each point. The
stationary apparatus, then, can tell us nothing about any time difference
between the two paths. When the apparatus is rotated by 90°,
however, the two paths change their orientation relative to the
hypothetical ether stream, so that the beam formerly requiring the
time tA (along parth A) for the round trip now required tB (along
path B) and vice versa. If these times are different, the fringes
will move across the screen during the rotation.
This information can be used to calculate the fringe
shift expected on the basis of the ether theory. The expected fringe
shift ‘n’ in each path when the apparatus is rotated
by 90° is given by
n = Dv2 / ?c2 ;
Here, D is the distance between half silvered
mirror and each of the other mirrors (made about 10 metres using
multiple reflections), v is the ether speed  which is the Earth’s
orbital speed 3x104 (m/s), c is the speed of the light = 3x108 m/sec,
and l is the wave length of light used, about 5000Å (1Å=1010m),
one then obtains n=0.2 fringe.
Since both paths experience this fringe shift,
the total shift should amount to 2n or 0.4 fringe. A shift of this
magnitude is readily observable, and therefore, Michelson and Morley
looked forward to establishing directly the existence of the ether.
To everybody’s surprise, no fringe shift whatever was found.
When the experiment was performed at different seasons of the year
and in different locations, and when experiments of other kinds
were tried for the same purpose, the conclusions were always identical:
no motion through the ether was detected.
The negative result of the MichelsonMorley
experiment had two consequences. First, it rendered untenable
the hypothesis of the ether by demonstrating that the ether has
no measurable properties – an ignominious end for what had
once been a respected idea. Second, it suggested a new physical
principle: the speed of light in free space is the same everywhere,
regardless of any motion of source or observer. As a result, the
MichelsonMorley experiment has become the most famous “failed”
experiment in the history of science. They had started out to study
the ether, only to conclude that the ether did not exist. But if
this were true, how could light move in “waves” without
a medium to carry it? What’s more, the experiment indicated
that the velocity of light is always constant.
It was a completely unexpected conclusion. But
the experiment was meticulous and the results irrefutable. Lord
Kelvin (18241907), said in a lecture in 1900 at the Royal Institution
that Michelson and Morley’s experiment had been “carried
out with most searching care to secure a trustworthy result,”
casting “a nineteenth century cloud over the dynamic theory
of light”. The conclusion troubled physicists everywhere,
though. Apparently, they were wrong about the existence of the ether
– and if they were wrong, then light was a wave that somehow
could travel without a medium to travel through. What’s more,
the Michelson  Morley results seemed to call into question the
kind of Newtonian relativity that had been around for a couple of
centuries and by this time was well tested; the idea that the speed
of an object can differ, depending upon the reference frame of the
observer. Suppose two cars are travelling along on a road. (There
weren’t many cars or roads in 1887, but one gets the idea.).
One car is going 80 kms per hour, the other 75 kms per hour. To
the driver of the slower car, the faster car would be gaining ground
at a rate of 5 kms per hour. Why would light be any different?
But that’s just what the Michelson and Morley
experiment had shown; Light does behave differently. The velocity
of light is always constant – no matter what. Astronauts travelling
in their spaceship at a speed of 2,90,000 km/sec alongside a beam
of light (which travels at 3,00,000 km/sec) would not perceive the
light gaining on them by 10,000 km/sec. They would see light travelling
at a constant 3,00,000 km/sec. The speed of light is a universal
absolute!
The Four
Dimensions
According to Einstein's views, space and
time are more intimately connected with one another than it
was supposed before and with in certain limits, the notion
of space may be substituted by the notion of time and vice
versa. To make this statement more clear, let us consider
a passenger in a train having his meal in the dining car.
The waiter serving him will know that the passenger ate his
soup, meals and dessert in. the same place, that is, at the
same able in the dining car. But, from the point of view of
a person on the ground, the same passenger consumed the three
courses at points along the track separated by many kilometres.
We Can hence make the following trivial statement: Events
taking place in the same place but at different times in a
moving system will be considered by a ground observer as taking
place at different places.
Now, following Einstein's idea concerning
the reciprocity of space and time, let us replace in the above
statement the word "place" by the word "time"
and vice versa. The statement will now read: Events taking
place at the same time but In different places in a moving
system will be considered by a ground observer as taking place
at different times. This statement is far from being trivial.
It means that if, for example, two passengers at the far ends
of the dining car had their afterdinner coffee sipped simultaneously
from the point of view of the diningcar waiter, the person
standing on the ground will insist that the coffee was sipped
at different times! Since according to the principle of relativity,
neither Of the two reference systems should be 'preferred
to the other (the train moves relative to the ground or the
ground moves relative to the train), we do not have any reason
to take the waiter's impression as being true and ground observer's
impression as being wrong or vice versa. Of course, this would
not be apparent to you If you were the ground observer. This
is so because the distance of, say, 30 metres between two
passengers sipping their after dinner coffee at opposite ends
of the dinning car translates into a time interval of only
108 seconds, and there is no wonder that this is not apparent
to our senses. It would become appreciable when the train
travels close to the speed of light.
The transformation of time intervals into
space Intervals and vice versa was given a simple geometrical
interpretation by the German mathematician H. Minkowski. He
proposed that time or duration be considered as the fourth
dimension supplementing the three spatial dimensions (x, y,
z) and that transformation from one system of reference to
another be considered as a rotation of coordinates systems
in this four dimensional space. A point in these four dimensional
space is called an event. Relativistic effects like the length
contraction and the time dilation then become consequences
of the rotation of these spacetime coordinates.
These effects being relative, each of the
two observers moving with respect to one another will see
the other fellow as somewhat flattened in the direction of
his motion and will consider his watch to be slow! 
