Scientific Understanding of Heavenly Phenomena

Scientific Understanding of Heavenly Phenomena

(A lecture delivered in Berhampur University, Berhampur, Odissa)

(Receiving Sri Ganesha from the Vice Chancellor of Berhampur University)

Debi Prasad Choudhary

Professor, Department of Physics and Astronomy

California State University Northridge

Associate Director

San Fernando Observatory

Profound scientific discoveries are made by following this simple method. Finding the common properties of similar phenomena under different situations and understanding them with a simple predictive model is central to scientific method. Over centuries, man asks questions about its surroundings, some of which are easy and some difficult. Attempting to answer them through generalization of observed results and extending their scope through creative imagination is a vital aspect of scientific method that resulted in a series of discoveries enriching our lives and brought us from caves to modern comfort. The important thing is that any new scientific theory or model must be able to explain the already observed phenomena and predict new results that can be used to test them. The latter is an important aspect, absence of which makes a theory unscientific. I have been working in physics of the sun for past three decade. I shall illustrate these statements using the understanding of “The Sun”, our closest life supporting star over past century.

Earth goes around the sun like other planets in the solar system. Our universe contains billions and billions of galaxies in an expanding space time fabric. Enormous amount of energy can be generated by breaking heavier elements or combining lighter ones. These are some of the profound discoveries made in past 100 years alone that changed our lives. By using some of these results, we can travel to faraway lands in few hours, light-up an entire city and remove darkness, communicate our loved ones live. These effects clearly enriched our living standards continuously, especially in past few decades or so. And you will be surprised to know that all these started with simple questions like “Is it true?”, “How does it happen?”. Each one of these discoveries has a fascinating grand story behind. I shall illustrate this process using one such story that lead us understanding our life supporting closest star – The Sun. I selected this story, because, I have been working for past quarter century to understand some aspects of this object.

The sun is a huge nuclear huge Furness, at the center of which 4.21 million tons of hydrogen is converted to helium every second producing 3.78 x 10²⁶ Joules of energy that takes about 4 to 40 thousand years to come out, making the sun shine. As shown in the figure, the energy is produced in the core, flows in “radiative” manner in Radiative Zone, and convectively in Convective Zone.  You might imagine heat flow on a solid object in radiative zone and boiling water in convective zone. The core and the radiative zone, which is 70% of the sun, rotate like a rigid body, while different parts of the convective zone rotate with different speed, that is called differential rotation. The interface between these two zones is known as techocline, where magnetic field in the sun is supposed to be created. As the energy escapes the sun, there are many complex physical processes occur on its surface, since it suddenly encounters low dense atmosphere. If you see through telescope, you will notice granule structures in the bottom of solar atmosphere, called photosphere, above which you will notice a highly structured (in form of for example prominences) chromosphere and transition zone leading to super-hot corona. The chromosphere and corona can only be seen from earth during total solar eclipse, whereas on ordinary day, you see only the photosphere, that produce most of the energy. In photosphere, occasionally you will notice sunspots, that are cooler regions, due to the isolation of solar material by intense magnetic field. Such regions appear more every 11 years, which is called a solar cycle. Complex sunspots support an entangled and highly unstable electric current system, that produce flare as a result of breakdown. Many times, the flares lead to events called Coronal Mass Ejections, that dump about a billion tom of hot material in to the space with tremendous speed of 1000 km/s. As the material hit earth, they cause polar lights and potentially might damage communication satellites and commercial flights over polar regions. So, understanding the cause of these events are important. When such events are not there, still material constantly flow from the sun in the form of solar wind, at a speed of about 400 km/s. Briefly, this the story of the sun, you take 20 years to learn!!

Figure 1: Structure of the sun. The size of the earth would be smaller than the size of "o".

