Elusive Particle of the Universe

Hi, welcome to you for the year of light and welcome to you for this interesting lecture.

Celebrating IYL 2015

Yes, we are talking about light, the light which is responsible for the diverse life on Earth and spreads in the unimaginable universe.  In the last lecture we spoke about the first light from the Big Bang called CMBR.  But in this lecture I don’t directly talk about light.  Instead I talk about atoms!!

Atoms are the building blocks of matter.  We have more number of atoms in our eye than the total number of stars in a galaxy.  This is true with any object which is of the size of an eye.  In principle we humans are all collection of atoms that have different names!  The matter which surrounds us is also a collection of atoms.  Suppose if I am drinking water from a glass.  If you shoot this in a video-camera which can only detect atoms regardless of their physical size, shape, and features, you can see that some arrangement of atoms drinking the same atoms which are in different arrangement.  This means that, you can form infinite number of structures by arranging atoms.  That is what the nature is doing from all these billions of billions years and it continuous do it in future also.  So, if you look at animals, birds, plants, humans, mountains, earth, stars and galaxies all these are just arrangement of atoms.

Image 4
Arrangement of atoms forms different structures. (Living and Non Living Things)

So it is important to study about atom.  Until the beginning of 20th century, scientist thought that atom is an indivisible particle of the universe and the fundamental particle of all the objects.  Later many observations and sensitive measurements by the 20th century scientist proved that atom is divisible.  Today we know that atom is made up of proton, neutron and electrons.  Protons and neutrons make up the nucleus which concentrates most of the atoms mass while the electrons revolve around the nucleus.  If I have to give you the feel of an atom or how big an atom is; imagine like this, consider this room (Auditorium) is of the size of an atom and this tennis ball (author is holding tennis ball) is a nucleus, than the smallest dust grain that you can find in this room is an electron!  This means atom mostly contains an empty space!  All the mass is concentrated in the nucleus.  This is a distinctive sketch of an atom.  But you might ask me a question… Do all atoms show the same characteristics?  The answer is no.  Atom with some fixed number of protons, neutrons and electrons have some physical and chemical characters.  But if you change the number of constituent particles of an atom, the characteristics also changes.  This means that if you change the number of electrons in an atom it exhibit different characteristics than the previous one.  Depending on the number of electrons in an atom a specific name is given to them, like hydrogen which has one electron, helium which has 2 electrons and so on… These are called elements.  These are arranged according to the ascending order of the number of electrons in their atoms.  This is called Periodic Table.  This table makes us to easily identify the element which has a specific character depending on its electron number.  This is about atom, and its constituent particles and their arrangement and how there characteristics changes.  But why am I talking about this, instead of light!

Yes, I will talk about light, but for a while let us go back to 1930.  Wolfgang Pauli an Astrian physicist was trying solve the mysterious violation of law of conservation of energy in process called Beta Decay.  I know all of you know about law of conservation of energy, in simple words the law says, energy can neither be created nor be destroyed.  It can only transfer from one form to another form.  And also the energy of the entire universe is constant.   In a given process the energy before the process and after the process should be equal.  No room for violation of this law in nature.  While doing math’s we may do errors in calculating the energies, but nature do not do any error.  It never violets the law of conservation of energy!  But something strange was happening with beta decay.  To know this let us learn about beta decay.  Since we know about atom, it is very easy to understand this process.  In certain elements the nucleus which contains protons and neutrons becomes unstable due to the more number of neutrons than the protons.  If something is unstable it has to give out or it has to accept something in order to attain stable position.  Here we have only protons and neutrons in the nucleus.  So, what happens to this unstable nucleus?  Yes, an extra neutron in the nucleus decays into proton and in this process an electron is emitted out of the nucleus as shown by the below nuclear reaction. (The elements which shows this behavior is called Radioactive Elements and the process is called Radioactivity). This process is called beta decay.  (Beta particle = Electron).  This is an observable process and the experiments have confirmed this nuclear reaction.  But what is the strangeness about this nuclear reaction?  You might be surprised to hear this; this nuclear reaction is actually violating the law of conservation of energy!  But the question is HOW?

n -> p + e

If you equate the energies in beta decay process, you will see that the total energy of the emitted particle is less than the energy of reactants (for now consider it as reactants).  Let me explain this… In beta decay process an extra neutron in the nucleus decays into proton and stays inside the nucleus.  But an electron ejects out from the nucleus and this electron does not belong to orbital electrons, because it is created in the nucleus and emitted out.  But the amount of energy that electron is taking out from the nucleus is less compared to the energy used in creation of the electron.  This tells us some energy is missing in this process.  When we do the experiment, there is no signature of any other particle taking the missing energy. Then where is the missing energy?  This is the question that haunted many scientists during the twentieth century.  So what do you conclude based on our experiment?  Is nature violating the law of conservation of energy or our calculations are wrong?

Pauli worked extensively on this problem of missing energy in beta decay and finally arrived at one conclusion.  He believed that the universe is governed by the order of natural laws.  And he had firm believes that nature does not violates these laws.  More importantly he also believed that his calculations are correct.  He said nature is not violating law of conservation of energy.  The missing energy in the beta decay is transmitted through a particle called ‘Neutrino’ which has zero mass but has the energy which corresponds to the missing energy!  He wrote down all the mathematical calculation to prove the existence of this particle which he called Neutrino and published the paper.  But many scientists did not believe Pauli and went on claiming that, this kind of particle does not exist.  But Pauli who was theoretical physicist, I mean the one who do only math and calculation to give the theory of nature had solid-believe on his theory.  I should say he trusted his calculations so much that, he always said this particle; I mean the neutrino should exist in our nature.  This is the beauty of understanding the nature.  This is where we should appreciate our language called maths and equations.  The numbers and equations hide the unseen exquisiteness of nature.

n -> p + e + nubar

Finally the beauty of Pauli’s calculation unfolded in the year 1956, when two physicist Frederick Reines and Clyde Cowan announced that they have indeed detected neutrino’s in beta decay process predicted by Pauli.  It nearly took 16 years to find the existence of the particle predicted by the great physicist Pauli.  But you know what, nearly trillions of trillions of trillions neutrinos have passed through your body while listening to this lecture.  For every minute billions of neutrino is passing your body.  The earth is in the shower of neutrinos from the sun, stars and galaxies endlessly.

Today I am here to talk about neutrinos.  When Pauli predicted this particle, he said it has energy but rest mass of the particle is zero, which means these particles never come to rest!!  So, how do we detect this particle?

Sir, I have question.
Go Ahead (Author)
Sir, Why do we need to detect neutrinos?  Should we detect them only to explain beta decay or is there any other use from them?

Very good question.  Beta decay problem is over, it is now confirmed that neutrinos are emitted from the nucleus and law of conservation of energy is successfully explained with this particle.  I will reframe your question like this; why do we need to detect neutrinos on a large scale? Does it give any information to us?  The answer is yes and let me give you one such example.  Let us talk about Sun for a while; the thermonuclear reaction happening at the core is powering sun’s total energy.  During this reaction photon (particles of light), neutrinos and other particles are emitted.  The light that warms the surface of the earth as well as you and me has come from the photosphere of the sun.  Photosphere is the visible disc of the sun.  As we all know that light contains photons.  These photons are generated at the core of the Sun.  It takes billions of years for a photon to reach to the surface of the photosphere; from there the photon takes only 8 minutes to travel to the earth.  So the photon which is warming you right now has left the sun’s interiors billions of years ago.  Yes….. Absolutely amazing right!  If you study this light you will be actually studying the sun’s interior which is present some billions of years ago.  So you cannot study real time sun’s core in the visible light.  But on the other hand the neutrinos which are created at the sun’s core travel to the earth in just 8 minutes.  This is because neutrinos do not interact (very very less interaction) with matter.  They just pass through it.  But photon suffers trillions of collisions with the matter spending billions of years inside the sun before emerging out of the photosphere.  So detecting these solar neutrinos is very helpful in monitoring real time sun’s core.  Not only Sun in all the high energetic explosions (Supernovae and other) that happens in our universe emits neutrinos and detecting them will give us clear picture of these events as well as our universe.

