Dear Friends,
Relativity - The Theory which shattered the year long belief of the word absolute.
There is no absolute East or West, Right or Left, Up or Down.
Every thing depend upon the observers view.
Here is an Article about Special Relativity Theory.
The Speciality of the article is
"Great concept expressed in easy way to understand "
Is It possible for a
person to be elder than his parents?
“yes” says Albert
Einstein.
Let us see “how”
Science is the
religion of all- AlbertEinstein
An introduction to
the Special Theory of Relativity
The theory of relativity of time was
proposed in the year 1905 by the greatest 20th century physicist,
Albert Einstein at the age of 25. It placed him among the giants of human
thoughts-Copernicus, Newton and others.
In this article, I wish to explain
some of the details about the relativity theory. I have a very little knowledge
about this topic. I propose to explain
the tip of the iceberg, with the aid of some books on the subject which I have
gone through.
If this article is able to make you
curious to go further on this subject, I think this work has served the
purpose.
Science makes our life very simple.
All the inventions are used by us in our day to day life. To mention a few,
mobile phones, computers, and vehicles.
This world
has created many great scientists and inventors. Even though every invention is
useful in one way or the other, some of them are superior to the others, in the
sense that without them nothing is possible today. In my opinion, the best
inventions are wheel, electricity and computers.
Many
scientists proposed scientific concepts, theories etc. They explain the cause
for the happenings around us. Some of the theories are very vital, as they have
the effect of making the belief of that time upside down. Let us consider few
such examples.
` It was
believed that the shape of the earth was flat. Subsequently, it was established
that the shape is almost spherical.
Dalton
stated that the atom is the smallest particle which cannot be divided further.
Scientists like J.J.Thompson, Rutherford proved that atoms canbe divided
further and named those particles as neutron, electron and proton.
Once light
was believed to have wave nature. It was proved that it has particle nature
also. The present theory is that light has dual behavior, wave and particle.
In my
opinion, the greatest of all such theories is the “Theory of Relativity” by
Albert Einstein.
Aristotle
believed that a constant force (pull or push) or an external agency is required
to keep the motion of a body.
Galileo
proved that this is false. He proved by performing a series of experiments with
inclined plane that if there is no friction, no external agency is required for
the continuous motion of any object. In other words, an object in motion will
continue its motion for ever if there were no friction.
Sir Isaac
Newton consolidated these ideas and formulated the famous “Newton’s laws”. This
subject is called the “Newtonian mechanics”, which was followed for almost for
400 years.
Albert Einstein introduced the
concept of relativity. He published two famous papers, “General Relativity” and
“Special Relativity”. This has almost shattered the basics of Newtonian
mechanics.
Let us begin with some important
terms used in this article.
Relative and absolute
Some
sentences have a definite meaning and some have not. Observe the following
sentences.
1.
The
Sun rises in the east. It is absolute. That is the direction in which the sun
rises is called the east direction. This is true for all places in the world.
Hence it is absolute.
2.
Our
post office is on the left side of the street. If we walk from bus stand to
temple, it is on our right side. If we walk from temple towards bus stand, it
is on the left side. Which is correct? The terms “left” or “right” are relative
to the direction in which we walk. So “left” or “right” are relative terms.
3.
The
terms “up” or “down” are also relative.
4.
Which
is bigger
In the following figure, the cowherd is bigger than the cow.
In the next figure the cow is bigger than the cowherd. In fact, both the
drawings were the same but drawn from different angles.
Now, let us introduce the following
terms, based on Newtonian mechanics.
Rest: An object which is not changing
its position from time to time is said to be at rest. For example, our office
is at rest since it is at the same place at different times.
Motion: An object is said to be in
motion, if it changes its position with reference to time. A bus which is going
from Srivaikuntam to Tirunelveli is in motion. The bus is at Srivaikuntam at
5.45 PM, at Puthukudi at 5.50 and at Tirunelveli at 6.45 PM.
Consider our
friend sitting in a train. His brief case is kept in the place for that purpose
which is above his seat, and just opposite to him. See the following figure.
We are in
the platform standing near the coach. The train is about to start. If we ask
our friend in the train that whether his briefcase is at rest or in motion, he
would say that it is at rest. For us also it is in rest.
Now the
train starts and going at a speed of 5 KMPH towards north. Now, if we ask the
same question to our friend in the train, he would give the same reply that the
brief case is at rest. Also he would say that we are going backwards towards
south at a speed of 5KMPH. But for us,
the brief case and our friend are in motion. Both are right and nobody is
wrong. Here comes the relativity. “Rest”and “motion” are taken as “absolute” by
Newton but for Einstein they are relative. This is the reason for the
contradictory observation by us and by our friend.
From the
above we can see that rest and motion are also relative terms.
