A GRAND TOUR OF PHYSICS

DR. GEORGE DERISE PROFESSOR EMERITUS, MATHEMATICS THOMAS NELSON COMMUNITY COLLEGE SPRING 2019

APR. 26, 2019 1:30 – 3:30 TNCC ROOM 328.

HYPERMODERN PHYSICS- UNIFICATION GUTS STRINGS & BRANES

LECTURE 6

CLASSICAL- NEWTONIAN MECHANICS

TERRESTRIAL MECHANICS

CELESTIAL MECHANICS

ELECTROMAGNETIC THEORY-MAXWELL

𝑬 = 𝒎𝒄𝟐

SPECIAL RELATIVITY - EINSTEIN

CLASSICAL NEWTONIAN MECHANICS

SPECIAL RELATIVITY RELATIVISTIC MECHANICS

c

FOUR DIMENSIONAL SPACETIME CLASSICAL ELECTROMAGNETIC THEORY LORENTZ TRANSFORMATIONS

QUANTUM MECHANICS

CLASSICAL NEWTONIAN MECHANICS

QUANTUM MECHANICS

ħ

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?

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!

THREE INDEPENDENT COUPLING CONSTANTS, WHY THEIR VALUES?

TWO PILLARS OF THEORETICAL PHYSICS QUANTUM

MECHANICS GENERAL

RELATIVITY

STANDARD MODEL

OF COSMOLOGY STANDARD MODEL OF PARTICLE PHYSICS

Electromagnetism

Strong nuclear force

Weak nuclear force

Big Bang, Black Holes

Gravity

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

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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.

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.

RECALL: BOSONS SPIN 0, 1, 2, . . . FORCES

FERMIONS SPIN 1/2, 3/2, . . . MATTER

ALGEBRA OF SUPERSYMMETRY RUTHLESSLY SIMPLIFIED

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

The harmonics, or normal modes of vibration are determined by the tension of the string.

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’ 𝒐(𝜶′)  ∼  𝟏𝟎𝟑𝟗 tons

a. Point particle- world line

b. String- world sheet

c. Closed string- world tube

VIOLENT FLUCTUATIONS OF SPACETIME AT

THE PLANCK LENGTH 𝟏𝟎−𝟑𝟓 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

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!!

NO ULTRA VIOLET (SHORT DISTANCE) DIVERGENCES

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.

g2 g4 g6

PERTURBATIVE STRING THEORY

http://www.superstringtheory.com/

E8 X E8 HETEROTC STRING THEORY,HE

ORIGINAL BOSONIC THEORY, 26 DIMS

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

Strings are not fundamental to M-theory

All five perturbative string theories are connected by DUALITIES.

Also connected to an eleven dimensional theory that at low energies is

described by supergravity.

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.

S=A

𝟒

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 INFORMATIONAL CONTENT OF ALL THE OBJECTS THAT HAVE FALLEN INTO THE HOLE MIGHT BE ENTIRELY CONTAINED IN SURFACE FLUCTUATIONS OF THE EVENT HORIZON.

THE MAXIMAL ENTROPY SCALES WITH THE AREA OF THE EVENT HORIZON, AND NOT THE VOLUME OF SPACE OF THE BLACK HOLE

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 MALDACENA’S AdS5-CFT4 CORRESPONDENCE (1997)

FIRST ACTUAL EXAMPLE OF A QUANTUM FIELD THEORY THAT IS A THEORY OF GENERAL RELATIVITY. A GRAVITATIONAL THEORY IS EQUIVALENT TO A QUANTUM THEORY!

TYPE IIB STRING THEORY ON THE SPACE ADS5

IS EQUIVALENT TO N = 4 SUPERSYMMETRIC YANG–MILLS THEORY ON THE FOUR-DIMENSIONAL BOUNDARY.

AdS: ANTI DE-SITTER SPACE maximally symmetric spacetime with negative curvature.

AdS5 : 5 DIMENSIONAL ANTI-DE-SITTER SPACE

CFT4: 4DIMENSIONAL CONFORMAL FIELD THEORY An ordinary (non gravitational) field theory which is conformally invariant.

N = 4 SUPERSYMMETRIC YANG–MILLS THEORY SUPERSYMMETRIC: bosons and fermions are in the theory.

YANG-MILLS THEORY: a theory of particle physics that uses non-Abelian groups. S(2)

Electro-Weak and SU(3) Strong force theories are Yang-Mills.

N = 4: number of supersymmetries.

MALDACENA’S AdS5-CFT4 CONJECTURE

CALABI YAU MANIFOLD (THE TINY 6 DIMENSIONAL SPACE)

M10 = P4 X K6

AN IMPORTANT IDENTITY: 10 = 4+6 √ 10 = 5+5 ?

A CALABI-YAU MANIFOLD WITH THE FIRST AND SIMPLEST HOMOTOPY GROUP (TOPOLOGY) (THE FUNDAMENTAL GROUP) IMPLIES

ELECTRIC CHARGES OF A PARTICLE CAN TAKE ON EXOTIC FRACTIONAL VALUES e.g.

1

5 ,  

1

11 ,  

1

13 ,  

1

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“PROFESSOR, WHAT IS E(8) ?” A calculation the size of Manhattan!! It involves 453,060x 453,060 matrices each of whose entries is a polynomial of degree up to 22!!

E8 X E8

E6 X E8

E6

SU(3) X SU(2) X U(1)

SU(2) X U(1)

U(1) SU(3)

HOW MANY DIFFERENT CALABI YAUS? CONSERVATIVE ESTIMATE:

Spring 2008 54

UNIFICATION OF FUNDAMENTAL THEORIES

Electricity

Magnetism

Light

Beta-decay

Neutrinos

Protons

Neutrons

Pions, etc.

Earth Gravity

Celestial Mech.

Electromagnetism

Weak Interaction

Strong Interaction

Universal Gravity

Spacetime Geom.

Electroweak Interaction

Standard Model

General Relativity

STRING THEORY

1864

1965

1971

1973

1976

1687 1916 ?

VAST ARRAY OF VACUUM STATES

WHAT IS THE LANDSCAPE?

“DAS IST NICHT EINMAL FALSCH” “THIS IS NOT EVEN WRONG!!”

A NEW PHILOSOPHY OF SCIENCE?

THE UNREASONABLE EFFECTIVENESS OF MATHEMATICS IN THE NATURAL SCIENCES Eugene Wigner http://www.dartmouth.edu/~matc/MathDrama/reading/Wigner.html LIE GROUPS: U(1) The Electromagnetic Interaction SU(2) The Weak Interaction SU(3) The Strong Interaction SU(3)XSU(2)XU(1) Standard Model of Particle Physics SU(5) A Grand Unified Theory (quarks and leptons) Poincare Group Special Relativity GRADE 2 LIE GROUPS SUPERSYMMETRY E(8)X(E8) The Gauge Group of the Universe (?) (String Theory)