time dilation & length contraction

SPECIAL THEORY OF RELATIVITY

TIME DILATION & LENGTH CONTRACTION

Submitted by :-AKASH SINGH CHAUHANB.TECH 1ST YEAR( 2ND SEMESTER)

Submitted to :-Ms. NISHA CHUGHASST. PROFESSOR

CONTENTS• INTRODUCTION• SPECIAL THEORY OF RELATIVITY• POSTULATES• TIME DILATION• LENGTH CONTRACTION• TWIN PARADOX• BIBLIOGRAPHY

BORN - 14TH MARCH 1879DIED - 18TH APRIL 1955

SPECIAL THEORY OF RELATIVITY

• A German scientist ALBERT EINSTEIN concluded that the concepts of space & time are to be revised . In 1905 , at the age of 26 . He proposed a theory which is known as SPECIAL THEORY OF RELATIVITY.

POSTULATES

• The special theory of relativity based on following two postulates :

1. THE PRINCIPLE OF RELATIVITY : All the laws of physics are the same in all inertial frame of reference.

2. THE PRINCIPLE OF INDEPENDENCE OF THE VELOCITY OF LIGHT : The speed of light in a vacuum is independent of the motion of the light source or receiver.

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”.

The total time for the light pulse to trace its path is given by

The length of the half path can be calculated as a function of known quantities as

Substituting D from this equation into the previous and solving for Δt' gives:

and thus, with the definition of Δt:

THE TWIN PARADOX

• The time dilation effect leads to the famous “THE TWIN PARADOX” of special relativity .let us consider a hypothetical experiment involving twin sisters SEETA and GEETA .After celebrating 20th birthday .the adventurous twin sets out a space voyage ….................

THE TWIN PARADOX

LENGTH CONTRACTION “Length contraction is the phenomenon of decrease in length

measured by the observer , of an object which is traveling at any non-zero velocity relative to the observer”.

• This contraction formally called Lorentz contraction or Lorentz - fitzgerald contraction after Hendrik Lorentz and George fitzgerald.

• This contraction 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.

• This effect is negligible at everyday speeds , and can be ignored for all regular purposes . only at greater speeds does it become relevant. At a speed of 13,400,000m/s(30 million mph,0.0447c),the contracted length is 99.9% of the length at rest: at a speed

LENGTH CONTRACTION DERIVATION

• Where

• L0 is the proper length (the length of the object in its rest frame),

• L is the length observed by an observer in relative motion with respect to the object,

• v is the relative velocity between the observer and the moving object,

• c is the speed of light,

and the Lorentz factor, γ(v), is defined as•

BIBLIOGRAPHY

• TIME DILATION

• L.LANDAU , YU.RUMER -1981-MIR PUBLICATION MOSCOW.

• LENGTH CONTRACTION

• R.RESNICK , D. HALLIDAY , FIFTH EDITION , JOHN WILLEY & SONS INC. SINGAPORE