How do we detect them?  As I said neutrinos interaction with matter is very less.  They can pass through humans, buildings and even mountains!!  That is why they are called as most elusive particles of the universe.  But if we detect them we get a lot of information about our universe.  So here it is an astronomical observatory built half a mile down the earth.  This is Super-Kamikonde Neutrino Observatory built under Mt Ikenoyama at Japan.  This is a human eye to watch supernovae in our milky way galaxy.

Image 1
Super-Kamikonde Neutrino Observatory (Screen grab from the documentary Cosmos hosted by Neil deGrasse Tyson)
Image 2
Super-Kamikonde Neutrino Observatory (Screen grab from the documentary Cosmos hosted by Neil deGrasse Tyson)

The observatory is built underneath the mountain.  This is because the instrument which detects the neutrinos is very sensitive.  Apart from neutrinos there are other elementary particles reaching earth.  If we have not shielded our instruments then the detector will pick up the signs of unwanted particles.  How to shield these particles? Yes, go underneath the mountain; let nature itself shield these particles (Most other particles can interact with matter).  Most of the neutrino observatories are built in the abanded mining places.   Since neutrinos don’t interact with matter, they just pass through the mountain and to the detector.  And because of zero interaction with matter for billions of years, they have the information of past!  If you detect them you can actually get oldest of old information regarding our universe.  Detecting even a single neutrino requires lot of big observatories like this and lot of patience because of its elusive nature.

In this observatory, 50000 tones of distilled water are stored and it is surrounded with scintillating tubes which detects the minute flash of light.  But how do you get this flash of light in distilled water?  In a minute trillions of trillions of neutrinos are passing through this huge detector.  Suppose if one neutrino interacts with the nucleus of water molecule, an electron is emitted.  This electron is detected by the very sensitive scintillating tubes by producing a flash of light.  Each flash of light can signifies the presence of neutron in the detector.  If the activity is more in outer space, I mean if there was a supernova in our galaxy, then flash of light increases indicating the presence of more neutrinos.  This has been observed during the Supernovae-1987A in the year 1987.

Image 3
Astrophysicist Neil deGrasse Tyson having boat journey inside the detector. (Screen grab from the documentary Cosmos hosted by Neil deGrasse Tyson)

A flash of light is used to detect one of the most elusive particles of the universe which hides rich information about our home.  It is again the light that is doing our work!

Happy International Year of Light.
Thanks a lot for listening to me, that’s it for today.
Have a great evening.

Image Credits:
First Image: Google Images
Second, Third and Fourth Images: Screen grab from the documentary Cosmos hosted by Astrophysicist Neil deGrasse Tyson

Year 2015 is celebrated as International Year of Light and Light Based Technology by UN as a global event.  This year mark the 150th anniversary of Maxwell’s Equations by James Clerk Maxwell, the man who unfolded the secret of nature and answered what light is made up of. 

More Information about IYL 2015
UN Anniversaries
IYL – 2015 Home Page
IYL – 2015 Blog

Upcoming Topics for IYL 2015

  • Biological Industry – Photosynthesis
  • Principe, Africa – 1919 TSE
  • Copy of Earth – Extraterrestrial Planet
  • ದೀಪವು ನಿನ್ನದೆ ಗಾಳಿಯು ನಿನ್ನದೆ ಆರದಿರಲಿ ಬೆಳಕು
  • Let there be light – Newton, Maxwell, Hertz and Einstein

Viswa Keerthy S

First Light – CMBR

Celebrating IYL 2015

     If you look at the modern periodic table you will find hundred and eighteen elements listed in it. Out of this, ninety four elements occur naturally.  All these elements can be found on Earth (exceptions are there).  Elements are building block of things that you see around you.  Whether it’s a human, animal, tree, building, roads, bridges, monuments, mountains, etc, everything is made up of elements.  But the question that comes to our mind is who brought all these elements on the Earth?  How are they formed?  The answer is… all these elements are formed inside a star.  Yes, in a sense, everything that you see around is cooked inside a star!  Richard Feynman, a famous physicist once said that, the stuff which we are made was once cooked in a star and spit out.

      The entire universe comprises trillions of trillions stars which cooks the matter that we see around us.  The next question that arises is how do these stars form?  Well, these kinds of questions will go on….. it’s a never ending process. But then, where do we begin?

Yes, we begin at the beginning.
We begin at the Big Bang!

Big Bang
Artist view of Big Bang before the explosion.

     The universe which includes stars, galaxies, nebulae etc. is expanding for billions of years.  If you look back, somewhere in the past there must exist a time where the entire universe is concentrated in a point of high density (infinite density).  According to the accepted theory, this high density state of a point, exploded violently, creating the universe that we see today.  This is the Big Bang theory proposed by Edwin Hubble in the year 1929.  The explosion that we consider in Big Bang is not at all a violent explosion, in fact it is one of the silent explosions that you can ever think of and it is neither big nor bang!  This is just a name given to the theory.  The reason is this, the space, time, sound, matter, elements and more importantly the light that we feel and experience today was created after Big Bang!  Big Bang is just an expansion of a point of infinite density, nothing more that.  But then, how do we verify this theory?

     If this kind of an expansion has happened in the past, then we must be able to detect, outer surface of the expanding sphere which contains the information of big bang in the form of light.  According to the theory, this sphere of light should uniformly exist all over the space. In a sense we have to detect the first light from the big bang.  This is called background radiation of the Big Bang.  If we succeed, it confirms the theory Big Bang.

   In the year, 1960 two astrophysics namely Dickey and Pebbles were working on the challenge of finding background radiation of the Big Bang.  They came to the conclusion that, since universe is expanding from billions of years, the energy of the photons of background radiation must be less because of the expansion in space.  (Expanding Universe:  The space and time fabric between the galaxies expand.  The light or the photon which travels in this fabric also expands.  When it expands the energy of the photon becomes less – this is predicted by Einstein’s General Theory of Relativity) When they did the calculation by using Wien’s Displacement law, they found that photon’s energy lies in the microwave region of light.
Few miles away from this group of scientist there were two more researchers from Bell Laboratory namely Penzias and Wilson designing the Horn antenna for radio astronomy.  They were trying to remove the background noise in the antenna which is detected by the detector.  No matter how much they tried they were unable to remove the background noise even-though they replaced the detector for many times.  Interestingly the detector was detecting the noise in all the direction and at all times of the day.  After their unsuccessful attempt of trying to remove this noise, they come to the conclusion that, this signal is not a noise, it is actually coming from outer space.

     Later it turned out that the noise of Penzias and Wilson’s horn antennae was actually the background radiation of Big Bang that Dickey and Pebbles were searching for!  Yes, it was an accidental discovery by two researchers from Bell Laboratory who have no idea about background radiation.  All they did was they tuned their antennae to receive a microwave radiation.  The detector was detecting first light from the Big Bang but Penzias and Wilson thought it was noise!!  The temperature of the background radiation was 3 kelvin and it was in perfect agreement with the measured value from the theory.  This is famously called as 3 kelvin black body radiation curve or 3 K curve.   Both of them were awarded noble price in physics in the year 1978 for their accidental discovery of Background Radiation.  Press Release from Bell Labs can be seen here. This observation confirms Big Bang theory.  (Big Bang theory is still a debatable theory for other reasons).

