Monthly Archives: February 2005

In what orbs to run

Friends,

 

        In yesterday’s math forum meeting some interesting questions regarding orbits of planets were raised. Since these would interest everyone in the VERITAS group I thought I should post the answers as a VERITAS article:

1) How do we know that earth orbits the sun and not the other way?

   This is actually a very valid question. We take it for granted that earth orbits the sun. But why? The Sun is not God! Why should earth orbit the Sun? When we look at the Earth-Sun system we realize that these are 2 bodies moving under the gravity of each other. Sun pulls Earth. Earth pulls Sun. SUch a system is called a two body system. In a two body system the bodies move around their centre of mass. So earth does not orbit the Sun. And the Sun does not orbit the earth. They both orbit their common centre of mass. But the sun is SOOOOOOOOOO massive compared to the earth. The centre of mass of the earth-sun system lies within the body of the Sun. See that! So the earth orbits the Centre of mass which is within Sun. It cannot be the other way round. No need to even observe. All this can be shown mathematically. The solution of the two body problem is well known and is textbook material.

   I would also like to mention that the three body problem is still unsolved in Physics. Physicists dont have an equation to describe how three bodies move under mutual attraction!!!! They have to do this approximately and numerically! Physicists talk about the universe but they cannot solve a 3-body problem. What to talk of the 10 body solar system!

 

      Remember Einstein’s words:

“Whoever undertakes to set himself up as judge in the field of truth and knowledge is shipwrecked by the laughter of the Gods.”

 

2) Why are the orbits of Planets elliptical and not round?

    I have struggled with this question a lot in my younger days.

It made me feel so miserable. Only after reading Herbert Goldstein’s “Classical Mechanics” did I felt better.

      Why do we have a desire for round orbits? Lets first look deeper at this question? This desire comes from our stupid educational system that gives us analogies to help our learning but does not warn us when we go too far with these analogies. In our school days we were told that earth orbits sun much like a stone tied to a thread can be rotated in a circular motion! And electrons also orbit the nucleus the same way! Nice for learning but these kind of analogies hamper any deeper reflections on these subjects.

   Lets understand the stone tied to a string rotation in detail. A stone tied to a string is rotated. It moves in a circular fashion. The stone’s “desire to move outward”(centrifugal force) is exactly balanced by the pull of the thread. Now rotate the stone faster. The stone’s velocity increases. Its centrifugal force increases. But it is exactly balanced by the increased tension in the string. Now increase the velocity further. More tension! …. it keeps going round and round till the string breaks and the stone goes far away!

 

   Now lets look at the earth sun example. first thing: there is no string. So there is no balance! It is something like this: The earth moves towards the sun… in this motion it gains a lot of velocity( think of it like falling toward the sun). When it comes near the sun the velocity is so huge that it whizzes past the sun. Now it is moving away from the sun.

In this motion it keeps getting slower( its direction is opposite to sun’s pull). It reaches a point where its “desire to move away” is exactly balanced by the sun’s attraction. Its velocity in a direction away from the sun becomes zero. And it falls again.

 Here are the major differences between the earth-sun orbit and the stone -string analogy:

a) In the earth sun system the balance between centrifugal force and pull happens only at the end points. In a stone with string thing every point is balanced.

b)If the velocity of the earth is increased it will make a bigger orbit around the sun. But if the velocity of the stone tied to a string is increased the orbit stays circular. This is because the thread can take more tension. And you have not let the stone move to a larger orbital.

You have taken a unstretcheble string. You have not allowed the stone to move away!

c)The pull of sun on earth decreases as earth moves away. The pull of the thread on the stone always adjusts to exactly match the pull of the stone.

So the analogy on which we base our desire to give a circular orbit to earth is not a valid one. A better analogy would be to imagine a stone tied to a flexible elastic. The elastic allows the stone to move away.

However even this analogy is not perfect.

    There is a point around the sun where if earth is placed with a particular velocity a perfect balance between opposing forces will be achieved. And a circular motion will follow! But the natural motion of planets around a star is not circular. It can be elliptical(least velocity of planet), parabolic( more velocity) or hyperbolic( highest velocity! The planet will not come back!)

 

            And, if each system in gradation roll

            Alike essential to th’ amazing whole,

            The least confusion but in one, not all

            That system only, but the whole must fall.

            Let earth unbalanc’d from her orbit fly,

            Planets and suns run lawless through the sky;

            Let ruling angels from their spheres be hurl’d,

            Being on being wreck’d, and world on world;

            Heav’n’s whole foundations to their centre nod,

            And nature trembles to the throne of God.