One and
the same place
Consider two friends are travelling
in the same coach of train from Tuticorin to New Delhi. Assume that they used
to write letters from the coach to their spouses daily at a particular time.
Assume that their spouses receive the letters on the next day.
Now we can find whether the term “one
and the same place” is absolute or relative.
If we ask the persons in the train,
they would say that all the letters are written from the same place, i.e. from
the same coach of the train. If we put the same question to the family they
would say that those letters are written from different places based on the
date stamp of the post offices. Both are right. Hence this term, “one and the
same place” is also relative.
Relative
speed
Assume we are going in a car at 50
KMPH. Also, another car is going at the same speed and in the same direction
nearby our car. If the suspension system of the car and road are good we cannot
feel the movement of the cars. All the persons in both the cars would say that
the other car is at rest. We might have experienced the same when one bus
overtakes another bus, when we are sitting in one bus. The reason for this is
the relative speed, which the difference between the speeds of the cars. In
this case it is zero (50-50).
When a car (A) going at 60 KMPH
overtakes another car (B) going at 50 KM in the same direction, the persons in
the car A will feel that the car B is going backwards at the speed of 10 KMPH
(60-50). The persons in B would feel that the car A going ahead of their car at
the rate of 10 KMPH.
If in the above case, if the cars are
going in the opposite directions, the relative velocity would be 110 KM
(50+60). In this case, both the cars would separate at the rate of 110 kmph.
That is the persons in both cars would feel that the other car is going at a
speed of 110 KM.
From the above, we see that when both
the cars are at rest or both moving with the same speed and in the same
direction the cars seem to be in rest.
In the above circumstances, whether
the cars are at rest or at motion?
In the same way, day and night are also
relative. While it is day in India, it is night in US.
Consider a train is moving in a
straight line with uniform speed. For a person in the train all the objects in
the train are at rest. If he tosses a ball up it will drop back to his hands.
The person will feel as if the train is at rest.
At the same time, a person in the
platform will see the movement of the ball in a different way which is shown in
the following diagram.
Some
facts about the light
The speed of light is almost 3 lakh
KM per second. To have an idea of this speed, if we have a rocket of this
speed, we can reach moon in 1 sec and the sun in 8.5 minutes. We can travel
around the earth almost 7.5 times in one second. The greatest speeds available
are those of a rocket with 12 km/sec. The speed of rotation of the earth on its
axis is about 30 km/sec.
Light does not have the relative
velocity. Its speed is always the same. It is a constant. It is independent of
the source which produces the light whether it is moving or at rest.
Naturally, it is possible to increase
or decrease the speed of a body artificially. For example, suppose a bullet is
fired from a gun. If we place a box or bag of sand in its way, it will slow
down the velocity of the bullet. The speed of the bullet depends on the type of
gun and the gun powder used in the gun etc. But for light the speed does not
depend on the source.
Sound requires a medium for propagation.
But light does not need any medium. Assume a bell and a bulb is placed inside a
glass jar. The air inside the jar is constantly pumped out. The sound of the
bell gets weaker and after some time we cannot hear the sound. On the other
hand, the bulb glows as usual. This shows that light requires no medium.
An experiment was conducted by Albert
Michelson to find the speed of light. His experiment showed that light travels
in all directions with the same speed. The speed does not vary with anything.
It was concluded that the velocity of light is not relative but absolute.
Time is
relative. Contraction of time
Assume a train which is 5400000 (fifty four lakh) long
which travels at a speed of 240000 (two lakh forty thousand) km/sec in a
straight line. Assume the train travels from west towards east direction.
There are two automatic doors one at
the first coach and another one at the last coach. There is a bulb in the
middle of the train. The doors are so devised so that they open immediately
when the light from the bulb reaches the doors.
We will find the observations made by
a person in the train and a person in the platform.
Person in
the middle of the train
Person in
the platform.
For this person, the fist coach is
going towards east at the speed of 240000 km/sec and light from the middle of
the coach also going in the same direction. For him, the relative speed is (300000-240000)=60000
km/sec. In order to reach the door in the first coach, light has to travel a
distance of 2700000 km. It will take 45 seconds (2700000/60000). Thus, he will
see the door open in 45 seconds after the bulb is switched on.
Hence, two identical functions,
opening of the doors in a train will happen at the same time for a person in
the train and with 40 seconds interval for the person in the platform.
It will seem to the people on the
platform that the doors open at different times, the rear door first and the
front door after 40 seconds. How it is?
There is a joke. One cow boy on
seeing a giraffe in the zoo exclaimed, “It cannot be”. The reason is that he
had never seen any animal other than cow. Likewise, the above phenomenon is
unbelievable since we cannot imagine the tremendous speed of 240000 km/sec.