The Special Theory of Relativity:
Surprisingly, Einstein never received a Nobel
prize for the most important paper that he published in 1905, the
one that dealt with a theory that came to be known as the special
theory of relativity.
He also tossed out the idea of the ether, which
Michelson and Morley had called into question. Maxwell needed it
because he thought light travelled in waves, and if that were so,
he thought, it needed some medium in which to travel. But what if,
as Max Planck’s (18581947) quantum theory stated, light travels
in discrete packets or quanta? Then it would act more like particles
and wouldn’t require any medium to travel in.
By making these assumptions — that the velocity
of light is a constant, that there is no ether, that light travels
in quanta and that motion is relative — he was able to show
why the Michelson  Morley experiment came out as it did, without
calling the validity of Maxwell’s electromagnetic equations
into question. But, where does “relativity” enter?
We mentioned earlier the role of the ether as
a universal frame of reference with respect to which light waves
were supposed to propagate. Whenever we speak of “motion”,
of course, we really mean motion relative to a “frame of reference”.
The frame of reference may be a road, the earth’s surface,
the sun, the center of our galaxy; but in every case we must specify
it. Stones dropped in New Delhi and in Washington both fall “down”,
and yet the two move in opposite directions relative to the earth’s
center. Which is the correct location of the frame of reference
in this situation, the earth’s surface or its center? The
answer is that all frames of reference are equally correct, although
one may be more convenient to use in a specific case. If there were
an ether pervading all space, we could refer all motion to it, and
the inhabitants of New Delhi and Washington would escape from their
quandary. The absence of an ether, then, implies that there is no
universal frame of reference, so that all motion exists solely relative
to the person or instrument observing it.
The theory of relativity resulted from an analysis
of the physical consequences implied by the absence of a universal
frame of reference. The special theory of relativity treats problems
involving the motion of frames of reference at constant velocity
(that is, both constant speed and constant direction) with respect
to one another; the general theory of relativity, proposed by Einstein
a decade later, treats problems involving frames of reference accelerated
with respect to one another. The special theory has had a profound
influence on all of physics.
The paper in which the young Albert Einstein in
1905 set out the special theory of relativity confronted common
sense with several new and disquieting ideas. It abolished the ether,
and it showed that matter and energy are equivalent. The new ideas
derive from the central conception of relativity: that time does
not run at the same pace for every observer. This bold conception
lies at the heart of modern physics, all the way from the atomic
to the cosmic scale. Yet it is still hard to grasp, and the paradoxes
it pose continue to puzzle and to stimulate each generation of physicists.
Two Axioms
The special theory of relativity is based upon
two axioms. The first states that the laws of physics may be expressed
in equations having the same form in all frames of reference moving
at constant velocity with respect to one another. This axiom expresses
the absence of a universal frame of reference. If the laws of physics
had different forms for different observers in relative motion,
it could be determined from these differences which objects are
“stationary” in space and which are “moving”.
But because there is no universal frame of reference, this distinction
does not exist in nature; hence the above axiom. Consequently, this
axiom implies that two observers, each of whom appears to the other
to be moving with a constant speed in a straightline, cannot tell
which of them is moving.
The second axiom of special relativity states
that the speed of light in free space has the same value for all
observers, regardless of their state of motion. This axiom follows
directly from the result of the Michelson  Morley experiment, and
implies that when both observers measure the speed of light, they
will get the same answer.
Neither of these axioms was new in itself. The
first axiom had long been implicit in the accepted laws of mechanics.
The second one was beginning to be accepted as the natural interpretation
of Michelson and Morley’s experiment in 1887. What was new,
then, in Einstein’s analysis was not one axiom or the other
but the confrontation of the two. They form the two principles of
relativity not singly but together. This is how Einstein presented
them jointly at the beginning of his paper.
So basically, in the special theory of relativity
Einstein revamped Newtonian physics such that when he worked out
the formulas, the relative speed of light always stayed the same.
It never changes relative to anything else, even though other things
change relative to each other. Mass, space and time all vary depending
upon how fast you move. As observed by others, the faster you move,
the greater your mass, the less space you take up and the more slowly
time passes for you! The more closely you approach the speed of
light, the more pronounced these effects become. Let us have a look
at some of the consequences of the theory of relativity.
Time Dilation
It follows at once from the two axioms combined
that we have to revise the traditional idea of time. By tradition
we take it for granted that time is the same everywhere and for
everyone. Why not? It seems natural to assume that time is a universal
“now” for every traveller anywhere in the universe.
But, according to the theory of special relativity, time cannot
run at the same pace for two observers, one of whom is moving relative
to the other, if they are to get the same speed (that is for light)
when they time a beam of light that is moving with one of them.
Consider this example.
If you were an astronaut travelling at 90 percent
of the speed of light (about 2,70,000 kms per second), you could
travel for five years (according to your calendar watch) and you’d
return to Earth to find that 10 years had passed for the friends
you’d left behind. Or, if you could rev up your engines to
help you travel at 99.99 percent of the speed of light, after traveling
for only 6 months you’d find that 50 years had sped by our
Earth during your absence!
Clocks moving with respect to an observer appear
to tick less rapidly than they do when at rest with respect to him.
If we, in the S frame, or the stationary frame of reference, observe
the length of time t some event requires in a frame of reference
S’ in motion relative to us, our clock will indicate a longer
time interval than the t0 determined by a clock in the moving frame.
This effect is called time dilation.
