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Can u tell anything absolute ?

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
We know that light travels at the same speed of 3 lakh km/sec. The light will reach the door in the first coach in 9 seconds. (2700000/300000). The person will see the door in the first coach opens in 9 seconds. Similarly, he will see the door in the last coach also opens at 9 seconds. Hence the person in the middle of the train will observe that both the doors will open at the same time.
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.

As the last coach moves in the east direction, towards the bulb and also the light moves towards the last coach, the relative speed is 540000 (300000+240000). Time taken for the light to reach the door in the last coach is 5 seconds. (2700000/540000). Thus, he will see the door in the last coach will open after 5 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,

1.     Relativity, The special and the General theory- Albert Einstein

2.     What is the theory of Relativity- L.Landau and Y.Rumer.

Science - The Religion of all


            “Science is the religion of all “- Albert Eienstein.
            “Physics is the study of the laws which govern each and every activity happening around us”
Dear students,

Kindly go through the following questions and try to answer them. Can you find the law or principle or rule which govern the following activities.

1.      A bus going at a speed comes to a sudden rest when the brakes are applied.

2.      A mighty ship floats whereas a small metal ball sinks in sea

3.      The launching of rockets.

4.      The glittering of diamond

5.      Principle of atom bomb.

6.      The taking off of an aeroplane

7.      The projection of cinema in a big screen at a cinema theatre

8.      Thunder arrester

9.      The continuous burning of wick stove or kuthuvilakku with the help of oil

10.  The blue colour of sky.

11.  Working of water heater.

12.  Using of red colour as a signal for danger.

13.  Electric motor or electric dynamo

14.  Covering the jewels made of silver with gold. (imitation jewellery)

15.  “Give me a place to stand and give me lever of suitable length. I will lift the earth”- said Archimedes. Had he been provided with these things would he been successful? If not, why?

Wish you all success,

Sri R.Hariharakrishnan,  

Next topic : Scientists

Are You Curious to Answer ?

These questions are solely intended for making curiosity in mathematics. It is a small effort to open a small window into the great world of mathematics. I hope while searching for the answers for these questions, you will get thrilled about the subject. If this search increases your interest in mathematics, I would be very happy. 
There are 3 famous mathematicians of the same family. Their last part of the names are the same. Who are they?

2.       What is special about the Ramanujam number 1729?

3.       Who are mathematicians who devised the subject “calculus”?

4.       Can you mention three mathematicians who have also contributed to physics?

5.       “Koningsbergbridge” is in Russia, which is starting point of a new branch of Mathematics. What is it? Who was the mathematician devised the new branch?

6.       Which prize is called the Nobel prize for mathematics?

7.       In which God did Ramanujanhad full faith in his findings in mathematics?

8.       Who is the English mathematician who helped Ramajujan and who brought his talents to the world?

9.       Which country contributed the number 0 (zero)?

10.   If the perimeter of any circle is divided by its diameter, we will get a constant. What is it?

11.   Who is called the Prince of Mathematics?

12.   What is the birthday of Ramajujan?

13.   Only one of the 7 problems called the millennium problems in mathematics is solved as on date. Who solved it? What is the problem?

14.   A great mathematician became deaf and blind at the age of 60. He made almost equal contributions to mathematics before and after becoming blind. Who is he?

15.   Ramanujan was not even a graduate. He was awarded the highest honour for his contributions to mathematics. What is it?

Courtesy : Sri R.Harihara Krishnan

Happy Teachers Day

Dear Friends,

Coming 5th is Vinayakar Chathurthi, which comes along with Teachers Day. Yes , Our Teacher is our God

Mathru devo bhava 
Pitru devo bhava 
Acharya devo bhava

Let us thank, our teacher, who opened the world with the  eyes of KNOWLEDGE.
Just Go and Meet your teacher, who inspired you and present a Gift and get his blessings.

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Venkat Pakkangal wishes its readers a Very Very Happy Krishna Jeyanthi.

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