Scientific Practice, Intuition and Temptation - Part I Intution

These Blogs are based on the lectures for a mini course on "Scientific Method for Non-Scientists".

Scientific Practice, Intuition and Temptation - Part I Intution

Debi Prasad Choudhary

Los Angeles

07/16/2015

Hypothesis, verification with experiment and revising based on the outcome are the foundations of scientific method. This straight forward sounding simple principle is really very complex in practice. The hypothesis is actually educated guess, in which intuition plays a major role that lead to path breaking discoveries in physics. Many times these intuitive ideas become so dominate that they prompt the experimenters   to tamper with their result. Let us discuss few famous examples here.

The dictionary definition and notion of Kent for intuition are, to large extent, practically adopted by practitioners of physics and astronomy. According to oxford dictionary intuition is the ability to understand something immediately without the need for conscious reasoning. The Kantian view of intuition is ¹“a non-logical mental form of representation, one that serves partly to render them concrete.” Physics practitioners create mental form of ideas based on the observational data that remains unexplained. Although the idea occurs immediately, the scientists keep thinking them for a long time. The concretization is realized by expressing the ideas in mathematical form that has predictive capability.

Formulation of Newton’s law of gravity, uncertainty principle in quantum mechanics, General Theory of Relativity and theoretical prediction of the existence solar wind are among few examples of result of intuition.

(1) Newton’s law of Universal Gravitation states that the gravitational force F is an attractive force that a body of mass m1 exerts on mass m2, such that F = G (m1 x m2)/r², where G is universal constant of gravitation. The force depends on both mass m1 and m2. The formula could have been F = G (m1+m2)/r², which would have been wrong. Here, Newton’s intuition guided possibly by Galileo’s experiment would lead to correct formulation. Galileo’s “Falling Body” experiment from Tower of Pisa showed that all bodies arrive at the surface of earth with same acceleration called “acceleration due to gravity”, which is 9.806 meters per second², which is the numerical value of (G x M/r²), where M is the mass of earth. So, without air resistance a hammer and a feather would fall at the same time that was observed on moon. The following simple mathematical analysis shows how Newton could have arrived at the correct formula.

 Newton’s second law of motion show that the force F = m x a, where “a” is acceleration. Let us assume the Universal Law of gravitation is that F = G (m1 + m2)/r². Here we have two definitions of force, which must be equivalent.

Equating the right hand side quantities of the two expressions for the force, we get,

m2 x a = G (m1 + m2)/r². m2 is the mass of apple.

If m1 is the mass of earth and m2 is mass of apple, in the above expression

m1 + m2 » m1, m2 being negligible.

That result: a = G m1 / (r² x m2), implying that large bodies would have smaller acceleration compared to smaller bodies, contrary to the Galileo’s experimental result.

By using m1 x m2, we get a = G m1 / (r²), where the acceleration “a” is independent of the mass of falling body, consistent with the observed experiment.

(2) The quantum physics or quantum mechanics was developed with a number of ideas that were proposed by physicists guided by intuition. Among them the most famous one is the Uncertainty Principle, which essentially comes from the idea that no measurement is possible with out disturbance. When we prepare to measure the position of a tiny object such as an electron, by shining light on it we shall move and change the position. So, it is impossible to measure the position and velocity (more precisely momentum) accurately at the same time. Although the “Uncertainty Principle” is being proved mathematically in the modern time, its effect was observed early in the shape of spectral lines and existence of electron degeneracy pressure of dying sun-like stars.

(3) The General Theory of Relativity is another shining example of scientific advancement guided by intuition. While proposing the Universal Law of Gravitation, Sir Isac Newton was uncomfortable with the proposition of “action at a distance” as existence of a force without mediator. The unexplained experimental result existed at the time was extra advancement of mercury’s perihelion position and a host of mathematical tools. Instead of an incremental correction to Newton’s theory, Einstein proposed space-time geometry that is shaped due to the presence of matter and energy in an elegant mathematical formulation. It was so nice that he said, he would be sorry for the God, if it were wrong!! The new General Theory of Relativity not only explained the existing results consistent with Newton’s Law, it predicted bending of light in the vicinity of massive objects among other things that were verified subsequently.