According to the theory of relativity, t and
to are related as
t = t0 /SQRT (1v2/c2 )
where v is the speed of the frame of reference
S’ (the moving frame) with respect to S (the stationary frame
in which the observer is situated). Obviously t is greater than
t0 as v cannot be greater than c. thus, a stationary clock measures
a longer time interval between events occurring in a moving frame
of reference than does a clock in the moving frame.
So the laws of relativity say that time is relative;
it does not always flow at the same rate for the two travellers
moving relative to each other. For example, moving clocks slow down.
In the 1960s a group of scientists at the University of Michigan
took two sets of atomic clocks with an accuracy to 13 decimal places.
They put one set of airplanes flying around the world. The other
identical set remained behind on the ground. When the airplanes
with the clocks landed, and those clocks were compared to the clocks
that stayed still, the clocks that had ridden on the airplanes had
actually ticked fewer times than those that had stayed on the ground.
It may also be remarked that when v approaches
c, the processes in the moving frame S’ appear to further
slow down to an observer in S. When v=c, t becomes infinitely long!
This equation then sets a speed limit on the moving frame S’
which is equal to the speed of light.
Let us now consider a common objection raised
against the theory of relativity. Since there is no absolute motion
of any sort, there is no “preferred” frame of reference.
It is always possible to choose a moving object as a fixed frame
of reference without violating any natural law. When the earth is
chosen as a frame, the astronaut makes the long journey, returns,
finds himself younger than his stayathome brother. All well and
good. But what happens when the spaceship is taken as the frame
of reference (S)? Now, it must be assumed that the earth makes a
long journey away from the ship and back again. In this case, it
is the twin on the ship who is the stayathome. When the earth
gets back to the spaceship, will not the earth rider be the younger?
If so, the situation is more than a paradoxical affront to common
sense. It is a flat logical contradiction. Clearly each twin cannot
be younger than the other! A paradox! Not really. The application
of the theory of relativity shows that the twin that travelled indeed
remains young than his twin stayathome brother!
The
Twin Paradox
Indeed, all sorts of objections were raised
against relativity. One of the earliest, most persistent objections
centred around a paradox that had been mentioned by Einstein
in his 1905 paper himself. The workd “paradox”
is used in the sense of something opposed to common sense,
not something logically contradictory. It is usually described
as a thought experiment involving twins. They synchronize
their watches. One twin gets into a spaceship and makes a
long trip through the space. When he returns, the twins compare
their watches. According to the special theory of relativity,
the traveller’s watch will show a slightly earlier time.
In other words, time on the spaceship would have gone at a
slower rate than time on the earth!
It may seem at first sight that the two
observers who part and then meet again must necessarily be
in a symmetrical relation. Whatever journey each has made
is, after all, relative; and it may therefore seem as if each
observer is free to say that he has not travelled at all and
that all the travelling has been done by the other. Indeed,
we may ask, does not the first axiom of relativity say this?
Does not the first axiom say that two observers cannot tell
which of them has moved and which of them has stayed still?
No, it does not. What the first axiom of
relativity says is something much sharper, something much
more restricted and more precise. The first axiom says that
if each of two observers seems to the other to be moving at
a constant speed in a straight line, they cannot tell which
of them is moving. But the axiom says nothing about observers
in arbitrary motion. It says nothing about them if they do
not move in straight lines and nothing about them if they
do not move at a constant speed.
Here is the crux of the matter. Two observers
who separate and meet again cannot fulfill the conditions
of the first axiom of relativity throughout such a journey.
Suppose one of them remains still. Then the other can travel
in a straight line going and coming, but if he does this,
he must turn back at some pointthat is, he must change his
speed. Or the traveller can move at a constant speed, but
if he does this, he cannot move in a straight linehe must
move in a curve if he is to come back to his starting point.
Two observers who part and meet again can fulfill one condition
of the first axiom of relativity, if they wish, but they cannot
fulfill both.
And at once, as soon as a traveller departs
from the conditions of the first axiom, he knows that he is
moving. He feels the outside forces that produce a change
of motion. If he is traveling in a straight line and has to
come to rest, he knows physically that he is decelerating;
he can tell that he is, by carrying an accelerometer and looking
at it. Indeed, all he needs to carry is a bucket of water:
if the surface begins to tilt, he knows that he is changing
speed. In the same way, if the traveler is rounding a curve,
he can tell that he is moving by the acceleration he feelsor
by carrying an accelerometer or a bucket of water. We cannot
detect a constant speed in a straight line: that is the first
axiom of relativity. But we can detect any accelerated motion:
that is a physical fact we have all experienced. Lying in
a sleeping compartment in the dark at night, we may not be
able to tell whether the train is moving or not. But we can
tell when the train brakes, and we can tell when it rounds
a bend. We can tell because we are thrown about; we act as
our own accelerometer.
Therefore if I stay at home and you go on
a journey and come back, the relation between us is not symmetrical.
You can tell that you have traveled, even if you travel in
a dark trainyou can tell by carrying an accelerometer. And
I can tell that I have stayed at home, because my accelerometer
has recorded no change of speed or of direction. The traveller
who makes a round trip can be distinguished from the stayathome.
Now consider what happens to your clock,
the traveller’s. Imagine your round trip broken down
into a series of short, straight paths, along each of which
you can keep your speed constant. Then along each short path
your clock seems to me to run slower than mine. When you return,
your clock should be behind mine, by the sum of these losses;
and you should have aged less than I. Can this be so? It can,
and it. The difference in our timekeeping does not contradict
any symmetry you may find in the situation. It does not contradict
your finding that, along any short path, my clock also seems
to you to be running slower than yours. Your findings do not
add up because you do not remain faithful to the first axiom
of relativity: your view of my time changes every time you
move abruptly from one straight path to another. Only my view
of your time losses accumulates steadily, because only I remain
faithful to the first axiom of relativity throughout.
