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Revolutions are celebrated when they are no longer dangerous ... ... Pierre Boulez, on !3 Jan, 1989 on bicentennial celebrationof the French Revolution

Lecture IREVOLUTION that began in 1900....

Quantum World is a strange world, a bizarre, mysterious world, where a particle can sometimes behave as a particle andsometimes as a wave. In other worlds, particles, like say electron and wave, say light, or X-rays, are same... By same, we meanthey are described by same laws of physics.

Scientists discovered the quantum world in the beginning of 20th century. It all began with Max Planck ( German Physicist,working in Berlin ) in 1900..... And it took physicists about 25 years to sort it all out and accept it as a NEW theory

It was a Revolution....

Let us understand what we mean by revolution... To understand what is meant by revolution, we need to understand where isthe revolution taking place and what is being affected by the revolution..

If I were to ask you to name some revolutions, let us confine to scientific revolutions.., perhaps most of you will say theinvention of WWW or Einstein’s theory of relativity....

Although both of the above were great revolutionary discoveries, the revolution we will be talking about is the one whichchanged the ”Laws of Physics”. It was not a small change, small modification, but a complete rewriting of laws of physics.

What is meant by Laws of Physics

The language of mathematics reveals itself unreasonably effective in natural sciences.....a wonderful gift which we neitherunderstand nor deserve.. ... Eugene Wigner, 1960

• How do we find the laws.. Guess...

• To check the laws, scientists try to test them in real world, in their laboratories..

• After many testing, the ”guess” gets accepted and becomes a Law.

• Some people continue to doubt the law ( even though the majority accepts it ) and this sets the stage for next revolution...For example, almost all physicists who developed QM did not believe in the validity of their own work... Like Planck,Einstein, Schrodinger, ....

Nature is complex. However, mathematics provides a universal language that reveals secrets of nature, showing its simplicity,universality and common sense symmetries.

Before 1900, the single theory that explained everything related to particles is Newtons’ Theory.

Physics has a history of synthesizing many phenomena into a few theories. We believe that there is one theory ( or perhapsjust one equation ) that can explain everything... THEORY OF EVERYTHING...

Classical World

Let us start with what is known as Newtonian Period or Newtonian Science ( 1700-1900). Sir Isaac Newton explained howparticles move... ” Laws of Motion”. (Very delightful link on the course web site, ” Tycho, Kepler, and Newton : a Story in theProgress of Science”).

In those days, Sir Isaac Newton’s theory could explain motion, sound, heat etc.... For example, phenomena of sound can beunderstood as motion of atoms in the air... Heat is also related to random motion of particles... So it is all Newton’s theory...,heat sound and motion of planets or anything else..

After the synthesis of the phenomena of motion, sound and heat, there was discovery of a number of other phenomenathat we call electrical and magnetic. In 1873 these phenomena were synthesized with the phenomena of light, and in fact all

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other radiations like X-rays, ultraviolet, radio waves... There is a single theory that describes all these, theory by James ClerkMaxwell: (13 June 1831 5 November 1879) was a mathematical physicist.

You might wonder what light has to do with electric and magnetic phenomena. It turns out light or X-rays are waves thattravel in vacuum ( unlike sound waves that require medium like air ) and these waves are made up of oscillating electric andmagnetic fields... ( will talk more about it later...)

Summary

In Classical world, there are three laws

(1) Newton’s Equations: Laws of Motion...(2) Maxwell’s Equations: Laws of Electricity and Magnetism(3) Laws of Gravity

First two were understood.. but theory of gravity remain unexplained. In fact even today, we do not understand gravity...There are many experiments where they are trying to detect gravitational waves ( Interesting book, ”Einstein’s UnfinishedSymphony: Listening to the Sounds of Space-Time by Marcia Bartisuak.

Can you think of some phenomena that you believe falls outside these theories.. ( except beauty, love.. sorry, happiness..)

IMPORTANT NOTE: Einstein’s Theory of Relativity: Was it a Revolution ??

Proposed in 1905 ( called special theory of relativity ) and General theory of Relativity (1916) were not revolutionarytheories.. There were considered extension of Newton’s theory to particles moving close to speed of light.... Just a brief notethat General theory of Relativity is the key to GPS... something Einstein may not have throughout about...

It can be viewed as a kind of mini-revolution, as speed of light emerged as the largest speed possible in Newtonian world, insome sense linking particles and light.

