Paradox, Confusion, Puzzle

This post is written by two of my students, I have suggested the title only…..

 

While traveling by train, both of us has gone through this experience many times…..we were in the train, the train was moving with high speed, suddenly another train comes in the side by line and it was going in the same direction of our train. We were watching the passengers of the side by train and suddenly felt that we are not moving at all, it appeared that our train and also the other train both are still. Then we immediately moved our heads on the other side and looked through the window and then we realized that our train did not stop, it was running with the same speed.

All of you have experienced it at least once while traveling by train.

So, what it says? This is a real life experience from where the concept “Relative” comes.

A moving train has a certain velocity for sure, but what is that velocity depends upon----with respect to which you measure it, generally we measure it with respect to earth, which is considered to be a “Rest Frame”---standing in the ground you measure the speed of a train(Say ‘Train A’)---obviously you will get a certain value, but if you try to measure the velocity of ‘Train A’ riding in another train (Train B)which is moving parallel to that ‘Train A’ and has same velocity then you will say that the speed of ‘Train  A’ is zero.

So, we can say everything is relative…depends upon from which frame you are measuring it.

Here some interesting incidents of Relativity have been discussed, hope you will enjoy it and will think about it….

 

Relativity:--

     We know that, the greatest scientist, Sir Albert Einstein is known as the "Father of Relativity". He informed us about relativity. Einstein formulated the 'Theory of Relativity' by which he described gravity more deeply. The theory of relativity consists of following two laws;.

 

(1) All laws in physics are same in every inertial frame; no change will take place (It is same for all non-accelerating observers).

(2.) Light has the maximum velocity (C) in the universe and it is same in every inertial frame.

Einstein made “Special Theory of Relativity’ which is generally applied where the curvature of space and time is negligible

This is what Sir Einstein said to simplify what is Relativity…

"To simplify the concept of relativity, I always use the following example: if you sit with a girl on a garden bench and the moon is shining, then for you the hour will be a minute. However, if you sit on a hot stove, the minute will be an hour."

Relativity deals with the phenomenon of ultra high speed that is the speed of light (C), this is the highest speed in this universe and this is the speed which can never be crossed.

Lorentz Transformation equations are the equations that deal with the phenomenon of “Moving frame” and “Rest frame” and also “time in moving frame” and “Time in rest frame”, we will share some interesting outcomes of Lorentz transformation equations.

 

Time Dilation: ----

      It is the theory of relativity which states that when a clock moves very fast then time starts to slow down in that clock.

 

Length contraction: ---

      From the relative theory of length contraction we can say that when an object moves very fast (velocity near  to 'C') and an observer is in rest parallel to the object, then the observer will notice that the moving object becomes shorter in length/ its length gets contracted.

Suppose there is a rod of 10 feet in a train and there are two observers, one is in the train and the other one is in earth, now if the train starts to move with a velocity near to ‘C’ then---

1) The observer who is in rest will measure the length of the rod as 8 ft, that’s shorter than original size. 

2)The observer in the moving train will measure it as 10 ft.

Now the question is----really it’s a length will contract if it travels with the speed of light?

Paradox: ----

    The term 'paradox' is from the Greek word 'Paradoxon' that means contrary to expectations existing belief of perceived opinion.

     It is a statement that appears to be self contradictory or silly but may include a latent truth. It consists of two meanings of the statement, both are true or both are false but meaning couldn't be true or false at the same time. It makes the reader to think deeply about it.

 

Twin paradox: ------

  It is a thought experiment in 'special relativity' in which identical twins, one of them travels in the space in a high speed ( appox 'C') rocket and then comes back to its original position to find his twin brother who was in rest in earth. It is likely to be happened that the travelled ones age will increase much slower than the rest one. We can prove it by the 'Lorentz transformation' rule and 'Relativity of time dilation'.

    Let us consider two twins Arun & Rahul. Both are 25 years old. Now, Arun makes a journey to the space in a rocket with a high velocity (approximate 'C', though it is not possible to apply this velocity in any object)suppose, It takes time 5 years to go to a destination and another 5 years to return…so total journey of 10 years, After coming back to its initial position, Arun will find that his age has become 35(25+5+5) but his brother Rahul’s age is 95 years.

