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 Einstein’s theory of Relativity.

1. Nothing travels faster than light2. 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’’ …

3. 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 Einstein’s 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.

• Maxwell’s Electromagnetic theory of light ( pre-20’th century ) when developed to incorporate the insights of quantum mechanics and relativity ( early 20’th century ) gives rise to a new framework :

Quantum field theory ( QFT ) – mid-20’th 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 N^2 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 70’s )

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 Newton’s 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 Einstein’s 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 gravitonsOr 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 ?