1. 1 Two-Time Physics The Unified View From Higher Dimensional Space and Time Itzhak Bars, USC One of the most important questions today: what is space and time? Such questions fascinated every civilization, from ancient to modern. Discussed in theology (the heavens & earth; beginning & end), and in philosophy, mathematics, astronomy, physics and cosmology. Einstein unified the concepts of space and time in the 20 th Century. String theory: consistent Quantum Mechanics + Gravity requires extra space dimensions (Kaluza-Klein idea: small, curled up,… ). How about extra time dimensions? (easy to ask, not so easy to realize!!)

2. 2 Symmetry Deeper order in space-time, leads to predictions of extra dims. Perspectives in higher space-time Same event in higher dims., different interpretations in lower dims. Reconstructing the substance from its shadows. Subtle phenomena in our space-time of 3+1 dims. Hard to notice, surprises, tests to confirm or reject theories Surprising and far reaching preliminary conclusion: The ordinary formulation of Physics in 3+1 LARGE dimensions is incomplete. One extra timelike plus one extra spacelike LARGE dimensions are needed to provide a more complete view of Nature at ALL SCALES of physics. Themes in this lecture: Related work : One corner of 2T-physics makes contact with work by Dirac, Salam, Adler, Ferrara, Siegel, Marnelius, Vasiliev,… (conformal symmetry)

3. 3 Students / Collaborators Shih-Hung Chen Yueh-Cheng Kuo Bora Orcal Guillaume Quelin Costas Kounnas (CERN and Ecole Normale, Paris) Cemsinan Deliduman (now Assoc. Prof., Istanbul Tech. Univ.) Oleg Andreev (now postdoc U. Munich) Sasha Vongehr Djordje Minic (now Prof. Virginia Tech) Moises Picon (now postdoc U. Padova)

4. space-time (where and when)  What is position in ordinary space ? –3 dimensions (location in space) = where  What is time ? – time on your watch = when many kinds of watches (atomic clock, sand clock, etc.)  What is a space-time event in space-time ? – an event at a specific time and specific place  What is space-time history ? – a collection of events, just like a movie ! – motion of a point is represented by a curve in space-time = worldline 4 x y z t x,y,z t Perspective: static observer free of forces, and emphasizing POSITION space This point of departure is a perspective not symmetric in momentum vs position

5. 5 Prediction : Special Relativity allows time travel to the future. Subtle effect: Too small to notice with common speeds. But experiments with short-lived particles in an accelerator confirms this. Subtle effect: Too small to notice with common speeds. But experiments with short-lived particles in an accelerator confirms this. Perfect identical watches may not measure identical time intervals. space-time perspectives (relativity) Ship’s watch: 1hr, but Earth’s: 320 yrs., as observed by astronauts. Time duration seen on a watch depends on the speed of the observer relative to that watch. Time Dilation

6. 6 More Perspectives: Space Contraction Identical rulers may measure differently the same space interval. You guessed it – it depends on the speed of the observer ! Identical rulers may measure differently the same space interval. You guessed it – it depends on the speed of the observer ! AT Subtle effects. The effect is too small to notice in daily phenomena because the speed is too small. But, particles in accelerators move at great speeds, and behave precisely as predicted. e.g. sphere looks like pancake.

7. 7 Close to the speed of light, or in very strong gravity, a watch appears to almost stop. Inside a black hole, time & space switch roles. Space and Time are not absolute they are relative to the observer Even more weird things happen close to the extremes. Such effects arise because observers are in relative motion, or under the influence of gravitational forces. Such effects arise because observers are in relative motion, or under the influence of gravitational forces. The observer’s coordinate systems get distorted relative to each other. The Equivalence Principle shows how to relate them. Then observers see same Law. The observer’s coordinate systems get distorted relative to each other. The Equivalence Principle shows how to relate them. Then observers see same Law. t x,y,z x t,y,z t x,y,z

8. 8 Equivalence Principle !! (Einstein) The laws of Physics are independent of the observer’s space and time perspective This is implemented as a symmetry of the equations: Invariance under “general coordinate transformations” Origin of Gravity The force of gravity exists because of this symmetry. All details of the gravitational force is controlled by this symmetry.

9. 9 But there is more to explain: Properties of matter other than history in space-time? Electric charge, … Non-gravitational forces?

10. Space-Time and Higher Dimensions  Kaluza (1921) and Klein (1926) considered 1 extra dimension. Explain charge and E&M (Gen Rel in 4+1)  String theory (so far unconfirmed) – requires 6 more space dimensions in addition to the usual 3 space and 1 time dimensions. This solves the puzzle of how to marry Quantum Mechanics and Gravity.  “M-theory”, which includes string theory, adds one more space dimension, for a total of 11 = 10 space + 1 time. 10 t x,y,z, … 7 more

11. Where is the Extra Space?  Scenario: soon after the Big Bang the extra space dimensions curled up into very tiny geometrical shapes, and remained small. How small ???  They may exist at every space-time point of our own 3+1 space-time, and they are supposed to explain charges, flavors, colors, families and more …  A tiny Christopher Columbus (e.g. electron) can explore the small dimensions and bring the information to us. 11 t x,y,z 7 more t x,y,z, …. 7 more subtle effect

12. Nobody discusses more time-like dimensions – why? 12 BBecause physicists are scared of them. TTwo kinds of disasters: 1) Ghosts! = negative probability 2) Causality (cause and effect) violation  time machines: Can kill your grandmother before your mother or you are born. ! BBoth are nonsensical, and kept physicists away from contemplating more time-like dimensions.