This is really doubtful and complicated for all. When Rahul becomes 95 years old then Arun also must be 95 years old, but it didn't happen. Such thing happened because Arun traveled with the high velocity and time went slowed down to him which did not happen for Rahul as he was in rest in earth.

 

 

Ladder paradox: ----

 It is an experiment which requires a ladder, a garage and an observer.

 Now, we consider that the ladder is longer than the length of the diagonal of the garage and does not fit inside the garage, as we all know that the maximum length of the ladder that can fit in the garage is the diagonal of the garage.  Now, the ladder is moving with a very high velocity (approx 'C') towards the garage and the garage is in rest….so, according to Lorentz Transf. Equation the length of the ladder will be shorter than its original length, so the observer who is seeing the ladder from a rest frame will see that ladder’s length has contracted and then the ladder can be fitted in the garage----this one will happen really?

Now think about the opposite situation, there is a ladder of very short length, say one foot, and there is a garage of 10ft/12ft/12ft, now if the garage starts to move towards the ladder with a very high velocity (Nearly C) then according to L.T. equation the garage will be shorter and the ladder will fit in it------Puzzled?

 

Example of paradox: ------

(1) Your enemy's friend is your enemy: ---

   Let us consider A, B & C is three persons.

 A is B's enemy.

C is A's friend.

Now, you can say that C is also B's enemy. But it always never happens. We read "Rajam & Moni", where Rajam & Moni are enemy to each other but Swaminathan is friend of both Rajam & Moni. So we can say that your enemy's friend could be friend of you, never always enemy.

So here it creates a conflict between many people.

 

(2) You shouldn't go into the water, until you know how to swim: ----

      This sentence is very complicated and everyone gets confused in it and thinks deeply.

    If anyone doesn’t go into the water then how and where he will learn to swim??????

   And if anyone doesn’t know how to swim then he must not go into the water as there will be chance of drowning.

So you can see that it creates conflict.

But, the real meaning of these sentences are --- you can go into the water from where you can survive yourself, so at first, learn swim in a lower deep water and then go into the deep water.

 

(3) The beginning of the end: ----

       When a task is going to be end then, how it is in the beginning?

   But if the task was not started then it will not meet end. So, both are right. Every task has a start point and an end point, which are dependent on time. The beginning of the end means the task is in the beginning period of the end stage, which means starting of the end period.

 

 

(4) When a fan doesn't run, we can clearly see the blades and its joints with the head of the fan. But when a fan runs very fast, at that time we only see the head, the joint portion looks like vacant and creates a ring (blank), it seems that the wings create circle.

So, during running period someone who is in rest(we all) will think there are no wings ----but it’s not true, because the person who is sitting in the blade will see that different blades because he is moving with the blades. So, it creates conflict between two people.

 

 (5) Let us consider a train is running with a high velocity (approx 'c') and a rod & an observer(A) are present inside the train and an another observer(B) outside the train who is in rest position. After sometime B will notice that the train as well as the rod will contract but A will not notice any change because he was inside the train and traveled with the same velocity of the train.

 

 

 

 

(6) When a lorry is on a bridge and both length are equal. If the bridge moves very fast (velocity near to 'C') then what will happen?? Will the lorry fall from the bridge or not?? You will think that the lorry will fall from the bridge but it will not happen. As the lorry is on the bridge and the bridge is moving so the lorry is also moving with the same velocity of the bridge, then both of their lengths will contract. So, the lorry will not fall from the bridge---at least L.T. Equations says so.

So it can’t be said exactly whether Arun’s age will increase much slower than Rahul or not, it can’t be said exactly whether the ladder which is much longer than the diagonal of a room will fit in the room or not----until we make a journey with a speed of light.

But we should remember one thing---if we measure the speed a certain train standing in “earth” then it will not match the speed when measured from another “moving train”…so which sped is correct? Which frame (Earth, moving train) is proper?

 

Written by:-

Arnab(Math Honors ,2^nd year)

Sanjiv(Diploma in Metallurgy, Final Year)

 

 

 

 

 

 

 

 

We are the destructors of the Universe

We are the destructors of Universe…

Surprised????

But it’s true, you can’t ignore it, you can’t stop it.

