Added Dimensions. Efforts to unify quantum physics and general relativity

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1 Added Dimensions Efforts to unify quantum physics and general relativity - Why are there only 4 extended dimensions? - Symmetry, elementary particles and the Standard Model - Supersymmetry - Kaluza-Klein theory: 5 dimensions - String theory: 10 dimensions - M-theory: 11 dimensions, branes and the multiverse

2 Why are there only 4 dimensions? (3 space and 1 time) - Gravity and electromagnetism would not have an inversesquare law if there were more than 3 space dimensions (first discovered by Immanuel Kant in the 1700 s) - Planetary orbits would not remain stable in more than 3 space dimensions (first discovered by Paul Ehrenfest in 1920) - Electrons would not remain stably in orbitals surrounding atomic nuclei in more than 3 space dimensions (discovered by F. R. Tangherlini in 1963) - Wave impulses would become distorted if there were a number of space dimensions other than 1 or 3 (Ehrenfest) - Protons and electrons would be unstable if there were more than 1 time dimension (Max Tegmark, 1997)

3 - When the number of dimensions is too great or too small, the equations of physics become unpredictable - When the number is too small, observers are not possible - In more than 3 space or time dimensions, atoms are unstable

4 Elementary particles - Fundamental constituents of matter and energy forces - Described by quantum field theory - Matter is made of quarks and leptons (collectively called fermions) There are three generations or families of matter - Energy forces are transmitted by bosons - Particles have anti-particles with opposite electric charges

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6 Elementary Particles MATTER ENERGY (FORCE CARRIERS) - Quarks - Bosons Up (u), Down (d) Photon (g) Charmed (c), Strange (s) Gluon (g) (8 flavors) Top (t), Bottom (b) W Z - Leptons ( Higgs) Electron (e) ( Graviton) Muon (m) Tau (t) Electron neutrino (n e ) Muon neutrino (n m ) Tau neutrino (n t )

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8 Particle interactions - Feynman diagrams world lines of particles - Example: two electrons exchanging a photon e - e - time g space - Particles intersect at single points in spacetime

9 Large Hadron Collider at CERN

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11 Example particle collision in a detector

12 Example particle collision in a detector

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14 Fermions matter particles - Fermions make up the atoms that make up the matter we experience in our everyday lives - Quarks: Make up atomic nuclei Massive: all but first generation (up and down quark) are short-lived and unstable - Leptons: Orbit atomic nuclei (electrons) and carry weak charge (neutrinos) Very low mass

15 Fermions matter particles

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17 Quarks and gluons the strong force - There are three strong force charges red, blue and green Each of the quarks in each generation of particles is available with each type of charge - Each charge has an anti-charge (anti-red, anti-blue, anti-green) - Combinations of quarks must be colorless - Gluons carry the charge of the strong interaction, unlike photons which do not carry the charge of the electromagnetic interaction - Leads to the consequence of asymptotic freedom As quarks get closer together the force gets weaker As they get farther apart the force gets stronger Means quarks can never be observed in isolation

18 Computer simulation of gluon flux tubes joining quarks within a baryon

19 The weak force - Changes one particle into another! - Muon and tau can turn into neutrinos - Quarks can turn into other types of quarks - Responsible for nuclear fusion in the sun - Responsible for beta decay in radioactivity - The neutrino interacts only via the weak force (and gravity) This is why it can pass through all types of matter without being stopped

20 Carriers of the weak force - For the weak force, there are three force carrier particles: W + W - Z 0 These are electrically charged in addition to carrying the weak force This one is electrically neutral - These particles are very massive almost as massive as the top quark (the most massive particle known) - This means the weak force is very short range

21 Relative strengths of forces Strength for 2 quarks at m Strength for 2 quarks at 3x10-17 m Gravity Weak Electromagnetic Strong Why do the forces have the strengths they do? - In particular, why is gravity so much weaker than the others? It s a mystery!