Now, the question is how do you know these are the facts, or that is possibly the real story of the sun? If you listen to a priest, or a scholar, who advocate the ancient wisdom, he might say a different story, that most of us might have heard in our childhood.  In my childhood, my grandmother told me that the Sun God, comes everyday on a chariot that has seven horses as shown in the picture 2. Depending on who makes the story, often the chariot is driven by a driver called Arun, who might possess a mustache or not. Every day, the sun god comes from east and goes in the west, and according to various versions distribute light on earth to sustain life and occasionally take interest on earthly affairs, especially when the supreme God like Sri Rama or Sri Krishna appear on earth. My mother worship sun god on a grand scale once in a year in winter. As a Brahmin, I often recite prayers called Gayatri Mantri, basically a prayer to the sun god. You would encounter similar and some times more exciting narrations in different societies. These are simpler and romantic than my story often told by people, who are considered to be closer to God that govern your lives. So, why should you believe me not them? You don’t have any way of verifying the two stories to ascertain, which is correct. You cannot now go through all the physics and mathematics that I learnt in past 40 years to appreciate my story. The only way to decide for yourself is to be doubtful of everything and ask simple questions and aim for simple answers. Doubtful of what I am saying and what they are saying. Follow the logic skeptically, verify them with evidences and decide. Blind believe is ok, but that should come in the end when you exhaust all your intellectual power. Take for example, a god-man or god-women producing a stuff (a gold ring) from nothing by waiving the hand. The simplest explanation is that he or she played a magical trick. The complex explanation is that he or she created the stuff from nothing by violating all known scientific principles. The other example is who created the universe, and why, like an excellent designer, where the fundamental particles are so uniform in size? These are the questions dealt in great Indian scriptures called Upanisheds. Answer is not straightforward and simple. You might get compiled to accept the grand creator. Anyway, let us continue with my story.

Each of the statements that I made in the third paragraph, were obtained by this process. The process is extensive, takes years of hard work by many scientists to come to these conclusions through a serious of rigorous experimentation and calculations. Hundreds of PhD thesis are written for each of these conclusions. Here, I shall illustrate the process that led us to know that sun is a huge nuclear Furness.

Figure 2: The sun God according to Hindu mythology.

Understanding the solar luminosity was central to the discovery of nuclear fusion, which is a perfect example of how a simple quest to understand a glaring phenomenon can also lead to vast engineering enterprise. In 19^th century, astronomers were convinced that gravity is the dominant force in the universe, so they conjectured that sun is shining by releasing energy by “gravitational collapse” that last for few tens of millions of years. By last 19^th century, geologists were confident that earth is much older, as we know today at least 4.5 billion years. There was a need to explain the source of energy in the sun. In 1920, Sir Arthur Edington, a brilliant British astrophysicist, presented to the British Association for the Advancement of Science by using the measurement of mass difference of hydrogen and helium that sun could shine for 100 billion years by converting 0.7% of mass equivalent energy in accordance with Einstein’s mass-energy relationship.

In 1939 two astrophysicists, Subrahmanyan Chandrasekhar and Hans Bethe, working independently, quantitatively showed the processes of gravitational collapse and nuclear fusion as the source of energy in the sun and stars. After this great achievement of intellectual gratification, the question was if we can use this physical process in earth. When so much energy is released in a tiny volume, that can be used as weapon and source of useful energy. Following the second world war and success of atom bomb, Edward Taylor of Manhattan Project worked on the problem and designed hydrogen bomb that is several times more destructive than atom bomb. This design required achieving the fusion reaction by bringing the deuterium nuclei very close to each other in a small volume unlike in the sun and stars, where this happens due to gravitational force. The conventional atom bomb is used to implode a container with deuterium to achieve this condition where energy is released in an uncontrolled fashion. The next step is to achieve controlled thermonuclear fusion that would be the source of useful energy for our daily application. This is not straight forward and needs several engineering research along with understanding the behavior of high temperature hydrogen plasma in a container. This is one of the hot research topics of contemporary physics and engineering at several leading centers around the world.

The difference between the two stories is that, my story gives you ways to verify and leads discoveries that can directly be used in our daily life. The other story does not have that scope, it can only entertain some times and collapse when simple questions are asked. So, in conclusion, I must say that be skeptical of everything, especially when people with “uncommon robe” speak. It is better to live in doubt than living with ideas that are false. Great Indian Scriptures like Srimad Bhagabat Gita promotes questioning and arguing. Sri Krishna says, you acquire knowledge by questioning, “Pariprasanan Sevaya¹”. He declares Himself as “Badaha Prabadatam Aham² – I am argument among discussion”.