Source: The Clock Paradox
by J. Bronowski 
Length Contraction
Relativity also says that the faster an object
moves, the more its size shrinks in the direction of its motion,
as seen by a stationary observer. This implies that the length of
an object in motion with respect to a stationary observer appears
to be shorter than when it is at rest with respect to him, a phenomenon
known as the Lorentz  FitzGerald contraction.
Because the relative velocity of the two frames
S and S’ the one moving with velocity v with respect to the
frame S, appears only as v2 in the equations, it does not matter
which frame we call S and which S’. If we find that the length
of a rocket is L0 when it is on its launching pad, we willl find
from the ground that its length L when moving with the speed v is
L = L0 Ö1v2/c2, while to a man in the rocket, objects on the
earth behind him appear shorter than they did when he was on the
ground by the same factor Ö1v2/c2. The length of an object
is a maximum when measured in a reference frame in which it is moving.
The relativistic length contraction is negligible for ordinary speeds,
but, it is an important effect at speeds close to the speed of light.
At a speed v=1500 km/sec or about 0.005 percent of the speed of
light, L measured in the moving frame S’ would be about 99.9985%
of L0, but when v is about 90% of the speed of light L would be
only about 44% of L0! It is worth emphasising the fact that the
contraction in length occurs only in the direction of the relative
motion.
A Striking Illustration
A striking illustration of both time dilation
and the length contraction occurs in the decay of unstable particles
called m mesons. m mesons are created high in the atmosphere (several
kilometres above the surface of the Earth) by fast cosmic ray particles
arriving at the Earth from space and reach sea level in profusion
travelling at 0.998 of the velocity of light. m mesons ordinarily
would decay into electrons only in 2 x 106 seconds. During this
time they may travel a distance of only 600 metres. However, relative
to mesons, the distance (through which they travel) gets shortened
while relative to us, their life span gets increased. Hence, despite
their brief lifespans, it is possible for mesons to reach the ground
from the considerable altitudes at which they are formed.
Heavier the Faster
One more interesting consequence of the special
theory of relativity is that as the objects approach the speed of
light, their mass approaches infinity. The mass m of a body measured
while in motion in terms of m0 when measured at rest are related
by,
m = m0 Ö1v2/c2
The mass of a body moving at the speed of v relative
to an observer is larger than its mass when at rest relative to
the observer by the factor 1/ Ö1v2/c2.
Relativistic mass increases are significant only
at speeds approaching that of light. At a speed one tenth that of
light the mass increase amounts to only 0.5 per cent, but this increase
is over 100 per cent at a speed nine tenths that of light. Only
atomic particles such as electrons, protons, mesons, and so on can
have sufficiently high speeds for relativistic effects to be measurable,
and in dealing with these particles the “ordinary” laws
of physics cannot be used. Historically, the first confirmation
of this effect was discovery by Bucherer in 1908 that the ratio
e/m of the electron’s charge to its mass is smaller for fast
electrons than for slow ones; this equation, like the others of
special relativity, has been verified by so many experiments that
it is now recognized as one of the basic formulas of physics.
Mass? Energy? Or Mass Energy?
Here is yet another astounding consequnce of the
theory of relativity. Using his famous equation, E=mc2, Einstein
showed that energy and mass are just two facets of the same thing.
In this equation, E is energy, m is mass and c2 is the square of
the speed of light, which is a constant. So the amount of energy
E, is equal to the mass of an object multiplied by the square of
the speed of light.
In addition to its kinetic, potential, electromagnetic, thermal,
and other familiar guises, then, energy can manifest itself as mass.
The conversion factor between the unit of mass (kg) and the unit
of energy (joule) is c2, so 1 kg of matter has an energy. content
of 9 x 1016 joules. Even a minute bit of matter represents a vast
amount of energy.
Since mass and energy are not independent entities,
the separate conservation principles of energy and mass are properly
a single one, the principle of conservation of “mass energy”.
Mass can be created or destroyed, but only if an equivalent amount
of energy simultaneously vanishes or comes into being, and vice
versa.
It is this famous mass energy conversion relationship
that is responsible for generation of energy in stars, atomic bombs,
and the nuclear reactors!
Where common sense fails
The consequences of relativity described in the
preceding paragraphs seems completely against all common sense.
But common sense is based on everyday experience, and things don’t
get really strange with relativity until you venture into the very,
very fast. Let us understand this aspect in some detail. Consider
a rifleman in a jeep moving with velocity v with respect to the
ground. The rifleman shoots a bullet in the forward direction with
the muzzle velocity V. Now, the velocity of the bullet with respect
to the ground, in accordance with the theory of relativity, will
be, not V+v, but (V + v) / (1 + vV/c2), where c is the velocity
of light. If both velocities V and v are small compared to the velocity
of light, the second term in the denominator is practically zero
and the old “common sense” formula holds. But either
V or v, or both approach the velocity of light, the situation will
be quite different. Consider V = v =0.75 c. According to the common
sense, the velocity of the bullet with respect to the ground should
be 1.5 c, i.e. 50 per cent more than the velocity of light. However,
putting V = 0.75 c and v = 0.75 c in the above formula, we get 0.96
c for the velocity of bullet with respect to the ground, which is
still less than the speed of light! In the limiting case, if we
make V, and the velocity of the jeep v = c, we obtain, (c + c) /
(1 + (c2) / c2) = c
Fantastic as it may look at first sight, Einstein’s law for
the addition of two velocities is correct and has been confirmed
by direct experiments. Thus Einstein’s theory of relativity
leads us to the conclusion that it is impossible to exceed the velocity
of light by adding two (or more) velocities no matter how close
each of these velocities is to that of light! The velocity of light,
therefore, assumes the role of a universal speed limit, which cannot
be exceeded no matter what we do! No matter how counter intuitive
the idea of relativity may seem, we may remember that every experimental
test of this theory till date has confirmed that Einstein was right!