(4) Finally, the story of Solar Wind. For a long time two observations were prominently existed. One: All photographs of the sun during the total solar eclipse showed the existence of a white light corona irrespective of its activity phase. Two: All comets showed the existence of a tail pointing away from the sun, irrespective of the position of the comet in heliosphere. These two observations showed that there must be a continuous wind existing perennially originating from the sun and blowing outward. Eugene Parker, from Chicago University, proved this using the known plasma physics in 1958, which was detected by space born instruments in early 1960s.

Often, while working in the frontiers of science, it is not easy to be guided purely by the observed facts or “data” that overcome one’s own prejudices, as selecting them may be tricky. This was vividly evident in the famous ²“great debate” between Curtis and Shapley in 1920 to decide the structure of our galaxy and nature of spiral nebular (which were newly discovered at that time). They selected the data to make their point in the debate. Curtis was right to argue that the spiral nebulae are external galaxies, while Shapley was correct to argue for the fact that the sun does not reside in the center of our galaxy.

¹Falkenburg, B., 2006, “Functions of Intuition in Quantum Physics”, Intuition and the Axiomatic Methods, E. Carson and R. Huber (eds), Springer, The Netherlands, 267-292.

²Trimble, V., 1995, The 1920 Shapley-Curtis Discussion: Background, Issues and Aftermath, Pub. Astron. Soc. Pac., 107, 1133-1144.

Empirical Facts and Scientific Results - Part II Understanding Atom and Light

These Blogs are based on the lectures for a mini course on "Scientific Method for Non-Scientists".

Empirical Facts and Scientific Results - Part II

Understanding Atom and Light

Debi Prasad Choudhary

Los Angeles

During my student days, I listened to Professor Chandrasekhar saying, the triumph of 20^th century science is that we are able to understand the tiniest objects atoms and giant objects stars with the same set of physical laws. Yet, one hundred ago structure and composition of atoms were mostly unknown. Let us explore how we came this long way. The story of atoms and light is intertwined and gives an excellent insight of scientific processes leading to extraordinary outcome.

The rainbow is dispersed sunlight that contains all visible colors from violet to red continuously with out gap. When we observe similar dispersed light from a fluorescent lamp, we notice gap between the colors. Of course, a highly dispersed sunlight also show gap. The gap in the dispersed light was a mystery in early days of physics about one hundred ago.  In fact, those days famous astronomer Joseph Fraunhofer from Germany, who discovered gaps in solar spectrum conjectured that light does not exist at the colors that show gap!! The fluorescent light contains mercury atoms that get excited through discharge and produce light. Hydrogen atom with a single proton produced light at systematic set of discrete wavelengths (or roughly speaking color) that became key to develop atomic model.

There was another important result in the beginning of 20^th century. In 1909 Ernest Rutherford at the Physical Laboratories of the University of Manchester conducted an experiment to observe the scattering pattern of positively charged particles when bombarded on to a thin foil of gold of thickness 0.00004 cm. The result was that while most particles passed through the foil, one in 20,000 of the particles bounced back. This is possible only if most of the gold atom was empty with a concentrated mass at the center. This experiment played a crucial role in developing current model of atoms.

Niels Bohr, one of the finest minds of 20^th century physics, utilized discrete emission from an atom and results from Rutherford experiment to propose an atomic model that may illustrate commonly used scientific method. Atoms are neutral, so the positively charged nucleus must be accompanied by negatively charged electron. They cannot remain stationary due to the effect of Coulomb force that is attractive. If the electrons move around the nucleus, according to classical electromagnetism, the electrons would loose energy by radiation and eventually fall into the nucleus. Considering the known physics at the time, Bohr in 1913 proposed that electrons orbit the atomic nucleus in discrete stable orbits and do not radiate as long as they remain in the orbit. They gain or loose energy by jumping from one orbit to the other. This is the reason for emission of spectral lines in specific wavelengths (or color) and removal of light from solar spectrum in selected wavelengths due to gaining of energy in the orbit of selected atoms in solar atmosphere. This scientific model explained a number of observations known at the time but had several limitations. It reproduced the spectrum of hydrogen atom successfully, but failed to explain the spectra of larger atoms such as mercury, sodium or Argon and when they emit in a magnetized environment. It laid the foundation for the development of sophisticated version of quantum theory by Heisenberg and Schrodinger. Here, it must be pointed out that the scientific models explain the data for which they are developed and not the final word in the subject. They have scope for constant refinement and development, as more information becomes available.  

