Transcript SPACE-TIME , GAUGE-GRAVITY AND STRING

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 !!
•
1.
2.
Some aspects of the new understanding of
space-time in Einstein’s 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’’ …
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 GRAVITY
in
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 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 ?