¹तद्विद्धि प्रनिपादेन परिप्रश्नेन सेवया । उपदेखयन्ति ते ज्ञानं ज्ञानिनः तत्व दर्शिनः ॥

Chapter 4, Verse 43

²अध्यात्म विद्या विद्यानाम , बादः प्रबदत।म अहम् ॥

Chapter 10 Verse 3

Scientific Method for Engineers

Scientific Method for Engineers

Debi Prasad Choudhary

Los Angeles

10/20/2016

As a religious youth, I used to meditate in front of a picture of Sri Ram every evening while in high school. One day, I noticed a speck of bright light right in the forehead of Sri Ram in the picture and was delighted. I told my parents, who were happy and advised me to continue quietly. I continued the practice of mediation, “as I understood”, for few more days. But, I used to have doubt about my achievement, because I knew from my father that getting God is not an easy affair. Many sages were meditating in forest for “thousands of years” before they could get anything close. My doubt intensified as time passed by and I started sealing the door and windows. The light disappeared. I was disappointed but did not tell other about the results. My doubt and the action to satisfy it was scientific method, but not telling other fall short of it. Scientific method is essentially investigating the observed phenomena and describe them with reasonable explanations. When a God man produces an object by hand waving, the reasonable explanation is simple magic trick, rather than complex method of producing the stuff from vacuum that cannot be repeated by any other individual.

Scientific Method in Fundamental Science: Profound scientific discoveries are made by following this simple method. One of the examples is to describe motion of heavenly bodies such as planets and objects on earth with the same set of physical laws. About 400 years ago, understanding the motion of “wondering stars” in the sky was a mystery. These are untwinkling bright start like objects in the sky, the planets, which appear to change position relative to background stars over the years. They appear progressively westward and suddenly reverse direction. It was clear in early days that these are unlike the stars and might go around the earth just like the sun. But, such a model was complex and was not able to predict their path easily. Using precise measurements of their position in the sky by Tycho Brahe, Johannes Kepler formulated three empirical laws that explain planetary motion around the sun that include the earth. Kepler was a religious person and thought God created the universe following musical rhythm. His devised following three laws to describe the observations of planetary motion in the sky. 

Kepler’s laws:

Keplers Law 1 (Law of Ellipses): All planets move around the sun in elliptical orbits with sun in one of it’s foci.

Figure 1a: Ellipses of different eccentricity e. Ellipse with zero eccentricity is a circle.    

Keplers Law 2 (Law of equal area): The orbital motion of planets around the sun is such that in equal time interval they swipe same area of the eclipse. As a result, when the planet is near the sun they move faster.

Figure 1b: The planet swipes equal blue shaded area in equal interval of time. As can be seen it moves faster near the sun. 

Keplers Law 3 (Law of Harmonics): Square of planetary period is directly proportional to the cube of planetary distance.

Figure 1c: The plot of T² (planetary orbital period in Astronomical unit) versus R³ (planetary period in years) is a straight line. One astronomical unit is the average distance between earth and the sun (1.496 x 10⁸  km).

So, even though his laws worked and could explain the motion of the planets in the sky precisely, it had no universal use until they were understood with physical mechanism given by Sir Isac Newton. 

Newton showed that two bodies with mass M1 and M2, separated by a distance R move around a common point in elliptical orbits. The mutual gravitational force between them is given by:

F_grav = G (M₁ x M₂)/R²

Or in case of sun-planet system,

F_grav = G (Msun x Mplanet)/R²       (1)

Where G is the universal gravitational constant. As the planet goes around the sun (in nearly circular orbit) with speed v, it experiences net centripetal force, which can be written as:

Fcentripital = G (Mplanet x v²)/R²    (2)   

The orbital velocity v can be expressed as:

v =(2pi x R)/T            (3)

Using these three equations, it is easy to show that:

T³/R³ = 4 pi² / (G x M_sun)       (4)

The right hand side of equation (4) is constant, same value for each planet regardless of planetary mass. This law is now universal and can be applied to any two objects orbiting around a central point. When Galileo discovered the moons of Jupiter, their motion around the planets could be described by the same equation (4) by replacing the mass of sun by Jupiter. We can use this formula to determine the speed of artificial satellites around the earth. We can show that the height of the geostationary satellites is 35800 km. By studying the movement of remote astronomical objects, the same law is used to discover dead stars as black holes and white dwarfs, supermassive black hole at the center of our galaxy, dark matter around the galaxies and planets around other stars.

