# predicty.net

## Data Science

- Why data science?
- Data Science Tools
- Getting Data
- Exploratory Analysis
- Statistical Inference
- Regression Models
- Machine Learning

### Why data science?

### Data Science Tools

### Getting Data

### Exploratory Analysis

### Statistical Inference

### Regression Models

### Machine Learning

## Machine Learning

### Why Machine Learning?

### Supervised Learning

### Unsupervised Learning

### Reinforced Learning

### Deep Learning

## Quantum Physics

- Nature of Physics
- Physics Prior to 1900
- Black-Body Radiation
- Photoelectric Effect
- Atomic Structure
- Wave Particle Duality
- Uncertainty Principle
- Quantum Wave Function
- Bra-Ket Notation
- Interpretations
- Double-Slit Experiment
- Experimental Validations
- Quantum Statistics
- Quantum Hall Effect
- Masers and Lasers
- Quantum Tunneling
- Superconductivity
- Josephson Effect
- Quantum Entanglement
- Quantum Computing

### Nature of Physics

Physics deals with physical items and processes. It does not deal with living beings, communal societies, or financial resources.

Physics deals with physical items and processes from physical perspective. It does not deal with their ownership, legality, or cost.

Physics gives general principles. It does not give principles for a particular rock, planet, or location.

Physics gives general principles in quantitative terms. It does not talk in qualitative or vague terms, which may be subject to interpretation.

Physics gives general principles based on or subject to observations. It does not make statements based on speculations or meditations.

Physics is an evolving science. It does not claim to be a rigid dogma dictated by someone.

### Physics Prior to 1900

Physics is not a new discipline of knowledge.

More than ten millennia ago, our ancestors found that a round item can be easily rolled and can help in transporting other items from one place to another. They also found that fire sparks can be generated by striking two rocks. The discipline of physics was born out of these revolutionary inventions of wheel and fire.

For several millennia thereafter, our ancestors studied stars and planets with a remarkable accuracy with whatever limited resources and knowledge they had. They tried their best to make some general derivations. It is unfortunate that some of these general derivations were misleading.

Formalization of physics as an exact science happened two millennia ago. Archimedes of Syracuse studied floating objects and derived the famous Archimedes principle, which states that weight of fluid displaced by a floating object is equal to the weight of the floating object. This principle was very important and a major milestone in physics.

Archimedes and some Chinese people studied passage of light through different shapes of glass. This led to the physics of light. It also led to the invention of spectacles, a biomedical device of great importance.

For more than a millennium thereafter, the human civilization got busy in other pursuits. There was no outstanding achievements related to physics. However, this period made another significant contribution to physics. It generated a lot of data on planetary positions and movements.

After a millennium of silence, physics roared in the fifteenth century with triumphs of the trinity of Nicolaus Copernicus (1473-1543), Galileo Galilei (1546-1642), and Isaac Newton (1642-1726). Copernicus analyzed the available data of planetary positions and movements. He gave a new concept of elliptical orbits and proved that the Earth revolves around the Sun, which was against the old belief of heliocentric universe. Galileo carried out experiments and proved that bodies falling freely from the same height take the same time for reaching the ground. This demonstrated the importance of experiments and shortcomings of common beliefs. His formula for pendulum oscillations led to an important instrument for measuring time. Newton was a genius, now known to all educated people around the world. His masterpiece theory of gravitational force not only explained the movements of planets and stars, but also made it possible to compute their trajectories with a great precision. His three laws of motion and concept of spectral distribution of light made physics a serious and important science.

The period of two centuries following Newton saw another great revolution in physics. Voltas and Coulomb studied static electricity in frogs, thunderstorms, rubbers, and other objects. Ampere studied electric currents. Michael Faraday (1791-1867) carried out lots of experiments related to electricity, and derived a connection between electricity and magnetism. James Clark Maxwell (1831-1879) consolidated others' findings on electricity and magnetism in the form of four beautiful equations. Based on these equations, he made an astonishing discovery that light is a form of electromagnetic waves. He proved that light can pass through vacuum, and disproved the earlier beliefs about aether. His equations also computed the speed of light in vacuum.