Horn Antenna
Penzias and Wilson in front of Horn Antenna

     Today we have some of the sophisticated scientific instruments in the on-board satellites which are revolving around the Earth.  WMAP (Wilkinson Microwave Anisotropy Probe) has mapped the background radiation.  The first light from the Big Bang is here….

CMBR – Cosmic Microwave Background Radiation by WMAP

The Light which is the sole responsible for life on earth was actually began its journey 13.5 billion years ago.

Through light on some atoms for billions of years, eventually you have life!

Image Details:
First Image: International Year of Light and Light Based Applications – 2015 Logo
Second Image: S. Harris Cartoon
Third Image : Bell Labs
Fourth Image:
APOD Images, March 25, 2013
Year 2015 is celebrated as International Year of Light and Light Based Technology by UN as a global event.  This year mark the 150th anniversary of Maxwell’s Equations by James Clerk Maxwell, the man who unfolded the secret of nature and answered what light is made up of. 

More Information about IYL 2015
UN Anniversaries
IYL – 2015 Home Page
IYL – 2015 Blog

Upcoming Topics for IYL 2015

  • Elusive Particles of the Universe
  • Biological Industry – Photosynthesis
  • Principe, Africa – 1919 TSE
  • Copy of Earth – Extraterrestrial Planet
  • ದೀಪವು ನಿನ್ನದೆ ಗಾಳಿಯು ನಿನ್ನದೆ ಆರದಿರಲಿ ಬೆಳಕು
  • Let there be light – Newton, Maxwell, Hertz and Einstein

Viswa Keerthy S


When Earth is close to Sun we have winter!!*

Seasons are the most wonderful thing that nature has gifted to Earth.  Without seasons, life on earth would have ceased long back.  But seasons have kept life alive on this Earth.  Changing landscape according to the seasons is the greatest beauty of nature.  Each living being on Earth can sense these changes and they adapt themselves to these changes to sustain their life on Earth. So, seasons play a crucial role in making Earth as a habitable zone for life in our solar system.

One of the age old questions is “How these seasons occur on Earth?”  Well, a fifth grade school child may answer this question. And the most celebrated answer among children is this, “Earth revolves around the Sun in an elliptical orbit with Sun at one focus.  So, when Earth is very close to Sun we have summer and when Earth is far away from Sun, we have winter.” The below image depicts what is said in the sentence.

Img 1
Seasons are mentioned with respect to Northern Hemisphere


At first stroke, this answer looks evident.  When the Earth is closest to Sun, Earth receives more sun light than at other position.  The hemisphere which is facing the Sun will have summer and the other hemisphere which is away from Sun will have winter. These conclusions can be derived from the above statement.  I studied this in my school days.  I firmly believed this explanation until I found that, this is totally wrong.  Yes, the most obvious statement that we make about seasons is wrong.  Some teachers still follow the same logic and teach wrong concept to their students!!
Let us have a closer look on how these seasons occur?

There are two motions of Earth which are evident to Img 4us.  Earth revolves around the Sun and Earth spins about its axis.  Earth takes nearly a year (365 days) to go around the Sun in an elliptical orbit and it takes a day (24 hour) to spin about its axis.  But there is a weird and wonderful thing about this axis of rotation of the Earth. (A body which rotates about its axis is called axis of rotation).  It is tilted at an angle of 23.5 degree from the vertical line as shown in the right side image. This angle or tilt is constant throughout the elliptical orbit.  And also the axis of rotation of the Earth points in the same direction at all positions of the orbit as you can see in the below image.  This direction is always towards the north.
Now let us come to our core topic seasons.  We have four seasons on Earth, summer, winter, spring and fall.


In the month of December Earth will be at position A.  At this position Earth is close to sun.  But northern hemisphere will receive less sun light than the southern hemisphere due to the tilt of the earth.  Because of this reason northern hemisphere will observe winter and southern hemisphere will observe summer!

Img 2Imag 3

But in the month of June, that is at position C the season reverses.  At this position Earth is far away from Sun compare to position A.  But now northern hemisphere will receive more sun light than southern hemisphere due to the same reason tilt of the axis of rotation of the Earth.  So, summer season at northern hemisphere and winter season at southern hemisphere.  But observe one thing; direction of the axis of rotation of the Earth is not changed.  It is still pointing in the same direction.

And the same explanation goes on for position B and D.  At position B, northern hemisphere will have spring and southern hemisphere will have fall.  Exactly reverse happens at position D.

We have got the answer!  The seasons occur on earth is because of the tilt of the axis of rotation of Earth (or Inclination of axis of rotation).

But we did not talk about the distance between Earth and Sun.  Because distance is not the cause of seasons!  Let me talk with numbers.  On Jan 4, Earth is closest to Sun with a distance of 148,000,000 km.  On July 4, Earth is at farthest point from Sun with a distance of 152,000,000 km.  The variation in distance is only 2%.  This small variation in distance cannot cause seasons on earth.

So we have seasons on Earth because, the axis of rotation of Earth is tilted. (23.5 degree).  If there is no tilt in the axis, then there are no seasons on Earth!!!

What I have learnt in school and wrote in exam is totally wrong.

Viswa Keerthy S
(*Title is with respect to northern hemisphere of Earth where I live. )


[G,c,h] = Our Universe

Richard Feynman said in one of his lectures that “The stuff which we are made was once cooked in star and spit out”.  This is true, humans, animals, birds, reptiles, rivers, oceans, mountains, buildings, bridges, earth, planets everything was made by the byproduct of stars.  The constituent elements of all these matters were created during the catastrophic explosion of stars, known as ‘supernovae’.  In other words, all living and non living things are star dust!  And also, as we see only matters around us and all around the universe, we can say universe is made up of matters.  On a fundamental scale matter is again made up of atoms and atoms are made up of elementary particles {ex. electrons and quarks (extensive study on elementary particles was done in 20th century)}.  Finally we can say elementary particles are the building blocks of the universe.  But the question is how does this universe behaves or works?  Over a period of 500 years the task of scientist or philosophers was to find the answer for these kinds of questions.  Some of them were succeeded in decoding nature’s secret and able to explain why nature behaves the way it is now or looks the way it is now? (Note: In this article Nature=Universe)

Let me ask you this question, why do you think the nature or everything should be the way it is now? Why can’t in some other way?  What made nature to restrict only to three dimensional worlds?  These are some of the fascinating questions which are still not understood to the full extent.  Nevertheless we still know some of the secrets of nature.  If a mechanical robot can give sensible answer to your question, if we can fly like birds through aeroplanes, if we can see the working heart without dissecting human body through NMR technology, it’s because we know some secret about nature and how it operates.  The laws of physics tell us how nature operates!  Many great peoples have spent their entire life in figuring out the correct laws of nature.  Today we have television, telephone, mobile, microwave, bread toaster, washing machine, air conditioner, car, train aeroplanes, etc, to make our life easy.  All these things have became our integral part of our life.  We are very fortunate to live in this privileged world.  All credits and applause should go to the people who dedicated their entire life to make our life privilege.

But now we will talk about some numbers.  These numbers show the mysteries of nature.  These numbers explains how nature operates.  These are very special numbers and hide many secrets of nature.  The numbers are as follows.


