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Physics 111 Class Lecture Notes 4/18/16 2:33 PM • • Final Exam Friday, March 18 th1-4pm • Quiz Next Tuesday through Next Mondays Lecture Today: • Intro to Physics and String Theory Reading for Tomorrow: • Look over Part I again • Start Part II, p23-37 Fundamental Forces: a. Gravitational o Examples: § Apple falling to earth § Moon falling to earth • Electromagnetic o Examples: § Holding Atoms together § Responsible for friction force § Light and more generally electromagnetic radiation (e.g., radio, cell phones, x-rays) • Strong Nuclear Force o Example: § Holds the quarks together to make up protons and neutrons • Weak Nuclear Force o Examples: § Decay of Neutron § Decay of the Muon Matter is composed of atoms, which in turn are made from quarks and electrons. According to string theory, all such particles are actually tiny loops of vibrating strings. Conflicts in Physics: • What does light “look like” when you try to catch up to it? – one of Einstein’s childhood thoughts o Resolution: The speed of light is the same regardless of your state of motion (moving fast or at rest). • Newton’s theory of gravity acts instantaneously across space (“breaking the speed limit of light”). o Einstein resolves this conflict with his theory of Gravity called General Relativity. • Incompatibility between General Relativity (GR) and Quantum Mechanics (QM) o Quantum Mechanics – the rules that describe the microscopic world. In particular the Electromagnetic, Weak and Strong Nuclear Force… or a quantum theory of gravity does not work! § If the fundamental particles (like electrons and quarks) are strings, the conflict of incompatibility between general relativity and quantum mechanics, is resolved! Goals of String Theory: • Resolution of Conflict between GR and QM o Possible technological applications o Better understand Black Holes o Better understand the early universe • Theory of Everything • Unification of the Forces 1/6/15 Today: • Questions • Finish Part I discussion • Start Einstein’s Special Theory of Relativity Reading for Tomorrow: • Continue Studying p23-37 • And p42 Muon Example In string theory, what are fundamental particles: • Fundamental particles cannot be broken down any farther. o In string theory, the fundamental particles (like electron and quark) are strings. An electron is different from a quark because they have different vibrations (they vibrate differently). • Note: String Theory simplifies the particles by saying there is only one, that vibrates in different ways to make the many matter and force particles. According to String Theory, the universe has extra dimensions curled up into a Calabi-Yau shape. Do physicists believe in String Theory? • Some say No! o Why? § It has not yet been proven by experiment. • Some say Yes! o Why? § It solves some compelling/unsolved problems in Physics. Reductionist Viewpoint: • If you have a theory of everything (know all the particles and their interactions or forces), you know everything including emotion (e.g., the love of a mother for their baby, etc.). Light = Electromagnetic Energy • What is it? o Oscillating (Wave) Electric and magnetic fields. § James Clerk Maxwell unified the electro and magnetic fields to come up with a theory for light! The foundation of Einstein’s Special Theory of Relativity: • Constancy of the speed of light o No matter how you move relative to light, the light always has the same speed. 1/7/16 Reading For Monday: • Continue Studying p23-37 and Start p37-47 Quiz Tuesday: • Through Monday’s Lecture (Lecture Focus Questions #1-5) C = Speed of Light = 670 million miles per hour Postulates of Special Relativity: • *1) Constancy of the speed of light. Light always moves at the same speed no matter how you move relative to the light. o Ex) Einstein trys to run and catch up to a beam of light. You might think the speed of light relative to Albert is half the speed of light…but No, the light still moves at the speed of light (c). § *This is a special paradoxical (miraculous) postulate. • 2) The Principle of Relativity. Constant Velocity Motion is relative. You cannot tell the difference between being at rest or moving at a constant velocity. Consequences of the Postulates of Special Relativity: • 1) Time Dilation. Moving clocks run slow relative to an identical clock at rest. • 2) Lorentz Contraction. Moving length shortens relative to an identical length at rest. I.e., A moving objet is shortened in the direction of its motion. • 3) The Relativity of Simultaneity. Events that are simultaneous for one group of observers is not simultaneous for another moving relative to the first. o UN Train Example o Consider the decay of a muon in the atmosphere moving towards the earth at 0.995c. Recall the muon decays (via weak force) to an electron, an anti-electron neutrino, and a -6 muon neutrino an about (lifetime at rest) 2 x 10 s. § How far does the muon travel? ú Fast moving muon actually lives ten times long (do math) or 2 x 10 -5s and the muon can travel the full 6000m and reach the earth! 