The General Theory of Relativity:
How does the general theory of relativity differ
from the special theory? Let us have a brief look.
Strangely enough, it was another four years after Einstein’s
publication of his papers on the photoelectric effect, Brownian
motion and the special theory of relativity, before he succeeded
in securing a teaching position at the University of Zurich —
and a poorly paying one at that. But by 1913, thanks to the influence
of Planck, the Kaiser Wilhelm Institute near Berlin created a position
for him. Ever since his 1905 publications, Einstein had been working
on a bigger theory: his general theory of relativity. The special
theory had applied only to steady movement in a straight line. But
what happened when a moving object sped up or slowed down or curved
in a spiral path? In 1916, he published his general theory of relativity,
which had vast implications, especially on the cosmological scale.
Many physicists consider it the most elegant intellectual achievement
of all time .
The general theory preserves the tenets of the
special theory while adding a new way of looking at gravity —
because gravity is the force that causes acceleration and deceleration
and curves the paths of moons around planets, of planets around
the sun, and so on. Einstein realized that there is no way to tell
the difference between the effects of gravity and the effects of
acceleration. So he abandoned the idea of gravity as a force and
talked about it instead as an artifact of the way we observe objects
moving through space and time. According to Einstein’s relativity,
a fourth dimension — time — joins the three dimensions
of space (height, length and width), and the four dimensions together
form what is known as the space time continuum.
To illustrate the idea that acceleration and gravity
produce essentially the same effects, Einstein used the example
of an elevator, with its cables broken, falling from the top floor
of a building. As the elevator falls, the effect on the occupants
is “weightlessness”, as if they were aboard a spaceship.
For that moment they are in free fall around the Earth. If the people
inside couldn’t see anything outside the elevator, they would
have no way to tell the difference between this experience and the
experience of flying aboard a spaceship in orbit.
Einstein made use of this equivalence to write
equations that saw gravity not as a force, but as a curvature in
space time — much as if each great body were located on the
surface of a great rubber sheet (A heavy object placed on
a streched rubber sheet makes an indentation. The presence of the
Sun "indents" spacetime in an analogous manner)
. A large object, such as a star, bends or warps space time, much
like a large ball resting on a rubber sheet would cause a depression
or sagging on its surface. The distortions caused by masses in the
shape of space and time result in what we call gravity. What people
call the “force” of gravity is not really a characteristic
of objects like stars or planets, but comes from the shape of space
itself.
In fact, this curvature has been confirmed experimentally.
Einstein made predictions in three areas in which his general theory
was in conflict with Newton’s theory of gravity:

Einstein’s general theory allowed
for a shift in a perihelion (the point nearest the Sun) of a
planet’s orbit as shown in (Figure). Such a shift in Mercury’s
orbit had baffled astronomers for years to which the general
theory of relativity offered an explanation.

Light in an intense gravitational field
should show a red shift as it fights against gravity to leave
a star. Indeed, comparing the vibration frequencies of spectral
lines in sunlight with light emitted by terrestrial sources,
astronomers have found that in the former case all vibration
periods are lengthened (or frequencies reduced implying the
"red shift") by about 2 x 104 per cent, which is
exactly the value predicted by Einstein’s theory. Consequenlty,
the spectrum observed appears to shift towards the red and as
observed on the Earth, exhibiting the gravitational red shift.

Light should be deflected by a gravitational
field much more than Newton predicted (The deviation
of light from a star when the light passes closed to the sun).
On March 29, 1919, a total solar eclipse occurred over Brazil
and the coast of West Africa. In the darkened daytime sky,
the measurements of the nearby stars were taken. Then they were
compared with those taken in the midnight sky six months earlier
when the same stars had been nowhere near the Sun. The predicted
deflection of the starlight was observed and Einstein was proved
right. He rapidly became the most famous scientist in the world,
and his name became a household word.
Always a Catalyst
Germany – one of the premier cradles of
great work in all the sciences – rapidly became less and less
hospitable to the large group of outstanding scientists who worked
there, especially the many who, like Einstein, were counted among
the Nazis’ Jewish targets. By the 1930s an exodus had begun,
including many nonJewish scientists who left on principle, no longer
willing to work where their colleagues were persecuted. In 1930,
Einstein left Germany for good. He came to the United States to
lecture at the California Institute of Technology, and never went
back to Germany afterward. He accepted a position at the Institute
of Advanced Study in Princeton, New Jersey, where he became a permanent
presence, and in 1940 he became an American citizen.
Always a catalyst among his colleagues for thoughtful
reflection, Einstein remained active throughout his life in the
world of Physics. But even this renegade found, as Planck did, that
Physics was changing faster than he was willing to accept. On the
horizon loomed challenges to reason that he was never able to accept
– such as Niels Bohr’s complementarity and Werner Heisenberg’s
uncertainty principle. “God does not play dice with the universe,”
Einstein would grumble, or “God may be subtle, but He is not
malicious.” During the last decades of his life Einstein spent
much of his time searching for a way to embrace both gravitation
and electromagnetic phenomena. He never succeeded, but continued
to be, to his final days, a solitary quester, putting forward his
questions to nature and humanity, seeking always the ultimate beauty
of truth.
Einstein received the Nobel prize in Physics for
the year 1921, not for relativity, but for the interpretation of
the photoelectric effect. It was given “for his services to
theoretical physics, and especially for his discovery of the law
of the photoelectric effect”.
