Strings, Gravity and Locality: An Overview ofModern Cosmology
Physics at the Dawn of the 20th Century: The Clockwork Universe Newton’s Third Law of Motion F=mdx/dt Universal Law of Gravitation F=GMm/r2 Maxwell’s Equations ▼∙E = ρ/ε ▼x E = −∂B/∂t ▼∙B = 0 ▼x B = µJ + µε∂E/∂t If one knew the positions of all objects occupying space, these laws would allow him to predict all events until the end of time : nothing could be uncertain; and the future just like the past would be present before his eyes.
Absolute, true, and mathematical TIME passes equably without relation to anything external, and thus without reference to any change or way of measuring of time. Absolute, true, and mathematical SPACE remains similar and immovable without relation to anything external. Physics at the Dawn of the 20th Century: Newton’s Absolute Space and Time
Physics at the Dawn of the 20th Century: The End of Physics "Everything that can be invented has been invented" U.S. Patent Office in 1899. The end of science is at hand… all that is left is working out details, refining the value of certain physical constants to a few more decimal places and mopping up of a few remaining but trivial questions.
General Relativity: A New Understandingof Gravity and Spacetime • Gravity is the curvature of space and time. • Equivalence of mass and energy (E=mc2). • Spacetime – Space and time no longer independent and absolute. • Time dilation and length contraction.
Curvature Tensor - Gµν Represents geometry of spacetime. Stress-energy Tensor -Tµν Distribution of matter and energy. Cosmological Constant- Λ - Property of space. - Needed for a static universe. The Field Equations Gµν = кTµν Static Universe Gµν + Λ = кTµν General RelativityEinstein’s Field Equations Space tells matter how to move. Matter tells space how to curve.
Early Unified Field Theories • Einstein spent last 30 years of life working on this vision without success. • Kaluza Klein Theory • Postulated curled up 5th dimension. • Offered hope of unifying electromagnetism and gravity. • Later experiments ruled this out. • No success.
Birth of Modern Cosmology • The expanding universe. • Uniform expansion. • v = H0r • Cosmic Microwave background. • Cosmological principle • 2.7K • From when Universe 300,000 yrs old.
The Big BangA Dynamic Universe - General Relativity. - Evolving from early homogenous state. - Decelerating expansion. - Possible beginning and end. • Fate determined by amount of mass (critical mass). • Finite/unbounded, infinite/bounded, etc…?. • ~ 15 billion years old (~ к/H0).
Quantum MechanicsThe Other Revolution • Wave-particle duality. • Heisenberg Uncertainty Principle. • Complementarity. • Causality, probability and clockwork. • Non-locality. • Copenhagen. • God does play dice!
Quantum Mechanics The Fundamentals Uncertainty Relationships ∆x∆P = ħ/2 ∆E∆t = ħ/2 ∆A∆B = ħ/2 Schrödinger's Equation −ħ2∂2Ψ(x,t)/2m∂x2 + U(x)Ψ(x,t) = iħ∂Ψ(x,t)/∂t Bell’s Inequality │P(a,b) – P(a,c)│ ≤ 1 + P(b,c)
Quantum Mechanics & Cosmology • Quantum fluctuations: The Genesis engine? • Quantum fluctuations: A vacuum alive with energy. • Quantum fluctuations: A natural source for a cosmological constant. • Quantum fluctuations: CMB anisotropies, the seeds of structure. • Evaporating black holes.
Forces Electromagnetic (QED) Weak Force Strong force (QCD) No gravity Misc. Electroweak unification. Particle masses are added in not predicted. Particles Fermions (matter) Quarks Leptons Matter/Anti-matter pairs. Bosons (forces) Gluon W and Z boson Photon Quantum Mechanics andThe Standard Model
Dark Matter and Neutrinos Dark Matter • Baryonic. • Massive Compact Halo Objects (MACHOS). • Supermassive Black Holes. • Non-Baryonic. • Weakly Interacting Massive Particles (WIMPS). • Neutrinos • Fundamental particle. • Weakly interacting (Trillions pass through our bodies every second). • Very small mass. • Under ground tank detectors.
