Lecture 26 Review of Course

The Great Ideas of Physics General Comments • What have we done this semester? t A Review 1 • We have studied the most important developments in physics, t2 t 4 stressing conceptual understanding. A A 34 12 Quantum • Science since antiquity (mostly Western) Mechanics • Revolutions in thought: t3 • Scientific Method, Classical Physics ~ 1300 – 1900 • Space-Time, Q u an tum B e h a vi o r Classical Key advances 1900 - 1930 Physics • This review does NOT cover the entire semester in detail • We have had two previous summaries. • Today: The overall picture Relativity More detail on the last part of the course: Quantum mechanics and the last 2 lectures.

Scientific Knowledge Timeline • Framework for Understanding: Asia, Egypt Middle “Modern” Greece, Rome Ages Renaissance Physics • “Logical Approach” Mesopotamia • Induction vs. Deduction (Bacon vs Descartes) Al-Khawarizmi Copernicus • The Problem of Induction: How to go beyond a collection of facts to new concepts? -1000 0 1000 2000 Plato Ptolomy • The problem of Deduction: How to demonstrate that an Fibanacci abstract idea applies to nature? Aristotle Galileo • “Historical Approach” Erastosthenes Euclid Gutenberg Kepler Aristarchus Printing Press • Normal science → crisis → extraordinary science (Kuhn) Franklin Ampere Maxwell • Paradigm Newton Coulomb Faraday • Anomalies exist only in the context of a paradigm • Revolution leads to a new paradigm 1600 1700 Volta 1800 1900 • We have followed historical approach • “Classical Physics” was complete around 1880 • Documented “Revolutions” • Set stage for understanding the way science worked and • See Timeline description of lives of various works in practice scientists on WWW pages.

Astronomy The Copernican Revolution • Initial Paradigm: The Two-Spher e U n i v e r s e • The Renaissance was a “rebirth” of knowledge in • Large sphere containing the stars on its surface many ways rotates about a small sphere, the Earth, with a period = 1 day. • Science and especially physics was at the center • Anomaly: The Problem of the Planets • Re-examination of the “ultimate questions” of cosmology • Five planets exhibit anomalous (within 2 sphere and the “practical questions” of understanding what we paradigm) motion. ie for some part of the year, observe in nature planets go “backwards”. • Is the earth the center of the universe or only a • Normal Science Response: Ptolemy → Tycho planet orbiting the sun? • Planets move on circles (epicycles) centered on another circle (deferent = Sun for Tycho) which • Ptolomy vs. Copernicus moves uniformly around the Earth. • Resolved by the simple description of Kepler, the earth and • Extraordinary Response: Copernicus → Kepler other planets move in ellipses • Copernicus: All planets (including the Earth) move • Copernican revolution about the Sun. • Kepler: abandons paradigm of uniform circular • Affects our understanding of our place in the motion: Elliptical orbits (Sun at one focus) with a universe – our world view varying speed (equal areas in equal times)

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The Classical Revolution The Classical Revolution • Continuing the Copernican revolution • Newton and Maxwell define “Classical Physics” • How do we understand motion on earth? • Newton’s Three Laws • Galileo (mathematician) introduces the experimental • Inertia: method and quantitative mathematical analysis • “Every body continues in its state of rest, or of uniform • Describes motion on earth by simple laws motion in a right line, unless it is compelled to change that state by a force impressed on it.” • Applies also to the heavens – the earth moves! • Force & Acceleration: • Basis for later developments ===> Newton • “The change in motion [rate of change of momentum] is • Next slide proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed. • Action = Reaction: • “To every action [change of momentum] there is always opposed an equal reaction; or, the mutual actions of two bodies are always equal, and directed to contrary parts.”

• Forces: Forces & Fields Paradigm of Classical Physics: • Free Fall (Galileo-- >Newton) Space & Time, Particles & Waves • Galileo: All bodies fall downward with the same acceleration • Experimental method

• Newton: F = m a + force of gravity near earth is Fg = m g • Galileo, ….. Test theories under controlled conditions • Universal Gravitation ( Kepler- - > Newton) • Space & Time • Kepler: Described motion of planets T2 = k R3 • Time is absolute (the same in all reference frames) 2 • Newton: F = m a + Universal law of gravity Fm = G m1 m2 / R • Particles • Conservation Laws: • Particles have mass which is conserved • Conservation of Momentum: • Newton’s 3rd & 2nd Laws ⇒ total momentum (p=mv) of • Particles obey Newton’s equations interacting objects is conserved (does not change in time). • Examples: Baseballs, electrons • Conservation of Energy: • Waves • Energy changes form but the total is always conserved • Waves are moving patterns • Fields: (Newton ==> Faraday ==> Maxwell) • Waves show interference effects • Electric Fields created by charges. • Examples: Light ( Maxwell’s equations), Sound • Magnetic Fields created by charges in motion. • Electromagnetic waves (speed = c) • Nature is Deterministic

Timeline - Modern Physics Space-Time Revolution Einstein • The Initial Paradigm: Classical Physics Bohr • Light is a wave (thought to be a medium called “ether”) Michelson Rutherford Nuclear Energy Thomson De Broglie Released Neutron Stars • The anomaly (crisis) for classical physics: Planck Schrodinger discovered Michelson-Morley Experiment Heisenberg • Found Speed of light to be the same in all directions even though 1900 1950 2000 the earth is moving around the sun Expansion of Universe Laser • Normal response Special Invented Relativity discovered • Try to explain the experiment as some anomaly of light Transistor All the General Quantum • Extraordinary Response (Revolution) Mechanics Invented Quarks Relativity discovered • Completely revise our notions of space and time • “Modern Physics” began with a two great revolutions starting around 1900, and ending ???? • See Timeline description of lives of various scientists on WWW pages.

