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Einstein’s Brane
Not his brain!
Paul K. TownsendDepartment of Applied Mathematics and
Theoretical Physics Centre for Mathematical Sciences, Cam-
bridge University
Zurich, November 13, 2015
Nor his favorite tipple!
Relativity GRAVITY
1632 1642
&
1687
1904 19051915
1907
161617th Century20th Century
E= mc2
1905 Special Relativity
1915 General Relativity
Gmn = 8π G Tmn
NEWTON’S GRAVITATIONAL
CONSTANT
SPEED OF LIGHT
1917 CosmologyEINSTEIN’S
COSMOLOGICALCONSTANT
Gmn + Λ gmn = 8πG Tmn
Gravitational Waves
Known Forces of Nature, circa 1916
Electromagneticfield theory
Gravity as a field theory
What’s next?
UNIFIED FIELD THEORY ?
Weyl, 1918 Kaluza, 1921 Klein, 1926
Einstein 1925
Some good ideas but
many ingredients are missing!
EXTRA SPACE DIMENSIONSGauge Invariance
The Ingredients
Three ``families’’ ofelementary particles!
DARK ENERGY
DARKMATTER
GRAVITON:Quantum of
Gravitational wave
+ +
+ =
Quantum ofElectromagnetic
wave
TWO GIFTS FROM the SEVENTIES
SUPERSYMMETRYUnifies matter and forces
QUANTUM STRINGS
``Predicts’’ Gravity (includes graviton)
Requires 6 extra dimensions (and supersymmetry)
Not (yet) seen!
Uniform tension T
Small amplitude wave:
Ideal StringsUniform mass density ρ
v2 = T/ρ
v ≤ c T ≤ ρc2
v
(kg/m)
(Newtons)
String
(Energy density)
Kinds of string
Guitar Strings T << ρc2
T = 0Spool of thread
String Theory Strings T = ρc2
Energy density
Closed Strings
Lowest oscillation state is the graviton
Quantum Gravity
But, need supersymmetry AND 9 space dimensions
Superstring Theory
There are just five of these
The 1980s
Open Strings
Open strings end on branes:
For example a membrane
(extended in 2 space dimensions)
p-Branes
• p=1. • p=2. • p=3. • p=4 .......
possible with extra space dimensions!
MembraneString
Three-braneSpace filling!
Kinds of Branes
TT
T
T
T
Surface Tension T
Mass density ρ
String theory branes saturate the bound:
T= ρc2
e.g. a drumT << ρc2
T ≤ ρc2
M-Theory : the unification of
superstring theories
Membrane in 10 space dimensions
String in 9 space dimensions
Kaluza-Kleinat work
1990s
Now, even strings are really branes
Brane DemocracyIn M-Theory, all branes are equal
(but some are more equal than others)
That’s because they areall made from the same
T= ρc2 ``stuff’’
String
3-brane (for example)
Supersymmetry ``justifies’’
these pictures
Brane-World
..
electronHiggs boson
positron
.
.
Quark
Multiple Branes
Particles are quanta of fluctuations of branes
BRANES vs BULK
Interact onlyvia gravity
Dark Matter
Branes
BULK
Dark Energy
Simplest explanation: Einstein’s cosmological constant Λ
Equivalent to filling space with a T= ρc2 tensile materiala
Georges Lemaître1927
A three-brane !
Vos calculs sont corrects mais votre physique est
abominable
Why is Gravity different?
Gravity resists unification with otherforces of nature.
As formulated by Einstein, it appears incompatible with Quantum Mechanics
M-theory explains why: Gravity governs the dynamics of the BULK
Other forces act only on BRANES
What is the BULK?Modern idea: it emerges holographically
from quantum fields on branes
Brane Bulk
Holographimage
fuzzyimage
Pointillism vs Ondulism
Seurat Monet
Brane Bulk