Mathematically speaking these are just numbers.  [G] is the Gravitational Constant, [c] is the speed of light and [h] is the Plank’s Constant.  These are called fundamental constants in physics which appear in Classical Mechanics, Special Relativity and Quantum Mechanics respectively.

As I said, mathematically these are just numbers but in physical world these numbers tell you the secrets of nature.  By using these numbers we can explain why earth and planets are going around the sun?  Why earth is trying to attract every other particle?  Through quantum mechanics we can able to go deep inside atoms and explain the properties and behavior of elementary particles.  Communication has made us to connect instantly throughout the globe.  Today we have all types of sophisticated medical instrument to diagnose various problems.  All these are possible because of these numbers!  Right from explaining planets going around the sun to NMR technology in hospital and live telecast in television sets at home, we need these numbers.  Nothing would have been reality without these numbers.  And again, we are leading privileged life because we know these numbers to some accurate level.

I said these numbers are secrets of nature because nature operates through these numbers.  We don’t know (we certainly do not know in future) why these numbers are (constants) as the way it is now.  But we can certainly say, nature looks the way it is now because of these numbers.  To some extent these constants are called universal constants.  If there are any changes in these numbers, nature never looks the way it is now!!  All our physics theories stands on these numbers and all theories are universal.  It means, if you change G , c and h values to some other numbers and if these numbers are applied to physics theories, the theories still give you result and it would suggest you a different kind of nature.  Do we have a different kind of nature with different values of G , c and h? Answer is, we don’t know! We have not yet found!

In basic physics Length, Mass and Time are called fundamental constants.  We can derive our basic fundamental constants (length, mass and time) in terms of G, c and h by using ‘Dimensional Analysis’ (mathematical process to equate two different quantities through dimensions).  Once it is done the values for length, mass and time are as follows.

Plank units

Here Length Mass and Time are called Plank length, Plank mass and Plank time respectively.  This derivation was first done by Max Plank, so the name.

The length in a centimeter scale starts from zero; we measure all our length with respect to zero.  And also we measure our time from zero seconds (i.e 0 1 2 3 4 5… seconds).  The way we measure all these quantities in our day to day life is by assuming length and time are continuous from zero.  This may workout exceptionally better for all our calculations, but in reality this is not true.  I mean, the length and time are not continuous from zero.  Plank length and Plank time are the lowest limit for the length and time.  We don’t know how length and time looks beyond this limit.  Theoretically, this is our nature’s limit.  Length cannot be defined beyond Plank length and also we cannot distinguish between two events which are happening less that of Plank time.  Right now our modern instruments are sensible to measure length at the order of 10^-18m and time 10^-23 seconds.  We have not yet reached Plank length and Plank time; it is still at the theoretical level.  But even in future no matter how sensitive our instruments, we cannot go beyond Planks length and Planks time.  This is the nature’s law!  And we don’t know and we never know how our nature (universe) looks beyond this limit.  And here the Plank mass has the order of 10^27kg.  It is the maximum mass that a point particle (like electron) can have in our universe.  That is, this is the upper limit for a point particle in our universe.  Electrons and quarks which are nature’s stable point particles are many orders less than that of Plank mass.  And again the Plank length, mass and time has those numbers because of G, c and h.  So, it is G, c and h numbers which makes nature operates in the way we see it now!

I must repeat this statement again, we don’t have any knowledge of why these quantities (G, c and h) have these numbers, but on a loose note we can easily say it’s because of these numbers our nature or universe looks the way it is now!!!  If there is any change in these quantities (G, c and h) nature never looks the way it is now.
[G, c, h]= Our Universe!

(All these fundamental quantities (G, c and h) are dimensional quantities.  The actual numbers may change if the units are changed.  In this article the units followed was SI units.  Whatever be the units the meaning of those numbers will be the same.  But in physics and mathematics there are some quantities which are dimensionless.  These quantities are independent of units that we use.  These are called dimensionless fundamental quantities.  Fine structure constant (α) and golden ratio (ϕ) are some examples.  Nature hides its beautiful features in these numbers.  And also the stories behind the discovery of Gravitational Constant (G), Speed of light (c) and Plank constant (h) are very fascinating and inspiring.  I will preserve all these topics for my coming posts.)

Viswa Keerthy S
Date: 27/12/2013

Wavefunction and Max Born

One of the beautiful theories in physics, which is more than hundred years old, is Quantum Mechanics (QM).  In 1900 when Blackbody Curve was satisfactorily explained by Max Planck, Quantum Mechanics saw its birth.  Later many great scientist of 20th century like Einstein, Bohr, Hertz, Heisenberg, Dirac, Schrodinger, Born, de Broglie developed quantum mechanics the way we see it now.  Almost all the people whom I have mentioned above have received Nobel Prize for their work on developing QM.  But to me the important thing is the idea behind the each stage of development in the QM.  Some of the concept and the experimental results were unable to explain with the knowledge of Classical Mechanics which was well developed during that time.  The new ideas and concepts which came up to explain these strange results were led to the development of this field.  Here I want to focus on some ideas/concepts of QM developed by different people and more importantly by a great mathematician and physicist Max Born.

Max Planck was the first person who broke the “continuity” concept of classical mechanics and introduced the “discreteness” in the energy called ‘quanta’ (packets) of energy in order to explain the “Blackbody Curve”.  The formula which he gave was in fact a perfect fit for the observed experimental curve.  His formula for the discrete energy includes the constant h = 6.023X10^-34 Joules, where h is Planck’s constant.  He was awarded Nobel Prize for his work in the year 1918.  Later in 1905 Einstein also came up with similar idea of ‘photon’ (packets of energy) to explain the energy concept in Photoelectric Effect.  The concept of ‘discreteness’ (Einstein called ‘photon’, Planck called ‘quanta’) again fits perfectly for the Photoelectric Effect.  So, it is the idea of quantization principle (discreteness) which led to the satisfactory explanation for all these experimental results.  And Einstein received his Nobel Prize for his work on Photoelectric Effect in 1921.  Another great scientist Neils Bohr who was a student of Rutherford and he was working on the model of an atom.  Rutherford atomic model was not satisfactorily explaining all the observed experimental results.  His student Bohr applied the same ‘quantization principle’ to angular momentum and by using Plank theory he was able to explain all the observed phenomena through his new atomic model.  Again quantization principle perfectly fits the theory.  So, in quantum world every quantity is quantized.  Today we know even space and spin is quantized!  But in classical world this is not at all true, everything looks continuous!  The idea of quantization by different people has led to the development of this unknown world known as ‘quantum world’.

scientist photo copyImage: Max Planck, W Heisenberg, E Schrodinger, Max Born. 