1/11/16 Quiz Tomorrow (through today’s lecture) Today: • Special Relativity Continued… • Postulates • Consequences Postulates: • Constancy of Speed of Light • The principle of relativity Consequences: (*Need to move fast, near the speed of light to easily “see” these consequences) • Time Dilation • Lorentz Contraction • The relativity of Simultaneity What is a muon? • Similar to an electron more massive What happens to a muon over time? • It decays Muon Example: • Muon traveling towards earth at V = .995c = approx. speed of light • On earth the muon lives 2 x 10 -5s • From the muon’s perspective: o Muon’s at rest -6 o Lives for 2 x 10 s o Earth and people are moving towards the muon § Does earth make it to the muon before decay? ú Yes, but why? • Lorentz contraction the moving 6000m shorts to 600m Relativity of Simultaneity: • U.N. Train Example o Train moving w/ light bulb in the middle of the train o Forwardland and Backwardland o Train is moving at the speed of light o For people off the train, the bulb is moving at the speed of light. § The distance between the outside observer to forwardland is shorter and his distance to backwardland is longer. ú Therefore for the person off the train, the light travels a shorter distance to forwardland. • The light reaches forwardland first then backwardland off the train • The light reaches these areas at the same time on the train though. ú However, on the train the light gets to both people (in forward and backwardland) simultaneously. Prove Time Dilation. Use Light clock (as in the text) • Be able to draw: o -9 • The time to go back and forth is 1.0 x 10 s (1 billionth of a second) at rest! • Back and forth distance is 30cm at rest. o D = R x T • Light clock moves relative to a person at rest. • Light is, at rest, moving at the speed of light • D = r x t • Larger = same x larger o Larger = time dilation 1/13/16 Reading for Tomorrow Start Reading Ch3 p53-62 Today: (Finish Chapter 2) • Questions • Twin Paradox • Motion Through Spacetime • E = mc 2 Twin Paradox: • Lecture example: Two identical twins, one stays on Earth, the other travels space and returns to earth. The traveling twin ages slower. o You can only see this easily if you travel fast (near light speed) o Note: Atomic clocks have the ability to measure nanoseconds -9 or 10 s (is one “tick of a light clock with mirrors separated by 15cm) o Yes, we have observed the twin paradox experimentally using planes and atomic clocks capable of measuring very small differences in time. o Claim: Paradox w/in the twin paradox § Both clocks in the above example run slow relative to each observer. ú For the traveling twin who returns, they need to slow down, stop (i.e., accelerate) , and speed back up (i.e., accelerate again) to get home. • This breaks the symmetry (of constant velocity motion) by accelerating (non- constant velocity motion). o P50 – Einstein – “Everything (including us) is traveling through spacetime at one fixed speed, the speed of light.” 1/20/15 Quiz Monday Through Tomorrow’s Lecture Reading for Tomorrow – p75-84 (end of chapter 3) Today: Einstein’s Theory of Gravity, G.R. continued… Examples of the equivalence principle: 1. Text example: Terrorist w/ bomb on scale. i. If the weight deviated by 50%, the bomb would go off. ii. Send it into space carefully such that the decreasing gravity in space is compensated by more acceleration. iii. Total gravity plus acceleration stays constant. • 2) Elevator rides. o Going upwards at the beginning you are accelerating upward which increases your weight. o At the top, slowing down, a negative acceleration makes you feel lighter. • 3) On earth classroom v. Deep space Recall: Acceleration = changing speed and/or direction Note: According to Einstein’s theory of gravity things are attracted to Earth because the space around it is being warped. Curved space due to acceleration we note that C > 2piR • Note: We only used arguments from special relativity with not reference to acceleration (off the ride). • On the Tornado ride: No one is moving relative to the other. But someone on the outside “feels” the greatest acceleration. Time also warps on the tornado ride: • Why? o Only using special relativity the motion through space is greatest on the outer edge, therefore, according to Special Relativity, the motion through time is slowest (works on and off the ride but the above example is off the ride). § Note: On the ride, the person w/ acceleration has a slower clock. The clock is slowest on the outside edge of the ride. In short, the greater your acceleration, the slower your clock runs. 1/21/16 Quiz Monday! • Its through Today’s lecture (the end of chapter 3) Today: • Einstein’s G.R. Continued… • Experimental Tests What’s wrong with the above picture? 1. It doesn’t show the warping of time 2. Only two spatial dimensions instead of three. 3. The orbiting planet doesn’t show any warped space. 4. There is no external agent pulling down the sun. Two Early Experimental Verifications of Einstein’s G.R.: 1. Precession of Perihelion of Mercury’s Orbit (See footnote 10, p394) 2. Need to wait until 1919 for total lunar eclipse to be able to see light from a distant star being bent around the sun’s gravitational field. More “recent” experiment verification: 1. 1976 NASA experiment compared an atomic clock on earth with an identical atomic clock 6000 miles above earth. The clock on earth ran 4 nanoseconds slower! In perfect agreement with experiment (footnote 9, p393-394) 2. Black Holes: The spacetime is so warped (or gravity is so strong) that not even light can escape. Observed in the center’s of galaxies and as stellar remnants! In 1907 before G.R. was done Einstein realized that light should be bent in a gravitational field using the equivalence principle. Note: In weak gravitational fields like the earth, time warping is a stronger effect than space warping. 1/25/16 Tomorrow: • Starting Quantum Mechanics (Q.M.) • Read p85-90 (Beginning of Chapter 4) Today: • Quiz #2 • Discuss Quiz #2 • Black Holes (continued…) • Einstein’s Biggest Blunder • Gravitational Waves Black Holes: • Found in centers of galaxies • Stellar remnants Evidence: • 1) “Heat” in the form of x-rays. • 2) Observe orbits to find very large mass in small locations (those orbits are black holes). 