Even though the equation (4) can be used to explain the orbital period of the most planets satisfactorily, precise measurements of the Mercury, the planet nearest to the sun showed anomalies. It arrived at the perihelion position (nearest distance to the sun) shifted by 43 arc seconds per century as seen from the earth. Now, we have observed similar phenomena when two massive compact objects, known as pulsars, move around each other. In a binary pulsar system PSR 1913+16, the periastron (shortest distance between two astronomical objects, here pulsars) advance by 4.2 degrees per years. Pulsars are compressed stars that are produced at the end of the life of massive stars. The compression is equivalent to keeping the entire sun in a volume of a sphere of earth. This anomaly of shifting the perihelion or periastron position cannot be explained by Newtonian formalism. Albert Einstein showed that massive objects shape or distort the space-time geometry around them, in which they move. This is the foundation of Einstein’s theory of General Relativity, the consequence of which is used in modern GPS system to get accurate positions. Apart from its utility value, the General Theory of Relativity is one of the most aesthetic discoveries of mankind about the material world.

Figure 2: Shifting the perihelion positions P1, P2 and P3 of planet Mercury (represented by red blob) on its successive orbit around the sun (represented by yellow blob)

Motion of massive objects studied by giants, from Kepler to Einstein, is a perfect example to illustrate scientific method. The “scientific method” in pure science is essentially searching the underlying systematics in observations and generalizing them to discover unknown effects. This is achieved by constantly revising the underlying principles based on new observations. For example, in case of Kepler’s law, the plot given in Figure 1c, was not same for solar system objects and the moons of Jupiter. This phenomenon can be explained using the Newtonian version of Kepler’s Law. Einstein’s discovery of the properties of space-time using the tiny departure of observations from Newtonian theory is an example of perpetual quest of scientists for universal principles through intuitive imaginations guided by mathematical foundations of prior work.

Application of Science: Apart from the intellectual satisfaction for individuals, science become relevant to society when it is applied to improve living conditions. For example, the Kepler’s Laws are important that opens up our view of solar system but, when applied to launch satellites, it became relevant for society and government funding is justified. The story of nuclear fusion is a perfect example of how a simple quest for understanding a glaring phenomenon can lead to vast engineering enterprise. In 19^th century, astronomers were convinced that gravity is the dominant force in the universe, so they conjectured that sun is shining by releasing energy by “gravitational collapse” that last for few tens of millions of years. By last 19^th century, geologists were confident that earth is much older, as we know today at least 4.5 billion years. There was a need to explain the source of energy in the sun. In 1920, Sir Arthur Edington, a brilliant British astrophysicist, presented to the British Association for the Advancement of Science by using the measurement of mass difference of hydrogen and helium that sun could shine for 100 billion years by converting 0.7% of mass equivalent energy in accordance with Einstein’s mass-energy relationship.

In 1939 two astrophysicists, Subrahmanyan Chandrasekhar and Hans Bethe, working independently, quantitatively showed the processes of gravitational collapse and nuclear fusion as the source of energy in the sun and stars. After this great achievement of intellectual gratification, the question was if we can use this physical process in earth. When so much energy is released in a tiny volume, that can be used as weapon and source of useful energy. Following the second world war and success of atom bomb, Edward Taylor of Manhattan Project worked on the problem and designed hydrogen bomb that is several times more destructive than atom bomb. This design required achieving the fusion reaction by bringing the deuterium nuclei very close to each other in a small volume unlike in the sun and stars, where this happens due to gravitational force. The conventional atom bomb is used to implode a container with deuterium to achieve this condition where energy is released in a uncontrolled fashion. The next step is to achieve controlled thermonuclear fusion that would be the source of useful energy for our daily application. This is not straight forward and needs several engineering research along with understanding the behavior of high temperature hydrogen plasma in a container. This is one of the hot research topics of contemporary physics and engineering at several leading centers around the world.

Use of electromagnetic signal has been the predominant single most important contribution of fundamental science facilitated by engineering research. In 1865, with the publication of Dynamical Theory of Electromagnetic Field James Clark Maxwell demonstrated that electric and magnetic field travel through the space at the speed of light in the form of waves, where these two fields vibrate in orthogonal planes that lie in plane perpendicular to the direction of propagation. Starting in the beginning of 20^th century, major effort is spent in using these waves for communication and other variety of application. This story illustrates the scientific method in engineering research, which is close to use in our daily life is the development of electronics from Vacuum Valves to IC circuits leading to the design of Apple by Steve Jobs, that incorporated both science and art. Vacuum tubes, invented by John Fleming in 1904, were used for half a century to receive, amplify and transmit by manipulating them for variety of purposes. Thery were replaced by solid state semiconductor transistors,  invented by John Bardeen and Walter Brattain in 1947 for which they received Noble Prize. Since than technological research made it possible to produce devices that are densely packed with components exponentially as shown in Figure 3.