These pioneering works on electricity and magnetism paved a way to the electric bulb, electric motor, radio, phone, and many other devices, which changed the human civilization in many different ways. Physics achieved a lot during 1490-1890. It achieved so much that a reputed physicist [not to be named here] commented in 1890: “Physics has achieved everything that was to be achieved. Only thing pending is a minor explanation for the black-body radiation distribution.”

That physicist could not foresee the future of physics and underestimated the black-body radiation distribution problem.

### Black-Body Radiation

All substances absorb a part of radiation they get and reflect the remaining radiation. A black-body, such as graphite, is a substance that absorbs almost 100% of radiation. When the black-body reaches a thermal equilibrium, it emits back the radiation that it had absorbed earlier. The radiation emitted this way is known as black-body radiation.

By 1890, physicists had measured intensity versus wavelength of radiation emitted by black-bodies at various temperatures. They had found that for a given temperature, intensity rises almost normally with wavelength for up to a certain wavelength, and then it tapers down with wavelength. In addition to academicians, industrialists were much interested in understanding the black-body radiation, expecting that it would lead to better filaments for the newly-invented electric bulb.

By 1899, several physicists presented theoretical models to explain the variation of intensity with wavelength, but they failed miserably. Wien’s model could explain the intensity variation for very high wavelengths, but it was upside-down for low wavelengths.

In 1900, when the 19th century was about to close, a senior German physicist named Max Planck tried a then-weird approach to explain the black-body radiation. Prior theoretical models had implicitly assumed that light of a given wavelength can have any energy value. Planck assumed that light of a given wavelength can have only discrete energy values. He treated light as packets or quanta of energy, and assumed that each quantum has energy equal to frequency of light multiplied by a constant value, which is now known as the Planck constant. Here, frequency is inverse of wavelength.

Based on this quantum theory of discrete energy levels, Planck was able to explain the black-body radiation pattern with a remarkable accuracy for any wavelength. This was the birth of the quantum theory.

Not many people realized the importance of this quantum theory at that very time. It took 5 years and a genius mind to understand and exploit its potential. It took 18 years for Max Planck to get a Nobel Prize of 1918. But, later is better than never.

Wikipedia article on black-body radiation

Illustrative page on black-body radiation

Wikipedia article on Max Planck

Nobel Prize in Physics 1918 to Max Karl Ernst Ludwig Planck in recognition of the services he rendered to the advancement of physics by his discovery of energy quanta

### Photoelectric Effect

By about 1900, some physicists had observed that some materials emit electrons when bombarded by gamma rays, which are electromagnetic waves similar to visible light but with higher frequencies. They observed that emission of electrons needs electromagnetic waves of some specific frequencies. This observation needed a theoretical explanation.

In 1905, while he was working in a Swiss patent office, Albert Einstein pursued his interests in physics in his spare time, and published 3 research papers. The first paper on random motion of small particles was a normal research paper. The second paper on photoelectric effect unraveled the potential of quantum theory, and won him a Nobel Prize in 1921. The third paper on theory of relativity brought forth many revolutionary results, and made him famous as one of the greatest scientists in the history.

In his paper on photoelectric effect, he explained the observations of emissions of electrons by applying the quantum theory. He assumed that: (1) electrons in atoms of matter are distributed in discrete energy levels, and (2) light is made of quanta of energy. Quanta of light, i.e. electromagnetic radiation, are now known as photons.

Based on Einstein’s assumptions for an electron to jump from one energy level to another higher energy level, a photon (light quantum) will be needed whose energy matches the difference between the electron’s new and old energy levels. If the new energy level is outside the atom, the electron will come out of the atom when it is affected by a photon of the required energy. Two photon of the same energy will knock out two electrons, and so on.

Einstein’s this theoretical model could explain an observation which could not be explained without invoking the assumptions made by Einstein. It thus provided a support to Planck’s quantum hypothesis, and made the quantum hypothesis an acceptable theory. In addition to providing an explanation to an observation, Einstein predicted the presence of stimulated radiation, which is a radiation emitted when an electron is stimulated to go from a higher to a lower energy level. This prediction later on led to masers and lasers.