In 1924 another great scientist de Broglie came up with a strange concept that almost all particles which has mass is associated with wave nature with a wavelength of h/mv, where v is the velocity of particle, m is mass and h is Planck’s constant.  This is called Wave-Particle duality, where all particle exhibit both the properties of wave as well as particle.  This was a big blow in the development of QM and its a strange concept when compared to Classical Mechanics.  The theory predicted that if a car (mass m) is moving at a velocity ‘v’ is actually associated with a wave of wavelength ‘h/mv’.  Classically it is impossible for a car to move like wave, but still the theory predicted wave nature of a car and gave the value of wavelength.  But in reality the effect of wave nature in a macroscopic world (mass is large) is very small and can be neglected, which means the car’s wavelength is very small and its wave nature can be neglected!  But when it comes to an electron which has very less mass, the wave nature of an electron magnifies and it can be studied under suitable condition.  The concept of QM is to study the dynamics of these tiny particles such as electrons and elementary particles.  Theory of QM is applicable to almost all particles, but for macroscopic particles the effects are very negligible and it is neglected.  This actually makes QM theory a Universal Theory to some extent.  For predicting the strange (classical sense) theory of wave-particle duality of nature de Broglie was awarded Nobel Prize in 1929.  Meanwhile in 1925 W Heisenberg explained the basic principles of QM through his papers ‘Quantum- Theoretical Mechanics based exclusively on relationships between quantities observable in principle’.  And in the very next year E Schrödinger came up with a different approach to QM through his ‘wave equation’, which is a very famous equation in physics called as ‘Schrodinger Equation’.  In classical mechanics we write the famous Newton’s law as F=ma, where ‘F’ is force applied, ‘m’ is mass of an object and ‘a’ is the acceleration of an object.  By solving this equation for a particular system (ex pendulum) we can get the equations of motion.  Which means the solutions can predict the motion of a system (ex Pendulum) after some time (t).  Newton’s law is actually the foundation to classical mechanics. And this equation holds good for almost all systems classically.  On the other hand in QM the same equation is replaced by ‘Schrodinger Equation’ which is given below.  Compare to Newton’s law, Schrödinger Equation is not so simple and difficult to solve.Equation

Meanwhile in 1927 Heisenberg came up with another law known as ‘Uncertainty Law’.  He said it is impossible to measure the position and momentum (mass x velocity) simultaneously for microscopic particles.  It means we cannot say the position and momentum of particle (ex. electron) at the same time.  This kind of simultaneous measurement is impossible in QM.  But in classical mechanics we can easily say the position of car and its momentum at any point of time simultaneously.  In macroscopic world everything looks simple and obvious, but the same is not true in microscopic world.  This restriction has reveled striking feature of microscopic world (nature) that we cannot pin point where is the electron in a system at a given point of time.  So, the traditional way of writing atomic model (fig a) breaks down and electron never revolve around the nucleus in a circular way as we have learnt in school.  Instead the circular line becomes a disk of width ‘a’ (two dimensional representation) (fig b).  Electron is present in the region of disk, but where in the region is unknown even today. There is a debate that may be we lack the technology of doing experiment and our instruments are incapable of doing such sensitive measurement.  But this is ruled out by scientist!  It is nothing to do with our technology or the sensitivity of instruments, Uncertainty Law is a law in nature! Neither our future technology nor our highly sensitive instruments in future can go beyond this level.  It is just there in the nature, and it magnifies in microscopic level.

model of atom

As I said the Schrödinger equation actually tells the dynamics of the particles (say electron).  It should describe how an electron moves in a given condition (ex. Infinite Square Well Potential).  While expressing this equation Schrodinger assumed that all the required information about the particle (electron) is hidden in the quantity called wavefunction (Ψ). By applying the given condition (given potential) to the equation one should get the value of wavefunction which is normally in complex form.  After obtaining the wavefunction in its form, the required information should be extracted from the wavefunction.  And this wavefuntion is a not a localized function but a spread function!  Uncertainty Law which is present in nature is actually a hidden property of Schrödinger equation and it shows up in the wavefunction as a spread function (not localized like classical mechanics).  But the question is how do we extract the required information about a particle from wavefunction?  Here comes Max Born a mathematician and physicist with his revolutionary approach to QM through Statistical Mechanics in the year 1926 said ‘modulus psi square(IΨ(x,t)I^2) is actually gives the probability of finding the particle at a point x and time t. Which means squaring of modulus of a wavefunction is actually a real quantity not a complex number! (But remember wavefunction is a complex quantity)  And Max Born was the first person to identify this quantity as the ‘probability’ of finding electron at x at time t.  This is called Born’s Statistical Interpritation.    I feel this concept is a revolution in QM, because without this concept we cannot interpret the wavefunction.  The normalization concept which is the direct product of this idea is a very handy tool in handling wavefunction.  I feel the statistical approach is the most significant step in the development of QM.  All credits go to Max Born who identified ‘modulus psi square’ is actually a probability.  Heisenberg and Schrodinger were awarded Nobel Prize in 1932 and 1933 respectively.  Max Born was awarded Nobel Prize on Dec 11, 1954 for his statistical approach to QM, after 29 years of his most important concept.  Coincidentally his Nobel Prize ceremony date was his 72nd birth anniversary (Born: 11 Dec 1882, Died: 5 Jan 1970)! In his Nobel Lectures he began his talk like this ” The work, for which I have had honour to be awarded the Nobel Prize for 1954, contains no discovery of fresh natural phenomenon, but rather the basis for a new mode of thought in regard to natural phenomena.”  What matters more is the way we think on some observed results/phenomenon.  All great scientist have just did that.  If you ask me what is QM, in simple words I can say Quantum Mechanics is just solving Schrodinger Equation.
(Max Born visited Bangalore in the year 1935.  He worked with Sir C V Raman at Indian Institute of Science for six months.)

On an application level QM has wide verity of application.  In a real world application it is applied in Laser, MRI, Quantum Cryptography, Transistor and many more.  It is also applied in the study of Atoms and Molecules, Nuclear Physics, Astrophysics, Solid State Physics and many more.  At some point of time I said QM is a Universal Theory, but still it fails to explain some important concepts.  Even today there is a debate on the fundamental concepts and principles of QM.  It is still not a complete theory even after more than hundred years.  Never the less it is one of the famous theories in Physics.

In the developing stages, the unique ideas by the scientist played a vital role in shaping QM in a proper way.  For student like us the important thing is the ideas behind each successful stage of development in QM or in general Science.  The ideas/concepts which are different from normal thinking can actually change the world totally.  This has actually happened in the history.  When I met my friend Suraj at Bangalore Planetarium, we were discussing about the great scientist and their concepts.  He said “look Einstein is famous for E=mc^2, Stephen Hawking is famous for his chair, Feynman is famous for his teachings, but there are other great scientist with their ideas/concepts, revolutionized the world, but they are not famous among us (to some extant this is true even among science students and teachers).  Everyone tells Faraday, Einstein, Edison, Hawking but nobody remembers Maxwell, Tesla, Born, Dirac, Pauli and many more who are equally important like others.  The reason is we never tell the stories of these great peoples among students.   I feel it is the stories of these great people and their ideas are important to students rather than the confined textbook chapters.

[If you are still interested in quantum mechanics and its development I strongly recommend you to read the preliminary chapters and Nobel Lectures in the book “Quantum Mechanics: Theory and Applications” by A.K. Ghatak and S. Lokanathan.     (S. Lokanathan was my Classical Mechanics teacher in REAP Course at Bangalore Planetarium)].

[I have just shown only four scientist pictures in this article, but all of them are equally important.]

Image credits: Google images.

Viswa Keerthy S

Place 7: Devarayana Durga and Namada Chilume

IMG_8671After my visit to Makali Durga in March, I had temporarily stopped visiting places due to other programs.  But one fine day when I received a call from Suhas (my frined), asking me to plan a weekend journey in bike, I instantly told him the place Deverayana Durga.  Devarayana Durga is a hill located at a distance of 65km from Bangalore and situated near Tumkur.  It has a fort, temples, mesmerizing nature and difficult trekking trails.

When we left Suhas home on Sunday it was already half passed seven in the morning.  We took Nice Road at Magadi Road junction reached NH4 which leads to Tumkur.  The sun was still hiding behind the cloud, with less temperature cold breeze and drizzling we felt like we are invited for a new day by nature.  With perfect climate, signal free National Highways and well maintained bike, all these were pushing digital speedometer to show the number 110!  I had an awesome riding experience that day.  After reaching Dabbaspete we took SH3 (State Highway3) and reached Udigere.  Following the KSTDC sign boards, we reached the base of Devarayana Durga.  From here one can start climbing the hill thorough steps or else bike can go up to a parking lot which is at haft way of the hill.  Before reaching parking lot we crossed 13 hair-pin-bends which are not so difficult compared to other hills.