Relativity – Any challenge?
True, there have been a few challenges to the theory of relativity
once in a while – both theoretical and experimental. Nearly
three decades ago, our own E.C.G. Sudarshan had predicted the possibility
of “Tachyons” – the particles that travelled at
a speed greater than light, but, in a different realm. They could
not travel at a speed lower than the speed of light. It may be noted
that such particles cannot carry any information.
There have even been challenges to the constancy of the speed of
light in vacuum. Recently, there has been a measurement by a team
of Italian physicists that appears to indicate that they can send
a fasterthanlight pulse of microwaves over more than a metre.
In Einstein’s theory, time races forwards as if on a light
beam. If an object were to travel faster than c, it would move backwards
in time, violating the principle of causality which says that cause
must always precede the effect. The alternative seems nonsensical
as illustrated by the following limerick:
There was a young lady named Bright whose speed
was far faster than light
She went out one day In a relative way And returned the previous
night.
General Relativity and Black
Holes
The Universe is expanding, exactly as the
pure equations of general relativity predicted in 1917. Then,
Einstein himself refused to believe the evidence of his own
theory! Indeed, Einstein’s equations provide the basis
for the highly successful Big Bang description of the birth
and evolution of the entire Universe. Within the expanding
Universe, general relativity is required to explain the workings
of exotic objects where spacetime is highly distorted by
the presence of matter where large masses produce strong gravitational
fields. The most extreme version of this, and one that has
caught the popular imagination, is the phenomenon of black
holes. Black holes would trap light by their gravitational
pull – or, in terms of general relativity, by bending
spacetime around themselves so much that it becomes closed,
pinched off from the rest of the Universe. If a star keeps
the same mass but shrinks inwards, or stays the same size
while accumulating mass, density increases. Eventually, the
distortion of spacetime around it increases until, a situation
is reached where the object collapses aand folds spacetime
around itself, disappearing from all outside view. Not even
light can escape from its gravitational grip, and it has become
a black hole The notion of such stellar mass black holes seemed
no more than a mathematical trick – something that surely
could not be allowed to exist in the real Universe, until
1968, and the discovery of pulsars which are rapidly spinning
neutron stars. A good deal of our understanding about black
holes is due to the work of the legendary physicist of today,
Stephen Hawking. 
Nobel Prizes awarded for work on Relativity and/or its applications.
1902 
Hendrik Antoon Lorentz

the Netherlands 
in Physics in recognition of his extraordinary
service he rendered by his researches into the influence of
magnetism upon radiation phenomena 
1907 
Albrt Abraham Michelson 
USA 
in Physics for his optical precision instruments
and the spectroscopic and metrological investigations carried
out with their aid 
1927 
Arthur Holly Compton 
USA 
in Physics for his his discovery
of the effect named after him 
1933 
Paul Adrien Mauric Dirac 
Great Britain 
in Physics for the discovery
of new productive forms of atomic theory 
1938 
Enrico Fermi 
Italy 
in Physics for his demonstrations
of the existence of new radioactive elements produced by neutron
irradiation, and for his related discovery of nuclear reactions
brought about by slow neutrons 
1961 
Rudolf Ludwig Mössbauer 
Germany 
in Physics for his researches
concerning the resonance absorption of gamma radiation and
his discovery in this connection of the effect which bears
his name 

Murray GellMann 
USA 
in Physics for his contributions and discoveries
concerning the classification of elementary particles and
their interactions 
1969 
Sir Martin Ryle 
Great Britain 
in Physics for his pioneering research in
radio astrophysics: for his observations and inventions, in
particular of the aperture synthesis technique

1974 
Antony Hewish 
Great Britain 
in Physics for his decisive role in the
discovery of pulsars 
1983 
Subramanyan Chandrasekhar 
USA 
in Physics for his theoretical studies of
the physical processes of importance to the structure and
evolution of the stars 
1984 
Carlo Rubbia 
Italy 
in Physics for their decisive contributions
to the large project, which led to the discovery of the field
particles W and Z, communicators of weak interaction 

Simon van der Meer 
the Netherlands 
do 
1993 
Russell A. Hulse 
USA 
in Physics for the discovery of a new type of pulsar,
a discovery that has opened up new possibilities for the study
of gravitation 

Joseph H. Taylor Jr 
USA 
do 
Note: It is interesting to note that Albert
Einstein – the father of relativity – did not receive
Nobel Prize for propounding the theory of relativity. He was awarded
Nobel Prize in Physics for his services to Theoretical Physics,
and especially for his discovery of the law of the photoelectric
effect.
Relativity: Glossary
Important terms used in connection with
Relativity are given below. The terms given do not necessarily appear
in the present article.
Aphelion: The point of a planetary
orbit farthest from the Sun.
Black hole: Black hole is a collapsed
object, such as a star, that has become invisible. It is formed
when a massive star runs out of thermonuclear fuel and is crushed
by its own gravitational force. It has such a strong gravitational
force that nothing can escape from its surface, not even light.
Thoush invisible, it can capture matter and light from the outside.
Cosmological constant: The multiplicative
constant for a term proportional to the metric in Einstein’s
equation relating the curvature of space to the energymomentum
tensor.
Cosmology: The study of the overall
structure of the physicala universe.
coulomb: A unit of electric charge,
defined as the amount of eletric charge that crosses a surface in
1 second when a steady current of 1 absolute ampere is flowing across
the surface. Abbreviated coul.
Curvature of space: The deviation
of a spacelike threedimensional subspace of curved spacetime from
euclidean geometry.
