Special Theory Of Relativity

Theory of R elativity Special By Nikhil Sharma

“…… ..Undoubtedly mechanics was a snapshot of slow and real motions, while new physics is a snapshot of fabulously swift and real motions……..” V.I.Lenin

History
Light also needs a Medium to propagate. (assumption)
This Hypothetical Medium was named as Luminiferous Ether.
Michelson and Morley Conducted an Experiment for proving the Existence of Ether.
Evolved after the failure of Michelson Morley Experiment.
The negative results were explained successfully by an German-American Physicist, Albert Einstein (1879-1955).

Postulates of Special Theory of Relativity*
“ The Laws of physics are same in all Inertial Frame of reference”
“ The Speed of Light in free space has the same value in all Inertial Frames.”
* These Postulates are taken from ~ Fundamentals of Modern Physics ~ Arthur Beiser ~ Fifth Edition ~1995

The Reference Frame
A Reference Frame is the point of View, from which we Observe an Object.
A Reference Frame is the Observer it self, as the Velocity and acceleration are common in Both.
Eg.:-
Let’s us see how the observation changes, with the change in Observer or we can say The Reference Frame.
1. A car moving on Earth.
2. A bomb dropped from a Rocket.

Here we can see the Effect of Reference frame on the Observations taken by the observer.

Constancy of Speed of Light
The speed of light does not depend upon the relative velocity between the Observer and the Source or the Medium in which light is traveling.

Consequence of Relativity
The Major Consequences To This Theory are:-
Length Contraction
Mass Expansion
Time Dilation

Length Contraction
“ It is the phenomenon of Shortening of Length which
is in the relative motion with respect to the observer”
Thus the length of a body appearing to an observer depends upon the relative velocity of the body with respect to the Observer.
And the Proper Length of a body can known by measuring it’s length when it is at rest w.r.t. the observer.
It is given by l = l o /(1-v 2 /c 2 ) 0.5

Mass Expansion , E = mc 2
“ This is a phenomenon of an increment in mass of a body w.r.t. an observer, moving with a Relative Velocity w.r.t. the observer.”
The Expansion of Mass of a body takes place according to m = m o /  1-v 2 /c 2 ) 0.5
Rest mass of a body is the mass measured by an observer who is at rest w.r.t. the observer.

Time Dilation
“ Time Dilation is the phenomenon of slowing down of a clock , as determined by an observer who is in relative motion with the Clock.” **
As it is an relative thus the Extent of Dilation depends upon
the Relative Velocity of the clock w.r.t. the observer.
It is an very important consequence of the Special Theory of Relativity .And is given by t = t o /(1-v 2 /c 2 ) 0.5
** This text is taken from Britannica 2005 DVD Edition .

Let us see the effect of Time dilation on a Radio active mass.

Here the active mass is moving at an velocity comparable to c.

This slide contains an Example which will help you to understand the Relativistic mechanics in a much Simpler & Easier manner.
Example:- A bust of 10 4  mesons having average life time period of 2.5x10 8 ,started traveling on a circular path of diameter 40 meters, Calculate the number of  –mesons left after the completion of one round.

The average life time period of an element is the time period in which the mass of the active matter decreases to 1/e times of its initial Mass.

Variation f Mass

Bibliography
What is the Theory of Relativity ~ L.Landau,Yu.Rumer~1981~ Mir Publication Moscow
Fundamentals of Physics ~ R.Resnick, D.Halliday,
Fifth Edition~ John Wiley & Sons, Inc.~ Singapore.
Fundamentals of Modern Physics ~ Arthur Beiser ~ Fifth Edition ~1995

Credits
Creator
Nikhil Sharma
ET-I st year (2007-08)
Special Thanks to
Shubham Srivastava (EN)
Kumar Gaurav (ET)
Sonakshi Aggrawal (IT)
Mohit (EN)
Shivam (ET)
And I also want to thank
all those who boosted my moral in the process
of completing this Presentation.

Explanations Slide 3 - 6 Slide 7 - 9 Slide 9 - 15 Slide 16 - 19 Slide 20 Slide 20 Contd. Please Zoom these pictures Separately.

Special Theory Of Relativity

by Nikhil Sharma

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