At this time, discrete nature of light was already known through photoelectric effect.  The violet light is of smaller wavelength compared to the red light. The violet to red is only a part of vast spectrum of electromagnetic radiation that is light. In photoelectric effect, it was observed that free electrons come out when the surface of a metal plate is illuminated by light. For a given material, the ejection of electrons did not depend on the intensity but wavelength of light. Einstein explained the phenomena by proposing quantum nature of light for which he received Noble Prize. If the wavelength is lower, the light quanta carried more energy, which resulted in electrons with higher velocity or kinetic energy. Quantum nature of light became a natural consequence of light in the Atomic model of Niels Bohr. He said, "Obviously, we get in this way the same expression for the kinetic energy of an electron ejected from an atom by photoelectric effect as that deduced by Einstein." This is another consequence of great scientific theory that encamps vast related phenomena to explain them in a unique fashion.

The fully-grown quantum theory (quantum mechanics) not only explained observed spectra and photoelectric effect, it was used to invent nuclear reaction leading to bomb and source of energy in the interior of the stars. In the center of a star, the pressure of overlying material become so huge that hydrogen atoms are heated to very high temperatures. They come very close and fuse to produce Helium and energy that is released as the light that we observe. The outflowing energy produce radiation pressure that balance inward material pressure leading to stability of stars. When, the internal nuclear combustion halts, the star collapses. For a sun like star this collapse is stopped by “electron degeneracy pressure”, which is also a consequence of quantum theory. One of the founding principles of quantum theory is known as “uncertainty principle”. According to this principle if electron is confined to a very small area, its velocity increases sharply (more precisely velocity x mass). The compressed star confines electron to such a small volume that the fast moving electrons generate enough pressure to stop further collapse for the stars whose mass does not exceed 1.2 times the mass of the sun. This is known as Chandresekhar limit. If the cores of the star exceed this limit they become a ball of neutron (or neutral star) or a blackhole that collapse endless. So the stability of the gigantic objects such as the stars and the stability of tiny particles atoms are understood using the same set of physical laws.

Each time, science is practiced to answer a well-defined precise question. Most basic assumptions are usually carefully designed such that they are not inconsistent with the experimental results. So, if a question is unanswerable with the contemporary science, it is not because the scientific method is incapable, it is because the tools to handle complex questions are not ready yet. Remember, one day we did not know the structure and composition of atoms, yet today we use them to understand the stars and obtain pretty pictures of our self and our loved ones!!

Empirical Facts and Scientific Results - Part I Understanding Gravity: Kepler, Newton and Einstein

These Blogs are based on the lectures for a mini course on "Scientific Method for Non-Scientists".

Empirical Facts and Scientific Results - Part I

Understanding Gravity: Kepler, Newton and Einstein

Debi Prasad Choudhary

Los Angeles

Science originates in human mind. It may not be easy to learn what propels mind to consider objects, a profound question that was posed in a great ancient Indian text known as Kenopnished. But, science has achieved many great things in about past 400 years that has improved our living conditions. Only in last ten years, we can reach our destination guided by a talking gadgets and no longer have to carry a map. We can see our loved ones at far away places and talk to them as if sitting in the next chair. We can locate the center of our galaxy and detect what happened soon after the universe was born. All these achievements make us think that there is something profound about science and the way scientists think. Many advocate that scientific thinking; temperament and the method are somewhat superior to all other ways of thinking. Being a practitioner of science for more than past 30 years, people ask me about the scientific method and seek justification and approval of their beliefs from “science”. My response has been random and non-scientific!! In these blogs, I address the issues related to scientific method, its limitations and justification of other methods of human endeavor. Before considering scientific method, let us learn some concrete example of great scientific achievements. I discuss understanding gravity in past about 400 years in this blog. This is an illustration of practicing science through observation of natural phenomena.