Curved spacetime: A fourdimensional
space, in which there are no straight lines but only curves, which
is a generalization of the Minkowski universe in the general theory
of relativity.
Equivalence principle: In general
relativity, the principle that the observable local effects of a
gravitational field are indistinguishable from those arising from
acceleration of the frame of reference. Also known as Einstein’s
equivalence principle; principle of equivalence.
Event: A point in spacetime.
FitzGeraldLorentz contraction:
The contraction of a moving body in the direction of its motion
when it speed is comparable to the speed of light. Also known as
Lorentz contraction: LorentzFitzGerald contraction.
Fourvector: A set of four quantities
which transform under a Lorentz transformation in the same way as
the three space coordinates and the time coordinate of an event.
Also known as Lorentz fourvector.
Fourvelocity: A fourvector
whose components are the rates of change of the space and time coordinates
of a particle with respect to the particle’s proper time.
Frame of reference: A coordinate
system for the purpose of assigning positions and times to events.
Also known as refrence frame.
Geodesic: A curve joining two
points in a Riemannian manifold which has minimum length.
Geodesic coordinates: Coordinates
in the neighbourhood of a point P such that the gradient of the
metric tensor is zero at P.
Geodesic motion: Motion of a
particle along a geodesic path in the four dimensional spacetime
continuum; according to general relativitiy, this is the motion
which occurs in the absence of nongravitational forces.
Gravitation: The mutual attraction
between all masses in the universe. Also known as gravitational
attraction.
Gravitational collapse: The implosion
of a star or other astronomical body from an initial size to a size
hundreds or thousands of times smaller.
Gravitational constant: The constant
of proportionality in Newton’s law of gravitation, equal to
the gravitational force between any two particles times the square
of the distance between them, divided by the product of their masses.
Also known as constant of gravitation.
Gravitational field: The field
in a region in space in which a test particle would experience a
gravitational force; quantitatively, the gravitational force per
unit mass on the particle at a particular point.
Gravitationalfield theory: A
theory in which gravity is treated as a field, as opposed to a theory
in which the force acts instantneously at a distance.
Gravitational radiation: A propagating
gravitational field predicted by general relativity, which is produced
by some change in the distribution of matter; it travels at the
speed of light, exerting forces on masses in its path. Also known
as gravitational wave.
Gravitational red shift: A displacement
of spectral lines towards the red when the gravitational potential
at the observer of the light is greater than at its source.
Gravitational wave: A propagating
gravitational field predicted by general relativity, which is produced
by some change in the distribution of matter; it travels at the
speed of light, exerting forces on masses in its path. Also known
as gravitational radiation.
Graviton: A theoretically deduced
particle postulated as the quantum of the gravitational field, having
a rest mass and charge of zero and a spin of 2.
Gravity: The gravitational attraction
at the surface of a planet or other celestial body.
LorentzFitzGerald contraction:
The contraction of a moving body in the direction of its motion
when its speed is comparable to the speed of light. Also known as
FitzGeraldLorentz contraction.
Lorentz fourvector: A set of
four quantities which transform under a Lorentz transformation in
the same way as the three space coordinates and the time coordinate
of an event. Also known as Fourvector.
Lorentz frame: Any of the family
of inertial coordinate systems, with three space coordinates and
one time coordinate, used in the special theory of relativity; each
frame is in uniform motion with respect to all the other Lorentz
frames, and the interval between any two events is the same in all
frames.
Lorentz invariance: The property,
possessed by the laws of physics and of certain physical quantities,
of being the same in any Lorentz frame, and thus unchanged by a
Lorentz transformation..
Lorentz transformation: Any of
the family of mathematical transformations used in the special theory
of relativity to relate the space and time variables of different
Lorentz frames.
Massenergy conservation: The
principle that energy cannot be created or destroyed; however, one
form of energy is that which a particle has because of its rest
mass, equal to this mass times the square of the speed of light.
Massenergy relation: The relation
whereby the total energy content of a body is equal to its inertial
mass times the square of the speed of light.
Minkowski metric: The metric
tensor of the Minkowski world used in special relativity; it is
a 4 X 4 matrix whose nonzero entries lie on the diagonal, with one
entry (corresponding to the time coordinate) equal to 1, and three
entries (corresponding to space coordinates) equal to –1;
sometimes, the negative of this matrix is used.
Minkowski universe: Space time
as described by the four coordinates (x, y, z, ict), where i is
the imaginary unit of c is the speed of light; Lorentz transformations
of spacetime are orthogonal transformations of the Minkowski world.
Also known as Minkowski world.
Minkowski world: Space time as
described by the four coordinates (x, y, z, ict), where i is the
imaginary unit of c is the speed of light; Lorentz transformations
of spacetime are orthogonal transformations of the Minkowski world.
Also known as Minkowski universe.
Neutron star: A star that is
supposed to occur in the final stage of stellar evolution; it consists
of a superdense mass mainly of neutrons, and has a strong gravitational
attraction from which only neutrinos and highenergy photons could
escape so that the star is invisible.
Principle of covariance: In classical
physics and in special relativity, the principle that the laws of
physics take the same mathematical form in all inertial reference
frames.
Principle equivalence: In general
relativity, the principle that the observable local effects of a
gravitational field are indistinguishable from those arising from
acceleration of the frame of reference. Also known as Einstein’s
equivalence principle; Equivalence principle.
Pulsar: Variable star whose luminosity
fluctuates as the star expands and contracts; the variation in brightness
is thought to come from the periodic change of radiant energy to
gravitational energy and back. Also known as pulsating star.
Pulsating star: Variable star
whose luminosity fluctuates as the star expands and contracts; the
variation in brightness is thought to come from the periodic change
of radiant energy to gravitational energy and back. Also known as
pulsar.
