String Theory to the Rescue Proof of String Theory & Extra Dimensions?

Transcription

1 String Theory to the Rescue Proof of String Theory & Extra Dimensions? EVERY POINT IN THE UNIVERSE IS NO MORE THAN ONE BLOCK FROM A STARBUCKS! Yale Physics 120 4/23/2018 Quantum Physics and Beyond John Harris 1

2 Physics 120 Quantum Physics and Beyond Announcements Final paper approvals by Wednesday April 25 Final paper due May 3 (before Finals commence) String Theory (Today) String and Tubes Extra Dimensions Cosmic Evolution Multiverse Illusion of Gravity Holographic Principle Planck Scale Hierarchy Problem & String Theory The BIG PICTURE (Wednesday) from the Big Bang to Unseen Dimensions Yale Physics 120 4/23/2018 Quantum Physics and Beyond John Harris 2

3 Reminder Remainder of the Term Today!! The Cosmic Conflict String Theory to the Rescue Extra Dimensions & the Multiverse Wed Apr 25 String Theory, Extra Dimensions, Multiverse 2 Paper approvals deadline Fri Apr 27 Thurs May 3 READING WEEK (begins end of day) Final paper due Yale Physics 120 4/23/2018 Quantum Physics and Beyond John Harris 3

4 Gravity Gravity - the Force We Think We Know Gravitational force equation What we can see and feel Everyday life, solar system What we can see but cannot imagine Black Holes, Pulsars, Quasars, etc. What we cannot see Gravitons (or gravity waves) The Force We Want to Get to Know Better Problems with Gravity Have not identified force carrier! Conflict with Quantum Mechanics on small scales! Purported to be resolved in String Theory & Extra Dimensions! Yale Physics 120 4/23/2018 Quantum Physics and Beyond John Harris 4

5 Gravity vs Quantum Mechanics Cosmic Conflict! Conflict with Quantum Mechanics on small scales! micro Smaller and smaller dimensions macro Yale Physics 120 4/23/2018 Quantum Physics and Beyond John Harris 5

6 String Theory to the Rescue In the quest for a Theory of Everything Physicists must reconcile the conflict between QM and gravity. In particle physics point-like objects interact at zero distance. Einstein s gravity doesn t make sense in this case! Strings have finite size, so interactions spread out. Theories now work better can combine QM and gravity Quarks and electrons not point-like 0-D objects but 1-D strings can be open or closed loops. Open loops end on a Brane surface. Different modes of oscillations of strings define the observed particles String theory has (at least) 9 space + 1 time dimension to make QM calculations work! (mem) Branes allow an extension of strings to higher dimensions 1-D Brane is a string Yale Physics 120 4/23/2018 Quantum Physics and Beyond John Harris 6

7 Particles as Strings Yale Physics 120 4/23/2018 Quantum Physics and Beyond John Harris 7

8 Black Holes, Extra Dimensions & String Theory All dimensions, except the 3+1 we observe are curled up and tiny! String Theory s best guess is 10+1 dimensions - equations connect to GR and QM - unifies forces and describes particle nature One way to think about extra dimensions Brian Green s description in video! Yale Physics 120 4/23/2018 Quantum Physics and Beyond John Harris 8

9 Parallel Universes & Extra Dimensions Yale Physics 120 4/23/2018 Quantum Physics and Beyond John Harris 9

10 Small Extra Dimensions Yale Physics 120 4/23/2018 Quantum Physics and Beyond John Harris 10

11 Gravity The Universe on a Wall? Our Universe may exist on a wall, or membrane, in extra dimensions. 3-D Universe rolled up! Gravity Extra Dimensions Yale Physics 120 4/23/2018 Quantum Physics and Beyond John Harris 11

12 Last Word on String Theory? Part 3 from The Elegant Universe Start here: 12:12 Hidden dimensions, String Theory 41:15 END Yale Physics 120 4/23/2018 Quantum Physics and Beyond John Harris 12

13 Reference Strings and Tubes from Reading Article Yale Physics 120 4/23/2018 Quantum Physics and Beyond John Harris 13

14 The String Landscape Energy of each configuration differs Most stable configurations will emerge. Different physical laws in each minimum. Yale Physics 120 4/23/2018 Quantum Physics and Beyond John Harris 14