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Special Relativity: The Postulates Special Relativity: The Consequences • A problem for classical physics: Michelson-Morley • Proper Time Experiment • Time for an object is measured in the reference frame where the • Found Speed of light to be the same in all directions even though object is at rest is called the proper time interval, ∆Tproper . the earth is moving around the sun • Space and Time differences • Einstein’s Postulates • ∆T = γ ∆T γ = 1 / sqrt ( 1 - (v / c)2 ) • Principle of Relativity: improper proper

• The laws of physics are the same in all frames of reference • Lparallel(moving) = Lparallel (rest) / γ which are moving at constant velocity • Speed of Light: • Lperpendicular(moving) = Lperpendicular (rest)t) • Light is always propagated in empty space with the same velocity c independent of the state of motion of the source or the observer • Nature’s speed limit • Relative character of “simultaneity” • Information cannot travel faster than the speed of light. • Adopting an operational definition of measurement of time at • Enforced by increase in relativistic mass: different places, we find that the meaning of “simultaneous” 2 depends upon the relative motion of the observer. • M = γ M0 E = M c • Time is not absolute! • Mass and energy are related!

Space-time & General Relativity The Quantum Revolution a=g • General Relativity • The Initial Paradigm: Classical Physics • Equivalence Principle • All motion is continuous; any energy is possible for particles or • Inertial mass = gravitational mass waves • “No experiment performed in one • Particles and waves are completely different place can distinguish a gravitational field from an accelerated reference • The anomaly (crisis) for classical physics: frame” Radiation from Hot bodies; Properties of atoms • Normal response • Consequences • Light “bends” in a gravitational field. • Completely puzzling • Gravitational “Red Shift”: Clocks at lower gravitational • Try to explain the experiment as some anomaly of matter potential run slower than those at higher gravitational potential. •Leads to objects like “Black Holes” • Extraordinary Response (Revolution) • Many people pointed the way: Planck, Einstein, Bohr • The Theory • de Broglie made the giant step: Particles act like waves! • Mass causes space- time itself to be curved • Describe gravity not by a force but by motion of bodies in a • Schrodinger and Heisenberg showed that our ideas of curved space determinism have to be completely revised, …..

Origins of the Quantum Theory Waves & the Quantum Theory • The concept of quanta • Wave nature of electrons • Blackbody Radiation: To get agreement with data, Planck • de Broglie proposed an electron has an “associated wave” with assumed light is emitted in packets or “quanta” with energy of wavelength determined by its momentum: λ = h / p each quantum related to the frequency by E = hν • Davisson & Germer showed electrons act like waves - show • Photoelectric effect: Einstein takes Planck seriously. Predicts interference. energy of electrons liberated in photoelectric effect because the light arrives in quanta of energy E = hν • General wave equation • Schrodinger proposed an equation which describes completely • Atomic models the time evolution of the matter wave Ψ. Probability of finding 2 • How can atoms be stable? the particle is given by Ψ • Completely puzzling in classical physics! • Successful -- describes electrons, atoms (periodic table), • Electrons should spiral into nucleus! molecules (chemistry) , elementary particles, ….. • Bohr proposed solution • Electrons can only be in certain orbits – quantized sates • Strange - The truth is stranger than fiction • Right idea but not fully correct

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The Uncertainty Principle The Quantum Revolution - Interpretation • Consequence: • Basic fact of quantum mechanics • Calls into question our very notion of “reality” • Heisenberg formulates quantum mechanics in terms of “observable quantities only” and obtains fundamental • Is there a “reality” external to ourselves? limits on how good an experimenter can be! • How do you know? ∆p ∆x > (1/2) h/2π or m ∆ v ∆x > (1/2) h/2π • Do experiments – test! • Conclusion ∆E ∆t > (1/2) h/2π • At the quantum level, the result of the experiment depends upon the experimenter! • Fundamental uncertainty in what we observe in nature • Not understood – a matter of debate

Scale of Sizes in Nature Elementary Particles • Fermions: particles with half-integer spin which can be transformed into other fermions or created (or destroyed) only in pairs with its anti-particle Person ~ 1 m • Example: electron, quark

• Bosons: particles with integer Fundamental particles spin which can be freely created or destroyed; carries forces between particles

Universe ~ 1026 m • Example: photon, gluon

Solar System ~ 1011 m • All matter described by the Earth ~ 107 m theory except gravity --- Present theories are incomplete

Important Quantum Effects in Our World The Universe and Cosmology • Galaxies and stars form from gases (mainly H) Lasers Due to quantum wave character pulled together by gravity of photons of light • Stars produce energy from nuclear fuel Due to quantum • Death of a star wave character of • Collapse when fuel runs out Semiconductors - electrons in crystals • Becomes a dwarf, neutron star (pulsar) Basis of all modern electronics or black hole Transistor invented at Bell Labs, 1947 • Rapid collapse causes a supernova (Bardeen, Brattain, Shockley • The Universe is Expanding • Hubble (1929) Measured by “Doppler Shift” • Expanding in all directions as if it came from a point Scanning Tunneling Microscope • Estimate for age of universe ~ 15 billion years “Sees atoms and electrons” Invented at IBM Labs, Switzerland,1985 • The BIG BANG

(Depends on quantum “tunneling”) • Future? • Expansion, gradual slowing, or collapse to the BIG CRUNCH

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The Great Ideas of Physics

t1 t2 t4 A A 34 12 Quantum Mechanics t3

Classical Physics

Relativity

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