Quasar: Quasistellar astronomical
object, often a radio source; all quasars have large red shifts;
they have small optical diameter, but may have large radio diameter.
Also known as quasistellar object (QSO).
Relative: Related to a moving
point; apparent, as relative wind, relative movement.
Relative momentum: The momentum
of a body in a reference frame in which another specified body is
fixed.
Relative motion: The continuous
change of position of a body with respect to a second body, that
is, in a reference frame where the second body is fixed.
Relativistic beam: A beam of
particles travelling at a speed comparable with the speed of light.
Relativistic electrodynamics:
The study of the interaction between charged particles and electric
and magnetic fields when the velocities of the particles are comparable
with that of light.
Relativistic kinematics: A description
of the motion of particles compatible with the special theory of
relativity, without reference to the causes of motion.
Relativistic mass: The mass of
a particle moving at a velocity exceeding about onetenth the velocity
of light; it is significantly larger than the rest mass.
Relativistic mechanics: Any form
of mechanics compatible with either the special or the general theory
of relativity.
Relativistic particle: A particle moving at a
speed comparable with the speed of light.
Relativistic quantum theory:
The quantum theory of particles which is consistent with the special
theory of relativity, and thus can describe particles moving close
to the speed of light.
Relativistic theory: Any theory
which is consistent with the special or general theory of relativity.
Relativity: Theory of physics
which recognizes the universal character of the propagation speed
of light and the consequent dependence of space, time, and other
mechanical measurements on the motion of the observer performing
the measurements; it has two main divisions, the special theory
and the general theory.
Schwarzchild radius: For a given
body of matter, a distance equal to the mass of the body times the
gravitational constant divided by the square of the speed of light.
Also known as gravitational radius.
Slowing of clocks: According
to the special theory of relativity, a clock appears to tick less
rapidly to an observer moving relative to the clock than to an observer
who is at rest with respect to the clock. Also known as time dilation
effect.
Space coordinates: A threedimensional
system of cartesian coordinates by which a point is located by three
magnitudes indicating distance from three planes which intersect
at a point.
Spacelike surface: A threedimensional
surface in a fourdimensional spacetime which has the property
that no event on the surface lies in the past or the future of any
other event on the surface.
Spacelike vector: A four vector
in Minkowski space whose space component has a magnitude which is
greater than the magnitude of its time component multiplied by the
speed of light.
Spacetime: A fourdimensional
space used to represent the universe in the theory of relativity,
with three dimensions corresponding to ordinary space and the fourth
to time. Also known as spacetime continuum.Spacetime continuum:
A fourdimensional space used to represent the universe in the theory
of relativity, with three dimensions corresponding to ordinary space
and the fourth to time. Also known as spacetime.
Special relativity: The division
of relativity theory which relates the observations of observers
moving with constant relative velocities and postulates that natural
laws are the same for all such observers.
Timedilation effect: According
to the special theory of relativity, a clock appears to tick less
rapidly to an observer moving relative to the clock than to an observer
who is at rest with respect to the clock. Also known as slowing
of clocks.
References:
 Concepts of Modern Physics Arthur Beiser McGrawHill Book Company,
1967 A standard textbook explaining concepts of the Modern Physics
in a simple, clear and lucid style.
 The History of Science From 1895 to 1945 Ray Spangerburg and
Diane K. Moser Universities Press (India) Ltd., 1999 Highly readable.
A set of five volumes on history of science from the ancient Greeks
until 1990s.
 Mr. Tompkins in Paperback George Gamow Cambridge University
Press 1965 A masterpiece from a master science popularisercumscientist,
combining Mr. Tompkins in Wonderland and Mr. Tompkins explores
the atom. Highly entertaining.
 Physics: Foundations and Frontiers
George Gamow and John M. Cleveland
Prentice Hall of India 1966
A wonderful exposition illustrating basic principles of physics
at elementary level.
 Observation of superluminal behavior in wave propagation
Mugnai, D., Ranfagni, A, and Ruggeri, R,
Physical Review Letters 84(2000)4830
This paper was about the indication that a fasterthanlight pulse
may be possible and hence challenging the constancy of speed of
light in vacuum.
 The Feynman Lectures on Physics (Vo. I)
Richard P. Feynman, Rober B. Leighton and
Mathew Sands
AddisonWesley Publishing Company 1963
A set of three volumes of lectures delivered by the Nobel Laureate
Richard P. Feynman to undergraduate students at California Institute
of Technology. Just superb.
 The ABC of Relativity
Bertrand Russel
(Revised edition, edited by Felix Pirani)
George Allen & Unwin Ltd. 1958
Though first published in 1927, this book has been a classic till
date.
 The Twin Paradox
in The Night is Large
collected essays (19381995)
by Martin Gardner Penguin Books, 1996
An entertaining article by a journalist and writer well known
for his recreational mathematicscolumn in Scientific American
and several books on the same topic.
 The Clock Paradox
by J. Bronowski
Scientific American
January 1963
A highly instructive article written in a lucid style.
 Dictionary of Scientific Biography
Vol. IV
EditorinChief, Charles Coulston Gillispie
Charles Scribner’s Sons, New York 1975
A wonderful resource in 14 volumes.
 A Brief History of Time: From the big bang to black holes
Stephen Hawking
Bantam Books 1988
This is probably the best single book on astrophysics and applications
of general relativity for the common reader.
 Introduction to Cosmology
Second Edition
J.V. Narlikar
Cambridge University Press 1993
An introductory text book on modern cosmology at undergraduate
level.
 htt://www.nobel.se
Official website of the Nobel Foundation – A treasure house
on Nobel Laureates.
