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Einstein, Notes and diagrams
Eun Ju Choi

Content

Preface

Einstein is the chief architect of 20th century physics. He was often called "the prince of physicists" , "the master guru of science" and "the father of the Atomic Age". Albert Einstein is indisputably a towering figure not only of the world of science but also of the 20th century culture. His theories, first thought to be bizarre and unreal, have survived triumphantly the rigorous tests of many and elaborate experiments. Much of his work had produced spin-offs that touched many aspects of our lives. Amongst them are nuclear energy, nuclear weapons, lasers, black holes and an expanding universe. It is strange that Einstein's science is more relevant today than during his lifetime. It has also literally touched everyone's life in one way or another. This is the main reason why every educated person must have a sense of the Einstein heritage.

Einstein's human side is just as rich and colorful yet unfortunately it is so often ignored or misunderstood. He was the eccentric genius with sheepdog like hair, dressed in baggy clothes and refusing to wear socks. A simple man full of humanity and humility, he detested materialism and believed in a God for all nature rather than an anthropomorphic God who cares only about the sins and problems of humans. A life-long pacifist, he disliked the military and fought passionately to bring about a nuclear disarmament. His position on many social issues is as much appropriate today as it was in his lifetime.

Biography

1879

Albert Einstein was born to a middle-class German family of Jewish ancestry. He was born with deformed head. His parents were concerned that he did not learn to talk until the age of three, but he was not so much a backward as a quiet child. He would build tall houses of cards and hated playing soldier. At the age of five he was fascinated with magnetic compass. He also learned the love for music and learned violin from his mother which companyed him through all his life. At the age of twelve he was fascinated by a geometry book.

1895

AT the age of fifteen Albert quit high school, disgusted by rote learning and martinet teachers, and followed his family to Italy where they had moved their failing electrotechnical business. After half a year of wandering and loafing, he attended a congenial Swiss school. The next year he entered the Federal Institute of Technology in Zurich.

1900

After working hard in the laboratory but skipping lectures, Einstein graduated with an unexceptional record. For two grim years he could find only odd jobs, but he finally got a post as patent examiner. He married a former classmate.

1905

Einstein wrote three fundamental papers, all in a few months. The first paper claimed that light must sometimes behave like a stream of particles with discrete energies, "quanta." The second paper offered an experimental test for the theory of heat. The third paper addressed a central puzzle for physicists of the day -- the connection between electromagnetic theory and ordinary motion -- and solved it using the "principle of relativity."

1909

Einstein became an assistant professor at the University of Zurich, his first full-time physics job. In 1911 he moved on to the German University of Prague. He continued to publish important physics papers, and was beginning to meet fellow scientists, for example at the exclusive Solvay Conference. The next year he returned to the Federal Institute of Technology in Zurich as Professor.

1914

Einstein moved to Berlin, taking a research post that freed him from teaching duties. He separated from his wife and two sons. When the First World War broke out, Einstein rejected Germany's aggressive war aims, supporting the formation of a pacifist group.

1915

After a decade of thought, with entire years spent in blind alleys, Einstein completed his general theory of relativity. Overturning ancient notions of space and time, he reached a new understanding of gravity. Meanwhile he continued to sign petitions for peace.

1918

As Germany collapsed, Einstein became more involved in politics and supported a new progressive party. The next year he remarried. And his general theory of relativity received stunning confirmation from British astronomers: as Einstein had predicted, gravity bends starlight. In the popular eye he became a symbol of science and of thought at its highest.

1921

Aided by his fame, Einstein championed the fledgling German republican government and other liberal causes. Partly as a result of this, he and his theory of relativity came under vicious attack from anti-Semites. He began traveling, attended an International Trade Union Congress in Amsterdam, and visited the United States to help raise funds for the Hebrew University in Jerusalem. The following year he received the Nobel Prize.

1924

Einstein contributed to the struggling new quantum theory. Meanwhile he searched for a way to unify the theories of electromagnetism and gravity. In 1929 he announced a unified field theory, but the mathematics could not be compared with experiments; his struggle toward a useful theory had only begun. Meanwhile he argued with his colleagues, challenging their belief that quantum theory can give a complete description of phenomena.