Johannes Kepler lived in early 16^th century when understanding the position of earth in the context of rest of the objects in the sky was of great concern, since it decided the power for a class of individuals. Is the earth center of the universe and govern its affairs through few individuals who have direct access to the creator? If that is so than rest of the human being should obey and serve these chosen ones. This question can be addressed by studying the motion of heavenly objects. There are three types of objects in the sky, which rise in the east and set in the west following a definite path. The stars describe simplest sky path. They appear four minutes late every day at the same location in the east sky and many of them seem to circle around a bright star in northern sky, called pole star or “Dhrub Tara” (Constant star). Some of them appear in the east and set in the west and some do not set by the morning. But, all of them repeat the same pattern annually. This pattern is however, not the same for an observer in the southern hemisphere, living say, in Sydney, Australia or Rio De Janeiro in Brazil, where there is no equivalence of a pole star.  As, most of the ancient astronomy was developed in the northern hemisphere, let is confine our story to northern sky for now. The other types of bright objects in the sky are the planets, which appear as non-blinking stars. The background stellar pattern around them change every day. They do not appear in the same location of the sky, although march in a narrow strip from east to west and also known as “wondering stars”.  The sun and the moon are very bright objects, which repeat their sky path in which planets move on annual basis.

About 600 ago, we did not understand the motions of all these objects in the sky in a comprehensive unified model. People thought, stars, planets, moon and sun revolve around the earth in which our Gods and we live. They invented complex geometrical models to describe these motions and predict their path with some success. For the first time, Nicolaus Copernicus of Poland proposed in 1514 that universe consists of eight spheres at the center of which resides the sun and not earth. The outer sphere contains motionless stars and the planets revolve in fixed spheres. Moon revolves around the earth on a sphere. Even though the concept or the idea was revolutionary that interested the Pope of the time, it had little practical consequence because of the basic assumption of circular orbit of the planets around the sun. Its predictive capacity (for the occurrence of eclipse for example) was limited and similar to the geocentric model. Copernicus considered circular orbits, since these are perfect geometrical shapes and did not have compelling reason for any other geometrical path.

About one hundred years later in about 1623 Johannes Kepler, a German Astronomer used accurate positional measurements of planets in the sky to devise laws that described their motion. He said in first two laws that the planets moves around the sun in elliptical and not in circular orbits in such a way that in equal time, equal area of ellipse is covered. As the sun occupies one of the focus of the eclipse, when the planet is nearer to sun it moves faster. The third law related the period of the planets with their distance. Of course there were other observations such as the phase of the planet Venus that also showed that the planets move around the sun. The introduction of elliptical orbit was crucial as it improved the predictability of the model considerably and offered a clear competitive choice to the geocentric model. Although these laws had profound impact by enhancing confidence on heliocentric model of the universe, they were confined to the planets of the solar system alone and did not have the capability of generalized application. The laws were based on purely empirical evidence of the data provided by Tycho Brahe.

The Kepler’s laws found robust foundation of physics after about 50 fifty years later when Sir Isac Newton showed that the motion of any two bodies with masses m1 and m2 separated by a distance r are governed by central forces F = G (m1 X m2)/r², where G is called gravitational constant (numerically: 6.67384 × 10^-11 m³ kg^-1 s^-2). Both the bodies (objects) would move around a central point, situated near the heavier mass, in elliptical orbits. In case of the solar system, the planets do not move around the sun, instead, the sun and planets move around a common point that is situated near the surface of the sun (not at the center of the sun). The Newton’s law of gravitation defined the force F in a quantitative manner that can be used to predict the orbit of any two bodies with masses and led to several new discoveries. We now know why the Kepler’s laws work. Using the Newtonian version of Kepler’s laws, faint and compact White Dwarf stars near bright stars and supermassive blackhole at the center of our galaxy were discovered. We use these laws to launch geostationary communication satellites for navigation. The scope and utility of data based empirical Kepler’s laws were enhanced by using the physics base that treated the planets and stars as simple matter that interact through a force called gravity. This scientific method of extracting systematics of a set of observations (data) and trying to find the underlying physical cause became useful when they provide scope to predict new phenomena to test their limitations.