 

Let me inform you one more thing---the hard workers are the biggest contributors in the destruction of the Universe. I am not blaming you, Okay? I am just informing you, what can I do? At least the theory says so, the lazy peoples, like me, are contributing very less in the destruction of this Universe.

 

There were times when I did not know this harsh truth and when I came to know about it then I started to work much less than before so that I don’t feel guilty for contributing a lot in this destruction.

 

OK let me start with some examples from day to day life….

Example ---1

 

Think about the situation when you boil something or cook something in the woven, let us consider, you are boiling water in a pan, so you have put the pan upon the woven and lit the woven, the heat energy (Fire) is being transferred in the pan and in the water and after sometime the water starts to boil, but the fact is---the amount of heat exerted by the woven is not totally transferred to the pan, some of the heat has spread out in the surroundings. Now if anyone is asked to collect the heat from the pan, from the water and specially from the surroundings and after collecting all the heats she/he has to create that amount of gas that has wasted in boiling---then she/he will not be able to do it----in short, if someone asks you to reverse the process collecting all the heats used, you have to recreate the gas wasted then you will never be able to do so----not only you, no one can do this, no one in this world.

 

Example ---2

 

We all switch on our fans (Table or ceiling), just notice what happens then---electric energy is being transferred into mechanical energy (moving the blades) and some amount of heat is being created (the fan become hot). Now the heat energy created in the fan---where is goes? It just simply spread out in the surroundings (Universe). Now try to reverse the process---collect the heat that has spread out, collect the mechanical energy and try to recreate the amount of electricity that has wasted to move the fan….it’s impossible.

 

Example---3

 

This example I taught one of my students to present in a science seminar in his college.

Select a blackboard (In school, or college), take a chalk, a new duster and take a glass plate whose length is same as the blackboard and width around 2 feet, now place the glass plate under the blackboard so that you can collect the chalk dusts. Now start to write something (you can write---“Jyotirmoy has said to do this”, just kidding) in the blackboard until the chalk becomes half of its size, now erase whatever you have written, collect the chalk dust from the glass plate and the duster and try to give the chalk its earlier size…let me inform you, you will not be able to do that, no one can.

So, why I am giving you all these examples!!!! Because if in the beginning I have written “Entropy” then am sure you would be afraid of the term (Generally it happens), you would have think…oh, here is something very complex theory of physics has been written.

 

So what Entropy is….in an easy phrase it can be said---Unavailable energy.

 

Now think about the Example---1, where you were boiling water, there the heat spread in the surroundings can never be collected again, it’s totally lost---this is entropy.

In Example---2, the same thing has happened.

Example ---3, I have written this to make it easy (loss of chalk dust) to make you understand that how it’s being lost. But one more thing---when you were writing in the blackboard there also some amount of heat generated due to friction of chalk and blackboard and like other two incidents the heat also has spread out in the Universe.

 

Any process in this Universe is irreversible and in any irreversible process the Entropy of the Universe increases and one day Entropy will get its maximum value.

 

Now you may think why I am focusing on heat, don’t think that I am suffering from hyper acidity or something like that, OK, jokes apart, let me help you to focus in the matter which you all know that the main source any energy is heat---because its due to sun that we all are surviving--- the main source of our energy is food and now you think about the food cycle, we take food and transfers it into other forms of energies and we all know the very fact that if sun collapses for some reason then we will not be alive anymore.

So sun is continuously supplying us heat energy and we all are surviving, but it will be a very foolish thought that sun will never stop to supply us energy, may be after trillions of years but sun will collapse for sure.

But why I said we all are the destructors of the universe?

Ok, before that I must remind you---why heat transfer happens---it happens due to difference in temperatures in between two bodies---take a hot ball and a cold ball, touch them and keep for few minutes, after sometime their temperature will be same….

This is what happening with us, with this Universe, the surrounding is in much cooler state and there are lots of stars with lots of amounts of heat (Huge fire), the stars are continuously spreading their heat in the Universe and the universe is being hot. And we here in this milky way galaxy, the sun is spreading its heat and we are also spreading the heat of Sun in the Universe---this is happening because there is a temperature difference between the surroundings and the sun, but one day will come when we will spread lots of heat in the universe and so the sun and the Universe will come into same temperature, then think what will happen…Sun will no more be able to give us heat…because everything will be in thermal equilibrium…everything in same temperature…no cooler, no hotter body will exist---so no more energy transfer….