1/26/15 Reading for next time: • p85-90 again • p91-97 Midterm Exam: • Tuesday Feb 9 . th Today: • Einstein’s “Blunder” • Gravitational Waves • Introduction to Quantum Mechanics (Q.M.) Einstein’s “Blunder”: • Einstein’s equations naturally account for an expanding or contracting universe. o Einstein modified his equations (by including a cosmological constant) to make the universe static. § It was a “blunder” because the universe is actually expanding. Looks like as of 2015, Gravitational waves have been detected as predicted by Einstein’s G.R. Einstein spent the rest of his life trying to unify the gravitational and electromagnetic (E&M) forces. Problems: • 1) E&M forces is a way stronger (10 42times) than gravity. • 2) He disliked the developments in quantum mechanics and he was ignoring the strong and weak nuclear forces that were newly discovered. Quantum Mechanics (QM) is needed to understand the subatomic level (“How an atom works”). Einstein detested the probabilistic nature of QM. Weird things in the Quantum Café (from in-class video) or h-bar (in the text): • Walking through walls • Everything is probabilistic “up to chance.” • There are many possibilities (or “Many Universes”) • Ice cubes going through glass. 1/27/16 Reading for Tomorrow: • P88-97 again • P97-103 Today: • Introduction to Quantum Mechanics continued…. Text uses H-bar (physics symbol) 8 C = Speed of Light = 3 x 10 mls, a big number. • Plays an important role in S.R. o In Q.M., h-bar play a similar role. § It is a constant but a very small number (h-bar = 1.05 -34 x 10 jewls) ú The smallness makes Q.M. mostly unobservable in everyday life. In H-bar or the Quantum Café, h-bar, is now a big number and quantum effects can be easily experienced. Quantum Weirdness in H-bar (From text): • 1) Disappearing cigar. • 2) Ice cubes left his class • 3) Walk through walls • 4) Ice cubes rattle around more vigorously in the small cup. Properties or Characteristics of Q.M.: • 1) Quanta – a packet or bundle of energy (ex: Photon is the quanta of the electromagnetic field). • 2) Particle/Wave duality: All fundamental particles are both wave and particle. o Ex: Light is a photon particle and an electromagnetic wave. • 3) Probabilistic Theory: If multiple outcomes of an experiment are possible, you can only determine the probability of a particular outcome. • 4) Uncertainty in Theory: Called Heisenberg Uncertain Relations. Experiments that demand the idea of quanta: • 1) Blackbody radiation: Anything with temperature (i.e., light bulb filament, you and me, hair straightener, the earth, etc.) radiates electromagnetic (or light) energy. The hotter something is, the more it radiates. • 2) Photoelectric effect. o Einstein won the Nobel prize for his quanta explanation. Maxwell’s theory of light (electromagnetic radiation) as a wave. Characteristics of a wave: • 1) Frequency (How fast back and forth) • 2) Period: Time to go back and forth once. • 3) Wavelength: The distance from one peak to the next peak. • 4) Amplitude: How big the peak is. 1/28/16 Exam Tuesday Feb. 9 th Reading: • P97-102 again • P103-112 Today: • Q.M. continued… • Blackbody Radiation • Photoelectric Effect • Double Slit? Blackbody Radiation and the Photoelectric effect are experiments that can only be explained by the quanta hypothesis. Blackbody Radiation • Examples: o Filament in “old” light bulbs o Hair Straightener o Humans o Earth, Sun o Oven Maxwell’s theory tells us that the radiation waves in an over have a whole number of crests and troughs—they fill out complete wave-cycles. Blackbody Radiation à Light or Electromagnetic waves à all waves: • Lambda = wavelength • F = frequency • Wavelength x frequency = speed of light = c Larger wavelengths require smaller frequencies or a smaller wavelength requires larger frequency because the product must equal the speed of light. Using classical physics, the energy emitted from a blackbody is infinite! But the energy is finite so the theory is wrong. • Why infinite? o Classical Physics says energy in a wave only depends on Amplitude. o All oscillators which create the light are excited, and there are an infinite number leading to infinite energy. Solution: • Due to Planck (who won the Noble Prize), if the energy is quantified, comes in clumps of energy (E) (called photons) with the energy proportional to frequency (f). • E = nhf o n = number of quanta o h = Plancks constant o f = frequency • Why is this a solution? o Not infinite, Yes. § Why? ú The high energy, high frequency quanta don’t have enough thermal energy to be emitted. Analogy: • Infinite: o People ßà Oscillators (Vibrating Atoms) o Temp. ßà Temp. o Payment ßà Energy o $1, $2, $5, $10, $20, $50, $100 ßà Frequency, or quanta of Energy • Catch: Landlord does not give change (does not make infinite money). Payment = $80. o Person with $50 only pays $50. o Person w/ $20’s pays 4 quanta = $80 o Person w/ $100 bill doesn’t have to pay o Only a finite number of people pay. Total finite amount of money (energy). 2/1/16 Reading for Tomorrow: • P97-112 again • P112-116 th Exam Tuesday February 9 ! Today: • Blackbody Radiation (Review) • Photoelectric Effect • Double Slit Experiment Properties of Q.M.: • Quanta: o Energy depends on frequency not amplitude o Lower frequency (Infrared) has lower energy than green light (all visible) and frequency. o You don’t get infinite energy because higher frequency protons need more thermal energy to be emitted. • Wave/Particle Duality • Probabilistic theory • Uncertainty in theory Photoelectric Effect: • First explained by Einstein (he won the Nobel prize for it) • If the photon has sufficient energy (i.e., high enough frequency) electrons are emitted. • When the energy of the photon matches the energy holding the electron to the metal (aka the Work Function), the electron can be emitted. • Lower frequency à No emitted electrons • Higher frequency à electrons are emitted and they have additional energy. Classically (not correct view): • Large amplitude of Low frequency light. o Might think the electrons will come off due to high energy but doesn’t happen! The individual phonons don’t have enough energy. Double Slit Experiment: If light was a particle, you might expect two bright spots. But you actually see an interference pattern (lots of light and dark spots) because light is acting like a wave. If we send photon’s, one at a time into the double slit. Individual photons hit the screen in different apparent random locations but after a long time an interference