Finding the common properties of similar phenomena under different situations and understanding them with a simple predictive model central to scientific method. The other aspect is the quest for “beautiful” and “elegant” mathematical explanation of observed phenomena. The General Theory of Relativity of Albert Einstein illustrates such an example. Newtonian mathematical approach is based on observations of experimental results, in which hypothesis are unnecessary. In fact Newton states that “Hypotheses non fingo (I frame no hypotheses). In 300 hundred years after Newton, several conceptual limitations of his theory was encountered as they were applied to study the dynamics of complex and sophisticated systems, chief among them being absence of inertial frame. This is when Einstein’s imaginative approach produced one of the most beautiful descriptions of the world. Einstein states, “Imagination is more important than knowledge. For knowledge is limited to all we now know and understand, while imagination embraces the entire world, and all there ever will be to know and understand.” Einstein proposed that mass and energy shape the space-time geometry, which in turn governs their motion. The consequence of this consideration is that the path of light deviates from the straight line while passing in the vicinity of massive objects, which is now clearly observed. We must note here that there was hardly any need for such consideration from experimental side for Einstein to think in this manner. It is the intuitive generousness that led him to this great discovery.  

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 later is an important aspect, absence of which makes a theory unscientific.

Scientific Method in Sociological Research.- Part II Law and Modern Physics

These Blogs are based on the lectures for a mini course on "Scientific Method for Non-Scientists".

Scientific Method in Sociological Research - Part II Law and Modern Physics

Debi Prasad Choudhary

Los Angeles, CA

The General Theory of Relativity and Quantum Mechanics are not only two great achievements of modern physics that enabled us designing devices such as GPS, computers and nuclear medicine for better living but also intellectually enriched us in better understanding the natural phenomena. In a sharp departure from the Newtonian paradigm, the space and time in the universe, according to General Theory of Relativity, is not uniform but gets structured or distorted in presence of matter and energy. Objects in the universe, such as stars, galaxies and planets move in the distorted space-time geometry. If the space-time were uniform, the motion of planets around the sun would be in an elliptical path following the Newton’s laws and the location of the shortest distance from the sun would shift slightly. The observations show that this is not the case and the location of the shortest distance of the innermost planet Mercury from the sun change faster. This observation showed that Mercury does not move in a flat uniform space around the sun, in stead moves in a curved space, distorted by the presence of the mass of the sun. The same theory is used to accurately determine the locations with GPS. On the other extreme, as we study the tine particles such as atoms and electrons, the observation process itself disturb its location. * So, it is impossible to simultaneously determine both the location and its time precisely. If we want precise spatial location of an atom, the time of it will not be precise and if the temporal information is desired precisely, the spatial information would be lost. This is one of the foundations of Quantum Mechanics that helped design almost all modern devices starting from computers to atom bombs.

Intellectually, these theories motivate us to observe the world in a completely different perspective. Here, we consider the governance of modern societies through constitution and law. The modern states have their constitutions and laws that must be in principle uniformly applied for all citizens for fairness, regardless of their social status or circumstances in which they leave. But, as discussed by Laurence H. Tribe¹, the uniform application may not be ideal and it would be advantages to consider the applicability of law non-uniformly depending on specific circumstances of a given case. He cites the example of a judgment relating the child abuse case, in which Joshua was repeatedly beaten by his father severely leading him to vegetative state. The state officers meticulously documented the evidence of torchers during the entire process but failed to intervene leading to fatal and permanent harm to the victim. After Joshua was permanently injured, his guardian local officials on the theory that “their failure to act deprived him of his liberty in violation of the due process clause of 14^th amendment and that Joshua was therefore entitled to recover damages under the civil rights status.”  The Supreme Court of Justice Rehnquist considered the “undeniably tragic” case and stated that, “nothing in the process of Due Process Clause… (that was enacted in the wake of the Civil War to enforce 14^th amendment) requires the State to protect the life, liberty and property of its citizens against the invasion of private actors. The Clause is framed as a limitation on the State’s power to act, not as a guarantee of certain minimal levels of safety and security.”

The majority view of the Court was based on the outcome of the simple questions such as “did the state of Wisconsin beat up that child?”. Inspired by General Theory of Relativity Tribe notes that the Court could have considered “Did the law of Wisconsin, taken in its entirety, warp the legal landscape so that in effect, deflected the assistance otherwise available to Joshua.” 