And the hard workers are accelerating this process---they are doing hard works, so they are spreading a lots of amount of heat in the Universe, making this Universe hotter, on the other way the lazy ones rarely performing any work so very less amount of heat they are spreading in the Universe so naturally contributing less to make the Universe hotter…so be lazy and contribute less in the destruction of the Universe.

                                        Lazy me---eating Samosa lying on rock of a Hill

Mainly we transfer heat energy (that exists in plants and vegetables which we take as food) into mechanical energy (walking, talking, and movements). We need foods to maintain our body temperature and to do works. If everything remains is thermal equilibrium then why we need food ? And what will we transfer?

 

So, what I have discussed above? ----Actually it’s a theory (an assumption) in Physics how the Universe will end, it’s called “Heat death of the Universe”---I have tried to make it interesting through some easy examples and my thoughts on it.

 

 

Unknown Indian(Part---4)---Unknown Girl, Unknown Pain

I was about to write an interesting post yesterday evening, which is very close to my heart but could not write a single word, even yesterday evening neither I accessed net nor I had done any work, lying in the bed I was thinking a lot, two incidents stirred my heart a lot, one is very heart wrenching and another one forced me to make analysis of God and his rules.

I am sharing the first incident here. When I started my new series “Unknown Indian” then I decided to make one post every week but this one is the second post in this week about an Unknown Indian.

This post is about a girl, whom I am seeing from last few months, in the beginning she did not caught my attention, in day to day life I have seen her, sometime in the morning, sometime in the evening.  After seeing her few times what I realized and observed is…

She is fifteen  years old girl(as i have guessed), She is not a member of the house where she lives now, the owner of the house has kept her to serve for his family, many times I have seen her to wash the utensils around 4:30AM-5:00AM during taking my morning tea, then I have seen her many times around 9:00 AM when she hangs the wet bed sheets and dresses in the rope but every time I have failed to find any happiness or peace in her face rather I have seen deep sadness and depression. She has the habit to spend the evening sitting in the garden, whenever I have seen her in that moment I have noticed that she is thinking something deeply or just sitting like a statue with lots of pains in her eyes. Yesterday when I saw her then she was in the garden, I noticed her eyes was full of pains and the face was very depresses than other days, I decided to observe her, so after sometime again I tried to see her and noticed that she sat like a drooping figure putting her head on her haunches, she was in that position for nearly two minutes and then lifted her face towards the sky and was making earnest prayer and was murmuring something, the prayer was very intense and deep, there was a restlessness in her attitude so it was very easy to understand that she needs something very badly, she was  demanding from God very earnestly---her intense prayer, painful eyes, sad and depressed face and restless attitude stirred my heart, I realized one thing very clearly that she is suffering from some troubles and problems and it is very easy to understand what the problem can be---its financial problem, otherwise at the age of fifteen she did not need to work in a house. It’s the age when she should go to school, it’s the time when she should enjoy his life playing with her friends but her fate has forced her to choose this path. It’s compulsory for her to work and thank to God that the owner of the house has kept her in his house otherwise she had to suffer from hunger and proper dress.

We all have the common feelings that we are suffering much more than others, we all think that our problem is bigger than others but this type of incident makes me feel that---“Kisi dusre ke nazar se dekho toh tumhare pass bahot kuchh hai”(Kaal Ho Na Ho, Released in 2003), yes this is what I felt observing her--- I have my own room, I have so many dresses(I have seen her only in two different dresses in last few months), I have good foods and have the liberty to decide what I will take in breakfast, lunch and dinner, I can move anywhere in my will, I can decide what works to do and when, I am not forced to obey any one’s order…

I know it’s not right to make comparison neither I want to mean that our problems are baseless, but it’s also true that if you observe these people and their struggles then you will get extra energy to fight with your problems and with your pains, this is what happens with me, whenever I see these types of people I become more stronger mentally, they encourage me a lot.

I don’t know exactly what the problems she is going through---but I know the life she is spending is not what she deserves in this age, as I have mentioned in my post “That Beggar and Me” that I don’t have enough financial condition to serve for these people for the life time, so what can I do is make prayers for her.

Hope you all will also make prayer for her.

If you can suggest me something to help her then I will remain grateful to you.