A PROJECT ON SPECIAL THEORY OF RELATIVITY

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.

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.

Galilean TransformConditions 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

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

The First Postulate of Special RelativityA 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.

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.

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.

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.

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.

x

y

z

S

x'

y'

z'

S' v

The Lorentz TransformationThe 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.

LORENTZ TRANSFORMATION EQUATION

Time DilationWe 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 the 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’  

Time

Dilation Equation

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.

Length Contraction equation