pattern emerges. • How is it possible? o 1) Schrodinger: § The photon has a probability to go through both slits . o 2) Feynman: Photon takes all paths simultaneously. Reading: p112-116 (Again) & p117-124 (Start ch5) Exam: • Next Tuesday • Bring Blue “Cal Poly” Scantron Today: • Double Slit • Matter Waves • Heisenberg Uncertainty Photoelectric: • Energy up à frequency up à Wavelength down (shorter) Frequency x wavelength = speed of light Higher “Amplitude” classically à Translates to more photons (Q.M.) Interference Patter: • Bright regions (Waves add constructively) & • Dark regions (no light – destructive interference) All Properties in the Double Slit: • 1) Quanta • 2) Wave/Particle Duality • 3) Probabilistic • 4) Uncertainty What is the particle nature of the double slit? • Note: we don’t know where a single photon will hit. But we know where photons won’t hit (i.e., Dark spots). We do we believe? • 1) There has never been an experiment that contradicts Quantum Mechanics. Einstein on the probabilistic nature of quantum mechanics, “God does not play dice with the universe.” More interesting facts about double slit experiment: • 1) Electrons also create an interference pattern • If you know which slit the photon or electron goes through the interference pattern goes away. 2/3/15 Reading: • P112-116 again • P117-131 (Ch5) • Exam Tuesday February 9 th Why is an electron (normally thought of as a particle) a wave? • Due to Louis de Broglie who “discovered” matter waves. o Mass (or energy) = 1/(wavelength) § Shows that mass and waves are related Heisenberg Uncertainty Relations • 1) (uncertainty in Position) x (Uncertainty in Momentum) > or = (h- bar)/(2) ß very small number o momentum (P) = mass x velocity o note: because h-bar is so small, this relation is easily satisfied for the macroscopic world. § Example: In h-bar or quantum café, Planck’s constant is large, the uncertainty applies to macroscopic objects. ú Ice cubes rattling in glasses: • Larger glass à slower ice • Smaller glass à faster ice • Ice cues going through class or going through walls. Wall (or glass) is a high energy barrier but you can borrow energy for a short period of time to overcome the barrier. § Example of Uncertainty: ú What is the length of a meter stick? 1.001 or 0.999m à uncertainty of 0.001m 2/4/16 Reading for Monday: • P117-131 again (Ch5) Midterm Through Monday’s Lecture (Finish Ch5) on Tuesday • Buy and Bring Cal Poly Scranton Big Blue Sheet Today: • Matter Waves and Measurement • Quantum Field Theories Matter Waves: • If you shoot electrons (matter) into a double slit they have interference patterns, therefore, they must be waves. o De Broglie: § Wavelength is proportional to 1 / mass or § Wavelength is proportional to 1/ energy o Ex) What is the wavelength of an electron (at rest)? (i.e., only the mass contributes to the energy) -10 § Electron Wavelength approx. = 10 m (very small) (electron mass) § Run electrons through a crystal you can “see” the wavelike nature. ú Why can’t we see the wavelength of a baseball? • The mass is too large! o To measure something of a particular size, we need to use a wavelength of at least size or smaller . § Ex: The wavelength of visible ranges from 700nm for Red to 400nm for Blue. ú These wavelengths are much smaller than what we try to see. § Ex: Hole in table. Need an object smaller than the hole to “see” hole (i.e., feel it when it passes over the whole) § Point: To locate something w/ high precision (i.e., small wavelength) we need high frequency (or Energy) Photons. § Recall: Heisenberg Uncertainty Principle: ú (Delta x) (delta p) > or = (h-bar)/(2) • Creates Quantum Foam at the smallest space and time scales. Which conflicts w/, o General relativity demands a smooth fabric of spacetime all the way down to all small scales. ú High Precision means small delta x (position uncertainty) • à delta p must increase Conflicts between G.R. and Q.M.: 1. Quantum Foam 2. A Quantum Theory of Gravity predicts infinite for processes that should be finite! 2/8/16 Exam Tomorrow • Buy CP Scantron No 10-11 Office Hour, but, new office hour 12-1:30 Today: • Standard Model of Particle Physics • Quantum Field Theories (QFT) Quantum Mechanic Uncertainty Principles Predict “Quantum Foam” • What is “quantum foam”? -31 o Down near the Planc Length 10 m, particles are created out of nothing by borrowing energy for a short amount of time. § Feynman (p120) Conflict of G.R. w/ Q.M.: 1. Quantum Foam is a problem for General Relativity which demands a smooth space-time. 2. A quantum theory of gravity predicts infinite answers for probabilities. i. These two conflicts go away if the fundamental particles are strings instead of point (no size) particles. S.M. = Standard Model of Particle Physics: • Experimentally proved w/ the Large Hadron Collider (LHK) o All experiments are consistent w/ the Standard Model. • Includes 3 of the 4 fundamental forces: o Strong o Electromagnetic o Weak o …the fundamental force not included is Gravity • The forces particles: o EM ßà Photon o Strong ßà Gluon o Weak ßà Weak gauge bosons § These particles mediate the forces. § Messenger particles = gluon, photon, weak gauge bosons § Example: Two electrons repel each other ú Feynman Diagram (look in notes) to visualize § Example 2: Gluons are being exchanged between quarks to create the strong force which holds the proton (or neutron) together. The Q.F.T. describing electromagnetism is called Quantum Electrodynamics (Q.E.D) • Q.E.D. provides the most precise agreement experiment and theory ever obtained. o The agreement is 1 part in about 10 . 