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Space-time
- 1. Space-time in the newmillennium La notion d’ESPACE-TEMPS au début du nouveau millénaire
- 2. PHYSICS STUDIES PHENOMENA ATVARIOUS SCALES SMALL STRUCTURES AND LARGE STRUCTURES
- 3. mediated by exchangeof other elementary particles SMALL STRUCTURES are accurately described by QUANTUM FIELD THEORY which postulates that matter is composed out of elementary particles bound together by forces,
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- 5. Particle interactions TAKE PLACEIN A FIXED SPACE-TIME BACKGROUND THE BEST EXPERIMENTAL TESTS IN PHYSICS
- 6. LARGE STRUCTURES ARE THE ARENAFOR THE THEORY OF GRAVITATION EINSTEIN’S GENERAL RELATIVITY theory
- 7. SPACE AND TIME Ineveryday life we see three spatial dimensions, and one temporal We also think that the GEOMETRY of SPACE is fixed and flat Also, we DO NOT FEEL that our presence changes any of these.
- 8. ALBERT EINSTEIN SHOWED SPACEand TIME are not independent. Measured by different observers they mix Any MATTER curves SPACE-TIME Space-Time curvature is felt by any Matter in the form of gravitational forces.
- 9. Imagine life in1+1 dimensions
- 10. Exploring the 1+1world
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- 12. The SUN curvesSPACE-TIME around it Free motion of the EARTH proceeds around the SUN
- 13. Small fluctuations ofspace-time fabric – gravitational waves
- 14. BLACK HOLES LARGE DEVIATIONSFROM FLAT IF A STAR IS VERY SMALL BUT MASSIVE THEN EVEN THE LIGHT CANNOT ESCAPE ITS GRAVITATIONAL FIELD VERY DIFFERENT FROM OUR SPACETIME 1918 Carl Schwarzschild found black hole solution in Einstein’s theory
- 15. UNIFY IDEAS? IS THEREA THEORY THAT WORKS WELL BOTH FOR SMALL AND LARGE?
- 16. Quantum field theory treatsgravitational waves as elementary particles – gravitons the same interaction picture as for the electrons and the rest
- 17. GRAVITATION as Quantum Field Theory? UNFORTUNATELY GENERALRELATIVITY AS QUANTUM FIELD THEORY MAKES NO SENSE
- 18. STRING THEORY NEW IDEAFOR AN ELEMENTARY OBJECT: a STRING
- 19. STRING TRAJECTORY TWO DIMENSIONALWORLDSHEET
- 20. Different vibration modes ofa single STRING look like different PARTICLES
- 21. STRING INTERACTION INSTEAD OF STRINGQUANTUM EFFECTS: NUMBER OF HANDLES ON THE WORLDSHEET
- 22. STRINGY GRAVITATION SPACE-TIME SHOULDBE 9+1 DIMENSIONAL ! FINITE, SOFT CORRECTIONS TO EINSTEIN’S THEORY BUT
- 23. EXTRA DIMENSIONS? Kazimir Malevich andhis Black Square which in fact hides a CUBE
- 24. MALEVICH: WHAT IS HIDDENBEHIND THE CUBE? 1919 THEODOR KALUZA 1928 OSCAR KLEIN PROPOSED THAT THE WORLD IS 4+1 DIMENSIONAL THUS UNIFYING ELECTROMAGNETISM AND GRAVITY
- 25. CALABI-YAU spaces The extra6 dimensions (9 - 3 = 6) are believed to be so SMALL that we do not observe them. For mathematical consistency, they should be wrapped on a special kind of space : a CALABI-YAU space.
- 26. BEFORE STRING THEORY 1978- Stephen Hawking (Cambridge) has explored this idea more quantitatively and gave a name to the fluctuating space-time: 1964 - John Wheeler (Princeton) suggested that at the Planck distances LPlanck=10-33cm the quantum gravity effects are so large that the geometry and topology of space-time fluctuate as mad
- 27. QUANTUM SPACE-TIME FOAM 1957Boris Vian ``L’ecume des jours’’ --- time foam
- 28. SPACE-TIME FOAM HAWKING ARGUED THATAT THE PLANCK DISTANCES SMALL , PLANCK-SIZED BLACK HOLES POP OUT OF VACUUM AND DISAPPEAR WITHIN PLANCK TIME : 10-43 sec
- 29. QUESTION CAN STRING THEORYDESCRIBE the QUANTUM SPACE-TIME FOAM?
- 30. QUANTUM STRING: EXPANSION INTHE NUMBER OF HANDLES GRAVITON SCATTERING DONE IN A STRINGY WAY gs STRING COUPLING CONSTANT
- 31. IMPOSSIBLE to seeBLACK HOLES SMALL DEVIATION OF FLAT GEOMETRY WORKING WITH FINITE STRING PRECISTION: FINITE NUMBER OF HANDLES FINITE NUMBER OF GRAVITONS
- 32. SIMPLEST STRING THEORIES with infinitenumber of handles under control: COUNT HOLOMORPHIC CURVES ON CALABI-YAU MANIFOLDS MATHEMATICALLY WELL-FOUNDED: GROMOV-WITTEN THEORY, BASED ON KONTSEVICH IDEAS OF STABLE MAPS TOPOLOGICAL STRINGS
- 33. FROM STRINGS TOCRYSTALS LAST YEAR, DURING THE FIRST SIMONS WORKSHOP AT STONY BROOK Andrei Okounkov(Princeton), Nikolai Reshetikhin(Berkeley) and Cumrun Vafa(Harvard) HAVE FOUND THAT:
- 34. TOPOLOGICAL STRING KNOWS ABOUTMELTING CRYSTALS!!!
- 35. DICTIONARY INVERSE ABSOLUTE TEMPERATURE GEOMETRYOF THE ORIGINAL CRYSTAL corresponds to the GEOMETRY OF CALABI-YAU MANIFOLD STRING COUPLING gS corresponds to the
- 36. THIS RELATION WAS EXPLAINEDMATHEMATICALLY IN DECEMBER 2003 Davesh Maulik(Princeton), Nikita Nekrasov (IHES), Andrei Okounkov(Princeton) and Rahul Pandaripande(Princeton)
- 37. MOST INTERESTING: PHYSICS OFTHIS CORRESPONDENCE MELTING CRYSTAL = FLUCTUATING CALABI-YAU GEOMETRY BOXES (ATOMS OF THE CRYSTAL) = THE SPACE-TIME FOAM BUBBLES = HAWKING’S VIRTUAL BLACK HOLES Amer Iqbal (Harvard), Nikita Nekrasov (IHES), Andrei Okounkov (Princeton), Cumrun Vafa (Harvard), building on ideas of the earlier work by NN and Harry Braden (Edinburgh)
- 38. THEREFORE STRING THEORY CANDESCRIBE the QUANTUM SPACE-TIME FOAM
- 39. FOR THE NEXTMILLENIUM QUANTUM GRAVITY EFFECTS IN MORE REALISTIC STRING THEORY UNIFICATION OF (QUANTUM) GRAVITIES: Loop Gravity Noncommutative SPACE-TIME Cosmological billiards …
- 40. In preparing thislecture the pictures from the following publications were used : • “The elegant universe”, by B.Greene • “The paths to paradise”, by P.Kornel • “Quantum foam and topological strings”, by A.Iqbal, N.Nekrasov, A.Okounkov and C.Vafa • Hubble telescope pictures, NASA • “Space goes quantum at Stony”, by G.Sterman and M.Rocek REFERENCES