Strings and Branes

Quantum Gravity

and Low-Energy Physics:The start of a

beautiful relationship?

C. Burgess, McGill University

String Theory

Outline

• The 20th Century Crisis• Quantum Mechanics vs Relativity

• String Theory• A Theoretical Balancing Act• Possible Problems?

• String Theory: One Mo’ Time!• D-Branes and M-Theory• Brane Worlds and Opportunities

• Outlook

String Theory

Outline

• The 20th Century Crisis• Quantum Mechanics vs Relativity

• String Theory• A Theoretical Balancing Act• Possible Problems?

• String Theory: One Mo’ Time!• D-Branes and M-Theory• Brane Worlds and Opportunities

• Outlook

String Theory

Outline

• The 20th Century Crisis• Quantum Mechanics vs Relativity

• String Theory• A Theoretical Balancing Act• Possible Problems?

• String Theory: One Mo’ Time!• D-Branes and M-Theory• Brane Worlds and Opportunities

• Outlook

String Theory

Outline

• The 20th Century Crisis• Quantum Mechanics vs Relativity

• String Theory• A Theoretical Balancing Act• Possible Problems?

• String Theory: One Mo’ Time!• D-Branes and M-Theory• Brane Worlds and Opportunities

• Outlook

String Theory

Two Pillars of 20th Century Physics

• Quantum Mechanics is the framework for studying the physics of very short distances.

• Special Relativity is the framework for describing the physics of objects moving at speeds close to the speed of light.

• General Relativity is the extension of this theory to include gravity.

Almost inconsistent with each other!

String Theory

Special Relativity

• The first completed revolution of 20th Century physics:• Relativity of

Simultaneity• Time Dilation• Length Contraction• E = mc2

• Speed of light as a maximum speed.

M.C. Escher ‘Relativity’

String Theory

It’s the Law!

• Absolutely nothing can move faster than light c = 300,000 km/sec

• All observers agree on this speed, regardless of their own motion.

• Causal influences cannot travel ‘outside the light cone’.

time

space

String Theory

Relativity of Simultaneity

• Observers can disagree whether A or B is earliest.

• Causality is not violated because no information can get from A to B since it cannot travel faster than light.

space

Light cone

Particle world line

time A B

String Theory

….Enter: Quantum Physics

String Theory

The Uncertainty Principle

The more precisely the position is determined, the less precisely the momentum is known in this instant, and vice versa.

Werner Heisenberg, 1927

2

xpx

String Theory

Precise Position Messes Momentum

• In Quantum Mechanics it is not possible to precisely specify a particle’s position and momentum (velocity) at the same time.• A particle does not really

have both position and velocity at the same time.

String Theory

Apparent Inconsistency….

• If particles are known to be precisely at positions A and B, then they move with arbitrarily high uncertainty in their speed.• In particular there is some

probability that they could be moving faster than light!

• How can events at A avoid acausally affecting events at B?

A

space

Light cone

Particle world line

time B Quantum Information?

String Theory

Consistency Restored!

• In Nature consistency is restored by ensuring that observers who disagree on the order of events A and B also disagree on whether influences pass from A to B or in the opposite direction.• This can work because every particle has an

anti-particle having an identical mass but opposite charge.

Richard Feynman

String Theory

Antiparticles Exist!

String Theory

Einstein on a Roll: General Relativity

• In General Relativity, gravity is attributed to the curvature of space and time.• Slowing of time in

gravitational fields.

• Bending of light by gravitational fields.

• Predicts the existence of Black Holes.

String Theory

General Relativity

• General Relativity requires test observers whose positions and times are precisely known, but with negligible mass.• They can map out space-time

without themselves gravitating.

• Another, more difficult, conflict with the Uncertainty Principle!

String Theory

Quantum Gravity?

• At small distances large ‘quantum fluctuations’ in the gravitational field make gravity very strongly-interacting.• Cannot predict using

General Relativity for distances shorter than the Planck length, ℓp.

• Absolutely no candidate theory before the mid 1980’s.

cmcGp333 10/

String Theory

Outline

• The 20th Century Crisis• Quantum Mechanics vs Relativity

• String Theory• A Theoretical Balancing Act• Possible Problems?

• String Theory: One Mo’ Time!• D-Branes and M-Theory• Brane Worlds and Opportunities

• Outlook

String Theory

String Theory: the idea

• All matter consists of small one-dimensional objects (strings).• Strings just look like particles

when they are not seen under sufficient magnification.

• Originally thought to be only a single unique theory which makes mathematical sense.

String Theory

String Theory: the idea

• Enormous economy of description:• All particle types are simply different kinds of oscillations

of the string.

String Theory

String Interactions

• All interactions consist of the splitting and joining of these elementary strings.• This is the only known

sensible description of gravitational interactions at very short distances!

• At long distances the theory looks like General Relativity plus other interactions at low energies.

• No parameters: the string length sets the units.

String Theory

String Varieties, circa 1990

• The consistency of gravity with Quantum Mechanics makes String Theories almost mathematically inconsistent.• Nevertheless there appeared to be more than one

kind of consistent string theory.