22 Summary of forces and carrier particles Interaction Carriers Act On Particles Gravitation (Graviton?) All (infinite) Weak force W +, W -, Z 0 Electrons, (10-16 cm) muons, taus, quarks, neutrinos Electromagnetic Photon Electrons, Force muons, taus, (infinite) quarks, W +, W - Strong force Gluons (8) Quarks, gluons (10-13 cm)

23 Some quantum numbers of particles Each particle has a characteristic - Charge Electromagnetic force charge: + / 0 / - Weak force charge Color charge (strong nuclear force): quarks/gluons only - Spin (angular momentum) Fermions: Integer spins (0, 1, ) Bosons: Half-integer spins (1/2, 3/2, ) There are actually many more quantum numbers involved in defining the behavior of particles Each quantum number is a conserved quantity: the total amount of it does not change in particle interactions

24 The Standard Model - Based on Quantum Field Theory Fields are quantized into particles (e.g. EM field -> photons) Consistent with Special Relativity (Lorentz invariance) Renormalizable does not give infinite answers - Explains observed behavior of all known particles; predicted new particles that were later observed - Unifies electromagnetism, weak force at high energies (electroweak unification) - Suggests possibility of unifying strong force with electroweak force at even higher energies (grand unified theory or GUT) - Does not include gravity or General Relativity

25 The unification of forces in physics

26 The unification of forces in physics? - The goal of unification theories (like string theory) is to explain the?

27 Symmetries in the Standard Model - Particle / anti-particle symmetry - Symmetry of structure of 3 generations of matter particles - Conservation laws Charge Mass/energy Spin (angular momentum) and other quantum numbers Parity (physics is the same for mirror images) True for electromagnetism, gravity and strong forces; Not true for weak force! - Gauge symmetry: invariance under local transformations of the spacetime system, due to the presence of gauge fields

28 Chen Ning Yang Chinese-American physicist - Nobel Prize, With Tsung-Dao Lee, proposed that parity is violated by the weak force; experimentally verified by C.S. Wu - With Robert Mills, developed modern gauge symmetry theory (non-abelian gauge theory, or Yang-Mills theory) - Married a 28-year-old graduate student at age 82 in 2005

29 Gauge Symmetry

30 Electromagnetic Gauge Field U(1) Symmetry

31 Gauge symmetry - A field has a magnitude and direction at every point in spacetime: this combination is the field s potential - Each circle represents the potential at a single point in spacetime a. Potential Magnitude value of = a radius field becomes of circle varied at different points in spacetime Direction = where the arrow in the circle is pointing b. Variation - Suppose of an value initially of potential symmetric is compensated static field: by gauge field (wavy lines) time

32 Gauge symmetry a. Potential value of field becomes varied at different points in spacetime b. Variation of value of potential is compensated by gauge field (wavy lines) c. Original symmetric field configuration is restored

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34 Gauge symmetry a. Potential value of a field becomes varied at different points in spacetime b. Variation of value of potential is compensated by gauge field (wavy lines) c. Original symmetric field configuration is restored

35 Gauge symmetry a. Potential value of a field becomes varied at different points in spacetime b. Variation of value of potential is compensated by gauge field (wavy lines) c. Original symmetric field configuration is restored

36 Internal symmetry space for gauge field space time world line of particle

37 Internal symmetry space for gauge field internal symmetry space (field potential magnitude) fiber bundle space time world line of particle

38 Path through internal symmetry space with no gauge field present internal symmetry space (field potential magnitude) space fiber bundle path of field magnitude through internal symmetry space time world line of particle

39 Path through internal symmetry space with internal symmetry space (field potential magnitude) space gauge field present fiber bundle path of field magnitude through internal symmetry space time world line of particle

40 Gauge symmetry - Electromagnetism: U(1) Unitary symmetry group with one degree of freedom Represented by rotations around a circle Gauge boson is the photon - Weak force: SU(2) Special unitary symmetry group with two degrees of freedom Represented by rotations on the surface of a sphere Gauge bosons are the W and Z particles - Strong force: SU(3) Special unitary symmetry group with three degrees of freedom Represented by rotations in a complex hyperspace Gauge bosons are the eight gluons

41 Symmetry Breaking - At high energies (e.g. in the Big Bang) all forces are the same (symmetrical) - At lower energies the forces become differentiated (the symmetry breaks) - Similar to the way hot steam has no directionality (it is symmetrical in all directions), but frozen ice crystals have specific directionality