Wikipedia article on photoelectric effect

Wikipedia article on Albert Einstein

Nobel Prize in Physics 1921 to Albert Einstein for his services to theoretical physics and especially for his discovery of the law of the photoelectric effect

### Atomic Structure

By 1905, experiments had made it clear that matter is made of atoms, and atoms are made of electrons and protons. They had not yet understood the arrangement of protons and electrons inside an atom.

Based on Einstein’s discrete-energy-levels model for matter, some physicists rationalized that an atom has protons in the center and electrons are in some discrete energy levels.

In 1912, Niels Bohr improved the atomic model. He stated that electrons are revolving around protons in some fixed orbits. The first orbit can have 2 electrons; the second orbit can have 8 electrons; and so on. The radius of an orbit and the speed of revolution of an electron are such that the outward centrifugal force of the electron matches the inward electric attraction force from protons, so that there is no net inward or outward force.

Bohr’s atomic model was quite understandable, and could account for most observations. Some refinements in the model were made later on to account for further observations. Bohr earned a Nobel Prize in 1922.

Wikipedia article on Niels Bohr

Nobel Prize in Physics 1906 to Joseph John Thomson in recognition of the great merits of his theoretical and experimental investigations on the conduction of electricity by gases

Nobel Prize in Physics 1922 to Niels Henrik David Bohr for his services in the investigation of the structure of atoms and of the radiation emanating from them

### Wave Particle Duality

Is light a wave or a particle? This question had puzzled and divided physicists for centuries.

In 17th century, Christiaan Huygen considered light to be waves. Isaac Newton treated light as made of particles. In 18th century, Thomas Young allowed light from a point source to pass through two slits and collected it on a wall on the other side. Light on the wall generated a pattern of multiple lines rather than a pattern of two solid lines. Such a pattern could be explained only in terms of waves. In 19th century, through his famous 4 equations, James Clark Maxwell showed that light is a form of electromagnetic waves. And then, the 20th century introduced the quantum theory in order to explain the black-body radiation. Max Planck had to treat light as made of particles, i.e. quanta or packets of energy.

Whether light is a wave or a particle remained a puzzling mystery until …

Louis de Broglie, an aristocratic noblemen, was studying physics for fun, rather than career. He pondered over the problem of whether light is a wave or a particle. He conjectured that light is both a wave and a particle; it can be described in both ways, as a wave and as a particle. He further conjectured that this duality applies not only to light, but it applies to everything; a thing is a thing, irrespective of whether we describe it as a wave or a particle.

In 1924, de Broglie wrote a small thesis on this novel concept of wave-particle duality. His thesis was sent to Einstein. Being a genius, Einstein could grasp the profound concept presented in the thesis. With Einstein’s endorsement, the concept of wave-particle duality got accepted by the physics community. de Broglie was awarded Nobel Prize in 1929.

The concept of wave-particle duality solved the age-old mystery, and opened doors for a new language in physics.

Wikipedia article on double-slit experiment

Wikipedia article on wave particle duality

Wikipedia article on Louis de Broglie

Nobel Prize in Physics 1929 to Prince Louis Victor Pierre Raymond de Broglie for his discovery of the wave nature of electrons

### Uncertainty Principle

A college teacher of mine told us a story. I do not know the authenticity or source of the story; but the story is worth-telling here.

In 1920s. Werner Heisenberg applied to a university physics department for a postdoctoral position. Two famous physicists interviewed him. The first interviewer asked him a question about optical microscopes. He could not answer. The first interviewer gave him a book on optical microscopes, and asked him to revisit for the interview.

While reading this book, Heisenberg got side-tracked. He thought deeply about optical measurements of waves and the new concepts from quantum physics, and came up with the uncertainty principle. In the next interview, he taunted the first interviewer, and narrated what he had come up with. The second interviewer, who was well-versed in quantum physics, immediately understood what Heisenberg was talking about, and helped him publish his work and later on get him a Nobel Prize in 1932.

Heisenberg’s uncertainty principle states that any measurement of a quantum system disturbs the quantum system. If we try to measure a variable of the system precisely, we cannot measure its corresponding canonical variable precisely. The product of uncertainty in the measurement of a variable and uncertainty in the measurement of the corresponding canonical variable is at least equal to the Planck constant h divided by 2 pi.