The theory of relativity of time and
its effects are usually known as special theory of relativity.
Assume that
we are travelling in a train called Einstein train along an endless railway.
The distance between two stations is 864000000(eighty six crore forty lakh) km.
The speed of the train is 240000 km/sec. If the train starts from one station,
at this speed, it will take 1 hour for the train to reach the second station.
There are
clocks at both stations. A person boarding the train at the first station sets
his watch by the station clock. On arriving at the second station he is
surprised to find that his watch is slow.
At the repair shop he was told that his watch was in good order.
To explain
the reason, consider the following. Assume that the traveler placed a torchlight
on the floor of the train and sends the light towards the ceiling. There is a
mirror in the ceiling which reflects the beam of light back to the torchlight. The
following figure shows the path of this beam as found by the person in the
train and by a person in the platform.
From the two
figures above, we may conclude that for the observer in the platform, the beam
travelled a greater distance than to those on the train. This is because of the
movement of the mirror and the torch along with the train. We already seen that
the velocity of light is absolute and hence it the constant for the traveler
and also for the person in the platform. We see that for the observer in the
platform, light travels more distance. From the basic formula,
time=distance/speed, we can see that it takes more time for the light to start
from the torchlight, reaches the mirror at the ceiling and to return to the
torchlight.
By a simple
calculation, we can find the difference of time between the traveler and the
person on the platform.Suppose the observer in the platform finds the time for
the light from the torch light to reach the mirror and then return back to the
torch light to be 10 seconds. Since the
speed of light is 300000 km/sec, and it took 10 seconds to complete its path,
the total distance travelled by the beam for this observer is 300000*10=3000000
km. This is the length of AB+BC in the triangle ABC. Hence, the length of
AB=length of BC=1500000 km. The distance AC is the distance travelled by the
train in 10 seconds, i.e. 240000*10=2400000.
In right
angled triangle ABC, BD is the height of the coach. We can find BD from
triangle ABD using Pythagoras theorem. It is 900000 KM.
For the
traveler in the train, the distance travelled by the beam is 1800000
(900000+900000 up and down). Speed of light is 300000. Hence, the time taken by
the beam is 1800000/300000= 6 seconds.
From the
above, it could be seen that while 10 seconds elapsed at the railway station,
only 6 seconds passed in the train. That is to say, if the train arrived at the
next station in 1 hour, for the observer in the platform, it would be only 36
minutes for the traveler. To be clear, if the train started at the first
station at 1100 AM, while reaching the next station, the time would be 11.36 AM
as per the clock of the passenger and would be 1200 as per the clock of the
person on the platform.
If the speed
of the train is increased so that it approaches the speed of light, it is
possible that only one minute will elapse on the train whereas one hour will
elapse in the platform.
Now assume
that the Einstein train travels along a circular railway. It will return after
a certain time to the point where it started. As already discussed, the
passenger will discover that his watch is slow. By increasing the speed of the
train we may reach a point where only a day passes for the passenger while a
number of years elapse for the station master. If the passenger were the
father, he would find his son elder than him.
A light year
means the distance travelled by light in one year. Usually the distances of
stars are measured in light years because of its enormous distance from earth. Assume
a star is at a distance of 40 light years. That is to say, if we go in a rocket
at a speed of light, 300000 km/sec, it will take 40 years to reach the star.
Suppose we
fly to the star in an Einstein rocket at a speed of 240000 km/sec, for the
people in the earth we will reach the star in 50 years. But as we seen earlier,
a time of 10 seconds in platform is only 6 seconds in the train, the actual
time taken for this travel is 50*6/10= 30 years.
If the speed
of this Einstein rocket is sufficiently increased, we can reach the star and
return to the earth within a minute. But on the earth 80 years will have passed
at the same time.
From
calculations, it is observed that if we travel for 6 months at an acceleration
equal to that of the earth, we may gain 6 weeks.12 months of flying in a rocket
will gain 18 months, for 2 years of travel the gain is 28 years, and if we
spend three years in interplanetary travel we will gain more than 360 years.
This can
only be theoretical and is impossible because of the expenditure involved. A
rocket of weight 1 ton and flying with a speed of 260000 km/sec consumes
250,000,000,000,000 (250 followed by 12 zeroes.) kilowatt-hours (units), which
it takes the world several months to produce. This is only for the travel. At
the speed of 260000 km/sec one year in the rocket will be equal to 2 years in
the earth.
The
requirement would be 200 times as mentioned above for the starting speed and
also for the safe landing of the rocket. This energy is approximately equal to
the power that the world produces in several dozen years.
Article by:
Sri R.Hariharakrishnan,
Reference:
1.
Relativity, The
special and the General theory- Albert Einstein
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