This document provides an introduction to Einstein's special theory of relativity. It discusses key concepts like Galilean transformations, Michelson-Morley experiment, postulates of relativity, and consequences like time dilation and length contraction. The document explains that special relativity applies to observers in uniform motion and the speed of light in a vacuum is the same for all observers, regardless of their motion. It also presents the Lorentz transformations and equations for time dilation and length contraction.

1. A PROJECT ON
SPECIAL THEORY
OF
RELATIVITY

2. Introduction to Relativity
The dependence of various physical phenomena on relative motion of
the observer and the observed objects, especially regarding the nature and
behaviour of light, space, time, and gravity is called relativity.
When we have two things and if we want to find out the relation
between their physical property i.e.velocity,accleration then we need
relation between them that which is higher and which is lower.In general
way we reffered it to as a relativity.
The famous scientist Einstein has firstly found out the theory of
relativity and he has given very useful theories in relativity.

3. What is Special Relativity?
In 1905, Albert Einstein determined that the laws of physics are
the same for all non-accelerating observers, and that the speed of
light in a vacuum was independent of the motion of all
observers. This was the theory of special relativity.

4. Galilean Transform
Conditions of the Galilean Transformation
Parallel axes (for convenience)
K’ has a constant relative velocity in the x-direction with respect to K
x`=x-vt
y=y`
z=z`
t=t`
Time (t) for all observers is a
Fundamental invariant,
i.e., the same for all inertial observers

5. Galilean Transformation Inverse Relations
Step 1. Replace vector ‘v’ with vector ‘–v’ .
Step 2. Replace “primed” quantities with
 “unprimed” and “unprimed” with “primed.”
 x=x’+vt
 t=t’
 where ‘v’ is speed of frame not speed of
object

6. The First Postulate
of Special Relativity
A person playing pool on a
smooth and fast-moving ship
does not have to
compensate for the ship’s
speed. The laws of physics
are the same whether the
ship is moving uniformly or
at rest.

7. The First Postulate of Special Relativity
Einstein’s first postulate of
special relativity assumes our
inability to detect a state of
uniform motion.
Many experiments can detect
accelerated motion, but none
can, according to Einstein,
detect the state of uniform
motion.

8. The Second Postulate of Special Relativity
The second postulate of special relativity states that the
speed of light in empty space will always have the same
value regardless of the motion of the source or the motion
of the observer.

9. The Ether: Historical Perspective
Light is a wave.
Waves require a medium through which to propagate.
Medium as called the “ether.” (from the Greek aither, meaning
upper air).
Maxwell’s equations assume that light obeys the Newtonian-
Galilean transformation.

10. The Michelson-Morley Experiment
Experiment designed to measure small changes
in the speed of light was performed by Albert
A. Michelson (1852 – 1931, Nobel ) and Edward
W. Morley (1838 – 1923).
Used an optical instrument called an
interferometer that Michelson invented.
Device was to detect the presence of the ether.
Outcome of the experiment was negative, thus
contradicting the ether hypothesis.

11. x
y
z
S
x'
y'
z'
S'
v
The Lorentz
Transformation
The relations between the primed and unprimed
spacetime coordinates are the Lorentz
transformations, each coordinate in one frame is
a linear function of all the coordinates in the other
frame, and the inverse functions are the inverse
transformation. Depending on how the frames move
relative to each other, and how they are oriented in
space relative to each other, other parameters that
describe direction, speed, and orientation enter the
transformation equations.

12. LORENTZ TRANSFORMATION EQUATION

13. Time Dilation
We explore the rate of time in different inertial frames by considering a special
kind of clock – a light clock – which is just one arm of an interferometer.
Consider a light pulse bouncing vertically between two mirrors. We analyze
time it takes for the light pulse to complete a round trip both in the rest frame
of the clock (labeled S’), and in an inertial frame where the clock is observed to
move horizontally at a velocity v (labeled S).
In the rest frame S’

14. Time
Dilation
Equation

15. Length Contraction
Length contraction is the phenomenon of a decrease in length of
an object as measured by an observer who is traveling at any
non-zero velocity relative to the object. This contraction (more
formally called Lorentz contraction or Lorentz–FitzGerald
contraction after Hendrik Lorentz and George Francis FitzGerald)
is usually only noticeable at a substantial fraction of the speed of
light. Length contraction is only in the direction parallel to the
direction in which the observed body is travelling.

16. Length Contraction equation