String Theory. Quantum Mechanics and Gravity: Cliff Burgess, McGill. The start of a beautiful relationship?

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1 Quantum Mechanics and Gravity: The start of a beautiful relationship? Cliff Burgess, McGill

2 Outline The 20 th Century Crisis Quantum Mechanics vs Relativity A Theoretical Balancing Act Possible Problems? D-Branes and M Theory Holography The Brane World Outlook

3 Outline The 20th Century Crisis Quantum Mechanics vs Relativity A Theoretical Balancing Act Possible Problems? D-Branes and M Theory Holography The Brane World Outlook

4 Outline The 20th Century Crisis Quantum Mechanics vs Relativity A Theoretical Balancing Act Possible Problems? D-Branes and M Theory Holography The Brane World Outlook

5 Outline The 20th Century Crisis Quantum Mechanics vs Relativity A Theoretical Balancing Act Possible Problems? D-Branes and M Theory Holography The Brane World Outlook

6 Two Pillars of 20 th Century Physics 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. Quantum Mechanics is the framework for studying the physics of very short distances. Almost inconsistent with each other!

7 Special Relativity M.C. Escher 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.

8 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

9 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. time space A Particle world line Light cone B

10 .Enter: Quantum Physics

11 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 x p x η 2

12 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.

13 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? time space A Particle world line Light cone Quantum Information? B

14 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

15 Antiparticles Exist!

16 Elementary Particle Detectors Particle detector (CDF) and particles detected (neutrinos at Super K)

17 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.

18 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!

19 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, p. Absolutely no candidate theory before the mid 1980 s. λ p = ηg / c 3 = cm

20 Outline The 20th Century Crisis Quantum Mechanics vs Relativity A Theoretical Balancing Act Possible Problems? D-Branes and M Theory Holography The Brane World Outlook

21 : 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.

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

23 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.

24 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 kinds of consistent string theory. Open strings, closed strings, heterotic strings, Type I strings, Type IIA strings, Type IIB strings

25 Uniquely Predictive String theory predicts space has 9 (or 10) spatial dimensions and 1 time dimension. Experimental update: observed number of (large) dimensions is 3 space and 1 time.

26 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 < cm Cannot yet predict the size of all dimensions.

27 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 cm. Theories without experiment guidance normally die through lack of progress λ p = ηg / c 3 = cm

28 Outline The 20th Century Crisis Quantum Mechanics vs Relativity A Theoretical Balancing Act Possible Problems? D-Branes and M Theory Holography The Brane World Outlook

29 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.

30 Why Consider This? Good Things Happen with both strings and D-branes: Previously-hidden duality symmetries emerge, and all known string theories become related to one another by these symmetries! Some weakly-interacting string theories are really the strongly-interacting limit of others! Led to discoveries of similar symmetries amongst ordinary particle theories. Conjecture: all known 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.

31 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» s Holography: Some string theories in 10 dimensions are equivalent with 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. R λ 2 s /R

32 The Brane World Some states are trapped on the branes, and others are free to wander through all of the dimensions of spacetime. It can happen that all of the known elementary particles and interactions (except for gravity) are brane bound in this way.

33 Brane Cosmology Cosmology describes the Universe given the distribution of matter within it. This can be dramatically different in the Brane World.

34 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.

35 Outline The 20th Century Crisis Quantum Mechanics vs Relativity A Theoretical Balancing Act Possible Problems? D-Branes and M Theory Holography The Brane World Outlook

36 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. The string length could very well be much longer than the Planck length. Size Matters: much better prospects for comparison with experiments. We may all be Brane bound. Important implications for very-early-universe cosmology.

37 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.

38 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.

39 Perhaps a beautiful relationship.

40 ...and a classic ending.

41 The Last Word