Brief Introduction of Einstein’s theory

The key point was the idea of ”space-time”, space and time are correlated and mathematically treated on equal footing. Also,E = mc2.

Special Theory of Relativity

(1) The speed of light in a vacuum is the same for all observers, regardless of their relative motion or of the motion of the lightsource. That means, two individuals, traveling on two trains moving in same direction will not feel that they are not moving...

(2) Relativity of simultaneity: Two events, simultaneous for one observer, may not be simultaneous for another observer ifthe observers are in relative motion.

(3) Time dilation: Moving clocks are measured to tick more slowly than an observer’s ”stationary” clock.

(4) Length contraction: Objects are measured to be shortened in the direction that they are moving with respect to theobserver. Mass-energy equivalence: E = mc2, energy and mass are equivalent and transmutable. Maximum speed is finite: Nophysical object, message or field line can travel faster than the speed of light in a vacuum.

General Theory of Relativity

General relativity is a theory of gravitation developed by Einstein in the years 1907-1915.

Einstein first proposed that space-time is curved. In 1915, he devised the Einstein field equations which relate the curvatureof space-time with matter and energy.

General relativity generalizes special relativity and Newton’s law of universal gravitation, providing a unified description ofgravity as a geometric property of space and time, or space-time. In particular, the curvature of space-time is directly related to

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FIG. 1: Schematic diagram of space-time curvature

the energy and momentum of whatever matter and radiation are present. The relation is specified by the Einstein field equations.

Rab =1

2Rgab = −8πGTab (1)

The above equation means that ”space-time curvature = energy density”. R and g describe the structure of space-time and Tmatter or energy that determines this structure.

NOTE: YOU DO NOT NEED TO UNDERSTAND THIS EQUATION. However, you may find it fascinating that these fewweird symbols encode all the complexity of the theory and that is what physicist call ”Mathematical Beauty”.

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Some of the consequences of general relativity are

(1) Orbits precess in a way unexpected in Newton’s theory of gravity. (This has been observed in the orbit of Mercury and inbinary pulsars).

(2) Rays of light bend in the presence of a gravitational field.

Classical World (1700-1900)(1) Newton’s Laws of Motion

(2) Maxwell’s Equations (light, electric and magnetic phenomena)(3) Gravitational Laws ( not understood)

Quantum World (1900- present)

NOTE: Einstein’s Theory of relativity is part of classical worldJames Clark Maxwell

1831-1879

Sir Isaac Newton1642-1726

Max Planck1853-1947 Albet Einstein

1879-1955Ervin Schrodinger

1887-1961Werner Heisenberg

1901-1976P.A.M. Dirac1902-1984

Gravitational Laws ( not understood): Waiting for Next Revolution

Quantum Mechanics (QM)

Quantum Field Theory (QFT)

QM replaces Newton’s equations

QFT replaces Newton+Maxwell’s equations

Quantum World: 1900-....

It was a revolution. The equations are not simple extension of Newton’s equations... Unlike Relativity which did not introduceany new ” Physical Constant”, quantum theory is fundamentally different as it introduced a new physical constant,

Planck’s constant...h or ~ = h/(2π).

h = 6.62606957(29) · 10−34 ( Joule-sec)(How many joules in 1 calories? The answer is 4.1858.)

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Quantum effects are not seen in macroscopic world because the constant h is very very small. One sees these quantum effectsas we try to peek inside the atom.

It turns out that one has to lose one’s common sense in order to perceive what is happening at the atomic level. The newtheory that replaced Newton’s equations was introduced in 1926. It is called Quantum Mechanics that replaced NewtonianMechanics. The world ”quantum” refers to a rather peculiar aspect of nature that goes against common sense. It is this aspectthat we are going to talk in this course.

Remark: We note that quantum mechanics could not explain how particle and radiation interact with each other. It turns outthat one has to change Maxwell’s theory in accordance with quantum mechanics and this new theory can explain light, particlesand their interaction. It is called Quantum Field Theory, which is beyond the scope of this course.

SUMMARY of HISTORY OF QUANTUM PHYSICS ( You may skip this summary)

• In 1900 Max Planck discovered that the radiation spectrum of black bodies occurs only with discrete energies separatedby the value hf , where f is the frequency and h is a new constant, the so-called Planck constant.

