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