11 9 11 § Example: A billionaire has 10 dollars or 10 pennies!!! ú 1 part in 1011 says your know about/keep track of all of your pennies. • Q.E.D. does have infinities in the probability calculations but the infinities are controllable. o In quantum gravity calculations you get an infinite number of infinities. They are not controllable. § In the 60’s Q.F.T. were applied to the Strong Force to create Quantum ChromoDynamics (Q.C.D.) In the 1970’s, Physicists (Glashow, Weinberg, and Salam….won Nobel prize) showed that the weak and electromagnetic forces could be unified into one force called the electroweak (no acronym) force. Matter particles of the Standard Model (see table 1.1) electron, electron neutrino, up and down quart (Family 1). 2/10/15 Exam’s back Tomorrow Reading for Tomorrow: • P131-152 Today: • Standard Model (Review and Problems) • String and String Theory History Problems w/ the Quantum Theory of Gravity: • Uncontrollable infinities • Doesn’t meld w/ the smooth spacetime needed for general relativity. Problems with the Standard Model: • Has about 19 unknown parameters (e.g., masses of particles, charge of particles, related to the force strength. • Why three families? • Doesn’t include gravity • Fundamental particles are points (take up no volume or have no size!) If the fundamental (particles) objects are strings: • All the Standard Model (S.M.) problems go away • Only one fundamental thing, a string. • The particle properties (mass and charge) depend on the string vibration. • The string are expected to be very very small, the planck length, -31 -33 10 m or 10 cm. History of String Theory: • 1968; Veneziano “accidently” discovered string theory. • Early years, string theory was used to try and describe Strong Nuclear Force. (Correct theory is Quantum ChromoDynamics) • 1973 J. Schwartz showed that the massless messenger particle could describe gravity if the string size were 10-31 m! o Problem: § Theory had anomalies (results like x = 1 and x =2 are both true) • 1984, Michael Green and John Schwartz showed the theory was anomaly free and had a rich enough structure to describe the four fundamental forces (p137-139) 2/11/16 (Next Tuesday is a Monday schedule) Reading for “Monday” • P152-174 Exams back at end of class Today: • Solution is Strings (Review) • String History 1984-1995 • How Strings Work o High String Theory Consequences “The answer my friend is string ing ing s” Solution is Strings (Review): • 1984: 1 stSuperstring Revolution o anomaly free and could explain all four forces in one theory. • 1988-1994: “Doldrums” – Why? o Complex equations § Because the equations are so complex (5 string theories) you need to use approximations. nd • 1995: 2 Superstring Revolution o Ed Witten used non-approximate (and other…) methods to show the five string theories are related by “dualities”. § All 5 String Theories are related to M-theory. How does string theory work? • Where does mass come from? • How is the G.R. vs. Q.M. conflict resolved? Recall: The strength of the gravitational force is weak • String tension is proportional to 1/strength of gravity o This implies the string tension is extremely large Consequences of Large String Tension: • Makes the string small (Planck length 10 -33cm) • Natural mass scale is large (Planck Mass) • Masses tend to be integer multiples of the Planck Mass If quantum mechanics is included, energy cancelations occur to give the massless graviton. • String theory easily predicts massless particles but has difficulty predicting small mass particles like electrons, neutrinos, quarks, etc…all the matter particles in the standard model 2/16/16 Quiz on Tuesday Extra Credit Reading for Tomorrow: • P162-174 Today: • Resolve conflict between G.R. and Q.M. Two answers of how to resolve the conflict between G.R. an Q.M.: • 1) Rough Answer: o To see small sizes (high energy) we use a small quantum mechanical wavelength which is inversely proportional to the energy at the LHC, the particle energy is roughly 14 TeV which can probe approx. 10 -21cm or 10 -19m. § Recall: The Planck length (the expected size of Strings is about 10-31m or 10 -33 cm. o To see (or probe) the quantum foam we need high energy (Planck energy) but at Planck energy the strings either gain mass or size and thus can’t probe the Planck sizes or smaller. • 2) More Precise Answer: o With strings (instead of point particles), the quantum foam is “tamed” (not as rough or chaotic). o At SLAC, they collide electrons (e ) and positrons (e ) (the anti-matter of electrons). o For strings (not points) the exact interaction point depends on your state of motion and thus is not unique. § Ex: Figure 6.8 ú Gracie “sees” the strings interact in the “middle” § Figure 6.9: ú George “sees” the strings interact closer to the “bottom” (in a different place) due to a different motion and the relativity of simultaneity. • Smoothing out of the interaction point for strings which also “tames” (or smoothes out) the quantum foam and the infinities for quantum gravities become finite and acceptable. 2/17/16 Office Hour Thursday only 10-10:30 Reading for tomorrow: • P174 – 183 Quiz Tuesday! Today: • Review G.R. vs. Q.M. resolution o In going from point particles to strings the quantum jitters at the Planck scale become smooth enough to mess with General Relativity. § The smoothing effect of strings is due to the finite size and the relativity of simultaneity (interaction point depends on your motion). o Previously physicists (Dirac, Feynman, Heisenberg, Paul:) did try to make non-point particle theories work but they failed. § Failures: ú Faster than light particles (Tacyons) • Will go away when you allow for supersymmetry ú Answers are outside the range of acceptable probabilities (i.e., 0 to 1) • Will go away when you allow for extra dimensions. § String theory encounters both these problems: ú 1) Tacyons go away w/ supersymmetry ú 2) Probabilities are acceptable w/ extra dimensions. • Super in Superstring stands for supersymmetry. o Symmetries found in nature related to space, time, and motion. § 1) Space ú Translations: • Experiments performed in different locations give same result. ú Rotations • Experiments performed in different orientations give same result. ú Time: • Same experimental results today and tomorrow. ú Motion: • The principle of relativity • The equivalence principle. § This is all the known space and time symmetries iunless you include quantum mechanics, then there is one more, supersymmetry. o What is Supersymmetry? § Background: ú Particles can have spin, an intrinsic property of the particle. § Examples: ú All matter particles (i.e., table 1.1) have spin of- bar/(2) (aka on half h), • If supersymmetry is true then all the particles in Table 1.1 would have super particles with spin = 0. • Particles w/ ½ (Fraction) integer spin or 3/2, 5/2, spin… = Fermions • Particles w/ integer spin (whole number, not fraction) (e.g., 0, 1, 2) are called bosons. o Boson Examples: § Higgs particle has spin = 0. § Force particles: ú Graviton has spin = 2. ú Strong (Gluon) has spin = 1. ú Weak Bosons has spin = 1. ú Photons also have spin = 1. • The super partner for the graviton is called the garvitino w/ spin = 3/2. 