A GRAND TOUR OF PHYSICS HYPERMODERN PHYSICS- UNIFICATION GUTS STRINGS & BRANES LECTURE 6 APR. 26, 2019 DR. GEORGE DERISE 1:30 – 3:30 PROFESSOR EMERITUS, MATHEMATICS TNCC THOMAS NELSON COMMUNITY COLLEGE ROOM 328. SPRING 2019 CLASSICAL- NEWTONIAN MECHANICS TERRESTRIAL MECHANICS CELESTIAL MECHANICS ELECTROMAGNETIC THEORY-MAXWELL SPECIAL RELATIVITY - EINSTEIN CLASSICAL NEWTONIAN c SPECIAL RELATIVITY MECHANICS RELATIVISTIC MECHANICS ퟐ 푬 = 풎풄 CLASSICAL ELECTROMAGNETIC THEORY LORENTZ FOUR DIMENSIONAL SPACETIME TRANSFORMATIONS QUANTUM MECHANICS ħ CLASSICAL QUANTUM NEWTONIAN MECHANICS MECHANICS QUANTUM FIELD THEORY – PARTICLE PHYSICS – STANDARD MODEL UNIFICATION There is a fifth dimension beyond that which is known to man. It is a dimension as vast as space and as timeless as infinity. It is the middle ground between light and shadow, between science and superstition, and it lies between the pit of man's fears and the summit of his knowledge. This is the dimension of imagination. It is an area which we call the twilight zone. Rod Serling Hey Rod, the fifth dimension is just the kaluza klein theory unifying the interactions of gravity and that of electromagnetism THE STANDARD MODEL SU(3) x SU(2) x U(1) ENCOMPASSES THE STRONG WEAK AND ELECTROMAGNETIC INTERACTIONS COMPLETELY DESCRIBES ALL THE PHYSICS CONDUCTED IN ACCELERATORS TO THE PRESENT TIME NO DISCREPANCIES 10-3 PRECISION (SOME TO 10 DIGIT ACCURACY) SU(3) STANDARD MODEL; WHAT’S WRONG? THREE INDEPENDENT COUPLING CONSTANTS, WHY THEIR VALUES? FAMILY PROBLEM; WHY 3 FAMILIES OF QUARKS AND LEPTONS? HIGGS MECHANISM WHY THE MASSES OF THE PARTICLES? WHY CP SYMMETRY BREAKING IN WEAK INTERACTION-NOT IN STRONG TOO MANY ARBITRARY PARAMETERS WHY DOES THIS MODEL WORK? WHY IS THERE MORE MATTER THAN ANTIMATTER? WHAT ABOUT DARK MATTER? DARK ENERGY? HIERARCHY PROBLEM; WHY m(H)<< m(PLANCK) DOES NOT INCLUDE GRAVITY! TWO PILLARS OF THEORETICAL PHYSICS GENERAL QUANTUM RELATIVITY MECHANICS STANDARD MODEL STANDARD MODEL OF COSMOLOGY OF PARTICLE PHYSICS Electromagnetism Gravity Strong nuclear force Weak nuclear force Big Bang, Black Holes QUANTUM MECHANICS GENERAL RELATIVITY Small; atoms, subatomic particles Large; (apples?), planets, stars, galaxies Linear equations Non linear equations Probabilistic Deterministic Quantum fuzziness Exact trajectory THE FERMION AND BOSON SPLIT ALL ELEMENTARY PARTICLES ARE EITHER BOSONS SPIN 0, 1, 2, . FORCES or FERMIONS SPIN 1/2, 3/2, . MATTER SUPERSYMMETRY A HYPOTHETICAL SYMMETRY BETWEEN FERMIONS AND BOSONS. For every known spin-1/2 particle type, there must be a spin 0 “superpartner” with the same charge and color and interactions. For every known spin-1 particle (gauge boson), there should be a spin 1/2 superpartner (gaugino fermion). The spin-0 Higgs boson has a spin-1/2 superpartner called the Higgsino. The spin-2 graviton (the carrier of the gravitational force) has a superpartner with spin-3/2 called the gravitino. 