13. 13 Easy! A new symmetry that unites (Position & Time) (Momentum & Energy) Indistinguishable at any instant for any motion. This wipes out the source of disasters. But requires 1 extra space and 1 extra time ! How? Here is the clue…  General setup of classical or quantum mechanics is symmetric under X  P, P  -X. They are at same level before a specific system or Hamiltonian is chosen.  Any Lagrangian :  Poisson brackets or quantum commutators  Boundary conditions  More general: GLOBAL symmetry, Sp(2,R) doublet  Even more general is symmetry under GLOBAL canonical transformations Invariant: 2T-physics emerges from demanding that this global symmetry turn into a local symmetry H

14. 14 X M =(Position & Time) P M = (Momentum & Energy) X M =(Position & Time) P M = (Momentum & Energy) indistinguishable at any instant. Gauge symmetries are so powerful that they highly constrain the equations that can be written down, sometimes fully determining them. All known forces in Nature are fully understood through some remarkable gauge symmetries, and follow from them: 1) Symmetry under general coordinate transformations give Einstein's General Relativity = Gravity 2) Yang-Mills gauge symmetry SU(3) x SU(2) x U(1) gives The Standard Model of Particles and Forces (strong, weak, and electro-magnetic) The new fundamental principle: A broader equivalence principle. To have the symmetry, the force must exist, its details fixed. A new gauge symmetry of the Laws of Mechanics Applied to all motion

15. 15 1)New symmetry allows only highly symmetric motions.  little room to maneuver. 2)With only 1 time the highly symmetric motions impossible.  Collapse to nothing. 3)Extra 1+1 dimensions necessary  4+2 !! No less and no more than 2T. 4)Straightjacket in 4+2 makes allowed motions effectively 3+1 motions (like shadows on walls). 1)New symmetry allows only highly symmetric motions.  little room to maneuver. 2)With only 1 time the highly symmetric motions impossible.  Collapse to nothing. 3)Extra 1+1 dimensions necessary  4+2 !! No less and no more than 2T. 4)Straightjacket in 4+2 makes allowed motions effectively 3+1 motions (like shadows on walls). Non-trivial: Gauge fix 4+2 to 3+1 (have 3 gauge parameters) many 3+1 shadows emerge for same 4+2 spacetime history. Each shadow contains only one timeline (a mixture of all 4+2) Non-trivial: Gauge fix 4+2 to 3+1 (have 3 gauge parameters) many 3+1 shadows emerge for same 4+2 spacetime history. Each shadow contains only one timeline (a mixture of all 4+2) How does it work? t2t2 w t 1,x,y,z, … (Position & Time) (Momentum & Energy) Indistinguishable at any instant Generalized Sp(2,R) generators Q ij (X,P) instead of the simpler Q ij (X,P)=(X 2,P 2,X.P) include ALL possible background fields. Generalized Sp(2,R) generators Q ij (X,P) instead of the simpler Q ij (X,P)=(X 2,P 2,X.P) include ALL possible background fields. Constraints: generators vanish !!!

16. Events in higher dims. 1357 One higher dimensional reality gives rise to many related lower dimensional “shadows” One higher dimensional reality gives rise to many related lower dimensional “shadows” From relations among many shadows could reconstruct full info in 4+2. Physicists who live only on the “wall” in 3+1 dims. can experiment only on the “wall”. The shadows appear to be independent phenomena to such observers. 16 Shadows in 3+1 capture different perspectives of 4+2 See ALL 4+2 ! Like many takes of a movie scene from different perspectives. Shadows in 3+1 capture different perspectives of 4+2 See ALL 4+2 ! Like many takes of a movie scene from different perspectives. Demos: hand, loop, sphere. See similarities to Plato’s Allegory of the Cave. But Plato does not have many shadows or their relations that are crucial in making the connections between 1T and 2T physics, & predictions.Plato’s Allegory of the Cave

17. 2T-physics Sp(2,R) X 2 =P 2 =X ∙ P=0. Background flat 6=4+2 dims SO(4,2) symmetry Massless relativistic particle (p  2 =0 conformal sy Dirac Massive relativistic (p  2 +m 2 =0 Non-relativistic H=p 2 /2m H-atom 3 space dims H=p 2 /2m -a/r SO(4)xSO(2) SO(3)xSO(1,2) Harmonic oscillator 2 space dims mass = 3 rd dim SO(2,2)xSO(2) Emergent spacetimes and dynamics, hidden symmetries & dualities from gauge fixing the 2T theory 17 2T-physics predicts hidden symmetries and dualities (with parameters) among the “shadows”. 1T-physics misses these phenomena. Holography: These emergent holographic images are only some examples of much broader phenomena. Free or interacting systems, with or without mass, in flat or curved 3+1 spacetimes Hidden Symm. SO(4,2) C 2 =1-d 2 /4= -3 singleton Hidden Symm. SO(4,2) C 2 =1-d 2 /4= -3 singleton Emergent parameters mass, couplings, curvature, etc. These emerge in 2T-field theory as well