42 Symmetry breaking of forces during Time from Big Bang (seconds) Big Bang

43 Evolution of the universe

44 Masses of elementary particles

45 Why do the particles have the masses that they do? (the hierarchy problem ) - It s a mystery! By gauge theory alone, particles should have no mass at all - The hierarchy problem : why are the particle masses so much less than the force unification energy? - In the Standard Model, particles get their masses from interaction with the Higgs field (whose gauge boson is the Higgs particle recently detected at CERN LHC) - But the model does not predict the specific sizes of particle masses (except for the W and Z bosons)

46 Higgs field vs. Electromagnetic field - Minimum Electromagnetic field potential is at zero energy

47 Higgs field vs. Electromagnetic field - Minimum Higgs field potential is not at zero energy, therefore symmetry breaks and particle gets positive mass

48 The former prime minister of England walks into a cocktail party

49 The former prime minister of England walks into a cocktail party

50 Strength Strength Supersymmetry one solution to the hierarchy problem Strong Strong Weak Weak Electromagnetic Electromagnetic Energy Energy - SM = Standard Model; MSSM = Minimal Supersymmetric Standard Model - Under MSSM the electromagnetic, weak and strong forces unify more precisely at high energy than under the normal Standard Model

51 Bruno Zumino - Italian-American physicist at U. of California - Berkeley: Dirac Medal, With Julius Wess, developed theory of supersymmetry in 1974 (independently developed by Golfand and Likhtman and by Volkov and Akulov in Russia) -The Minimal Supersymmetric Standard Model (MSSM) was first proposed in 1981 by Howard Georgi and Savas Dimopolous

52 Supersymmetry - Basic to String and M Theory

53 What Is Supersymmetry? - Superpartner particles have higher masses than ordinary particles (corresponding to their higher energies) May be detectible by LHC at CERN Supersymmetry breaks at much lower energy than force unification (solves hierarchy problem) - Superpartner particles spins are ½ less than those of their ordinary partner particles

54 History of unification theories in physics

55 Problems in unifying quantum field theory and general relativity - To quantize the gravitational field involves quantizing spacetime itself - The quantum particle of this field is the graviton, a massless spin-2 boson All other particles either have spin ½ (fermions) or spin 1 (bosons) No consistent gauge theory exists for spin-2 particles - The resulting theory is not renormalizable Particle interaction sites are single points in spacetime Single points have zero size Gravitational fields at single points can t be calculated Equations produce infinite results - singularities

56 Theodor Kaluza German mathematician - Spoke 17 languages (favorite was Arabic) - Developed unified theory of gravity and electromagnetism in 1919 by generalizing Einstein s theory of general relativity to 5 dimensions - Sent his results to Einstein, who sat on them for two years before finally encouraging Kaluza to publish in 1921

57 Oskar Klein Son of chief rabbi of Stockholm; physicist at University of Michigan and Stockholm University - Independently discovered 5-D unification of gravitation and electromagnetism in Proposed that the 5 th dimension is curled up ( compactified ) into a sub-nanoscopic circle (r=10-34 m), which is why it is not observed in nature

58 - What we see: Compactification

59 - What we see: Compactification - What an ant sees: Compact dimension

60 Kaluza-Klein space (1 compactified dimension) - Compactified dimension exists at all points in space - It is shown only at grid line intersections for clarity

61 Kaluza-Klein theory - In the 5-D space there is only one force: Gravity - In the 4-D space of our experience this becomes three forces: Gravity (same as Einstein s general relativity) Electromagnetism (electric charge corresponds to the component of the momentum of particles in the 5 th dimension, while electric force corresponds to the component of the gravitational force in the 5 th dimension) A third force (the radion )

62 Problems with original Kaluza-Klein theory - Singularities in the equations describing the behavior of electrons - Electromagnetic and gravitational forces of equal strength - Predicts an extra field (the radion ) not observed in nature - Predicts a tower or set of very massive particles at extremely high energies that are not observed in nature (yet) These are caused by the effects of normal particles entering the extra dimension with enough energy or momentum