21 Infinities generally arise because of the vertices. Fermions and Bosons contribute with opposite signs to the mass. Maybe they can be arranged to cancel? Supersymmetry automatically provides exactly the cancellation needed to solve the hierarchy problem. Supersymmetry must be a broken symmetry. DESPERATELY SEEKING SUSY SUPERSYMMETRY ALL ELEMENTARY PARTICLES ARE EITHER BOSONS SPIN 0, 1, 2, . FORCES FERMIONS SPIN 1/2, 3/2, . MATTER SUPER YANG MILLS THEORY: SUPERSYMMETRIC EXTENSIONS OF THE STANDARD MODEL explains inflation, large scale structure, the origin of Higgs mass, and the origin of right-handed neutrino mass and how the microwave background radiation appears isotropic.. SUPERGRAVITY (11 SPACETIME DIMENSIONS) THE SUPERSYMMETRIC GENERALIZATION OF EINSTEIN’S EQUATIONS OF GENERAL RELATIVITY Supersymmetry solves the hierarchy problem. SUSY provides an excellent candidate for dark matter: the spin ½ partner to the photon (lightest SUSY particle- the photino) is cosmologically stable. ALGEBRA OF SUPERSYMMETRY RUTHLESSLY SIMPLIFIED RECALL: BOSONS SPIN 0, 1, 2, . FORCES FERMIONS SPIN 1/2, 3/2, . MATTER EVEN ELEMENTS: Bα BOSE ELEMENTS ODD ELEMENTS: Fa FERMI ELEBENTS [Bα, Bβ]≈ Bγ [Bα, Fa] ≈ Fb {Fa, Fb} ≈ Bα SPACETIME GROUPS 3+3+1+3=10 EACH A SUBGROUP OF THE 10 DIMENSIONAL THE POINCARÉ GROUP ALGEBRA OF MINKOWSKI SPACETIME- SPECIAL RELATIVITY SUPERGRAVITY (11 SPACETIME DIMENSIONS) THE SUPERSYMMETRIC GENERALIZATION OF EINSTEIN’S EQUATIONS OF GENERAL RELATIVITY STRINGS ELEMENTARY 1 DIMENSIONAL MOVE THROUGH SPACETIME VIBRATE Each vibrational mode of a string corresponds to a particle. CAN JOIN, SPLIT, TWIST OPEN OR CLOSED HAVE A STRING TENSION α’ 풐(휶′) ∼ ퟏퟎퟑퟗ tons The harmonics, or normal modes of vibration are determined by the tension of the string. a. Point particle- world line b. String- world sheet c. Closed string- world tube VIOLENT FLUCTUATIONS OF SPACETIME AT THE PLANCK LENGTH ퟏퟎ−ퟑퟓ m THE PROBLEM OF QUANTUM GRAVITY: FLUCTUATIONS OF THE METRIC ACTION: GENERALIZATION TO A STRING LEAST ACTION PRINCIPLE: THE STRING SWEEPS OUT A WORLD SHEET OF MINIMAL SURFACE AREA STRINGS ‘LIVE’ IN SPACETIME OF 10 DIMENSIONS M10 = P4 X K6 NO ULTRA VIOLET (SHORT DISTANCE) DIVERGENCES SUPERSYMMETRY IS NECESSARY FOR CONSISTENCY (HENCE: SUPERSTRINGS) GRAVITONS EXIST; GENERAL RELATIVITY ‘POPS OUT OF THE AIR” NON ABELIAN GAUGE THEORIES (YANG-MILLS THEORIES) LOW ENERGY LIMIT, SUGRA + STANDARD MODEL SUPERSTRING THEORY UNITES QUANTUM MECHANICS AND GENERAL RELATIVITY A QUANTUM THEORY OF GRAVITY!! THICKENED FEYNMAN DIAGRAMS The interaction of two point particles portrayed by thickened Feynman diagrams. Lines and points become tubes and surfaces. Smearing of the interaction avoids the singularity at vertices String Theory is not plagued by the infinities as in point particle quantum field theories. Perturbation theory is used to expand the interaction into a sum of individual diagrams. First one: a tree-level diagram. The others with increasing number of holes: loop diagrams. If the interaction strength is small, (like QED)the series would converge rapidly, grows. PERTURBATIVE STRING THEORY g2 g4 g6 ORIGINAL BOSONIC THEORY, 26 DIMS E8 X E8 HETEROTC STRING THEORY,HE http://www.superstringtheory.com/ PRINCETON STRING QUARTET Gross Harvey Martinec Rohm THE HETEROTIC STRING 10 DIMENSIONAL 26 DIMENSIONAL EXTRA 16 DIMENSIONS- (INTERNAL DIMENSIONS) RESPONSIBLE FOR SYMMETRIES OF THE YANG MILLS FORCES SYMMETRY IN MATH DUALITY DUAL POLYHEDRA The centers