From here we started to climb the hill through steps, which are neatly constructed.  This hill has two temples, Boga Narasimha temple which is at base and Yoga Narashimha temple on top of the hill.  The total height of the hill is around 3940ft above sea level.  History says, this hill was called as Jadaka Durga (Jadaka is a ruler of this region), later when Mysore King Chikka Devaraja Wodeyar conquered this region, the name of the hill was changed to Devarayana Durga.  This hill is also called as ‘Karigiri’, that is kari means Elephant and giri means hill.  When you see this hill from far you can see the hill in the shape of Elephant.  The fort which was constructed here was a very huge fort and has seven doors to enter.  Today you can see the remaining of this fort.  The hill also houses the river Jayamangala’s and river Shimsha’s origin.  After having the glimpse of fort, we


IMG_8469entered through one door, half way through the temple we met with a deity of Garuda, Rama and Anjaneya.  This deity was very huge in its size and an open temple too, which means no garbhagudi.  It is unique in its construction because all three of them are seen on a single stone.  You can have a splendid view of surroundings from this point.  After this we reached stone mantapa, and then entered the Yoga Narasimha temple.  This temple is very beautifully constructed with a waranda outside and garbagudi dedicated to the deity of Narasimha an awathar of Lord Vishnu.  You can also find the deity of Ganesha and Lakshmi inside the temple.  Beside the temple there is another sacred place called ‘Pada Theertha”, where the water after abhishekha flows here.  This water finally reaches the sacred Kalyani near the temple formed between the rocks.

IMG_8513IMG_8508IMG_8496Mesmerizing nature, view of other mountains looks amazing at this point.  But the real journey is yet to come.  After the temple, there are no steps to climb the hill to reach the final point called as ‘Khumbi Shikhara’ (top of the hill).  You should trek to reach the top.  We went on searching for route and ended up in wrong direction in our first search.  Later finding the right direction, we started our trekking for next half of the journey.  The trekking path is moderately difficult, searching the correct path in a densely spread bushes was very difficult.  At some point you should crawl under the bushes to reach other point.  After having a 5min trekking from temple, you will reach another plain rocky surface which is directly above the temple.  This is a huge plain rocky area that you can see on this hill.  You can get amazing views from this point.




The climbing becomes very difficult (especially for beginners) from this point.  As I and Suhas have got little experience of trekking, we started climbing the hill up to the last point.  At one time I was unable to climb the hill by hanging my camera to neck.  Noticing the difficulty, I packed my camera and then started climbing.  With our good habit of climbing, without any trouble we reached top of the hill, which was called as “Kumbhi Shikhara” It has stone mantapa and a bell.  One who climbs the top should ring the bell, and the sound from the bell spreads all over the hill indicating somebody has reached top.  It was our first business to do after reaching the top and we did it.  We took photos of beautiful landscape, chains of mountains, and even the top view of Yoga Narasimha temple.





The view from tip of the point is breathtaking.  High breeze which hits on your face, surrounding view of mountains will make you forget your tiredness.  I feel that even though nature gives you a difficult path to climb, but once when you accomplish it, nature always displays its charming beauty, mesmerizing views in front of your eyes, which is an unforgettable vision for every nature lovers.  This is true at this place and even at all places.  After spending an hour on top, and listening to Bhavagethe (our routine practice at every hill), we started our descending journey.  During trekking, downwards journey is always difficult than upward journey.  But with our experience, we came down easily without having any problem.  At the base of the hill, you can get Fruit Juice, tender coconut and chaats.  We had light lunch by having chaats and juice and then moved on to our next place Namada Chilume.



Namada Chilume is a small place just 8km from Devarayana Durga towards Kyathsandra.  If you follow the KSTDC sign boards, it is not difficult to reach this place from the hill.  It is said the lord Rama and his team visited this place during their 14 years exile.  During their stay, Rama searched for water to apply tilaka on his forehead.  But he could not find water nearby, then he shot an arrow at the rock, arrow made small hole in the rock and water came down from the hole.  Rama used this water to apply tilaka on his forehead.  So the place got its name Namada Chilume (Spring of Tilaka).  Today you can see this spring of water here and it is been well protected from government.  Some region at this campus is fenced and visitors can see Deer in this protected area.  Just opposite to Namada Chilume, Karnataka Forest Department has a nursery of medicinal plants.  A nominal entrance fee is collected and this place can also be visited.  After having a nice walk in both the campus, and taking photos, chatting with other peoples, we left the place for our final destination of the day!


Our final destination was “Pavithra Hotel” Kyathsandra.  Kyathsandra is a place situated next to NH 4 before Tumkur.  It is famous for its Butter Tatte Idli’s (Plate Idli’s).  Like Bidadi Tatte Idli, Kyathsandra Tatte Idli is also very famous.  Coming to a places like this (a place with a special food) and not eating is literally a crime! (Sentence copied from Rohan who hosts “Strictly Street” TV Show in TravelXP HD channel, one of my favorite programs)  We both had Tatte Idli’s until we satisfy our stomach, and then started our Bangalore journey late in the evening.  Again the riding was wonderful; we followed the same route, and reached Bangalore in time.  After a long time of not having a trip, this trip was accomplished in its high fashion.  Before leaving Suhas home, I told him, hey our next destination is “Kailasa Parvatha” near Chintamani Road.  He smiled at me and said OK WE WILL GO!

Devarayana Durga and Namada Chilume are packed with historic stories, sacred temples, wonderful nature, hard trekking trails and what not!  In my opinion if a place includes all this, it is worth visiting these places by making our time in our busy schedule.  Do visit once.

How to go:
By Road: Bangalore- NH4- Dobbespete- Udigere- Devarayana Durga- Namada Chilume

Fruit Juices, Tender Coconut, Chat etc., are available at Devarayana Durga.
For hotels you should come to Kyathsandra.

When to go:
All through the year.

-Viswa Keerthy S (July 28, 2013)

Six Easy Pieces from Feynman

The subject which was called Natural Philosophy during olden days is relatively called Physics in today’s world.  Physics is a study of nature in particular the ‘laws’ of nature.  It means, Physics involves the study of why ‘things’ has to happen the way it is happening and figuring out the law behind it?  What is so special about these laws?  Can we explain everything (I mean the working of nature) with these laws?  For centuries people have struggled with these questions and exhausted their life on searching out the correct laws of nature.  Some of them have succeeded in figuring out.  They are the great persons (Archimides to Stephen Hawking) who revolutionized our understanding about nature.  From last fifty years due to the rapid growth in the field of science and technology, the question we can ask is, have we figured out all the laws of nature?  Can we say how nature works?  The answer is no! We have not yet reached such level of understanding.  We can bravely say we still don’t know many ‘things’ and how it works!  Yet, our small understanding about nature has put all of us to lead privileged life, which none of our ancestors experienced.  Now if you ask, what we have did, and what we have understood about nature, I better show you this book- “Six Easy Pieces Essentials” by Richard P. Feynman.

