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SPACE-TIME , LIGHT and GRAVITY in STRING

THEORY

S. Ramgoolam , Queen Mary, PPARC Wednesday

04/10/2006

Why theoretical physics ?

- Theoretical Physics, despite its use of

sophisticated mathematical tools and sometimes

highly specialized language, reveals surprising

connections between simple concepts which we use

in daily life. - These connections are often easy to state and

have profound consequences for the measurement of

simple physical quantities of universal

relevance.

- The theory of relativity ( of Einstein )

provided examples of this kind of novel

connections between basic concepts - Time and Space
- String Theory provides equally surprising

connections between - Light and Gravity

TIME and SPACE in RELATIVITY THEORY

TIME

- Time, as a physical quantity, reminds us of

duration, measuring instruments sand clocks,

watches, atomic clocks.

- It provides signposts along the sequence of

experiences we live through --- thus providing a

meter in our personal histories. - Time is something we feel we know first hand.

SPACE

- Space reminds us of distance

- and Perspective

- Of places to get to

- And Expanses far from our daily experience

Space-time

- Einstein comes along and teaches us that space

and time are entwined in a remarkable way, which

makes it useful to think about space-time as one

entity.

THE SURPRISES !!

- Some aspects of the new understanding of

space-time in Einsteins theory of Relativity. - Nothing travels faster than light
- A clock travelling at a speed close to that of

light will be found to be slower by an observer

at rest !! This is time dilation - Relativistic dynamics is simple in terms of

space-time diagrams, where notions of distance in

space are generalized to distance in space-time.

- Later, direct observation of time dilation in

particle physics experiments - Time dilation Twin travelling to a distant

galaxy near the speed of light and travelling

back will be found to be much younger than twin

who stayed at home.

LIGHT and GRAVITYin STRING THEORY

STRING THEORY

- String theory offers us surprises of comparable

magnitude. - The elements in Einsteins synthesis were space

and time. - The surprising synthesis emerging from String

theory in the last decade or so involves two

other familiar elements of our experience Light

and Gravity.

- Maxwells Electromagnetic theory of light (

pre-20th century ) when developed to

incorporate the insights of quantum mechanics and

relativity ( early 20th century ) gives rise

to a new framework - Quantum field theory ( QFT )
- mid-20th century

Light and Photons

- In QFT, light can be viewed as an elementary

particle, called the photon - QFT provides a new way to understand force

Force is due to the exchange of elementary

particles - Electric Force between particles e.g.

electrons is due to the exchange of photons (

light )

QFT and Strong Force

- Electrons spread to the outskirts of atoms. The

core of atoms consists of nuclei, made of

protons and neutrons. Protons and neutrons are

themselves made of quarks. - QFT can also account for sub-nuclear forces

between quarks. - The mediators of the ( strong ) force between

quarks are gluons.

- Hence QFT is the language of the Standard model

of Particle Physics (discovered by Weinberg

and Salam ) which has been tested to extremely

high accuracy in accelerators around the world.

Photons, Gluons , Large N

- Photons force between electric charge.
- One kind of charge ( one number, positive or

negative ) . One kind of photon. - Quarks come in 3 colours. Hence gluons come in

multiple types, depending on which quarks they

mediate between. - A simple mathematical generalization consists of

imagining theories with N quarks and N2 gluons.

WHY STRINGS ?

- QFT , while successful in describing

electromagnetic and sub-nuclear forces, is not so

successful in describing the force of gravity. - Rather we need String Theory, which is a new

paradigm whereby fundamental constituents of the

world are lines not points. - A multiplicity of particles arises from different

vibration modes of the same string.

STRING gluon and graviton

- Vibrations of an open string give rise to gluons.
- Vibrations of closed string -- graviton ( since

70s )

Gravitons and Gravity

- Graviton exchange . force of gravity.
- Charges replaced by masses.
- Photon replaced by graviton.
- By using symmetries of the string
- world-sheet, one can recover the equations

of general relativity.

Weak Gravity

- In the limit of weak gravity, we recover Newtons

gravity, which describes most planetary orbits to

reasonable accuracy.

Strong Gravity

- In the limit of strong gravity, the Einstein

equations describe black holes

- ON very large cosmological scales, it describes

the expansion of the Universe.

A String duality between Light and Gravity

- In string theory, light ( and its large N

generalization ) arises from the same object as

gravitons. This leads to the unexpected relation

- Gravity for space-time in the shape of a solid

ball in five dimensions is equivalent to a theory

with no gravitons but with large N-light

propagating on the four dimensional surface - of the ball.

ADS/CFT

- The five dimensional ball is ADS
- ( Anti-de-Sitter ) space a solution to
- Einsteins equations with negative

cosmological constant. - The large-N-light theory is a limit of open

string theory, called a CFT ( conformal field

theory ). - This is the celebrated ADS/CFT duality discovered

in 1996.

Duality and Probability

- Subject of my current work ---
- Correlators, probabilities, topologies in

AdS/CFT ( with a student at QM and

international collaborators ) - Finding probabilities for interactions
- between gravitons and their spacetime

geometries, using the dual large-N-light theory

FIVE dimensional space-time geometries

interpolating between gravitons Or between their

corresponding geometries are summed ( in a

Euclidean Path integral ) to compute

probabilities for transition between

gravitons/geometries

DUALITY to the rescue !

- This sounds complicated. And it is !!
- A direct computation of such probabilities in

quantum gravity is not possible yet. - But thanks to the duality between gravity and

light, we can use calculations with light to get

the answers

Probabilities in String Landscape ?

- What are the implications of this new string

duality between gravitons and gluons ? There are

bound to be many. - One aspect of string theory is to build precise

models of universes. The new picture is that

there is a huge multiplicity ( string landscape

) of models that have to be considered in

String theory. - It has been argued that the time evolution of the

Universe, in the form of eternal inflation ( at

times close to the Big Bang ) , allows the use of

a probabilistic scenario in explaining the

fundamental constants of particle physics from

String Theory.

- WHAT are the odds that a universe like ours will

emerge from cosmological evolution close to the

big bang, where quantum gravity is important ?

- What does Light-Gravity duality tell us about

this ?

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