Unlike in physical science, where is it possible to precisely measure the effect of curvature or distortion of the space caused by the presence certain amount of mass, it is not possible to quantify the influence on humane considerations. Cautiously, Justice Rehnquist stated that before influenced by grievous situations such as that of Joshua the judgment should rest on more conservative view. “Had the state moved too soon to take custody of the son away from the father, they would likely have been met with the charge of improperly intruding into the parent-child relationship, charge based on the same Due Process Clause”.

Justice Brennan on the other hand considered the local circumstances, which might be thought as consistent with modern view. He asked, “whether the state of Wisconsin – by establishing a child welfare system specifically to help children like Joshua, by creating a system for investigating reported instances of child abuse, and by outlawing private intrusions into a home where a child seems imperiled – effectively channeled all reports of such abuse, and all actions in response to such reports, to specific agencies. In this way, the state invited citizens and others to depend on local departments of social services … to protect children from abuse”.

According to Tribe, as illustrated with the Joshua’s case was adjudicated by a Newtonian judge who viewed the case from a objective vantage point that easily absolved the state of responsibility of his plight. “A post-Newtonian judge on the other hand would view the perspective of those whom her ruling affects as no less legitimate than her own, and ask what social space the body of legal rules help to define and may not distance the state from the helplessness of the most vulnerable”. This would help achieve philosopher John Rawls’ conclusion fundamental fairness of the society is achieved by fairly treating the least disadvantaged in the society.

As stated earlier, another powerful finding of the modern physics is to realize that in the process of observing tiny particles such as electrons by shining light or using a probe, we actually change its original position that we desire to determine. The particle is so small that as the light particle collide or the probe touches it moves!! This is known as “Uncertain Principle”. This simple sounding principle is used to understand the nuclear reactions that keep the sun shining and design “tunneling microscopes” to examine very small objects. Besides, this principle has tremendous social implication and used by both philosophers and sociologists to shape their concepts of working of the world.  This post Newtonian physics-like effect is seen in the process of awarding appropriate relief by due process of the law that alter the physical system under observation by the “process” it self. The case of Wooley Vs. Maynard, in which common citizens did not want to display state mandated statement “Live Free or Die” in their car license plate, illustrates the process of observation altering the material being observed. The Supreme Court extended the scope of First Amendment of free speech stating that “the proposition that the right of freedom of thought protected by the First Amendment against the state action include both the right to speak freely and the right to refrain from speaking at all.”

In the recent time, Chief Justice John Robert’s view on the Health Care Law that “Congress passed the Affordable Care Act to improve health insurance markets, not to destroy them. If at all possible, we must interpret the act in a way that is consistent with the former, and avoids the latter” may also be used to illustrate his judgment on “Individual Mandate” in 2012 as the observation influencing the case being observed. He wrote in majority opinion that “The Affordable Care Act’s requirement that certain individuals pay a financial penalty for not obtaining health insurance may reasonably be characterized as a tax. Because the Constitution permits such a tax, it is not our role to forbid it, or to pass upon its wisdom or fairness.”² This judgment became a major first victory for the survival of the act.

Finally, we might consider the recent Supreme Court judgment on Obergefell v. Hodges case³ (on same sex marriage) effected by the “curved space time”. Justice Kennedy pointed out “in interpreting the Equal Protection Clause, the court has recognized that new insights and social understandings can reveal unjustified inequality within our most fundamental institutions that once passed unnoticed and unchallenged”. This is important as, in a sense, it provides tools to our legal institutions to deal with social dogma that govern our societies unofficially. Physical laws that have been so successful in improving our material lives can shape our intellectual views and provide wisdom to devise tools to improve our intellectual social lives.

* Precisely the quantum mechanical uncertainty principle states that it is impossible to simultaneously determine both the location and its momentum (mass x velocity) or Energy and time.

¹ The Curvature of Constitutional Space: What Lawyers can learn from modern physics. By Laurence H. Tribe, Tyler Professor of Constitutional Law, Harvard Law School, Harvard Law Review, 1989, 103, 1- 38.

² NewYork Times, ADAM LIPTAK JUNE 28, 2012

³ Suhrith Parthasarathy, Emulating the U.S’s rainbow movement, The Hindu, Tuesday, June 30, 2015