63 Kaluza-Klein spaces (2 compactified dimensions) 2 dimensions compactified in the shape of a sphere 2 dimensions compactified in the shape of a torus - Compactified dimensions exist at all points in space - They are shown only at grid line intersections for clarity

64 Attempts at revised Kaluza-Klein theories -1938: Klein tries a 6-D theory including the nuclear strong and weak forces as well as gravity and electromagnetism Theory predicted numerous massless bosons not observed in nature -1938: Einstein, Bergmann and Bargmann try a 5-D theory in which the 5 th dimension is rolled up along one of the other space dimensions into a sub-nanoscopic tube Theory predicted that electromagnetism and gravity should be similar in strength : Cremmer, Julia and Scherk propose an 11-D theory of supersymmetric gravity in which 6 dimensions roll up into sub-nanoscopic hyperspheres

65 String theory - Began in the late 1960s and early 1970s as an attempt to describe bosons as vibrations of stringlike objects Different vibrational modes equate to different quantum number configurations (different particles and particle characteristics) - Later expanded to represent all particles including gravitons Predicts and requires supersymmetric particles - Unifies gravity with electromagnetism, strong and weak forces - Explains hierarchy problem - Can t be tested experimentally at present Energies required are far too large to probe strings directly LHC at CERN may detect supersymmetric particles

66 Example: string vibrational modes and particle mass Low energy mode = low particle mass Intermediate energy mode = intermediate particle mass High energy mode = high particle mass - Above illustration is for a closed string particle vibrating in 2-D only

67 Strings and world sheets time space space

68 Particle interactions in string theory e - e - time g space space - No single points of intersection = no singularities

69 Uncertainty in string theory - Quantum field theory: basic measure of uncertainty given by Planck s constant h = x ev sec Momentum (or position) can t be defined more precisely - String theory: new basic measure of uncertainty given by the string size a = cm 2 Spacetime can t be defined more precisely

70 String theory requires 10 dimensions - Why? Accommodates enough degrees of vibrational freedom to represent all the different quantum numbers (mass, charge, spin, etc.) Incorporates all standard model gauge symmetries Mathematically consistent (no negative probabilities, no singularities, etc.) - What happens to the other 6 dimensions? They may compactify, as in the Kaluza-Klein theory Or they may be large, but inaccessible to us (leads to concept of branes in M-theory) - Size of the compactified dimensions: ~10-34 m (as in Kaluza-Klein theories)

71 How do the extra dimensions compactify? - Not all compactification mechanisms lead to valid physics The shape of the compactified dimensions must allow for the proper kinds of string vibrations to generate the particles and quantum properties we observe in nature - In 10-D theories: Extra 6 dimensions compactify into Calabi-Yau spaces

72 Shing-Tung Yau Chinese-American mathematician, chair of Harvard University mathematics department; Fields Medal, In 1976, proved a conjecture of Eugenio Calabi about the existence of good metrics on complex manifolds, thereby discovering Calabi-Yau spaces

73 Animation of 3-D projection of 6-D Calabi-Yau space

74 3-D projection of a 6-D Calabi-Yau space - The pattern of holes in the space affects the vibrational patterns of the strings, which determines the quantum numbers of the particles (charge, spin, etc.)

75 3-D projection of another 6-D Calabi-Yau space -There are tens of thousands of Calabi-Yau spaces and very few criteria for choosing which one represents our universe - It should have 3 holes, since there are 3 particle families

76 10-D space with 6 dimensions compactified in a Calabi-Yau shape - Compactified dimensions exist at all points in space - They are shown at grid intersection points only for clarity

77 Summary of string theories Type IIB Type IIA E 8 x E 8 Heterotic SO(32) Heterotic Type I SO(32) String Type Closed Closed Closed Closed Open (& closed) 10d Supersymmetry N=2 (chiral) N=2 (nonchiral) N=1 N=1 N=1 10d Gauge symmetry none none E 8 x E 8 SO(32) SO(32)