18. Energy (n) 0 1 2 3 Angular momentum (L) “Seeing” 4+2 dimensions through the H-atom 18 (Position & Time) (Momentum & Energy) Indistinguishable at any instant 4 states at the same energy. 1 at L=0 3 at L=1, etc Why L=0,1 same energy? H-atom orbitals Demo : the 4 th dimension shadow of rotating system Seeing1 space (the 4 th ), and 2 times : At fixed angular momentum (3-space) the energy towers are patterns of space-time symmetry group SO(1,2) Seeing1 space (the 4 th ), and 2 times : At fixed angular momentum (3-space) the energy towers are patterns of space-time symmetry group SO(1,2) Shadow of free motion in 4+2 subject to : Subtle effects:

19. “Seeing” the 4 th dimension in celestial mechanics 19 2T-physics says A is just the component of angular momentum for rotating from ordinary 3-space into the 4 th dimension. The unchanging L and A are due to rotation symmetry in 4 dims. Demo with shadows: eccentricity and orientation of ellipse arises from orientation of orbit in 4 space dimensions. Unchanging ellipses – No precession. WHY? An accidental symmetry – meaning? Unchanging ellipses – No precession. WHY? An accidental symmetry – meaning? (Position & Time) (Momentum & Energy) Indistinguishable at any instant. Laplace-Runge-Lenz vector (axis of ellipse // to A) constant at any point in orbit. It determines the eccentricity and the orientation of the ellipse in the plane. Angular momentum (defines plane) constant of motion (same at any point in orbit) because of rotation symmetry in 3 dims. One of the shadows in 3+1 of free motion in 4+2, subject to symmetry Subtle effects:

20. 20 What are the true constituents of matter? Macroscopic matter   molecules  atoms  nuclei (many isotopes)  (protons + neutrons +…)  quarks + leptons Deeper into matter: 2T-physics and Field Theory All known matter is made up of quarks, leptons and “force particles” that hold them together. Matter particles spin ½, fermions 6 quarks (in 3 colors) 6 leptons (Including right-handed or Majorana singlet neutrinos) and their anti-particles (anti-matter) Matter particles spin ½, fermions 6 quarks (in 3 colors) 6 leptons (Including right-handed or Majorana singlet neutrinos) and their anti-particles (anti-matter) Currently we don’t know their sizes, and what, if anything, is inside quarks, leptons or force particles (maybe “superstrings” ?).

21. 21 plus Higgs unconfirmed Four interactions or forces govern all known phenomena in the Universe. Understood in the framework of Quantum Field Theory (computational framework). The Standard Model of Particles and Forces Describes Nature down to 10 -18 meters. Exquisite agreement with experiment. This SM emerges as a “shadow” of a 4+2 field theory. With better features. AND there are more shadows  duals This SM emerges as a “shadow” of a 4+2 field theory. With better features. AND there are more shadows  duals

22. 22 Unsolved Mysteries: CP (time reversal) violation problem in the strong interactions (but axion not seen?)  2T-physics solves this (a property of 4+2 dims.) – no need for axion! Why these degrees of freedom? And why in these patterns? 25 parameters : masses, couplings, mixings – is there a theory that determines them from first principles? Is Higgs the answer to the origin of mass ? LHC 2008 !!  2T-physics modifies Higgs (adds dilaton). Also new possibilities for mass ! Is there Supersymmetry (to resolve the mass hierarchy problem: stability) ?  a) If SUSY exists, there are new constraints from 2T-physics ! Tests !  b) 2T-physics may provide an alternative (conformal symmetry, 6 dims.!!) ? What is dark matter ? 25% of the matter in the Universe. What is dark energy? 70% of the energy in the Universe. How do we solve the Quantum Gravity problem (strings 9+1 dims, M-theory 10+1 dims, curled up dimensions) ? This is a framework ! Not a theory yet !  2T-physics requires extra 1-space + 1-time. M-theory in 11 space + 2 times !! Possible candidates for these exist among the degrees of freedom above. So far 2T-physics  known physics, but in new light with new predictions related to 1+1 dims. Are there predictions of disagreements with 1T-Physics?? Yes, only in hitherto unknown realms.

23. 23 In conclusion … These old Greeks eventually discovered the concept of the atom. Hidden information is predicted by 2T-physics. A new idea on unification. Similarly, you can’t ignore 2T-physics. A lot more remains to be done with 2T-physics. New testable predictions at every scale of physics are expected from the hidden dualities and symmetries. A lot more remains to be done with 2T-physics. New testable predictions at every scale of physics are expected from the hidden dualities and symmetries. 1T-physics on its own cannot capture these hidden symmetries and dualities, which actually exist. 1T is OK only with additional guidance.

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