 

                              ( Alexander Pope)

 

 

 

kanwar

 

 

|======================================================|

  Go, wondrous creature! mount where Science guides:                 

  Go, measure earth, weigh air, and state the tides:                 

  Instruct the planets in what orbs to run,                          

  Correct old time and regulate the Sun;                             

|======================================================|

Maxwell’s Demon

 

Friends,

 

        We know that the disorder in a system always increases. This is the law of increase of Entropy. For those of you who have not read this, let me give you an example: place 100 red balls on one side of a box. On the other side place 100 white balls. So the balls are neatly seperated.

Now shake the box. When you open you will see that the red and white balls are not in the ordered state in which you placed them. They are now mixed with each other. So our ordered state is lost. A disordered state is reached. So the law of entropy says that all closed systems move from order to disorder. Never the other way! A glass tumbler may break into small pieces. But small pieces will never join together to make a tumbler. The law of entropy is remarkable because there is no other law of Physics that differentiates between the past and the future. The law of entropy does. The future time is the time when the system becomes disordered. Thus the law of entropy defines the arrow of time.

    In today’s VERITAS we will discuss a remarkable “thought  experiment”.

A “thought experiment” is a theoretical Physicist’s delight. The theoretical Physicist just sits on his chair and imagines the experiment.

So it is an imaginary experiment. A flight of fancy. It is supposed to be analyzed using mathematics.

 

       In the year 1871 the great Physicist James Maxwell proposed this thought experiment: Imagine two compartments of a box filled with a gas. There is a wall separating the two compartments. There is a tiny trapdoor on this wall. A tiny “demon” sits near the trapdoor. If he sees a fast moving molecule of gas coming he opens the trapdoor. If he sees a slow moving molecule coming he does not open the door. Over time all the fast moving molecules would collect in one compartment and the slow moving in the other compartment. So we would have created order from disorder. Would this not violate the law of entropy? And by separating the fast moving molecules on one side and slow moving on the other we have made one side hot and the other cool. We can even extract heat from the system!

      You may not find this such a strange thing! You would say: “Hey I can tidy my desk! I can make it ordered from disordered! Is this a violation of the law of increase of entropy?”. When you clean your desk you are using up energy. To have and consume energy you must eat food. And the consumption of food increases the entropy of the world! You are breaking down complex ordered food into simple less-ordered things in your stomach! So you may be tidying up your desk but you have created a lot of disorder in the universe in order to do so!!!!!! The total disorder in the universe will always increase.

     In the Maxwell’s thought experiment we are hoping that we can use less energy by merely deciding whether the trapdoor should be opened/closed. We are trying to beat the entropy backlash by creating a simpler more energy efficent machine!

     So we want to create a trapdoor that is nearly frictionless. We want to create a decision making demon( a small compter) that will just look at the molecule’s speed and make a decision to close/open the door. We want to burn very little energy (or create very little disorder) and create a lot of order!

   In the year 1929 Leo Szilard wrote a paper “On the decrease of entropy in a Thermodynamic system by the intervention of Intelligent beings”. In this paper ( which came much before the advent of computers) he wrote that for the demon, in order to learn through measuremnt the speed of the molecule and to make the decision,there has to be a use of atleast : kT log 2 amount of free energy. So Szilard was saying that collection of information and its processing must involve at least a minimum amount of energy( and therefore entropy increase). This is called the “Szilard limit”. This paper formed a relationship between information and thermodynamic energy. THis paper’s definition of information found a lot of use by Shannon in the field of communication science!

      In other words Szilard showed that the law of entropy increase cannot even be violated by an intelligent being merely making decisions because information gathering and processing will cause a lot of disorder in the universe.

   In 1983 W.H Zurek showed that even a quantum computer cannot behave like an efficient Maxwell’s demon. The “Szilard limit” holds there also.

       So the demon has been killed. The law of entropy increase holds! The universe will move towards disorder and neither you nor you compters can do anything about it. Order can only be created in localized pockets. But any creation of order at one place will result in a huge amount of disorder elsewhere!

      Someone has beautifully summarized the three laws of thermodynamics:

1) You cant win. You can only break even 

( Enery cannot be created. It is conserved)

2) You cannot break even

      ( You cannot return to same energy state because there is always

  an increase in disorder)

3) You cannot even get out of the game

      ( zero energy is unattainable)

Kanwar

 

|======================================================|

  Go, wondrous creature! mount where Science guides:                 

  Go, measure earth, weigh air, and state the tides:                 

  Instruct the planets in what orbs to run,                          

  Correct old time and regulate the Sun;                             

|======================================================|

Light and Life – Part 1

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This post was written on Wednesday, February 02, 2005

Friends,

       Today we are starting a new series in VERITAS. Just like our “Mysteries of the Brain” series this series will last for several months(or years!). In this series we will explore the complex relationship that life has with light.