The book contains six chapters, taken from most famous book in physics “The Feynman Lectures on Physics”.  Six Chapters are Atoms in Motion, Basic Physics, The Relation of Physics to other Science, Conservation of Energy, Theory of Gravitation and Quantum Behavior.  Unlike the great physicist, Feynman was considered as a greatest physicist and teacher of all time.  He has a remarkable talent of explaining most difficult ‘things’ in a very simple way.  This makes him very special among all other scientist.  His legendary lectures at Caltech, now it is called Feynman Lectures, considered as ‘The Bible’ in physics.  And the six chapters which were mentioned above are the selected topics from these books. It’s a popular science book and does not require any knowledge of science to read.  But, if you have interest in science you must read this book.   He explains how each simple observation and some simple experiments have changed our understanding about nature.  It is true that we have revolutionized our level of understanding compare to the Aristotle period or even at the beginning of 20th century.  Yet, we have not fully discovered the entire laws.

The title of the book says “Six Easy Pieces Essentials” in reality these are the six pieces, which are very essential to understand our nature. And Feynman does not make you to understand these topics; instead he explains why these are very important, what is so special about them, in his typical ‘Feynman Style’.  Read the book to get experience yourself.  At last let me ask you this.  By some way all our scientific knowledge is destroyed and only one sentence (Scientific Idea) is to be conveyed to the future generation.  What will you convey in one sentence, which contains nearly all information of our scientific idea? Answer: Read this book!

You can Google it and get E-copy of the book.
For purchase…

-Viswa Keerthy S (21/07/2013)

“Symmetry, Symmetry, Symmetry”

tarasov-this-amazingly-symmetrical-worldWhen we see the word ‘Symmetry’, we used to think vo! It is a topic in elementary particle physics, crystal structures, rotational symmetry, transnational symmetry and other things… full theory, and we feel it’s a boring topic.  Once we decide it’s a boring topic, no matter what happens we never ever even try to look at it.  I feel this is the nature of normal student.  But now, I am here to tell you about a book which is written on “Symmetry”!, believe it or not once you read this book you will surely say, without ‘symmetry’ atom, matter, earth, life, etc,.… nothing would have existed!

      Symmetry is one of the most general properties of nature.  And Symmetry is not restricted to Chemistry, Crystal Structure and Particle Physics.  It can be visualize everywhere in nature.  It can be seen in animals, plants, birds, humans, snowflakes, non living objects… what not! Everywhere you can see symmetry.  In the book “This Amazingly Symmetrical World” the author quotes a sentence said by M Gardner (mathematician and science writer) that “On the earth life started out with spherical symmetry, than branched off in two major directions: the plant world with symmetry similar to that of cone, and animal world with bilateral symmetry.”  Yes it is true! If you see any plant from top, the structure of the plant looks like cone.  The cone structure ensures equal sharing of sun light to all parts.  And all animals do exhibit bilateral symmetry.  Symmetry controls the structures of all living organisms.  Amazing!

     Throughout the book author puts above sentence in this way “Symmetry limits the diversity of structures in nature.”  And he gives many examples of which one of the interesting examples is this one… Many of our science fiction stories portraits that extraterrestrials may look very different than organisms found on earth.  But symmetry tells you, whatever the extraterrestrials looks like, they must exhibit bilateral symmetry.  The reason is our laws of physics are universal in nature.  That is, whatever the planet, the planet will have gravity, and our physics laws works same as it worked here.  And again all our symmetric conservation laws of nature works the same in that world.  If the conditions present in other planet and here is same then, extraterrestrials should exhibit bilateral symmetry.  What fiction stories tell such as, a single eye, and single ear or any wired organisms is not possible just like that.  Symmetry of physics laws restricts those structures.  For example if extraterrestrials has ear, it should have two ears with same size and shape on opposite side.  At the same time it does not mean that symmetry can predict the possible structures in nature; instead it can predict structures which are not possible in nature.  Whatever the topics in which you study symmetry, symmetry always tells you what is not possible in nature.  Symmetric laws are sometimes called as ‘Prohibition Laws’.  These are some of the examples which I liked, but in book it covers many aspects of symmetry found in nature.  And lot more interesting examples. You will  really enjoy reading this book.

     “This Amazingly Symmetric World” is a book written by L. Tarasov and published by MIR Publication.  It is a general science book written in a very lucid language, and requires knowledge of elementary school physics to read.    Book begins with the conversation between author and reader (who is yet to know the world of symmetry) and finally ends with another conversation between them, but now reader has seen the beauty of symmetry.  Conversations are joy to read.  The book has two parts, ‘Symmetry Around Us’ which will show you symmetry found around the nature that we live.  And the second part is ‘Symmetry at the Heart of Everything’ which talks about the symmetry found in elementary particles and how our conservation laws are said to be universal laws.  I feel reading about symmetry is like reading nature’s beautiful power!  This book really shows  you that.   I am sure when you read this book, you will definitely say, beautiful and powerful tool of nature is symmetry!  Without this nothing would have existed!

     And also we always study many topics in science in a narrow field, and think why we need to study all these? What is so special about these things?  But when we come out of it and start looking at these beautiful things in a big picture, it wonders us, and gives more clarity about why we need to study these things, and what are the roles they play in nature.  This is true with symmetry or for that matter any topic in any subject.

e-copy of this book can be downloaded here…


(I would like to thank my teacher Mr Madusudhan sir [Scientific Officer at Bangalore Planetarium] who showed this book and inspired me to read this book.)

-Viswa Keerthy S (06/07/2013)

Maxwell and his ‘c’

     If you ever type “Maxwell Equations” in ‘Google Images’ you get many images, like the one mentioned below.

God Said Maxwell Equation

     Have you ever thought why it is been shown like this.  What is so important about these equations.  If you want to know, read this article

     If you ask me about these equations, I will say these are the greatest equations in the history of physics.  These equations may not look beautiful to a common man.  But truly, it looks beautiful for a physicist.  I am writing this article not to tell you the mathematics or the physics behind these equations.  But to tell you the beauty of nature, which is hidden in these equations!

    Let me first tell you this,

  • E= Electric Field
  • B= Magnetic Field
  •  ρ = Charge Density
  •  ɛ = Permittivity of free space (Property of medium)
  •  μ = Permeability of free space (Property of medium)
  • J = Current Density
  • Inverted triangle symbol is called ‘del’ It is just a differential operator

(read ɛ and μ as “epsilon not” and “mu not”)

That’s all about these equations.

     Before Maxwell, Electricity and Magnetism are two separate theories in physics.  They were independent of each other.  But this person called “Maxwell” unified these two theories as a single theory, called “Electromagnetic Theory”.  He said, a moving charge produces a magnetic field, and a change in magnetic field produces current in a wire!  True, this looks obvious to us now.  But during Maxwell time (year 1865) this is a remarkable achievement in the field of Physics.  Later it said that, this is the second Greatest Unification Theory in the History of Physics since “Newton’s Universal Law of Gravitation”.  Einstein once remarked on Maxwell theory that “Most profound, most truthful that physics has experienced since the time of Newton”.  Believe it or not all his work on “Electromagnetic Theory” stands on the above four equations!  If you exploit each equation, hidden natures beauty will unfolds to you.  If you ask me what these equations means, in a crude language I will say, disturbance of Electric and Magnetic fields travel in space (medium/vacuum) as Electromagnetic Waves obeying above equations.

     As I mentioned in the first paragraph, I want to show one such hidden beauty from these equations.  Before that let me introduce you to a “Wave Equations”.  It is just a mathematical equation which governs the propagation of wave in space.  And the equation is…

Wave Equation

     Here, Ѱ is a wave, V= Velocity of the wave.  Don’t worry about the differentiation; just see the form of equation.  We will come back to this equation later on.