of the faces of a cube are the vertices of a regular octahedron and the centers of the faces of a regular octahedron are the vertices of a cube. Also works for the dodecahedron and the icosahedron DUALITY TRANSFORMATIONS WEB OF INTERCONNECTED STRING THEORIES All five perturbative string theories are connected by DUALITIES. Also connected to an eleven dimensional theory that at low energies is described by supergravity. Strings are not fundamental to M-theory P BRANES – D BRANES BRANE - a physical object generalizing the notion of a string to higher dimensions. They are dynamical objects which can propagate through spacetime They have mass and can have other attributes such as charge. A p-dimensional brane is generally called "P-BRANE". BLACK HOLES CLASSICALLY: Black holes are black. They do not radiate. “BLACK HOLES HAVE NO HAIR” Mass, charge, angular momentum completely describes a black hole. QUANTUM MECHANICALLY: Black holes are thermal radiators with a (Hawking) temperature and an entropy BIG QUESTION: IS THERE A STATISTICAL MECHANICAL INTERPRETATION? This exact entropy formula can be derived microscopically by counting of quantum states of strings and D-branes which correspond to black holes in string theory. The class of black holes used (extremal black holes) are described by 5-branes, 1-branes and open strings traveling down the 1-brane all wrapped on a 5-dimensional torus, which gives an effective one dimensional object-a black hole. A S= ퟒ BLACK HOLE ENTROPY FORMULA Microscopic Origin of theBekenstein-Hawking Entropy Strominger- Vafa, 1996 THE HOLOGRAPHIC PRINCIPLE (t’Hooft 1993) ALL OF THE INFORMATION CONTAINED IN SOME REGION OF SPACE CAN BE REPRESENTED AS A `HOLOGRAM' – A THEORY WHICH `LIVES' ON THE BOUNDARY OF THAT REGION. THE HOLOGRAPHIC PRINCIPLE was motivated by BLACK HOLE THERMODYNAMICS which conjectures that THE MAXIMAL ENTROPY SCALES WITH THE AREA OF THE EVENT HORIZON, AND NOT THE VOLUME OF SPACE OF THE BLACK HOLE THE INFORMATIONAL CONTENT OF ALL THE OBJECTS THAT HAVE FALLEN INTO THE HOLE MIGHT BE ENTIRELY CONTAINED IN SURFACE FLUCTUATIONS OF THE EVENT HORIZON. The entropy (or disorder) of a black hole is proportional to the surface area of the black hole, not its volume. This is one of the arguments in support of the holographic principle, BLACK HOLE INFORMATION PARADOX S: ENTROPY a measure of randomness; S counts the number of microscopic Quantum States. BEKENSTEIN 1970: Black Holes have Entropy. S (black hole) ̴ A (event horizon) PROBLEM: Entropy is a concept of Quantum Mechanics. Black Holes are a concept of General Relativity FOUR LAWS OF BLACK HOLE MECHANICS – HAWKING et al. 1973 PARTICLE CREATION BY BLACK HOLES – HAWKING 1975. Black Holes have temperature and they emit particles. Black Holes evaporate. Throw ‘information’ (a mass) into a Black Hole. Black Holes evaporate. The information is that of the wave function ѱ, i.e. all the quantum numbers (information), e.g. mass, spin, charge are lost. Schrodinger’s equation is one of time evolution; it predicts (probabilistically) the future. But the information disappears into the singularity. HAWKING’S SOLUTION: The information comes out via the emitted particles. ADS-CFT