• A few years later Albert Einstein used this discovery in his explanation of the photoelectric effect. He suggested that lightwaves were quantized, and that the amount of energy which each quantum of light could deliver to the electrons of thecathode, was exactly hf .

• The next step came in 1911 when Ernest Rutherford performed some experiments shooting alpha particles into a gold foil.Based on these results he could set up a model of the atom in which the atom consisted of a heavy nucleus with a positivecharge surrounded by negatively charged electrons like a small solar system.

• Rutherford model was in conflict with the laws of classical physics. According to classical mechanics and electrodynamicsone might expect that the electrons orbiting around a positively charged nucleus would continuously emit radiation sothat the nucleus would quickly swallow the electrons.

• At this point Niels Bohr entered the scene and soon became the leading physicist on atoms. In 1913 Bohr, visitingRutherford in Manchester, put forward a mathematical model of the atom which provided the first theoretical supportfor Rutherford’s model and could explain the emission spectrum of the hydrogen atom. The theory was based on twopostulates:

(1) An atomic system is only stable in a certain set of states, called stationary states, each state being associated with adiscrete energy, and every change of energy corresponds to a complete transition from one state to another.

(2) The possibility for the atom to absorb and emit radiation is determined by a law according to which the energy of theradiation is given by the energy difference between two stationary states being equal to h.

• Bohr model ran into problems, nonetheless, when one tried to apply it to spectra other than that of hydrogen. So there wasa general feeling among all leading physicists that Bohr’s model had to be replaced by a more radical theory.

• In 1925 Werner Heisenberg, at that time Bohr’s assistant in Copenhagen, laid down the basic principles of a completequantum mechanics. In his new matrix theory he replaced classical commuting variables with non-commuting ones.

• The following year, Erwin Schrdinger gave a simpler formulation of the theory in which he introduced a second-orderdifferential equation for a wave function.

• Schrodinger could not explain the meaning of the wave function. However, already the same year Max Born proposed aconsistent statistical interpretation in which the square of the absolute value of this wave function expresses a probabilityamplitude for the outcome of a measurement.

• Paul Dirac obtained relativistic generalization of Schrodinger theory, that is replaced Einstein’s theory with a new theorythat is consistent with both relativity and Quantum mechanics.

• Finally Feynman, Schwinger and Tomonaga in 1948 generalized Maxwell’s equations in accordance with quantum me-chanics. New theory called ” Quantum Field Theory” can explain interaction of matter and radiation.

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NEXT REVOLUTION...

Present Theory is inadequate... There will be a next revolution.. When.. We do not know... Newtonian physics survived for200 years... How long Quantum Physics will survive, It has survived little more than 100 years... By that we mean there hasbeen NO experiment that has violated the theory

Although there has been no violation of the theory, it cannot explain gravity??

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Lecture II

Quantum World is a strange world where a particle can sometimes behave as a particle and sometimes as a wave. In otherwords, particles and waves have dual personality. A particle is an object so small that its size is negligible; a wave is a periodicdisturbance in a medium. These two concepts are so different that one can scarcely believe that they could be confused. Inquantum physics, however, they turn out to be deeply intertwined and fundamentally inseparable.

We note that almost all Nobel prizes in Physics ( since its beginning in 1901 )has been award in Quantum Science. The firstNobel prize was for discovery of X-rays and you will learn soon what it has to do with Quantum science.

To comprehend the Quantum world, we begin with what we know about particles and waves. In other words, we will beginby talking about particles and waves in our familiar world, that is the ”Classical” world which is described by rules of classicalphysics.

CLASSICAL PHYSICS- Particles and Waves

The term classical physics was coined in the early 20th century to describe the system of physics begun by Isaac Newton( 1643-1727) and many contemporary 17th century natural philosophers, building upon the earlier astronomical theories ofJohannes Kepler, which in turn were based on the precise observations of Tycho Brahe and the studies of terrestrial projectilemotion of Galileo.

It should be noted that Einstein’s theory of relativity, is also part of Classical physics, it represents classical physics in itsmost developed and most accurate form.

PARTICLES: The Classical or Newtonian physics, is solely based on one single mathematical equation that describes themotion of the particle. This equation, known as Newton’s equation says that Force acting on a particle is equal to its mass mtimes acceleration.