1933

Unwilling to live in Germany under the new Nazi government, Einstein joined the Institute for Advanced Study in Princeton, New Jersey. He turned away from strict pacifism, and warned world political leaders to prepare for German aggression. He also worked to rescue Jewish and other political victims of the Nazis.

1939

Einstein signed a letter that informed President F. D. Roosevelt of the possibility of nuclear bombs, warning that the Germans might try to build them. The next year Einstein became an American citizen.

1952

Einstein was asked to become the second President of the State of Israel, but declined. He was supporting many causes, such as the United Nations and world government, nuclear disarmament, and civil liberties.

1955

The search for a true unified theory -- for a more profound understanding of nature -- continued to fill Einstein's days. While corresponding about a new antiwar project and writing a speech for Israel, he was stricken and died.

Physics before Einstein

Gravity

• Aristotle:

• Galileo:

• Newton:

  • Too small canon ball will fall down, too big canon ball will permanently leave the earth but idealized right speed will set the ball in orbit

  • Gravity is a universal law. The same force of gravity that makes an apple fall keeps the moon in orbit.

  • Force of attraction : masses attract each other. the bigger mass has more gravity. as the distance increase the gravity become smaller.

  

  F=(Gm*M)/r**2

  F=force of gravity, G=constant, M and m=mass, r=distance between M and m

Light

SPEED OF LIGHT C = 3 exp 8 meter/sec

• Newton

  

• Maxwell

  • discovered that light is an Electromagnetic Wave.

  • Electromagnetic means that the characteristic of each light have electricity.

  • All the waves have to have a medium to travel through (ex: sound waves need air to travel through). Then, there must be a medium which is very rigid but so light that is responsible for transmission of light waves.

The Mystery of the Ether

Ether was thought to be the substance responsible for the transmission of light. It was thought to be everywhere, even in space. It was suspected to be very thin since we cannot feel it and with rigidity of thousand times that of steel to generate the speed of light.

The Earth in Ether

Beams of light are expected to have different speeds in different directions depends upon the streams of ether.

Michelson and Morley Experiment to prove the existence of the ether -- proved to be death certificate of Ether

• Fringes : caused by interference of the two lights

• If the speed of light changes the pattern of fringe will change.

• Expectation: Fringe pattern will change as apparatus was rotated which means that two light beams were to change orientation with respect to Ether.

• Result: Fringe pattern remained unchanged which means beams of light have always same speed.

Energy

The "Earthquake' OF 1896

• X - rays( by a German scientist Roentgen)

• The Electron (by Thomson)

• Radioactivity (by Curies and Bequerel)

19th century believed Law of Conservation of Energy : "Energy cannot be created out of nothing, nor can be destroyed." However, this Law of Conservation of Energy was threatened by the discovery of radioactivity.

The mystery of Radioactivity

• Where does the energy come from?

• Does this violate the Law of Conservation of Energy?

• This radioactivity can be explained by Einstein's E=mc

Special Relativity

1905, The Special Theory of Relativity

Special = limited

Postulates

• All laws of nature remain the same in inertial frames of reference.

• No matter how-or-who measures the speed of light is always the same.

Ramification

• "Death" of universal NOW

  "We are not only separated by distance but also by time"

• Death of Simultaneity

  Andrew .. Simultaneous explosion of the stars A and B
  Mary .. A ------> B
  Peter.. B ------> A
  All are right from their perspective

• Time dilation

  • The faster a clock will travel the slower it will tick. Because the speed of light is the same no matter how fast a clock travel.