Figure 3: Density of components in electronic device as a function of time.

These two examples illustrate the similarity and difference between methods in the field of fundamental science and engineering. The similarity is in both fields the approach is to work towards finding solution to a problem and build models that explain the observations. The difference is in selecting the problems. In case of fundamental science the problems are related to investigate natural process irrespective of their utility value.  In engineering research, on the other hand, the utility factor is prime.

Regional and Economic for Engineering Research: While the fundamental science is universal and driven by pure curiosity, engineering research is primarily driven by application. The applications are always derived from experience and hence regional. So, engineering research would mostly benefit if they are driven by regional needs. Global needs definitely drive engineering research, but such work may not be suitable to all organization. It is possible to invent products that has global market value. While Dr. C. V. Raman was giving a tour of Raman Research Institute to Mahatma Gandhi, one of his associates asked if the institute can engage in improving Charakha (that span threads for making cloths). This might sound funny, but that is what should be inspiration for engineering institutes to work on the local social needs. Princeton University campus proudly display a bridge that was designed by the undergraduate student. Let us discuss some possible ideas that are especially relevant to developing countries.

Water Management: There is a water shortage in rural and urban habitats in developing countries. In many places in developing countries, for example in Odissa, there is draught followed by flood. The ground water level has been receding. In smaller towns, where there are locations of public distribution of water, the water flows from public taps uncontrolled. These are some of the problems a casual onlooker could gather without much effort. The scientific method for engineering research is rooted in these observation.

The problem is glaring, but the solution would be complex. The first step is to isolate a problem that can be solved with reasonable effort. This step can be called as the Project Design. Let us say, we want to find the solution for ground water level depletion in a specific location. This step is very important; it defines the problem. Once the problem is well defined, we need to gather all relevant information related to this problem. We need to know the amount of rain fall over past couple of decade in the area and adjacent locations. We need to know how much water level has been depleted in past decade. Associated with this, we need to know the water usage pattern of the habitants, water discharge through the rivers and cannels, the depth of the rivers and cannels, number of open wells and ponds that store water and charge the ground aquafer, water usage in agriculture, forest coverage etc. This phase can be considered as background research, since all these factors contribute to the water management of the area. The next step is to specify the requirements for the solution. Let us say, the goal of the project is to solve a part of water crises by supplying enough water for 50% of needs from natural resources and charge ground water. The last step to complete the project design is to outline a solution after weighing various options. At this stage, the best practices for such problems should be studied carefully. In our example, the goal can be filling the existing ponds or creating new one. Identifying aquafers and direction water streams to recharge ground water. Once the outline is prepared, the next step is to create an implementable mini project and examine if it works. May be one or two villages can be taken for such a study. Learn the problems that must be improved. Finally, the project must be continuously revised and improved on existing infrastructure. While this is an example, most such engineering projects are based such steps. The key to success for engineering projects is to divide the problem to smaller units and solve them in an integrated fashion. The difference between the approaches in basic science and engineering is that of objective of explaining the unknown phenomena and using known explanations in an efficient manner to solve a problem. On completion of the project, writing a report is the final step that helps others in the field and verify what is achieved.

While the problem described here is a common problem that can be found in most regions, engineering research generally adopt two key steps design and implement. When an engineer is equipped with frontiers of basic science, they can do great discoveries. The story of discovery of cosmic microwave radiation by Penzias and Wilson in 1964 is an excellent example, for which they received Noble Prize in 1978. On the other hand, the discovery of blue Light-Emitting Diode by Isamu Akasaki, Hiroshi Amano and Shuji Nakamura received Noble Prize in 2014, which is an excellent illustration of technological invention based on the urge to know basic physical laws that govern material properties. There are several technological innovations such as CCD detector, fiber optics communication and Liquid Crystal received Noble prize. These achievements require engineering skill and knowledge of basic physical principles.

Finally, in engineering research the projects are essentially application oriented and require team work. While the leader must have the vision of the goal and a clear path to achieve the same, the project should be divided in to smaller units that can be handled by subgroups of individuals in a timely fashion. That would be the key to success and an vital part of engineering research.

Home work:

1. Write an essay on the evolution of electronic devices from vacuum tube era to the modern time.

2. Design an ideal village that could be self-sufficient and sustainable.

3. House building is a problem in many developing societies. Use of bricks and cements and agriculture land and destroy the environment that is unsustainable in long term. Write a project for a possible solution.