Transcript Strings, Gravity, and Locality

Strings, Gravity and Locality:
An Overview of
Modern 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.
Physics at the Dawn of the 20th Century:
Newton’s Absolute Space and Time
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: 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.
The 20th Century Revolutions:
General Relativity & Quantum Mechanics
General Relativity: A New Understanding
of 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.
General Relativity
Einstein’s Field Equations
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
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 Bang
A 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 Mechanics
The Other Revolution
• Wave-particle duality.
• Heisenberg Uncertainty
Principle.
• Complementarity.
• Causality, probability
and clockwork.
• Non-locality.
• Copenhagen.
God does play dice!
Quantum Mechanics The Fundamentals
Schrödinger's Equation
−ħ2∂2Ψ(x,t)/2m∂x2 + U(x)Ψ(x,t) = iħ∂Ψ(x,t)/∂t
Uncertainty Relationships
∆x∆P = ħ/2
∆E∆t = ħ/2
∆A∆B = ħ/2
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.
Quantum Mechanics and
The Standard Model
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
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
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–
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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?
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QM ≠ Gravity
Unification of forces
Homogeneity of CMB
Flatness of space
Mass question
Dark matter
Extensions
• Inflation
–
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• Unified Field Theory
– Grand Unification
– Quantum Gravity
(graviton)
• Higgs interaction
– Higgs boson
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
Superstring Theory:
The Theory of Everything?
History
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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:
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-Theory
The Real Theory of Everything?
• 11- dimensional theory.
• Unites 5-string theories while including supergravity and pbranes.
– 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.
String/Brane Cosmology
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
Cosmic Acceleration!
• 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
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Gravity not confined to brane
Leaks puts tension on brane
inherent warp→ Einstein’s Λ
Measurable large distances
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 for
21st 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
The Landscape of Cosmology