Some of the sets of canonical variables are:

_{x}p

_{y}p

_{z}

This principle has profound implications in what we can measure and comprehend about microscopic quantum things and processes. For big things and processes, the uncertainty is still there, but the uncertainty becomes insignificant due to large values of variables.

Wikipedia article on uncertainty principle

Wikipedia article on Werner Heisenberg

Nobel Prize in Physics 1932 to Werner Karl Heisenberg for the creation of quantum mechanics the application of which has inter alia led to the discovery of the allotropic forms of hydrogen

### Quantum Wave Function

The concept of wave-particle duality needed a mathematical language to describe waves and particles alike.

In 1920s, while staying in a sanatorium due to his illness, Erwin Scrodinger pondered over the quantum theory, wave-particle duality, wave propagation, and statistics, and came up with a brilliant equation, now known as Scrodinger equation. He got a Nobel Prize in 1933.

A typical Scrodinger equation looks like:

[i] (h bar) (d/dt) (psi) = (H caret) (psi)

Here:

(psi) is the quantum wave function of the item being described.

(H caret) is the Hamiltonian of the environment of the item.

(d/dt) is the time derivative operator.

(h bar) is the Planck constant divided by 2 pi.

[i] is the square root of minus one.

The quantum wave function (psi) is a quantum description of the item under consideration. It has complex, i.e. real plus imaginary, values.

*A complex number and its conjugate have same-valued same-signed real parts, but same-valued opposite-signed imaginary parts; thus, conjugate of a+[i]b is equal to a-[i]b . Multiplication of a complex number and its conjugate is equal to sum of square of real part and sum of imaginary part; thus, multiplication of a+[i]b and a-[i]b is equal to a ^{2}+b^{2} .*

The quantum wave function (psi) represents the amplitude of probability of existence of the item at a space-time point. Its multiplication with its conjugate represents the probability of existence of the item at a space-time point.

The quantum wave function (psi) varies in space and time. The space-time variation depends on the Hamiltonian operator.

What does the Hamiltonian (H caret) mean? Suppose that: you are to drive a car through some locations; you have a map of these locations; and the map shows that region **a** has good roads while region **b** has bad roads.
Then, you would almost certainly predict that you will be driving fast in region **a** and slow in region **b**. The Hamiltonian is like a map, which highlights ups and downs in the space and thereby helps us predict
the space variations in (psi). Just as governments and map companies develop territorial maps, many physicists and chemists spend much of their time in defining the Hamiltonian for various scenarios. Mathematically speaking,
the Hamiltonian is a space derivative operator.

The time derivative operator (d/dt) describes time variation of (psi).

The presence of Planck constant divided by 2 pi (h bar) leads to quantum effects of the item.

The presence of [i] introduces complex oscillatory behavior of (psi).

Wikipedia article on Schrödinger equation

Wikipedia article on Erwin Schrödinger

Nobel Prize in Physics 1933 to Erwin Schrödinger and Paul Adrien Maurice Dirac for the discovery of new productive forms of atomic theory

### Bra-Ket Notation

Schrodinger’s equation in terms of a quantum wave function gave a feeling that matter is inherently of wave type and it is of particle type only indirectly. This was not a problem for most physicists.

Quantum physics was a very hot subject in 1920s, and attracted many brilliant minds from all over the world. One such brilliant mind was Paul Dirac, a brilliant, but shy, British mathematician.

Dirac was not satisfied with Scrodinger’s approach. He thought that if waves are particles, there should exist a particle-based description of the matter. He looked for various possibilities, and came down to vectors, matrices, and linear algebra.

In Dirac’s approach:

For example, if A* is an annihilation operator, A is a creation operator.

Dirac and Scrodinger shared Nobel Prize in Physics 1933.

Wikipedia article on Dirac equation

Wikipedia article on Paul Dirac

Nobel Prize in Physics 1933 to Erwin Schrödinger and Paul Adrien Maurice Dirac for the discovery of new productive forms of atomic theory

### Interpretations

The core concepts of quantum physics (wave particle duality, uncertainty principle, and quantum wave function) were and are beyond human intuition. Many physicists have attempted to give some meaning to these concepts.