    

  • Speed = Distance / time , time = Distance / speed = 2d / c , c = speed of light

  • time for an event = pulse of light to go up and down

    

  • rocket with light clock

  • time for the event (pulse of light to go up and down) = 2D / c

Experiments that prove time dilation

• Atomic clocks placed one on North Pole and one on equator

  the clock on equator moves faster by 900mph

• One atomic clock on the ground and one on a 747 plane

  the clock on the plane runs slower

• using particles called muons

  Birth and death at a lab which is stationary : 10 exp-6 s (one millionth of second)

  Muons' life in motion(in a accelerator machines at 95% of speed of light)

  extended by 1000 (10 exp-3 s : thousandth of second)

• Space contraction

  space shrinks in the direction of motion.

  the faster the motion, the more the shrinkage

  "space" must be viewed as spacetime. Time and space are affected by high speed.

  • EX) Muons are born in the upper atmosphere by cosmic rays

  • We know their life is 10 exp -6 seconds

    

  • Explanation : Because the muons move at high speeds, their "clocks" slow down, therefore they live long enough to reach the earth - Time dilation. On the other hand, from muons point of view, space contract. They live normal life but, the atmosphere appears shrunk because of their high speed.

• E = mc

  Energy and mass are manifestations of the same thing. Energy can become mass and mass can become energy. This can be proved by radioactivity (mass -- energy), nuclear energy (mass -- energy), energy from a star (mass -- energy) and Big-Bang model of universe (energy -- particles -- Galaxies)

General Relativity

1915, The General Theory of Relativity : A new theory about gravity

Postulates

• The Principle of Equivalence : "It is impossible to distinguish between the force of gravity and the force caused by acceleration.

  EXAMPLE: A spaceship without window is traveling at constant speed. All of sudden the astronaut find himself standing on the floor. This can be caused either by force of acceleration or by force of gravity. The astronaut cannot distinguish the two different force.

  

  

  E = mc, then, m = E/c : mass equivalent for light

  Eddington (astronomer), in 1919, proved that light from a star is bent by the gravity of the sun. He observed the position of a certain star during a total eclipse. He found it to be displaced. This was so because its starlight was bent by the gravity of the sun.

  

• Impact of gravity on light

  • It can change its path (Eddington, 1919)

    

    Black Holes

    • no light can escape them due to super strong G.

    • condensed "corpses" of giant stars

  • "color" of light

    • Gravitational Red Shift

    • As a beam of light escape gravity it changes color from blue(high energy) to red(low energy). Because it has to spend energy to escape gravity. However, the speed of light stays the same.

  • curved space (3-D space + time + gravity): the more the curvature, the stronger the gravity and the slower the clock

Nuclear energy

1832, M. Faraday in England produced Electricity by moving a magnet inside a coil. All power plants that produce electricity use the same method -- coils spinning inside magnets. The sources of power that make the coils spin are various including windmill, waterfall, and steam turns turbines. Steam to turns turbines are generated by burning coal(70%), by burning oil, and nuclear fission(20%). Nuclear fission split atoms which produce heat then, this heat is used to heat up steam. Nuclear is becoming a major source of our electricity.

Science behind Nuclear Energy

• Electron - (negative electric charge)

• Proton +

• Neutron (Proton and Neutron make Nuclear)

Rules of Atom : must be electrically neutral

• # of Electrons = # of Protons (Atomic number)

• # of (Protons + Neutrons) = Mass number

EXAMPLE: Uranium : 238-U-92
238: mass number
92: Atomic number
: this means Uranium has 92 Electrons and 92 Protons
(238 - 92) = 146 Neutrons

EXAMPLE: Carbon 12-C-6

Isotopes:

• 6 electrons, 6 neutrons, 6 protons

• 14-C-6 : 6 electrons, 6 protons, 8 neutrons

Isotopes : Atoms with identical, physical and chemical properties which means same number of electrons(protons) but have different number of neutrons.

EXAMPLE: Uranium isotopes

• 238-U-92 (most abundant)

• 235-U-92 (used in nuclear fission)

EXAMPLE: Hydrogen isotopes

• 1-H-1 Protium

• 2-H-1 Deuterium (used for nuclear fusion)

• 3-H-1 Tritium (used for nuclear fusion)

  H-2-O = water, Heavy water made with 2-H-1 is used for nuclear energy

Nuclear Fission : process in which an unstable nucleus splits in two smaller nuclei accompanied by the release of energy using 235-U-92 as fuel. This split is only possible by using neutron as a bullet.

these three neutrons will cause chain reaction of splitting atoms.