Cosmology in the Early 1990s • Big Bang • General Relativity • Smooth & homogeneous • CMB anisotropies (QM) • Expanding universe • Decelerating • Fate dependant on mass • Vacuum energy • Standard Model • Fundamental particles • Electroweak unification • Universe seems flat. Something missing? • QM ≠ Gravity • Unification of forces • Homogeneity of CMB • Flatness of space • Mass question • Dark matter
Unified Field Theory Grand Unification Quantum Gravity (graviton) Higgs interaction Higgs boson Inflation 10-35s A.BB 10-32s duration 1050x expansion Symmetry breaking/ Vacuum energy/ cosmological constant Homogeneity Smooth curvature Seed structure Supersymmetry fermions → bosons bosons → fermions Every particle has a super partner Predicts Higgs boson Extensions
History String theory – ‘70. Initially strong force. Fails, but… Predicted massless spin 2 particle – graviton? Quantum gravity? Supersymmetry + gravity = 11-D supergravity. Supersymmetry + strings = 10-D superstrings – ’80. Theory of everything. 5 versions. Duality and the relationship between theories – ’95. 0-9-D P-branes. Superstring Theory:The Theory of Everything?
Superstring Theory:What is it? • 1-dimensional strings – 10-33cm. • Particle - mode of vibration. • Matter • Force • 10-dimensional spacetime. • QM and gravity. • By doing away with dimensionless point. • In fact, requires gravity! • Spacetime not fundamental – Emergent on a classical scale?
M-TheoryThe Real Theory of Everything? • 11- dimensional theory. • Unites 5-string theories while including supergravity and p-branes. • Duality - Simply different aspects of same theory. • Ends of open strings confined to move within brane. • Properties of branes revealed by examination of strings which endpoints it contains. • Dimensionality may only emerge in semi-classical contexts as an artifact of particular solutions. • Do not know the final form yet.
Big Bang model No singularity. Same mechanism as for QM/GR. Space may not be fundamental on these scales. Cosmic strings – seeding structure The Universe as a brane. 3 dimensional space as a 3-brane. Open strings constrained to brain would not “see” outside. So large dimensions could be unnoticed. Gravity not constrained: measurable consequences. Measure extra dimensions Ekpyrotic Universe Universe as a 3-brane afloat in a higher dimensional space with other 3-branes Initially cold and flat 3-branes collide Energy results in matter and radiation Finite temperature Inflation Cyclic Model Self dual point Contraction until dual to large scale String/Brane Cosmology
1998 studies - Rate of expansion increasing! Dark Energy – Cosmological constant Quantum vacuum energy Too much though General relativity – negative pressure Gµν + Λ = кTµν Gµν = Λ + кTµν Property of space ↔ form of energy M-Theory – Leaked Gravity Gravity not confined to brane Leaks puts tension on brane inherent warp→ Einstein’s Λ Measurable large distances Cosmic Acceleration!
Cosmic Composition • 95% Universe mystery. • 30% Dark matter. • Non-baryonic. • 65% Dark energy. • 5% normal stuff. • .3% Neutrinos.
Multiverse • Level I – Cosmic Horizon • Same physics. • Different Initial conditions. • infinite space - Infinite regions • Level II – Bubble Inflation • Same equations • Possibly different constants, particles and dimensionality. • Chaotic inflation – bubble regions • Level III – QM Many Worlds • Level IV – Mathematical • Any mathematical model. • Any laws of physics.
9 Questions for21st Century Physics • Are there undiscovered principles of nature: new symmetries, new physical laws? (M-Theory, etc…) • How can we solve the mystery of dark energy? • Are there extra dimensions? • Are all forces simply one aspect of a single force? • Why so many kinds of particles? • What is dark matter and how can we make it in the laboratory? • What are neutrinos telling us? • How did the universe come to be? • What happened to all the antimatter?
How Do We Know What We Know • Nature shows us only the tail of the lion. But I do not doubt that the lion belongs to it even though he cannot at once reveal himself – Einstein. • Scientific knowledge is a body of statements of varying degrees of certainty – Feynman • It is 'Scientific' only to say what's more likely and less likely– Feynman • It is wrong to think that the task of physics is to find out how Nature is. Physics concerns what we say about Nature. - Niels Bohr • All of us live with the knowledge that there is an ultimate truth and our mistakes will be discovered. - Persis Drell