First lecture
Introduction
Probably no physical theory in 20th century has been the
subject of more discussion amongst philosophers and
scientists and at the same time caught the imagination of
the( intelligent) layman, than the Einstein's theory of
relativity discovered in the vintage year 1905 .The year 2005,
marking the century of that remarkable year, has been
declared the international year of physics by organizations
such as UN and UNESCO This is essentially due to the fact
that the concepts underlying the theory of relativity are not
only radically new but also provide a framework which
embraces practically all the branches of physical sciences .
Indeed Einstein's revolutionary theory revolutionized our
understanding of the physical universe in major ways.
Inertial frames of reference
Classical mechanics is based on the conception that the free
space is empty and the position of a point in this free space
can be given in terms of three real numbers (x,y,z) , which
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are called the coordinates of a point since the position of a
point or body can be stated only relative to some other
points or bodies , the description of these observation
requires a coordinate system of a frame reference. A frame
of reference is a technical term for the combination of a set
of spatial coordinates axes and time variable .
Galileo and other scientists realized that the form of the
laws of nature depends on the choice of the frame of
reference. Among all the possible frames of reference , there
exists a class called the inertial frame of reference , in which
the laws of nature take a simple form. Inertial frames of
references are those frames in which a particle or a body
that is not acted upon by external forces , moves with
constant velocity with respect to each other , and one of
them is inertial frame then the other frame will also be an
inertial frame fig (1). The laws of mechanics remains
invariant in all inertial frames.
No frame connected with any material object in the universe
can serve the purpose of perfect inertial frame of reference
for the earth and other planet as they revolve round the sun
which itself is moving . Stars are also not fixed .Relation
between the two coordinate systems is determined by the
functional relation between their respective coordinates
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Galilean transformation
Consider two inertial frames of references
that
their
coordinate
axes
coincide
S
S
and
at
time
such
t=0
moves with velocity v along the x- axis w.r.t. S frame
.Obviously , the relation between the coordinates in the two
frames can be expressed by the following equations
x  x  vt
y  y
z  z
t  t
These equations are called Galilean transformation. In
obtaining Galilean transformation equations it is assumed
that (i) it is possible to define a time t which is the same for
all inertial frames of references , and (ii) the distance
between two points is independent of frames of reference. It
is to show from Galilean transformation that the velocities
u  u  v
and accelerations in the two frames of references are related
a  a
by the equations
between
two
frames
where v is the relative velocity
along
the
x
direction
and
respectively. It is worthwhile to mention that the Galilean
transformation
are
not
consistent
electromagnetic theory .
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with
Maxwell`s
and
S
Velocity of light
It is follows from Maxwell`s electromagnetic theory that
electromagnetic waves travel in vacuum with a speed equal
to the ratio of electromagnetic unit to the electrostatic unit of
charge. This ratio is essentially equal to the speed of light
and hence light is considered as a form of electromagnetic
radiation .
Now the question arises , how does the velocity of light
transform from the inertial frame to another? Galilean
transformation reveal that the velocities are different in
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different frames of references and are related by the
previous equation. However , Maxwell`s equations for
electromagnetic fields have no reference to the velocity of
inertial frame. Michelson-Morley experiment also suggests
that the speed of light is independent of the velocity of light.
The search of the ether
In spite of the great success of Maxwell`s equations in
describing the behavior of electromagnetic phenomena in
space and time, it was quite disturbing to find that they are
not covariant under a Galilean transformation. Obviously
,the Galilean transformation which permits a covariant
description of mechanical forces , does not hold for
electromagnetic forces.
Another serious difficulty arose from Maxwell`s
electromagnetic theory in connection with a medium , which
was postulated to sustain wave character of light .We know
that every wave motion has something that “waves” . Sound
waves has air and water waves has water .Surely it was
argued that light waves must involve the waving of
something even in free space . No one knew what it was , but
it was given the name luminiferous ether . Maxwell`s
equations and experimental observations , particularly on
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polarized light , show that light is a transverse wave motion .
This implies that the ether is a solid . Transverse waves
involve shear force and can occur only in solids , which can
support shear .Obviously , the ether must be a rigid solid .
The propagation velocity of mechanical waves in various
materials depends on the elastic constants of the material.
These are much greater for steel than for air. The very great
velocity of light thus implies that they must have very large
shear modulus . It is rather hard on the imaginations to
suppose that all space is filled with this rigid solid and the
material objects move through this rigid solid with
resistance , yet it was supposed to exist . It was then natural
to assume that the ether was in a state of absolute rest, the so
called “ stationary ether “. Accordingly ,the ether become an
absolute reference , through which the material bodies move
without resistance
If the ether is assumed to be at rest then the interesting
question is ; how fast are we moving through the ether ?
Since all speculation
about the ether stem from its
properties as a medium for carrying light, an optical
experiment is indicated .It is not very difficult to know how
sensitive the apparatus must be required in order to
measure the ether drift. Assuming , for the sake of
simplicity, that the sun has no ether drift , the velocity of the
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earth through the ether must be its orbital velocity. If the
sun has an ether drift , then the drift of the earth will be
even greater than its orbital velocity for the same reasons.
Knowing that the radius of the earth`s orbit is about 93
million miles , we find the orbital velocity to be about 18.5
miles/s (about 30 km/ s). By performing the experiment at
the best season of the year, we know that, we should be able
to find an ether drift of at least 30 km/s . The velocity of light
is
3  108
m/s
. The orbital velocity of the earth is about 10-4
times the velocity of light .Obviously, we need a very
sensitive experiments to detect the ether drift. A number of
experiments were devised to measure the earth`s motion
through the ether ,i.e., to detect an ether wind with respect
to the earth .The most famous of these experiments was the
Michelson-Morley experiment, which will be described
inshaa allah in the next lecture .
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