Nuclear Fusion : process in which two smaller nuclei combine to form a new larger nucleus and the release of energy by using Hydrogen. Hydrogens are abundant and cheap. However, this process requires 10 million degree of heat( C) which challenges current technology.

Radioactivity

first discovered in 1896

• Alpha particle (2P and 2N) (*)

• large unstable nucleus

• Beta particle (*)

• Gamma rays (*)

(*) 3 forms of Radioactivity

Ionization
Atom missing one or more electrons --- Ion
Ionization can be caused by either extreme heat or collisions.
All forms of Radioactivity can cause ionization.
Alpha : most ionizing, least penetration
Gamma : least ionizing, most penetrating

Background of Radioactivity
Geiger counter : instrument to detect radioactivity
MREM : Millirem (unit of radioactivity, as far as damage to human body) Roentgen Equivalent Man

Maximum allowed for worker in nuclear plant is 3 - 5000 MREM/yr.

• Cosmic rays from outer space : 45 MREM

• Soil : 20

• Water, food, air : 25

• Home Brick : 50 - 100

• concrete : 70 - 100

• wood : 30 - 50

• chest x - ray : 20

• trip to Europe from USA : 5

• ----------------------------

• Average total 2 - 300 MREM

Uses of Radioactivity

• Medical

  • kill cancerous cell using Cobalt 60 - gamma rays

  • Diagnostic purpose by injecting Radioactive liquids internally Target organ under examination which now gives off gamma rays

• Industrial

• Food Sterilization

• Archeology : Carbon dating system

Stellar Evolution

• The story of the Universe -- Cosmology

  

  • Aristotle - Earth is the center of the universe (Geocentric) Ptolemy supported Aristotle but in Epicycles

    

  • Copernicus, in 1543, proposed Heliocentric model - Sun is the center

  • Galileo ("the Father of modern Science) supported Heliocentric model

  • Newton proved the Copernican model

  Bishop Usher in 17th century said the universe began 4004 B.C. Tuesday 9:00 by interpreting the bible. But science tells us the universe is 14 billion years old.

• Information in star light-beam

  location, how far away, chemical composition, temperature, age, speed, rotation speed and possibly surrounding planets.

  

  Galaxy is a cluster of stars. The Milky way is the name of our galaxy estimated to have 100 billion stars. It will take 120,000 LY to cross. LY which stands for Light Year is a unit of distance that light will travel in one year.

• Age of our universe

  1929, Hubble discovered universe is expanding by observing light of galaxy and analyzed. He measured the rate of expansion and by using this rate backward he proved that the universe is 14 billion years old.

  

  Hydrogen spectrum on galaxies was found to be shifted to the red which is called Dopper Red Shift. This phenomenon can be explained only if the galaxy is moving away.

Cosmological theories

• The Big-Bang Model : Birth of universe

  

  

  

  

  • Energy expands ( universe is born -- space and time begin)

  • Leftover radio signals -- temperature one that relates to -270 C (3 K) : very cold

  • Penzias and Wilson accidentally discovered leftover radio signals from Big-Bang from satellite communications and won the Nobel Prize in 1965

• The Death of the Universe

  • Open universe model

    Expansion continues -- universe will get colder -- stars will dim

  • Closed universe model

    Expansion slows down -- stops -- universe begins to condense -- (collapse)

    if there is enough dark matter

  • Oscillating universe

    universe will expand and condense back then, start all over again ... go round

• The "Birth" and the "Death" of a Star

  • Embryo stage -- self generated gravity causes cloud to condense into itself and not shining yet

    

  • Stable -- Nuclear fussion takes place, gravity fight expansion created by nuclear fusion, 10 - 15 million degrees

    

  • Red Giant -- first step to death

    

  • Nebula -- small stars are formed, our sun is at this stage

    

    Our sun ends in Nebulas stage

    It has been in stable stage for 5 billion years and will stay for another 5 billion years.

