## 28 Dec 2012

### Special Theory of Relativity - Full Lecture

Before i start my topic i will tell you about frame reference What is frame of reference? you will find much detail about this but here i will tell you a little. Let first define it "A frame of reference is any coordinate system relative to which measurements are taken". For example suppose some measurements for an experiment are taken in laboratory then laboratory is the frame of reference. Another example is suppose a body is palced in car then car is a frame of refence. Lets move further. There are two types of frame of reference.
1) Inertial frame of reference
2) Non inertaial frame of reference
In above example if the body is at rest or moves with consatnt velocity so that no acceleration is produced then it is called inertial frame of reference.
And if the body moves with some variable velocity so that acceleration is produced then it is called non inertial frame of reference.
Special theory of relativity treats the problems involving inertial frames of reference and do you know? there is another theory called general theory of relativity that treat the problems involving non inertial frames of refernce.
In 1905, a paper entitled " on the electrodynamics of moving bodies" Einstein offered the following postulates which are the basis of the special theory of relativity.
The two postulates are:

#### 1) Principle of relativity:    The laws of physics are same in all inertial frames of reference.2) The constancy of the speed of light:    Speed of light in free space(vacum) is constant(has same value c) in all inertial frames of reference.

Now we will discuss the above two postulates.
The first postulate declares that the laws of physics that hold for an observer in inertial frame of reference cannot be violated for an observer in an other inertial frame of reference.
To accept the second postulate we consider the three observers at rest in three different inertial frames of reference.

The flash of light emitted by observer A is measured by him to be travel at speed c. If the frame of
observer B is moving away from A at a speed of c/4, then Galiliean kinematics predicts that B
measures the c-c/4=3c/4 for the speed of light emitted by A. If the observer C is moving towards A
with a speed of c/4, then the Galilean kinematics predicts that C measures the value c+c/4=5c/4 for
the speed of light emitted by A.
BUT
Second postulate tells that all three observers measures the same speed c for the speed of light.
However, some experiments are conducted which satisfies second postulate. This is a big problem
and confusion which must be solved in future.
Now we will discuss some consequences(results) of special theory of realativity. There are many
consequences but here i willl discuss only three consquences which are important.
These are
i) Time Dilation
ii) Length Contraction
iii) Mass Variation
Here i will more focus on time dilation. Lets discuss these consequences one by one.
1) Time Dilation:
From centuries it is considered that time is an absolute quantity. Time is running, running and running.
But
Einstein said time is not an absolute quantity it depends on velocity, it depends on motion of frame of
reference.
Now suppose an observer is stationary in an inertial frame of reference. He observes the time interval
between the two events in this frame let it be t0 . This is called proper time. If the observer is moving
with velocity v with respect to frame of events, then the time measured by observer would not be it
will be t0
given as

As the quantity of right hand side is less than 1, so t is always greater than t0.
There are many verses in Holy Book Quran that tells that time is not an absolute quantity. Time is not
same for all. It is different for diffferent persons.
In Quran,
"The angel and spirit ascend to Him in day whose length is fifty thousand years"
(Chap.29, Surah Al-Maarij 70:4)
AND
"They ask you to hasten the punishment God will not break His promise. A day with your Lord is
equivalent to a thousand years in the way you count" (Al-Quran 22:47)
Now focus on this picture.

Here people are working together and time is passing on Earth which is t0 and time passing on
spaceship is t. Focus on above two clocks you can see that
More time pass on Earth
Less time pass in spaceship
So from above verses and example it is clear that time is not an absolute quantity.
2) Length Contraction:
Suppose an observer in spaceship is at rest in space. The observer measured the length of a rod
(say 1 meter), which is ℓ0 and called proper length. And if the observer moves with spaceship in a
space then the length measured by the observer will not be 1 meter it will be less than 1 meter, denoted
by ℓ and
given as
3) Mass Variation:
Suppose an observer in a spaceship is at rest in space. The mass of an object meaured by the
observers m(say 1kg), called proper mass. Now, if the observer moves at high speed, then the
time maesured by observer will not be 1 kg, it will be greater than 1 kg. denoted by m and
given as