The most workable interpretation of the quantum wave function was given by Max Born, who was expert in mathematical treatment of the physics of light. According to Born's interpretation, the quantum wave function (psi) represents the amplitude of probability of existence of the item at a space-time point, and the qyantum wave function's multiplication with its conjugate represents the probability of existence of the item at a space-time point. Born's interpretation is able to explain the wave particle duality and uncertainty principle. Yes, Born did earn a Nobel Prize in Physics.

Richard Feynman, who is famous for his lectures on physics, gave an alternative interpretation in terms of path integrals. While Born's interpretation is in terms of existence, Feynman's interpretation is in terms of movements.

In order to rationalize this probabilistic nature of quantum systems, many physicists now believe that while the actual space-time continuum has more than 4 dimensions, we human beings are confined to a space-time continuum of only 4 dimensions. Similarly, many physicists now believe that while there exist multiple parallel universes, we human beings are confined to a single observable universe.

There is a theory known as string theory, according to which, basic building blocks of the universe are strings. Roughly speaking, a string is a wave with a beginning and an end, and a string with a certain winding pattern leads to a particle.

A typical solution of a Scrodinger wave equation is a linear superposition of pure harmonic oscillators. A pure harmonic oscillator has no beginning and no end. However, we see that each particle has a beginning and an end. Sudarshan and Glauber were able to show that an alternative solution of a Schrodinger equation is a linear superposition of coherent states. Each coherent state is a bundle of many pure harmonic oscillators, and it has a beginning and an end. Glauber earned a Nobel Prize in Physics for this important finding. Sudarshan was not so lucky.

Wikipedia article on interpretations of quantum mechanics

Nobel Prize in Physics 1954 to Max Born for his fundamental research in quantum mechanics, especially for his statistical interpretation of the wavefunction

Nobel Prize in Physics 1965 to Sin-Itiro Tomonaga and Julian Schwinger and Richard P. Feynman for their fundamental work in quantum electrodynamics, with deep-ploughing consequences for the physics of elementary particles

Nobel Prize in Physics 2005 (shared) to Roy J. Glauber for his contribution to the quantum theory of optical coherence

### Double-Slit Experiment

If light from a point source is allowed to pass through two slits [or holes] and collected on a wall, the wall shows a pattern of multiple lines [or concentric rings] instead of two lines [or two dots]. This is easily understandable based on the wave nature of light.

Based on the concept of wave particle duality, it was predicted that if electrons from a point source are allowed to pass through two slits [or holes] and collected on a wall, the wall should show a pattern of multiple lines [or concentric rings] instead of two lines [or two dots].

And lo and behold, this is indeed what they observed in experiments in 1960s. Such a confirmation of the prediction was a big step in the general acceptance of the concept of wave particle duality.

### Experimental Validations

Experiments conducted by Davisson and Thomson found that electrons get diffracted by crystals, and their diffraction patterns could not be explained without treating electrons as waves. These and several other experiments helped in the validation of the quantum physics concepts.

Nobel Prize in Physics 1937 to Clinton Joseph Davisson and George Paget Thomson for their experimental discovery of the diffraction of electrons by crystals

### Quantum Statistics

Particle statistics is a way of computing the population density of various energy states.

According to classical physics, particles of the same type can be distinguished and can share an energy state. Particle statistics based on these classical conditions is known as Maxwell-Boltzmann statistics.

According to quantum physics, particles of the same type cannot be distinguished.

In 1920s, Otto Stern and Walther Gerlach performed some experiments. Based on their findings, physicists determined that particles have an intrinsic property known as spin. A particle’s spin is similar to an angular momentum, but it is fixed for a particle. Physicists then determined that photons and certain other particles have integral spin (0, 1, 2, …) and electrons and certain other particles have half-integral spin (1/2, 3/2, 5/2, …).

Wolfgang Pauli concluded that particles of integral spin can share an energy state, but particles of half-integral spin cannot share an energy state. Pauli earned a Nobel Prize in Physics for this conclusion known as Pauli exclusion principle.

SN Bose and Einstein formulated statistics for particles of integral spin. These particles are now known as bosons.

Enrico Fermi and Dirac gave formulated statistics for particles of half-integral spin. These particles are now known as fermions.