  • Super Nova -- factory of all heavy atoms like metals

    

Lasers

"Laser" - Light Amplification by Stimulated Emission of Radiation

Ordinary light : incoherent light -- different colors going in different directions and mixture of many different colors

Laser light : Electrons can perform a unique dance called Metastable state. This produces coherent light which is pure(-only one color) and moves in step in one direction.

Einstein discovered that light stimulated other atoms to give off similar light : Light is Amplified. This discovery leads to the discovery of laser light.

Quantum theory and Unified field theory

The "Failure" of Einstein in Science

• The use of the cosmological constant in general theory of Relativity

  The universe was static. After Hubble's discovery, Einstein admitted that he was wrong. Then, he removed the cosmological constant from his theory -- universe is expanding.

• Unified Field Theory -- remained incomplete

  • Gravity

  • Weak Nuclear

    takes place inside nuclear, act like glue.

    second weakest force in nature and related to radioactivity

  • Electromagnetic

    keep electrons to stay in orbit motion

    if electromagnetic does not exist everything will disintegrate because no atoms can exist without this force

  • Strong Nuclear

    keeps nuclear together, without this force the electrical force between same force ( ex; protons with protons) will appulse apart only appears inside nuclear.

• Einstein and Quantum theory

  • 1905 Photoelectric effect (won Nobel prize in 1922)

    "Light comes in particles called protons."

  • 1920 New Quantum Physics

    look for probability rather than defined

    • use of Probability (by Shroedinger)

      mathematical tool in describing nature

      "God does not play dice with the universe," said Einstein

      

    • Uncertainty principle (by Heisenberg)

      no absolute measurements in position and speed of particles.

      "Nature is built on error." -- The act of observation (which involves light) creates errors which cannot be eliminated

      

Einstein's Humanity : Selected Quotes

Humanity

"How strange is the lot of us mortals! Each of us is here for a brief sojourn, for what purpose he knows not, though he sometimes thinks he senses it. But without deeper reflection one knows from daily life that one exists for other people -- first of all for those upon whose smiles and well-being our own happiness is wholly dependent and then for the many, unknown to us, to whose destinies we are bound by the ties of sympathy. A hundred times every day I remind myself that my inner and outer life are based on the labors of other men, living and dead, and that I must exert myself in order to give in the same measure as I have received and am still receiving..."

"I have never looked upon ease and happiness as ends in themselves -- this ethical basis I call the ideal of a pigsty. The ideals that have lighted my way, and time after time have given me new courage to face life cheerful, have been Kindness, Beauty, and Truth. Without the sense of kinship with men of like mind, without the occupation with the objective world, the eternally unattainable in the field of art and scientific endeavors, life would have seemed empty to me. The trite objects of human efforts -- possessions, outward success, luxury -- have always seemed to me contemptible."

"My passionate sense of social justice and social responsibility has always contrasted oddly with my pronounced lack of need for direct contact with other human beings and human communities. I am truly a lone traveler and have never belonged to my country, my home, my friends, or even my immediate family, with my whole heart; in the face of all these ties, I have never lost a sense of distance and a need for solitude..."

"The most beautiful experience we can have is the mysterious. It is the fundamental emotion that stands at the cradle of true art and true science. Whoever does not know it and can no longer wonder, no longer marvel, is as good as dead, and his eyes are dimmed. It was the experience of mystery -- even if mixed with fear -- that engendered religion. A knowledge of the existence of something we cannot penetrate, our perceptions of the profoundest reason and the most radiant beauty, which only in their most primitive forms are accessible to our minds: it is this knowledge and this emotion that constitute true religiosity. In this sense, and only this sense, I am deeply religious man...I am satisfied with the mystery of life's eternity and with a knowledge, a sense, of the marvelous structure of existence -- as well as the humble attempt to understand even a tiny portion of the Reason that manifests itself in nature."