2/18/16 Quiz on Tuesday Reading for Monday: • P184-202 Today: • Supersymmetry (continued…) SuperSymmetry: • Fermions: o Have ½ (or 3/2, 5/2, etc.) integer spin o Example: § Matter Particles in the Standard Model (Table 1.1) • Bosons: o Have whole integer spin 0, 1, or 2. o Example: § Force particles in Standard Model • What is spin? o Intrinsic spin of the particle itself which creates a magnetic field. • How do you detect spin? o Can use magnets to see particle deflections. • Definition of Supersymmetry: o Bosons and fermions come in pairs. o For every fermion particle (e.g., electron) in the Standard Model, there is a superpartner boson (e.g., selectron w/ spin = 0) o If supersymmetry exists for every particle in the standard model their would be a superpartner particle. § No superpartners have yet to be discovered! ú People were expecting superpartners to be discovered at the Large Hadron Collider (LHC). Non yet! • Particle (Spin) Superpartner (Spin) Electron (1/2) – fermion Selectron (0) – boson Photon (1) – Boson Photino (1/2) – fermion Non Standard Model: Graviton (2) – Boson Gavitino (3/2) – fermion • Why do physicists expect supersymmetry (SUSY) to be a symmetry? o 1) Why wouldn’t nature use this symmetry? § Nature has used all the other known symmetries of space, time, and motion. o 2) Fine Tuning Problem (p174): § Parameters in the Standard Model need to be fine tuned to 1 part in 10 . ú The fine is not needed if nature obeys supersymmetry. o 3) At high energy or small distances the tree forces of the standard model (E&M, Weak, Strong) unify if SUSY is true! • How do forces, like the electromagnetic change with distance? o For example, at higher energy, the E7M force gets stronger. § How does this happen? ú Two electrons repel ú Zoom in on an electron ú Particles are being created an annihilated ú The created and annihilated particles diminish (or screen) the electron charge or force like fog diminishes a streetlamp’s brightness. ú Closer to the electron, there is less screening and a stronger force. 2/22/16 Quiz Tomorrow: • Lecture Focus 21-25 Today: • Supersymmetry (review) • Superstring Theories • Extra Dimensions Note: • Mistake w/ Fig. 7.2 • Energy not distance on the axis. Why SUSY? • 1) At high energy and superpartners, strong E&M and Weak Unify! • 2) Why shouldn’t nature use it? Uses all the rest! • 3) Fine Tuning Problem Original String Theory by Veneziano: • The theory only described bosons and 26 total dimensions. • Problems: o 1) To describe nature you need to have fermions (matter particles) o 2) The Tachyon Particle: § Moves faster than the speed of light! The new versions of superstring theories have fermions pair w/ bosons (i.e., the theories have SUSY built in to it.) In some sense, superstring theory predicts supersymmetry. Turns out, string theorists discovered five consistent string theories: • Heterotic O • Gerotic E • Type I • Type IIA • Type IIB The five superstring theories appeared to need ten total space and time dimensions. 1995: M-Theory relates the five superstring theories to each other and M – theory in 11 spacetime dimensions. Note: Superstring theories require extra dimensions in order for the acceptable range of probabilities (is 0 to 1). Know universe has 3 spatial dimensions and 1 time dimension. • Where are the other 6 dimensions? (i.e., 10 – 6 = 4) Dimensions cone in two types: • 1) Large, extended, easily visible • 2) Small, compact, hidden In 1919 Kaluza introduced the idea of a small compact hidden dimension, to understand E&M and unify this force w/ gravity! 2/24/16 Reading for Tomorrow: • P221-234 Quiz 4 Next Wednesday Poem Due on Last Day of Class (Lecture) ~ 1 page in length Compact Dimensions: • Original String Theory has 10 total space and time dimensions • M-theory has 11 total space and time dimensions • These extra dimensions are needed to give an acceptable (0 to 1) range of probabilities. • Fig 8.4: o 2 large extended dimensions o 1 small compact (hidden) dimension • Lineland is a one-dimensional (1-D) Universe • • • • • Perhaps line land has a small compact dimension that got large o o o o o o o o Only case you can properly visualize w/ a drawing both large and compact dimensions o Note: we are only talking about the surface of the garden hose • Fig 8.7: o Only the surface of the sphere is available, providing two compact dimensions. • Big Deal? o Shape and characteristics of the compact dimensions influence the way strings vibrate and hence all the properties of particles and forces. • Simple low dimensional example of how dimensions influence vibration: • A) 1-D: o • • o only open strings o vibrates by stretching and contracting • B) 2-D o o o o open and closed strings o stretch and contract o also vibrate back and forth • From video: o Shape of French horn gives rise to different vibrations (notes) or particles in string theory. • Only Super String Theory o 10 spacetime dimensions o 4 known space and time dimensions o 6 spatial dimensions § if they are all small String Theory Stringent requirements allow calabi-yau spaces ú ex) Fig 8.9 is a cartoon of 6-D compact space. • Fig 8.10 shows: o Large extended dimensions: 2 o Small compact dimensions: 6 o 6 + 2 = 8 total spatial dimensions • Calabi-Yau spaces are not unique! ~ 10,000 of them. o Note: One of these 10,000 can still give rise to a different shape with small deformations. § 2-D analogy: Space w/ 3 holes fig 9.1 is different from figure 9.2 with 3 holes. • What is the big deal w/ 3 holes? o A Calabi-Yau space w/ three holes predicts three families (like we see in nature table 1.1) of particles. Unfortunately, thus is not a unique prediction of string theory. There are many possibilities with three holes. 