     Now, What Maxwell did is, he took two of his last equation, that is…

Last Two Equation

     And his aim was to write down the final equation, which “looks like” wave equation, the one I showed you in the above paragraph.  He did some mathematical manipulation to his equation, and finally arrived what he wanted.  His final equation was this…

Final Equation

     One for Electric Field, another for Magnetic Field.

     Here, if you compare these two equations to the wave equations.  You can identify E and B are Electric and Magnetic Wave respectively.  But notice that, these two equations don’t have the v term in it.  Instead, it has some other terms.  If you equate these two terms, you get…

V square

V final

     So, you (he) finally got the velocity in which Electric and Magnetic Wave travel in space.  Alright, until now everything was fair enough.  But the beauty lies after this.  Let me tell you, we have…

V final

     I said, in the first paragraph that  ɛ and  μ are the properties of medium in which wave is travelling.  And it’s a constant number for a given medium.

For instance, if you consider medium as vacuum.


(Ignore the units)

If you substitute and calculate the velocity you get…


This happens to be precisely the velocity of “Light”!

     Before Maxwell people had did experiment and found velocity of light.


     But Maxwell did not even think of light, he took electricity and magnetic theory, combined these two theories to get “Electromagnetic Theory”.  And said the disturbance of electric and magnetic field will travel as “Electromagnetic Wave”.  And now he has calculated the velocity of “Electromagnetic Wave”, it turns out that it will travel at a velocity, precisely equal to the velocity of light.  This means, “Light is also an Electromagnetic Wave”!

     Up to Maxwell time, Mankind did not know, what constitute the light, which was the most abounded form of the energy right through human civilization.  Maxwell unfolded this greatest mystery of nature by saying “Light is a wave made up of electric and magnetic field and they are called as Electromagnetic Wave”.  Truly a remarkable achievement by Maxwell!

     It doesn’t stop here, there is another beautiful thing which is hidden in this formula.  Let me again tell you.  Now we can safely write, Velocity of light is…

C formula

     Again, as I said ɛ and μ are constant for a given medium, and they are the properties of medium itself.

     Isn’t it strikes you that just a properties of a medium tells you the velocity of light, which is the ultimate speed in our universe!  And, what is also interesting is, experiment involving measurement of  ɛ and μ has nothing to do with ‘c’.  But yet their combination gives rise to ‘c’!  Velocity of light is controlled by the properties of medium!  Amazing result.  The same kind of argument can be seen in connection with velocity of sound. That is, you can write velocity of sound in terms of bulk modulus (property of medium) of the medium in which sound is travelling.  But in light, the bulk modulus turned out to be ɛ and μ of the medium.  Nature works same everywhere, and Maxwell showed us the beauty of nature through his equations.  I don’t have many words to say about these things, but this is truly amazing!  Let me remind you, Maxwell did not studied light, he just wrote down his equations on Electric and Magnetic field.  But all these things are just hidden in his equations; he himself did not know about these things.  But his results showed everything, about the hidden quantities.  He himself was surprised!  I have just showed you one example.  You can find many of them, if you exploit the equations.  Truly they are beautiful equations of Nature.

     Now, I hope you got to know why people write Maxwell equations like the one which I showed you at the beginning.  Light is all about Maxwell’s equations.  I personally believe, existence of God is zero. But, if he is there, and if he controls the nature, then surely he must have said this!  Because that is how nature is working.  And this genius Maxwell unfolded the God’s secret to Mankind!

     450px-James_Clerk_Maxwell_statue_in_George_Street,_EdinburghJames Clerk Maxwell (13 June 1831- 05 Nov 1879) was a Scottish man, and one of the greatest physicist during 19th century.  Apart from his “Electromagnetic Theory” he also worked on “Maxwell-Boltzmann Distribution” which is statistical way of describing “Kinetic Theory of Gases”.

Right: Maxwell Statue at Edinburgh. (Image from wikipedia)

-Viswa Keerthy S (29-06-2013)

Place 4:Makali Durga

indian railwayMakali Durga is a fort hill which is 60km from Bangalore.  The place is located in the state high way of Bangalore-Gauribidanur and it is just 10km from Doddaballapur.  The height of the hill is around 1350mts above sea level.  As I said it’s a fort hill, on top you will find the wreckages of the fort, built by Tippu Sulthan.  At the base of the hill, there is a temple of lord Shiva and Nandi.  The railway line which passes near the hill ads up to the beauty of Makali Durga.  There is a small railway station near the hill, which makes easy accessible to Makali Durga through trains.  Unlike the other places for example Savandurga, this place is isolated from common people.  That is, you hardly find peoples here.  No shops, no hotels, no people around makes you still more exciting.

This place is a paradise for trekkers.  It’s a moderately difficult trekking place.  The hill is covered with small thorny shrubs, trees and rocks.  Route markings for climbing the hill are not so good.  Better to search our own route and explore the place.  This makes trekking really exciting and challenging.  If you are a first time visitor it is advised to take at least one person with you who has seen this place earlier.  There is high degree of chance that you may go in a wrong way and end up in worst situation.  As I said there are no shops, hotels around this place, it is good to pack your food.  Most importantly you must take plenty of water.  Remember you don’t get water at this place.  And make sure to drink less water during trekking.  While climbing, the sight from top of the hill is magnificent.  The view of Gundumgere Lake is really an awesome experience.  And the view of the passage of trains and goods carriages through the curved paths will make you still more exciting.  On top of the hill there is a fort built by Tippu Sulthan.  It is almost at its last stage of destruction, and it needs proper maintenance from government. Breathtaking view of the chains of mountains from top is unforgettable.  You could see Nandi Hills and Skandagiri Hill from top.  Night trekking can also be done, but it needs proper planning and arrangement. Overall this place is one of the best one day trekking destinations for Bangalorians.




IMG_9622I and my friends (Pramod, Naveen, Achyut) left Hebbal Fly over at 9pm in the morning, reached Makali Durga in Naveen’s Innovae car.  Innova car took all the responsibility of making sure that our journey was comfortable.  Thanks to Innova!  My frined Achyut was a professional trekker.  Except Achyut, for all of us, it is our first time visit to Makali Durga.  With Achyut professional guidelines we started to climb the hill.  At first, we felt hard to climb due to rocks and shrubs. But after adjusting to the surroundings climbing was very easy and we took many pit stops while climbing.  Based on Achyut guidelines we took plenty of water with us.  During our trekking we were making sure that we were not dehydrated.   At half way through our climbing, we met other group from ‘Suvarna TV’, who had come for trekking.  After meeting, all of us went together.  The sight from high altitude was awesome.  After reaching top and having the glimpse of the Tippu’s fort, we finished our lunch.  Our descending journey was equally difficult like the climbing; searching route was very difficult while descending.  At last we came down and all through the day our lens was making noise and took some beautiful photos.  Finally Innova took the job of returning us safely to home.  Thanks to Naveen and his Innova.  A one day trek was completed in its high fashion.





How to go:

Makali Durga is well connected by road.  The state highway to Gauribidanur from Bangalore will pass through Makali Durga.

By Road: Hebbal Flyover- Yelahanka- Rajankunte- Doddaballapur- Follow the Gauribidanur Raod until you get Makali Durga Railway Station. (There is no proper notice board beside the main road. It is advised to ask locals after Doddaballapur)

By Train: There is train which runs all day from Yeshwanthpur at 08:15am and stops at Makali Durga Railways Station.  Return train is at 02:00pm at Makali Durga Railway Station.  Except this train no other train stops at this railway station.


No hotels, no shops nothing.  Pack your food.  Take plenty of water.

When to go:

It is difficult to climb during monsoon season.  Summer season is the best.

Some of our photos…

Viswa Keerthy S