78 Summary of string theories Type IIB Type IIA E 8 x E 8 Heterotic SO(32) Heterotic Type I SO(32) String Type Closed Closed Closed Closed Open (& closed) 10d Supersymmetry N=2 (chiral) N=2 (nonchiral) N=1 N=1 N=1 10d Gauge symmetry none none E 8 x E 8 SO(32) SO(32) - At low energies, the E 8 x E 8 Heterotic theory compactified on a Calabi-Yau space resembles the Standard Model

79 How E 8 x E 8 heterotic theory compactified on Calabi-Yau space resembles SM physics Flat 10-D Superstring E 8 x E 8 theory 6 compact dimensions, 4 ordinary dimensions Superstring E 8 x E 8 theory Calabi-Yau compactification Massive particles with fractional electric charges shadow matter Magnetic monopoles Unified U(1) x SU(2) x SU(3) + supergravity + U(1) x SU(2) x? New forces Electromagnetism Weak force Strong force Gravity Particles Superparticles

80 Edward Witten Physicist, Institute for Advanced Study, Princeton; Fields Medal, Key developer of string theory, along with Andre Neveu, John Schwarz, Michael Green and Pierre Ramond - Originator of M-theory as a unifying concept uniting several different types of string theories - String theory is a part of 21 st century physics that fell by chance into the 20 th century

81 Witten s question: Search for a realistic Kaluza-Klein theory What is the minimum dimension of a space which can have SU(3) x SU(2) x U(1) gauge symmetry? U(1) = electromagnetic field symmetry (represented by rotations around a circle): needs 1 dimension SU(2) = weak force symmetry (represented by rotations on the surface of a sphere): needs 2 dimensions SU(3) = strong force symmetry (represented by rotations in a space with several complex variables): needs 4 dimensions Adding these 7 dimensions to the 4 dimensions of spacetime gives 11 total dimensions

82 M-Theory - 11 dimensions (10 space, 1 time) - Not all the extra dimensions are compactified some are extended - Our universe is a 4-dimensional subset (4-brane) of the whole 11-dimensional space (the bulk ) - There may be other subsets besides ours!

83 Heterotic SO(32) Heterotic E8 x E8

84 Virtual string pair formation and space string coupling constants space time String interaction String splits into virtual string pair Strings recombine Interaction termination - Coupling constant determines the probability of one string splitting into a virtual string pair - Weak coupling (constant <1) means probability can be ignored for multiple successive loops; strong coupling (constant >1) means it can not be ignored - S-Duality: physics of one theory s strong coupling = physics of another theory s weak coupling

85 Closed string winding modes on compactified dimensions r radius of compactified dimension - Winding creates energy in addition to the string vibrations and the motion of the string along or around the dimension - In certain cases the sum of winding and vibration/motion energy is the same for radius = r and radius = 1/r - In these cases the physics of large and small dimensions and unwound and wound strings is the same: T-duality

86 M-Theory and relationships among different string theories - T-duality: Physics of theory compactified at radius r = physics of alternate theory compactified at radius 1/r - S-duality: Physics of one theory s strong coupling = physics of alternate theory s weak coupling

87 Shrinking a 2-D toroidal brane s radius to zero to form a closed string 11-D M-theory 10-D Type IIA string theory r - r = radius of toroidal brane

88 Example: Relationship between M-theory in 11 dimensions and Type IIA string theory in 10 dimensions 11-dimension M-theory compactified on sub-nano-circle Wrap 2-D brane on circle, join ends to form torus and reduce radius of torus to zero Shrink membrane to zero size IIA in 10 dimensions IIA superstring point particle Unwrapped brane Wrap 5-D brane on circle flat plane 4-D space-time

89 Large Extra Dimension Models - By experimental limits, extra dimensions could still be as large as 0.1 millimeter This will be tested by gravity, which behaves as F ~ M 1 M 2 / r n+2 for n extra dimensions - Large extra dimensions would show up in experiments at the LHC as invisible missing energy disappearing into the extra dimensions, or as one micro black hole a second being produced

90 String Theory (or M-Theory): Multiverse - Particles = vibrating strings in 11-D space-time (the Bulk ) - Universes = subsets of the Bulk (ours is a 4-D brane ) - String vibrational patterns determine particle characteristics (e.g. charge, mass-energy, spin, etc.) - M-theory parameters specify and restrict strings behavior Hundreds of parameters ( moduli ) - Countably infinite number ( 0 ) of branes (universes) Each described by a different M-theory Vast majority will be unstable and vanish Tiny fraction but still huge number (~ ) of stable ones remain, of which ours is one - Because of this huge number we can t tell exactly which M-theory describes our specific universe