2/25/16 Quiz next Wednesday Reading for Monday: • P231-246 Today: • Questions • Possible Predictions of String Theory Big Picture: • Strings resolve conflict between G.R. and Q.M. o Stings have no clear interaction point (depends on relative state of motion b/c relativity of simultaneity) therefore: § Strings smoothed out quantum foam and gets rid of infinities in calculations o Predict Extra Dimensions § 6 (pre 1995) § 7 (post 1995) ú What do these extra dimensions look like? • If all compact space: Calabi=Yau meets the stringent requirements. ú What do these extra dimensions do? • Influence how the strings vibrate which determines mass, charge, energy, force (or interactions). o They influence everything about how the universe works! ú Do we believe? • We would like to see predictions verified. Possible Predictions: • 1) A Calabi-Yau (C-Y) space w/ three holes, creates three families of particles! o But this is not unique. § The equations w/ today’s tools are too complicated to predict a universe space (C-Y) w/ 3 holes! • 2) A spin 2 massless particle called a graviton “Prediction of String Theory” Witten says, “String theory predicts gravity.” o The graviton does not depend on the shape of the compact dimensions “Robust Feature of String Theory.” § But the Electromagnetic, weak, and strong forces do depend on the structure of the compact space. • 3) SUSY – If SUSY is discovered is string theory right? o There are other point particle SUSY theories. § But, since string theory requires SUSY, this is a step in the right direction. • 4) Extra Dimensions - If observed at the LHC, is string theory right? o Not necessarily. § Example: Supergravity is a SUSY point particle in 11- dimensions • 5) Directly observe a macroscopic string in telescope that grew large form the time of the early Universe! (Hasn’t happened!) • 6) Fractional Charges besides 1/3 (e.g., 1/5) o This can be described “easily” with string theory but for point particle theories it is like, “a bull in the china shop.” • …. • 9) Dark Matter – observed in nature, by watching stars orbit in galaxies. o Helps hold stars in galaxies § Dark amounts to about 25% of the known energy and matter in the Universe. ú String theory could possibly predict what the dark matter is (but it hasn’t yet). • Dark Energy: o The universe is filled w/ energy in empty space. Makes up about 70% of the known matter and energy in the Universe. § Note: the stuff you and I are made of (ordinary matter) only accounts for about 5% of the matter and energy in the universe. § The dark energy makes the universe accelerate in its expansion. 2/29/16 - Poems due Thursday March 10 - Extra credit due Thursday March 10 Quiz on Wednesday! • Lecture Focus 27-31 Today: • Quantum Geometry Background: • Einstein’s theory of gravity is based on smooth curved spacetime and uses the mathematics of Riemannian Geometry. o Riemannian Geometry is based on the idea of pints as the fundamental entity. § In string theory, strings are the fundamental entity. Quantum geometry is based on the fundamental object being a string. We expect quantum geometry to be important at the Planck length. Consider a 2-D universe. • 1-Dimension large and extended • 1-Dimension is compact o i.e., cylinder Motivation: • Prove that the smallest a dimension can be is the Planck length. o So what? § We know this is true, interesting. § Black holes would not be infinitely dense (i.e., a singularity). ú If this is right black holes have some size. ú This would say the Universe did not spring forth from nothing. There was size to the early Universe. ú Note: Only one type of motion, uniform motion, for points. • A string can experience uniform motion and wrap around the compact dimension. Winding Modes: • The wrapping of a string around compact dimension. • The winding number (w.n.) is the number of times the string wraps. • Winding Number Energy = Ewn = NwnR • Assume Planck Units: -33 o R = 1 (actually R=10 cm) o R = 2 (2 x 10 -33cm) o … o R = 10 (10 x 10 -33= 10 -3cm) • Ex: o R = 10 o Nwn = 3 o What is the Winding Number Energy? (in Planck Units) § Ewn = NwnR § = 10 x 3 § Ewn = 30 Planck Units Vibration Modes: • 1) Ordinary Vibration (wiggling String) • 2) Uniform Vibration (Quantum Mechanical Wavelength or vibration associated with motion). 3/1/16 Quiz Tomorrow Quantum Geometry continued… • Big Picture: o Results from fundamental objects being strings, not points. • Prove: o The smallest a dimension can be is Planck length. • New Idea: o Two notion of distance o Duality § The physics remains the same (e.g., total energy) under different circumstances (R = 10 or R = 1/10) • Strings can wind and translate across space • Points can only translate across space • Winding Energy = Ewn = NwnR • Uniform vibration: o Quantum mechanical wavelength or vibration associated with motion and energy. • Recall: The wavelength (or frequency) and quantum mechanical are related. o Energy is proportional to frequency which is proportional to 1/wavelength • Ex: o R = 10 o Consider a string w/: § Nnw = 2 § Nuv = 3 o Calculate the total Energy (Etotal) § E total = Ewn + Euv § E total = NwnR + Nuv/R § E total = 2 x 10 + (3/10) § = 20.3 Planck Units • Ex2: o Consider the R = (1/10) (R went to 1/R) and interchange the Nwn and Nuv § N wn = 3 § Nuv = 2 o What is E total? o E total = Ewn + Euv