• Open strings, closed strings, heterotic strings, Type I strings, Type IIA strings, Type IIB strings…

String Theory

Uniquely Predictive

• String theory predicts space has 9 (or 10) spatial dimensions.• Experimental update:

observed number of (large) dimensions is 3 space and 1 time.

• Falsifiable or False?

String Theory

How Would We Know?

• There may be 9 spatial dimensions, since we would not know about the extra ones if they were extremely small.

r < 10-17 cm

• Cannot yet predict the size of all dimensions.

String Theory

Experimental Tests?

• Strings were thought to have to be very short in order to properly reproduce the strength of Newton’s Law of Gravity.

• Since strings are so short, it is extremely difficult to find decisive experimental tests for the theory using only experiments on distances larger than 10-17 cm because short-distance physics decouples.

Theories without experiment guidance normally die through lack of progress…

cmcGp333 10/

String Theory

Outline

• The 20th Century Crisis• Quantum Mechanics vs Relativity

• String Theory• A Theoretical Balancing Act• Possible Problems?

• String Theory: One Mo’ Time!• D-Branes and M-Theory• Brane Worlds and Opportunities

• Outlook

String Theory

D-Branes

• String theory is bigger than previously thought. • Normally, the ends of open

strings move freely at the speed of light.

• Strings can also exist whose ends are anchored onto surfaces.

• These surfaces are interpreted as large, massive objects, called D-branes, in spacetime• Much like magnetic monopoles.

String Theory

Why Consider This?

• Good Things Happen with D-branes:• Previously-hidden ‘duality’ symmetries

emerge, and the known string theories become related to one another by these symmetries!

• Some weakly-interacting string theories turn out to be the strongly-interacting limit of others.

• Led to discoveries of similar symmetries amongst ordinary particle theories.

• Conjecture: all string theories are different solutions to a more fundamental (11-dimensional) theory (called M Theory). • Sometimes it is the strings which are

‘fundamental’, sometimes it is the branes.

String Theory

Outline

• The 20th Century Crisis• Quantum Mechanics vs Relativity

• String Theory• A Theoretical Balancing Act• Possible Problems?

• String Theory: One Mo’ Time!• D-Branes and M-Theory• Brane Worlds and Opportunities

• Outlook

String Theory

The Brane World

• Some states are trapped on the branes, and others are free to wander through all of the dimensions of space-time.• It can happen that all of the known elementary particles and interactions

(except for gravity) are brane bound in this way.

Can enormously change the low energy perspective.

String Theory

Strings Might Be Big

• String size is inferred from the (very weak) strength of gravity compared with other interactions in 4 dimensions.

• String theory predicts these strengths in 10 dimensions.

• Strings can be as large as the present experimental limit if gravity ‘sees’ more dimensions than other interactions.• If so, experimental tests may be

around the corner….

20 dr

eQA

200 dr

GMh

String Theory

New Approaches to Low Energies

• If strings are close to the experimental limit in size, then it may be that two of the extra dimensions are as large as r ~ 10 m across.• This assures GF/GN ~ (r/ℓs)2 has the

correct size.• Such an r is close to the present

experimental limit for deviations from Newton’s Law.

• The observed Dark Energy is of order 1/r4 in size.

• Branes usefully expose previously hidden assumptions about what is possible at low energies!!

r ~10 microns

You are here

String Theory

Branes and Symmetry Breaking

• Branes also suggest new low-energy ways to understand naturalness problems related to symmetry breaking.• Each brane breaks some (super)symmetries but bulk does not.

• All supersymmetries broken once all branes are considered.

• Bizarre effective interactions and symmetry breaking patterns:• Higher-dimensional locality requires brane actions to arise as

sums of terms involving different numbers of supersymmetry.

'4)4(8 21 NLNLNLL bbB

String Theory

Brane Cosmology

• Cosmology describes the Universe given the distribution of matter within it.• This can be dramatically

different in the Brane World.

Brane Inflation or Ekpyrosis

WMAP

String Theory

Outline

• The 20th Century Crisis• Quantum Mechanics vs Relativity

• String Theory• A Theoretical Balancing Act• Possible Problems?

• String Theory: One Mo’ Time!• D-Branes and M-Theory• Brane Worlds and Opportunities

• Outlook

String Theory

String Theory Summary

• String theory is the only known theory where gravity and quantum mechanics co-exist at high energies.• Major Lesson of the 20th Century: Relativity and Quantum

Mechanics are almost inconsistent, and so together impose extremely strong self-consistency conditions.

• Strings could very well be much longer than the Planck length.• Size Matters: much better prospects for eventual

comparison with experiments.

• We may all be Brane bound.• Important broadening of the low-energy mind.

String Theory

The Theory of Everything?

• For the first time in history we have a candidate which could be a Theory of Everything.• It appears to consistently

include gravity down to arbitrarily small distances.

• It appears to be so tightly constrained by consistency as to be unique.

• It must make contact with experiment, but there is not a time limit so long as progress is made.

String Theory

New Approaches to Old Problems

• Perhaps some particles can move faster than others?• Perhaps not all interactions ‘see’ the same number of

dimensions of space?• Perhaps ‘space’ and ‘time’ only make approximate

sense on very large distances.

String Theory

Perhaps a beautiful relationship….

String Theory

Thanks for your time….