15 Extra Dimensions from Article Solutions of equations in String theories depend predominantly on the configuration of the other dimensions Physics observed in our 3+1 world affected by the other 6 dimensions # doughnut handles Geometry of each handle # and location of branes Yale Physics 120 4/23/2018 Quantum Physics and Beyond John Harris 15

16 Cosmic Evolution Start with vacuum at point A. One of the flux lines decays Since they are now different topologies the physics is different. This point begins to expand rapidly (the rest also expanding). Can become billions of light years across. Other decays then occur within this region i.e. green region - new physics again Each region cannot catch up with previous region This is happening all over manifold All possible minima eventually explored Our universe just one small bubble! Yale Physics 120 4/23/2018 Quantum Physics and Beyond John Harris 16

17 Our Large Scale Universe. Yale Physics 120 4/23/2018 Quantum Physics and Beyond John Harris 17

18 Multiverse? Yale Physics 120 4/23/2018 Quantum Physics and Beyond John Harris 18

19 Scientific American, November 2005 Example gravity in 3 spatial dimensions projected onto 2 spatial dimensions Describe the Juggler in 2 and 3 D! Physics is identical but with different descriptions Yale Physics 120 4/23/2018 Quantum Physics and Beyond John Harris 19

20 Illusion of Gravity We know we live in 3-dimensions of space & 1 of time or do we? Clouds of quarks and gluons on the boundary surface can describe equivalent complex objects (such as this apple) in the interior. The advantage of this holographic theory is that interior objects experience gravity even though a distinct gravitational interaction does not exist on the surface. Yale Physics 120 4/23/2018 Quantum Physics and Beyond John Harris 20

21 Space-time Curvature Yale Physics 120 4/23/2018 Quantum Physics and Beyond John Harris 21

22 Anti-de Sitter Space de Sitter space - positively curved space + time positive curvature - outside of a balloon anti-de Sitter space - negative/hyperbolic curvature space + time hyperbolic curvature - saddle like Anti-de Sitter space shown on right, boundary has two dimensions length of cylinder and its circumference Similar for other dimensions. Imagine a 4-D anti-de Sitter space, whose spatial boundary is a 3-D sphere 2-D representation of anti-de Sitter space Quantum gravity theory Quantum particle theory Yale Physics 120 4/23/2018 Quantum Physics and Beyond John Harris 22

23 Nuclear physicists have now demonstrated that the material essence of the universe at a time microseconds after the big bang consists of a ubiquitous quark-gluon liquid. Scientific American, November 2005 One particular calculation shows that a black hole in 5-D corresponds to a hot system of quarks and gluons in 4-D (i.e. our world!) Yale Physics 120 4/25/2018 Quantum Physics and Beyond John Harris

24 What the bleep? A Black Hole in the 5 th dimension? Explain.. We know about Black Holes! But, what s this about 5D? Yale Physics 120 4/25/2018 Quantum Physics and Beyond John Harris

25 What s this about 5D? We all know we live in 3 dimensions! Up Down Yale Physics 120 4/25/2018 Quantum Physics and Beyond John Harris

26 But do we? Up Down Take 3D space and time 4 dimensions necessary to describe world we live in! Yale Physics 120 4/25/2018 Quantum Physics and Beyond John Harris

27 Holograms on a 2D Flat Film Up Down Left Right Consider only spatial dimensions for the moment! is encoded a 3D World! Yale Physics 120 4/25/2018 Quantum Physics and Beyond John Harris

28 Imagine our World as a Hologram Up Imagine we live on a 3D hologram Down Left Right Consider only spatial dimensions for the moment! Can a 4D World be painted onto our 3D surface? Yale Physics 120 4/25/2018 Quantum Physics and Beyond John Harris

29 Take into Account the Time Dimension Up We then live on a 4D surface (3 space + time) Down Left Right Now consider also the time dimension! That is equivalent to a 5D World? Yale Physics 120 4/25/2018 Quantum Physics and Beyond John Harris

30 4D Representation of a 5D World Known as the Holographic Principle (co-founders t Hooft and Susskind) Gerhard t Hooft Nobel Prize, 1999 The Universe is a 4D system has volume and extends in time that is equivalent to a 5D space-time. Father of String Theory If this Holographic Principle holds - a difficult calculation on the 4-D boundary, such as behavior of quarks and gluons, can be traded for an easier calculation in 5-D. Yale Physics 120 4/25/2018 Quantum Physics and Beyond John Harris

