2. Strings and Branes Quantum Gravity and Low-Energy Physics: The start of a beautiful relationship? C. Burgess, McGill University

3. String Theory Outline The 20 th 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

4. String Theory Outline The 20 th 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

5. String Theory Outline The 20 th 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

6. String Theory Outline The 20 th 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

7. String Theory Two Pillars of 20 th 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!

8. String Theory Special Relativity The first completed revolution of 20 th Century physics: Relativity of Simultaneity Time Dilation Length Contraction E = mc 2 Speed of light as a maximum speed. M.C. Escher ‘Relativity’

9. 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

10. 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.

11. String Theory ….Enter: Quantum Physics

12. 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

13. 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.

14. 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?

15. 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

16. String Theory Antiparticles Exist!

17. String Theory Elementary Particle Detectors Particle detector (CDF) and particles detected (neutrinos at Super K)

18. 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.

19. 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!

20. 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, ℓ p. Absolutely no candidate theory before the mid 1980’s.

21. String Theory Outline The 20 th 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

22. 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.

23. String Theory String Theory: the idea Enormous economy of description: All particle types are simply different kinds of oscillations of the string.

24. 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.

25. 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…

26. 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?

27. 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.

28. 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…

29. String Theory Outline The 20 th 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

30. 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.

31. 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.

32. String Theory Is Space-time Emergent? In some circumstances physics at distances smaller than the string scale is identical with physics larger than the string scale. Suggests that notions of distance may only be approximate, applying only for distances R » ℓ s Holography: Some string theories in 10 dimensions are equivalent to ordinary particle theories on the 4 dimensional boundaries. In a proper formulation of the theory space and time should not be assumed, but should emerge in the long-distance limit.

33. String Theory Outline The 20 th 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

34. 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.

35. 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….

36. 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 G F /G N ~ (r/ℓ s ) 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/r 4 in size. Branes usefully expose previously hidden assumptions about what is possible at low energies!!

37. 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.

38. 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

39. String Theory Outline The 20 th 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

40. 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 20 th 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.

41. 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.

42. 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.

43. String Theory Perhaps a beautiful relationship….

44. String Theory ….…..and a classic ending.

45. String Theory Thanks for your time….