To understand the difference between the three types of statistics, let us see how 2 particles p1 & p2 can be arranged in 3 states s1 & s2 & s3. With [distinguishable and sharing] classical particles, there can be 3 double occupancies and 6 single occupancies. With [indistinguishable and sharing] boson particles, there can be 3 double occupancies and 3 single occupancies. With [indistinguishable and non-sharing] fermion particles, there can be no double occupancy and 3 single occupancies.

Wikipedia article on particle statistics

Wikipedia article on Stern–Gerlach experiment

Nobel Prize in Physics 1943 to Otto Stern for his contribution to the development of the molecular ray method and his discovery of the magnetic moment of the proton

Nobel Prize in Physics 1945 to Wolfgang Pauli for the discovery of the Exclusion Principle, also called the Pauli Principle

Wikipedia article on Satyendra Nath BoseNobel Prize in Physics 1938 to Enrico Fermi for his demonstrations of the existence of new radioactive elements produced by neutron irradiation, and for his related discovery of nuclear reactions brought about by slow neutrons

### Quantum Hall Effect

In 1879, Edwin Hall had found a classical physics phenomenon. If electrons are flowing in one direction and a magnetic field is applied perpendicular to the flow of electrons, then electrons are deflected perpendicular to the flow direction and field direction, and this deflection builds up an electric voltage. This phenomenon is known as the Hall effect. The ratio of the built-up electric voltage to the initiating electric current is known as the Hall resistance.

Around 1975, a few physicists predicted a strange phenomenon based on quantum physics. If electrons are flowing through a very thin plate in a strong magnetic field in a cold environment (where thermal vibrations are negligible), the build-up of electric voltage will be such that the Hall resistance can have only quantized values, in multiples of Planck constant divided by square of electron charge. This phenomenon is now known as quantum Hall effect.

In 1980, experiments conducted by von Klitzig confirmed the existence of quantum Hall effect. They earned Nobel Prize. Their experiment was significant and important, because it showed that quantum phenomena are not restricted to atoms and microscopic objects as previously thought; even large objects can exhibit quantum behavior.

Quantum Hall effect has applications in measurement instruments and some electronic devices.

Later on, some other physicists observed large-scale quantum phenomena related to excitations in electron fluids.

Wikipedia article on quantum Hall Effect

Nobel Prize in Physics 1985 to Klaus von Klitzing for the discovery of the Quantum Hall Effect

Nobel Prize in Physics 1998 to Robert B. Laughlin and Horst L. Störmer and Daniel C. Tsui for their discovery of a new form of quantum fluid with fractionally charged excitations

### Masers and Lasers

Light from an ordinary electric torch is incoherent. It gets diffracted and vanishes after traveling some distance.

Masers are devices for coherent microwave radiation. Lasers are devices for coherent visible light radiation. Laser is an abbreviation for Light Amplification by Stimulated Emission of Radiation.

Radiation from a maser or a laser is so much coherent that it can travel a very very long distance without getting diffracted. No wonder why lasers have found many great applications in many different fields.

Generation of radiation in a maser or a laser is based on quantum physical photoelectric effect. Maser or laser has a cavity with special mirrors to reflect the radiation multiple times before it is sent out. This arrangement makes the radiation coherent.

Radiation from a maser or a laser displays many quantum phenomena.

Nobel Prize in Physics 1964 to Charles Hard Townes and Nicolay Gennadiyevich Basov and Aleksandr Mikhailovich Prokhorov for fundamental work in the field of quantum electronics, which has led to the construction of oscillators and amplifiers based on the maser-laser principle

### Quantum Tunneling

According to classical physics, a particle thrown against a high-rise wall gets reflected back by the wall, and therefore, cannot reach the other side of the wall.

It is not so according to quantum physics. According to quantum physics, a particle is also a wave. A particle thrown against a high-rise wall travels like a wave to make an effort to get through the wall. If it overcomes its attenuation while traveling through the wall, it reaches the other side of the wall. Thus, there is a non-zero possibility of the particle overcoming a barrier and tunneling through the wall.

Tunneling microscopes and many electronic devices are based on this quantum tunneling effect.

Wikipedia article on quantum tunnelling [Source of the above gif illustration.]