31 4D Representation of a 5D World Juan Maldacena conjectured that String Theory in a particular 5D universe can be painted onto our 4D boundary universe. Juan Maldacena Edward Witten Ed Witten has shown that a black hole in a particular 5D space-time corresponds to a hot system (quarks and gluons!) on the 4D space-time boundary. Yale Physics 120 4/25/2018 Quantum Physics and Beyond John Harris

32 Tests of Gravity and String Theory? Tests of string theory At LHC Predicts new particles (higher order vibrations) possibly at TeV range - seeable by experiments - No candidates observed yet, watch the news Missing energy, carried off by gravitons - None observed yet, watch the news Evidence of mini-black holes - CMS measure lower limit on mass > ~4 TeV at 95% confidence Tests of gravity at very small scale Table top experiments does gravity vary by something other than 1/R 2 - tested at distances down to few 10s of micrometers. Thus far no deviation from Newton's gravitational inverse-square law has been found Further tests in Relativistic Heavy Ion experiments at LHC and RHIC Detection of dark matter and/or further studies of gravity waves Yale Physics 120 4/23/2018 Quantum Physics and Beyond John Harris 32

33 Planck Scale Energy/mass/length where quantum effects of gravity become sizable: = 1.22 x GeV = x 10 8 kg = x m At the Planck scale, quantum field theory - the theory describing subatomic particle interactions - breaks down....because gravity needed & doesn t fit into current Quantum explanations. String theory may be a possible explanation that includes gravity. At Planck scale Force of gravity comparable to other forces. All forces become unified Concepts of size and distance break down, as quantum indeterminacy becomes virtually absolute! Yale Physics 120 4/23/2018 Quantum Physics and Beyond John Harris 33

34 Hierarchy Problem and String Theory The Hierarchy Problem: Why are there two distinctly different energy scales in Universe? "electroweak scale ~ 100 GeV, mass of W and Z, unites strong, electromagnetic and weak forces. Planck scale, ~ GeV, gravitational interactions. Why is gravity 39 orders of magnitude weaker than other forces? Possible solution: Density of field lines decrease as area increases Gravity falls off as 1/R 2 If there are 3+k spatial dimensions at small scales Area in this space grows as R 2+k Gravity will fall off as 1/R 2+k Gravity appears weak in our 3+1D world Once R large compared to extra dimension scale Gravity falls as 1/R 2 Yale Physics 120 4/23/2018 Quantum Physics and Beyond John Harris 34

35 Why Extra Dimensions Only Affect Gravity? Gravity uniquely tied directly to geometry of space-time in our 4 dimensions. Brane an n-dimensional surface. Strings can be open loops as long as motion confined to a brane. Lowest mode of open string analogous to spin 1 gauge boson (photon) Toy models of electromagnetic, weak & strong forces, can be confined to a 3-brane! In this case only gravity s (graviton spin 2) strength is diluted by extra dimensions Graviton is a closed loop - not fixed to our brane. Yale Physics 120 4/23/2018 Quantum Physics and Beyond John Harris 35

36 Mini-Black Holes at the LHC BH in universe are massive Energy LHC collision = 2 mosquitoes - Not enough mass to form BH String theory - at small distances extra dimensions Hence, gravity may be larger than expected in LHC collision BHs unstable due to Hawking radiation Decay away fast If BH at CERN then BH from Cosmic rays Cosmic rays > ev = 5x10-14 /sec/cm 2 Earth s surface 5x10 18 cm 2 Earth 4.5 billion years old > 3x10 22 cosmic rays have struck Earth CERN will have ~10 17 p-p collisions over planned running LHC Yale Physics 120 4/23/2018 Quantum Physics and Beyond John Harris 36

37 The String Theory discussion will continue The New Yorker, Jan Yale Physics 120 4/25/2018 Quantum Physics and Beyond John Harris

38 Return Graded Quiz 2 4 Grades on Quiz F D C C+ B A- A A+ Quiz 2 Score Range (# students) A+ 69 (99%) (3) A 64 ( 92%) (4) A- 63 ( 90%) (2) B 56 ( 80%) (2) C+ 52 ( 75%) (1) C 49 ( 70%) (1) Yale Physics 120 4/23/2018 Quantum Physics and Beyond John Harris 38