91 Strings and branes in the bulk Open strings (attached to brane) Closed strings (can leave brane) Brane Another brane

92 The Multiverse

93 The M-Theory Multiverse Landscape - Graph axes show only 2 out of hundreds of M-theory parameters ( moduli ) that determine how strings behave Potential energy density - Each point on the Landscape represents a single Universe with a particular range of string behaviors - Each Universe could be realized in a separate post-inflation bubble

94 Lisa Randall Professor of Physics, Harvard University - Winner of Westinghouse Science Talent Search as high school student - With student Raman Sundrum, authored seminal 1999 paper suggesting that extra dimensions did not need to be compactified and that gravity could move among branes while other forces would remain stuck to individual branes

95 String size = cm Randall-Sundrum Model (RS-1) String size = cm ( Bulk )

96 Paul Steinhardt Albert Einstein Professor of Physics, Princeton University; Dirac Medal, With Neil Turok of Cambridge, developed the ekpyrotic universe theory, in which the big bang is replaced by a cyclic collision between branes (with a cycle time approximating 1 trillion years)

97 M-Theory: Two Branes Colliding in the Bulk - The distance between the branes in the bulk may be about 0.1 millimeter

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99 Issues with M-theory and string theory - Can not be experimentally tested (yet) Hopes placed on LHC at CERN to detect supersymmetric particles, but this will not prove the theory - Mathematics to fully develop the theory largely doesn t exist General relativity and quantum field theory: mathematics mostly developed 50+ years before the physics M-theory: similar to development of calculus with Newton and Leibniz physics is stimulating the creation of completely new mathematics (e.g. non-commutative geometry, quantum geometry) - Does not really describe a specific universe No principles for selecting which of the zillions of choices in the multiverse landscape represents our universe

100 Actually, I would not even be prepared to call string theory a theory imagine that I give you a chair, while explaining that the legs are still missing, and that the seat, back, and armrest will be delivered soon; whatever I did give you, can I still call it a chair? Gerard t Hooft, Nobel Prize winner in Physics

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102 Matter and force carrier particles and their major characteristics - Note the three generations or families of matter particles (fermions) every particle also has an anti-particle

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104 space time

105 Bosons Force carrying particles (8) massless

106 Kinds of quarks and anti-quarks

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108 The unification of forces in physics - Strong Force - Weak Force -Electro Magnetic Force - The goal of unification theories (like string theory) is to explain the?

109 Relative strengths of forces in Standard Model ( hierarchy problem ) -The hierarchy problem is the problem of explaining the difference in the strengths of the four forces

110 Gauge symmetry 1. Potential value of a field at different points in spacetime

111 Gauge symmetry 1. Potential value of a field at different points in spacetime 2. Variation of value of potential at different points in spacetime

112 Gauge symmetry 1. Potential value of a field at different points in spacetime 2. Variation of value of potential at different points in spacetime 3. Variation of value is compensated by gauge field (represented by curved arrows)

113 Gauge symmetry 1. Potential value of a field at different points Variation of value of potential at different points 3. Variation of value is compensated by gauge field (represented by curved arrows) 4. Original field configuration is restored - Quantum of the gauge field is called a gauge boson

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116 The Higgs Field - Minimum potential is not at zero - Therefore symmetry breaks and particle gets positive mass

117 Feynman diagram of neutral weak current (muon neutrino scattering off electron) n m Z o e n m e

118 Symmetry breaking of forces during Big Bang

119 Supersymmetry one solution to the hierarchy problem - SM = Standard Model; MSSM = Minimal Super Symmetric Model - Under the MSSM the electromagnetic (EM), weak (W) and strong (S) forces unify more precisely at high energy than they do under the standard model

120 Supersymmetry one solution to the hierarchy problem - MSSM = Minimal Super Symmetric Model - Under the MSSM the electromagnetic (U(1)), weak (SU(2)), and strong (SU(3)) forces unify more precisely at high energy than they do under the standard model