F = ma (2)

The beauty of this equation is, it applies to all particles, no matter whether it is on the earth, or in space or on Mars. It appliesto all kinds of forces, such as gravitational force or electric or magnetic force.

WAVES: In physics, a wave is disturbance or oscillation that travels through matter or space, accompanied by a transferof energy. Wave motion transfers energy from one point to another, often with no permanent displacement of the particlesof the medium-that is, with little or no associated mass transport. They consist, instead, of oscillations or vibrations aroundalmost fixed locations. Waves are described by a wave equation which sets out how the disturbance proceeds over time. Themathematical form of this equation varies depending on the type of wave.

There are two main types of waves

(1) Mechanical waves propagate through a medium. Examples are sound waves and water waves. Sound waves propagate viaair molecules colliding with their neighbors. When air molecules collide, they also bounce away from each other . This keepsthe molecules from continuing to travel in the direction of the wave. Wave equation in this case can be obtained from Newton’sequation.

(2) Electromagnetic Waves: The second main type of wave, electromagnetic waves, do not require a medium. Instead, theyconsist of periodic oscillations of electrical and magnetic fields generated by charged particles, and can therefore travel througha vacuum. These waves include radio waves, microwaves, infrared radiation, visible light, ultraviolet radiation, X-rays, andgamma rays. These waves are described by equations called Maxwell’s equations which cannot be obtained from Newton’s law.

Unit of Frequency: Heinrich Rudolf Hertz (German: 22 February 1857 1 January 1894) was a German physicist who firstconclusively proved the existence of electromagnetic waves theorized by James Clerk Maxwell’s electromagnetic theory of light.

Intellectual crisis of 20th Century : Birth of QUANTUM THEORY

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frequency = 1/period

velocity=frequency * wavelength

FIG. 2: Characterization of Waves: Amplitude A, wave length λ, frequency f , period T , velocity v.

(A) Radiations from hot objects cannot be explained by classical theory

(B) Planetary Model of Atom: It is unstable

Detail Historical account: ” A Revolution with No Revolutionaries: Planck-Einstein Equation for the Energy of a Quantum,by Graham Farmelo ( supplementary material I ).

QUANTUM PHYSICS- WAVE PARTICLE DUALITY

Distinguishing Particles and Waves in an Experiment

Two-Hole ( Double Slit ) experiment

In a macroscopic world, we can look at the particle and wave and there is NO further testing needed to determine theircharacter. However, in microscopic world, where we cannot see the ”electron” or ”proton” , how do we know whether it is aparticle or wave.

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speed of light, c = 300,000,000 meter/s = 3.10^8 m/s=186,000 miles/s

Velocity of Sound =340 meter/sec

FIG. 3: Electromagnetic Spectrum: ”nm” stands for unit of Wave length in Nano Meters. For example, 800nm = 8 · 10−6m.

Experiment, called Two-hole or double slit experiment can distinguish particles and waves. Feynman’s video, and the text (supplementary material II ) are perhaps the best resource for this important topic.

Home Work Assignment

Watch the video 1 and submit five questions and five comments based on the video.

(Video 1) Double Slit Paradox by Richard Feynman[2]

You may also watch the following video,

(Video 2) Quantum Physics and Microscopic Universe[3]

This includes double slit or Two hole experiment at time intervals10-20 minutes ( over lap with first video) .

This video goes beyond the scope of this course after about half-hour and has the following format

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0-10 minutes: Quantum Entanglement and Quantum Computer10-20 Two hole Experiment18-23 Uncertainty principle23-25 Quantum Tunneling————————————-

The following topics will not be covered in this course25-28 Parallel Universes28-33 Dark Matter33-34 WIMP ( Weakly interacting massive particles ): May exist at very small size or another dimension36 String theory: All particles are vibrations of tiny loops39 Plank length: size of the string; If we blowup H-atom to the size of the observable universe, we may see the Plank length andstrings.41-42: Grid in space time, space-time are emergent phenomena

(Video 3) No ordinary genius: A very delightful Video about Richard Feynman: [4]

[1] http://www.learner.org/courses/physics/unit/text.html?unit=5&secNum=3[2] <https://www.youtube.com/watch?v=hUJfjRoxCbk>[3] <https://www.youtube.com/watch?v=PpQdMM6Vr70>[4] <https://www.youtube.com/watch?v=Fzg1CU8t9nw>