Nobel Prize in Physics 1973 (shared) to Leo Esaki and Ivar Giaever for their experimental discoveries regarding tunneling phenomena in semiconductors and superconductors, respectively

### Superconductivity

We all know that when electrical current flows through a conducting wire, the wire gets heated. This is because electrons of the current collide with matter of the wire and these collisions tend to resist the flow and convert electrical energy into heat. This electrical resistance prevents the wire from carrying a large current for a long time.

In 1911, Heike Kamerlingh Onnes discovered something weird. He found that if the conducting wire is cooled below a certain temperature, the wire’s electrical resistance drops and becomes almost zero. This means that at low temperatures, the wire can carry large currents for long times. Quite understandably, this property was named as superconductivity. Onnes was awarded a Nobel Prize in Physics for this pioneering work.

For four decades thereafter, physicists were puzzled and could not explain the sudden drop of resistance at a certain temperature, which varied from material to material. In 1956, Bardeen, Cooper, and Schrieffer proposed a theory, which could fairly well explain the superconductivity. Their explanation is somewhat as follows.

Since electrons are fermions, they cannot share energy states, meaning that an energy state cannot hold more than one electron. This non-sharing behavior at normal temperatures leads to electrical resistance. Just as below the boiling point, vapor molecules condense to form water, and below the freezing point, water molecules condense to form ice, {and just as above a certain age, each animal feels an urge to get married,} below the superconducting temperature, electrons marry with each other to form electron pairs. The spin of an electron is half, but the spin of an electron pair is one. Now remember that particles of half-integral spins are ferminons, but particles of integral-spin are bosons. Fermions cannot share an energy state, but bosons do not mind sharing an energy state. This sharing behavior at superconducting temperatures removes electrical resistance.

If a metal bar is surrounded by a conducting wire and electrical current is passed through this wire, the metal bar becomes magnetic. This electromagnetism is what is behind all electrical motors and many other electrical machinery. At normal temperatures, magnetic field lines are inside as well as outside a magnet. This characteristic prohibits a magnet from roaming around freely. It was found that at superconducting temperatures, magnetic field lines cannot pass inside a magnet. This characteristic allows a magnet to roam around freely and to levitate as shown in the above video.

Superconductivity has lots of applications and is a great subject in itself. For example, MRI machines use superconducting magnets.

For several decades, superconductivity was possible only at very very low temperatures, below 6 degree Kelvin, that is, below -267 degrees Centigrade. Due to superconductivity’s vast applications, physicists and chemists all over the world hunted for the superconductivity at higher temperatures. This hunt has now discovered superconductivity in copper oxide cuprates at temperatures as high as 133 degree Kelvin, that is, -140 degree Centigrade.

Wikipedia article on superconductivity

Nobel Prize in Physics 1913 to Heike Kamerlingh Onnes for his investigations on the properties of matter at low temperatures which led, inter alia, to the production of liquid helium

Nobel Prize in Physics 1972 to John Bardeen and Leon Neil Cooper and John Robert Schrieffer for their jointly developed theory of superconductivity, usually called the BCS-theory

Nobel Prize in Physics 2003 to Alexei A. Abrikosov and Vitaly L. Ginzburg and Anthony J. Leggett for pioneering contributions to the theory of superconductors and superfluids

Wikipedia article on high-temperature superconductivity

The Path of No Resistance: The Story of The Revolution in Superconductivity by Bruce Schechter, published by Simon and Schuster, 1989

YouTube video on superconductivity-based lavitation [Source of the above YouTube video]

YouTube video on applications and hunt for high-temerature superconductors

### Josephson Effect

Let us consider two superconductors separated by an insulating plate. Let us now consider that an electrical current is passed through one of the two superconductors.

According to classical physics, electrons cannot cross the insulator barrier and get into the second superconductor, and therefore, there will not be any electrical current in the second superconductor.

Based on quantum physics, physicists thought that electrons can tunnel through the insulator barrier, and these electrons would create a little electrical current in the second superconductor.

In 1962, at the age of 22, Brian Josephson predicted that not only electrons but also electron pairs of the first superconductor can tunnel through the insulator barrier, and these electrons would create a high electrical current in the second superconductor.