121 What is supersymmetry? - All particles have superpartners that exist only at very high energies force-carrying bosons have matter fermion partners and vice versa Names of boson superpartners of fermions all start with s e.g., squark, selectron, etc. Names of fermion superpartners of bosons all end with ino - e.g., photino, Wino, gravitino, etc. - Superpartner particles have higher masses than ordinary particles (corresponding to their higher energies) May be detectible by LHC Supersymmetry breaks at much lower energy than force unification (solves hierarchy problem) - Superpartner particles spins differ by ½ from spins of their ordinary partner particles (superpartners spins are ½ less) - Supersymmetry is a basic assumption of string and M-theory

122 Evidence for supersymmetric particles? Observed rotational speed based on Doppler shift data Rotational speed models based on visible light observations of galactic halo, disk and gas - Rotation of galaxies (for example NGC6503) is much faster than predicted from the mass of the visible matter in them - This is evidence for dark matter which could be made up of supersymmetric particles (other explanations possible)

123 A Bit of History of Unification Electricity unified with magnetism (M. Faraday and J. C. Maxwell). Relativity and General Relativity (A. Einstein). Quantum Mechanics (Planck, Bohr, Schrodinger and Heisenberg). Relativistic quantum mechanics (P. Dirac). Quantum Electrodynamics (R. Feynman, Tomonaga, Schwinger). Quarks and Quantum Chromodynamics (Nemann, M. Gell-Mann and G. Zweig). Unification of Electromagnetism with Weak Interactions to form Electroweak theory (S. Weinberg, A. Salam). Grand Unified Theories Supersymmetry Superstring Theory of Everything including gravity.

124 Symmetries and conservation laws Symmetry Under Implies Conservation of Time dimension translation Space dimension translation Rotation Energy Momentum Angular momentum

125 Closed string vibrating in 3D

126 Gauge symmetry We can illustrate the concept of gauge symmetry as follows: - Electric and magnetic fields can be expressed using potential functions. - These can be exchanged (gauge-transformed ) according to a certain rule without changing the fields. The simplest transformation is to add a constant to the electric potential Physically this illustrates the well-known fact that electric potential can be calculated from an arbitrary zero point, since only the differences in potential are significant. This is why a squirrel can walk along a highvoltage cable without being injured. - That the zero point can be moved in this way is perceived by physicists as a symmetry in the theory, gauge symmetry.

127 How E 8 x E 8 heterotic string compactified on Calabi-Yau space resembles SM physics

128 Type I SO(32) Heterotic M-Theory Type IIA 11-D Supergravity E8xE8 Heterotic Type IIB

129 - Exist in M-theory Branes - N-dimensional membranes or hypersurfaces that are subsets of the whole 11-dimensional spacetime (the bulk ) - Our universe is a 4-dimensional brane (or D4-brane ) - There may be other branes of varying dimensionality - Open strings live on branes (are permanently attached) If open strings represent fermions and bosons, it means that all normal matter plus the strong, weak and electromagnetic forces are stuck in our own D4-brane - Closed strings can move through the bulk If closed strings represent gravitons, it means that gravitational forces can be felt across branes Suggests another possible explanation for dark matter

130 Collision of proton and antiproton in a brane - Collision produces normal particles (blue balls), graviton (ripples in brane), and Kaluza-Klein mode of graviton (ball going up out of brane)

131 M-Theory Multiverse - Different universes may be formed by different branes in the bulk - Each universe may have a different number of dimensions, different laws of physics, etc. Based on a number of free parameters in the M-theory describing each universe - There are an infinite number of different universes in the multiverse landscape Each described by a different M-theory The vast majority of them will be unstable and vanish A tiny fraction but still huge number (estimated at > ) of stable ones will remain, of which ours is one

132 Strings, Branes and Black Holes Surface of 5D torus - Hawking radiation: open strings travel in both directions down the D1-brane, emitting closed strings (radiation) when they interact. The system decays into the configuration on the right

133 Ekpyrotic vs. Big Bang model with inflation EKPYROTIC EKPYROTIC MODEL