       If we examine our senses and pick one that is the most important we would no doubt pick sight. All other senses are local in range. We have
to be near something in order to touch,smell or hear or taste it. The range of these four senses is very limited compared to the range of sight.
We can see the moon and stars( which are millions of kilometres away)!

       But what is sight? It is to detect light and to be able to get information about things from which this light comes. But what is light?
It is an electromagnetic wave( a wave with an electric and a magnetic field moving perpendicular to each other). So seeing means to detect
photons( particles of light). It seems like a very complicated thing to do.

 In today’s VERITAS we will try to understand how the sense of sight evolved. Light had always existed in this world. But when did the first
living thing realize that there is something( a em field) around it which it can use to detect the shape and size of things without touching it? And
how did this realization evolve into something as complicated as the eye?! So how did the first blind creatures realize light???!!!

       When Darwin proposed his theory of evolution he realized that the eye would be very difficult to explain in terms of evolution. Indeed, the
creationists ( people who do not believe in evolution. According to them the world was created by a Supreme Being. This world is a perfect world-
No need to evolve) frequently use the example of the eye to state their point. They say that the eye could not have evolved from something
simpler. And this is because the eye is something so complicated and several complicated parts come together to make the functional eye.
Any one part of the eye is useless without the other. SO the creationists believe that any one part could not have given the bearer of this part any
advantage in terms of survival. So this part could not have evolved into the eye!

 But people who believe in evolution have an answer to these. And in recent years a lot of scientific evidence has shown that the eye did evolve from something much simpler.

       Lets go back to  the Cambrian period( about 550 million years ago). The world is full of primitive creatures that feed on other creatures. Predation has started. SOme creatures are the prey and the others are predators. But none of them can see. They touch each other and
decide to eat or move away. One of these creatures develops a small light sensitive cell( out of nowhere! Mutation! He was just born with it). That
one cell gives this creature a small sense of light or darkness. He gets a slight advantage in terms of survival. This creature passes on this trait
to its offspring. They too get this survival advantage. Slowly after several hundreds of generations this light sensitive cell becomes a group
of light sensitive cells. Organisms that have this group get a survival advantage over the ones who have lesser number of cells. And then
after generations a hole of light sensitive cells is formed which gives a much better idea of not only light and darkness but also relative
brightness. Then in some creatures this hole is filled by a liquid that bends light to form a blurred image. And much much later a lens is formed
that can focus to form a sharp image by bending light. That is how the eye evolved. So each generation that had the additional light sensitive apparatus had a slight survival advantage over the creatures that did not have this apparatus. Scientists have found fossil records of each of these stages.

       How much time would this evolution from a light sensitive cell to a primitive eye take. According to a group of scientists( Nilsson and Pelger)
this would take no more than 400,000 years( assuming a generation lasts for 1 year as it is in case of fish). So the eye has had a lot of time to
evolve since the first light sensitive cell appeared(550 million years ago)

       But there are several questions that I still dont know the answers to:

a) Why was detection of light(photons) a survival advantage. Why not detection of say electrons/atoms? Why didnt a creature with a electron
  sensitive cell not survive and evolve?
b) How is the detection of light actually done by the eye? Is it a photoelectric thing ?

c) We can detect only a small range of frequencies of light. Why only  these? Did evolution decide something here?

   If I find any of the answers to these questions I will post them in a future part of our VERITAS series “Light and Life”.

Friends, see how such  complicated things as the eye can evolve out of almost nothing over millions of years. The people who dont believe in
evolution dont do so because they are overwhelmed by the complexity of the living organisms. And they cannot understand how something as simple as evolution explain  this. But dont underestimate the power of a million years. It is a  VERY VERY long time. Our life spans are nothing compared to this. And things do change in a million years.

        To appreciate our sense of sight lets recall the sonnet that Milton wrote after he became blind. In this sonnet Milton tries to come to terms with his lack of vision:

    When I consider how my light is spent
    Ere half my days in this dark world and wide,
    And that one talent which is death to hide
    Lodg’d with me useless, though my soul more bent
    To serve therewith my Maker, and present
    My true account, lest he returning chide,
    “Doth God exact day-labour, light denied?”
    I fondly ask. But Patience, to prevent
    That murmur, soon replies: “God doth not need
   Either man’s work or his own gifts: who best
   Bear his mild yoke, they serve him best. His state
   Is kingly; thousands at his bidding speed
   And post o’er land and ocean without rest:
   They also serve who only stand and wait.”

Kanwar

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 Go, wondrous creature! mount where Science guides:
 Go, measure earth, weigh air, and state the tides:
 Instruct the planets in what orbs to run,
 Correct old time and regulate the Sun;
|======================================================|

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