This was a great prediction. It was confirmed by several experiments only within a year. Josephson was awarded Nobel Prize in Physics for this prediction.

A circuit consisting of two superconductors separated by an insulator is known as a Josephson junction. Circuits of this type have many practical applications in devices for measurements and diagnostics. Some inventors are thinking of designing transistor-type electronic circuits by using Josephson junctions, so as to reduce power consumption and improve the performance. Stay tuned!

Wikipedia article on Josephson effect

Nobel Prize in Physics 1973 (shared) to Brian David Josephson for his theoretical predictions of the properties of a supercurrent through a tunnel barrier, in particular those phenomena which are generally known as the Josephson effects

### Quantum Entanglement

Suppose a particle of zero angular momentum and zero linear momentum decays into two identical particles. According to the law of conservation of angular momentum, one of the two particles will have clockwise angular momentum and the other particle will have anticlockwise angular momentum. According to the law of conservation of linear momentum, one particle will go in one direction and the other particle go in the opposite direction.

Let us say that Alice measures angular momentum or linear momentum or some other property of one of the two particles, and Bob measures the same property for the other particle at exactly the same time as Alice.

According to quantum uncertainty principle, measurement by Alice cannot be predicted with 100% certainty, and likewise, measurement by Bob cannot be predicted with 100% certainty, and therefore, measurements by Alice and Bob need not be correlated. However, if Alice and Bob get different results, that will violate the conservation laws. It is reasonable to assume that the conservation laws are more powerful than the uncertainty principle. According to the conservation laws, Alice and Bob should get the same results. If Alice and Bob get the same results, we would say that the two particles are entangled. This is what is meant by quantum entanglement.

Einstein was skeptical about quantum entanglement. He called it a spooky action at a distance, which was against his belief that nothing can travel at a speed beyond the speed of light.

Many experiments have been performed to find out whether quantum entanglement really exists. Many claims of having seen quantum entanglement have been rejected by reviewers. However, based on claims not disputed so far, quantum entanglement has been noticed for distances of a few miles.

If quantum entanglement is proved to be correct, it will provide a means of secure and instantaneous communication. Quantum communication is currently a great topic of research.

### Quantum Computing

Regular computers currently in use are based on deterministic logic gates. They store and process information in the form of bits. At a given time, a bit can have a value of either 0 or 1, but never both 0 and 1.

Quantum computers will be based on quantum probabilistic gates. They will store and process information in the form of quantum bits, nicknamed as qubits. At any given time, a qubit can have both values of 0 and 1, as allowed by quantum physics principles. Only after a measurement is made, a qubit will display a value of 0 or 1.

Richard Feynman stressed the need of quantum computers for simulating and understanding quantum processes.

An algorithm is a set of steps for finding or computing something. An algorithm, which is possible to run only on a quantum computer is called a quantum algorithm.

In 1994, David Deutsch and Richard Jozsa published a quantum algorithm, which can classify some information much faster than a classical algorithm can do.

Peter Shor published a quantum algorithm, which can factorize a large number, a task almost impossible on a classical computer.

Lov Kumar Grover published a quantum algorithm, which can *detect a needle in a large hay* much faster than a classical algorithm can do.

These and several other algorithms have shown that quantum computers will revolutionize the way we encrypt and process information. Quantum computers will simplify the handling of big data of high volume, high variety, and high velocity.

A few years back, IBM claimed that they have succeeded in building a quantum computer. Their claim was subsequently rejected.

Recently D-Wave, a Canadian company, has built a computer, which they are claiming to be a quantum computer. Google and a few other organizations have jointly purchased one such computer for understanding its operations. At this stage, it is not crystal clear whether this computer is truly a quantum computer.

When our future generations get quantum computers, they will laugh at our current computers the way we are laughing at those old-age computers.

Wikipedia article on quantum computing

David Deutsch's lectures on quantum computing - excellent for algorithms

FAQ on quantum computing - good for understanding applications

## Quantum Computing

- Quantum Principles
- Quantum Entanglement
- Quantum Gates
- Fourier Transform
- Period Factoring
- Grover Algorithm
- Observable
- Continuous Systems
- Spin Qubits
- Current Status