"Knowledge and skills alone cannot lead humanity to a happy and dignified life... Humanity has every reason to place the proclaimers of high moral standards and values above the discoverers of objective truth. What humanity owes to personalities like Buddha, Moses, and Jesus ranks higher than all the achievements of the inquiring and constructive mind."

"It is strange to be known so universally and yet to be so lonely."

Religion and Science

"What I see in nature is a magnificent structure that we can comprehend only very imperfectly, and that must fill a thinking person with a feeling of ‘humility.' This is a genuinely religious feeling that has nothing to do with mysticism.... My religiosity consists in a humble admiration of the infinitely superior spirit that reveals itself in the little that we, with our weak and transitory understanding, can comprehend of reality."

"I want to know how God created this world. I want to know his thought, the rest are details... What really interests me is whether God had any choice in the creation of the world"

"Knowledge of what is does not open the door directly to what should be."

"What characterizes the aspirations of a person who gives me the impression of being religious: a person who is religiously enlightened appears to me to be one who has, to the best of his ability, liberated himself from the fetters of his selfish desires and is preoccupied with thoughts, feelings, and aspirations to which he clings because of their superpersonal value.

"Science can only ascertain what is, but not what should be, and outside of its domain value judgments of all kinds remain necessary. Religion, on the other hand, deals only with evaluations of human thought and action: it cannot justifiably speak of facts and relationships between facts... Science can only be created by those who are thoroughly imbued with the aspiration toward truth and understanding. This source of feeling, however, springs from the sphere of religion. To this there also belongs the faith in the possibility that the regulations valid for the world of existence are rational, that is, comprehensible to reason. I cannot conceive of a genuine scientist without that profound faith. The situation may be expressed by an image: science without religion is lame, religion without science is blind."

Education :Education for Independent Thought

From the New York Times, October 5, 1952.

"It is not enough to teach man a specialty. Through it he may become a kind of useful machine but not a harmoniously developed personality. It is essential that the student acquire an understanding of and a lively feeling for values. He must acquire a vivid sense of the beautiful and of the morally good. Otherwise he--with his specialized knowledge--more closely resembles a well-trained dog than a harmoniously developed person. He must learn to understand the motives of human beings, their illusions, and their sufferings in order to acquire a proper relationship to individual fellow-men and to the community. These precious things are conveyed to the younger generation through personal contact with those who teach, not--or at least not in the main--through textbooks. It is this that primarily constitutes and preserves culture. This is what I have in mind when I recommend the "humanities" as important, not just dry specialized knowledge in the fields of history and philosophy. Overemphasis on the competitive system and premature specialization on the ground of immediate usefulness kill the spirit on which all cultural life depends, specialized knowledge included. It is also vital to a valuable education that independent critical thinking be developed in the young human being, a development that is greatly jeopardized by overburdening him with too much and with too varied subjects (point system). Overburdening necessarily leads to superficiality. Teaching should be such that what is offered is perceived as a valuable gift and not as a hard duty."

"All our lauded technological progress -- our very civilization -- is like the ax in the hand of the pathological criminal."

Politics

"My political ideal is democracy. Let every man be respected as an individual and no man idolized. It is an irony of fate that I myself have been the recipient of excessive admiration and reverence from my fellow beings, through no fault, and no merit, of my own. The cause of this may well be the desire, unattainable for many, to understand the few ideas to which I have with my feeble powers attained through ceaseless struggle. I am quite aware that for any organization to reach its goals, one man must do the thinking and directing and generally bear the responsibility. But the led must not be coerced; they must be able to choose their leader. In my opinion, an autocratic system of coercion soon degenerates; force attracts men of low morality...The really valuable thing in the pageant of human life seems to me not the political state, but the creative, sentient individual, the personality; it alone creates the noble and the sublime, while the herd as such remains dull in thought and dull in feeling."

"The topic brings me to that worst outcrop of herd life, the military system, which I abhor... This plague-spot of civilization ought to be abolished with all possible speed. Heroism on command, senseless violence, and all the loathsome nonsense that goes by the name of patriotism -- how passionately I hate them!

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