o E toal = NwnR + Nuv/R o E total = 3 x 1/10 + 2/ (1/10) o E total = 3/10 + 20 • Notice: Same energy appears to have the same physics! o Example of duality. • How we measure distance depends on the probe we use. • Quantum Geometry has two types of probes: o Uniform vibration o Winding • The size you can measure depends on probe you use. • Recall: Wavelength size ~ 1/Eprobe • Ex: o If this 2-D space were the size of our universe, R would be = 61 10 . o For lightest, least massive probes Nwn = 1, Nuv = 1. o Only probe very small Please do professor evaluation GE Science Assessment Return Quizzes Read p283-303 for tomorrow Poem due Thursday Today: • Questions • Orbifolding and mirror symmetry • Tearing Space If one space is dual to another space, the physics (total energy) remains the same. Brian Greene discovered (w/ colleagues) another duality in string theory called mirror symmetry. How does this work? • Greene and others played w/ orbifolding: o Attachments of points in one Calabi-Yau (CY) using precise mathematical rules, to create a new distinct CY space. Found and Later Proved: • Number of even dimensional holes in one CY space was dual to another CY space w/ the same number of odd-dimensional holes. Definitions: • Even dimensional hole: Hole in 2,4,6… dimensions (ex: hole in piece of paper (b/c paper is 2-D)) • Odd dimensional hole: Hole in 1,3,5,… dimensions (ex: hole in a sphere, human w/ a hole through them, etc.) This technique solved math problem of Yau and Collaborators. Ex: Roughly ~ calculate the number of spheres in a CY shape. In some CY space the math is very hard but in the space the math is easier. Can space Tear? • On GR space cannot tear! (Needs to remain smooth) • On string theory, can space tear? Yes. Greene and collaborators showed this. Motivation: • Why might we want to tear space? o Create a wormhole to travel to another location the universe. Space tearing flop transition. Is this OK for string theory? • Greene and collaborators constructed the dual (mirror symmetry) space and compared the before and after tear. Poems due Thursday Please do course evaluation Please do assessment survey Reading for Tomorrow: • P303-319 Today: • Tearing Space • “String Theory Unification” 3/9/16 Poems due Tomorrow…print out! Please do course evaluations Please do Assessment Survey Today: • “String Theory Unification” • Perturbation Theory • Strong/Weak Coupling Duality Final Exam Next Friday 1-4pm • Through Lecture Focus 37 (through ch12). “String Theory Unification”: • Pre-1995, String understanding looked like figure 12.1 (five separate string theories) • Physicists used perturbation to understand string theory. But perturbation theory only works at weak string coupling (constant) o Weak coupling § String coupling constant << 1 o Strong coupling § String coupling constant >> 1 • The use of strong/weak duality and the R and 1/R duality (T- duality) related all the 5 string theories to each other and M-theory. • Pre-1995, physicists did not have the tools to investigate the theory at strong coupling. o To investigate the strong coupling regime, string theorists uses BPS states. § What is a BPS state? ú A special string excitation with minimal mass for a given charge which obeys supersymmetry. § Why are BPS states special? ú 1) Don’t depend on whether the string coupling is strong or weak ú 2) Highly constrained • What do we mean by highly constrained? o Ex: syzygy o Analogy: what other words in the English language have three y’s? § Type I (Strong coupling) is duel to heterotic O (Weak coupling) § Type I (weak coupling) is dual to heterotic O (strong coupling) § Type IIB (strong coupling) is dual to Type IIB (weak coupling) § Heterotic E (Strong coupling) (10 spacetime dimensions) is dual to M-theory (11 spacetime dimensions) Note: the extra dimension grows a dimension of the string to a ribbon. The strength of the string coupling tells you how big the extra, 11 , th dimension is. § Type IIA (strong coupling) is dual to M-theory (see fig. 12.8 for picture of the extra dimensions.) ú Same physics ú Same bps states § T-duality ú Teroritic O (size R) is dual to Heterotic E (1/R) • And vice versa ú Type IIA (size 1/R) is dual to Type IIB (Size R) • And vice versa • First: What is Perturbation Theory? o An approximation technique w/ the first term giving a ballpark estimate. Each successive term is smaller. Lecture 27-31 Focus Questions 4/18/16 2:33 PM Lecture 27 Focus Questions: 1. Name three reasons why we might expect supersymmetry to be a symmetry of nature? • 1) If all standard model and matter particles have superpartners, the E&M, strong, and weak forces unify at high energy (small distance). • 2) Why shouldn’t nature use it? Uses all the rest! The math works. • 3) Fine Tuning Problem: Without SUSY, physicisists have to fine- tune their equations. 2. Under what conditions do the strong, electromagnetic, and weak forces unify? • When all standard model, force, and matter particles have superpartners - at high energy (small distance) strong E&M and Weak Unify! 3. Explain with a picture why the electromagnetic force gets stronger when probed at small distance or high energy? • At a large distance, energy fluctuations shield the bare charge of the electron. Therefore, the charge strength is less. However, at a small distance, there is less shielding. Therefore, a stronger charge and force. 4. What type of particles did the first string theory explain? • Original String Theory by Veneziano only described bosonic vibrations. 5. Why do string theorists no longer have to worry about the tachyon particle traveling faster than the speed of light? • Five new SUSY theories were discovered, none of which had tachyons. o These theories also need 10 space-time dimensions. 6. In what sense did supersymmetry find its beginning in string theory? • Found that outside bosonic string vibration there is a corresponding fermion
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