1. 1 Two-Time Physics The Unified View From Higher Dimensional Space and Time Itzhak Bars, USC One of the most important questions today is, 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:

3. space-time (where and when)  What is position in ordinary space ?  What is time ?  What is a space-time event in space-time ?  What is space-time history ? – motion of a point is represented by a curve in space-time = worldline 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

4. 4 It took 17 centuries, From Ptolemy to Copernicus, for humans to be convinced the Sun, and not the Earth is the center of the Universe. And even this is not right !! It took 17 centuries, From Ptolemy to Copernicus, for humans to be convinced the Sun, and not the Earth is the center of the Universe. And even this is not right !! Today we believe in an expanding Universe that has no center!! Expansion not uniform, slightly accelerating (DE). Importance of perspective

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) Watch on ship 1hr, Watch on Earth 320 yrs. Measured time depends on speed of observer. 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.

7. 7 Close to the speed of light, or in very strong gravity, the other observer’s 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 observers’ coordinate systems get distorted relative to each other. The Equivalence Principle shows how to relate them. Then each observer sees the same Laws of Physics in their own coordinate systems. The observers’ coordinate systems get distorted relative to each other. The Equivalence Principle shows how to relate them. Then each observer sees the same Laws of Physics in their own coordinate systems. 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 for all physical phenomena: Invariance under “general coordinate transformations”

9. SYMMETRY AND 9 Now substitute the “temple” with “Equations that describe Laws of Physics” to grasp the notion of symmetry and perspective, and Equivalence Principle. Local symm. Rotate white tiles individually Global symm. Rotate picture tiles everywhere One temple, many perspectives  relations Search for subtle effects

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11. 11 But there is more to explain: Properties of matter other than history in space-time? Electric charge, … Non-gravitational forces?

12. 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. t x,y,z, … 7 more

13. 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. t x,y,z 7 more t x,y,z, …. 7 more subtle effect

14. Not much discussion of more time-like dimensions – why? Because the road to 2T is dangerous and scary: 1) Ghosts Some events can happen with negative probability. 2)Murderers! You can kill your grandmother before your mother is born, so you prevent your own birth Causality violation (cause and effect disconnect)  time machines, impossible paradoxes! But there are some clues for more T’s in the search of the mysterious theory: Extended SUSY of M-theory is (10+2) SUSY (Bars -1995), F-theory (10+2 or 11+1), S-theory (11+2), U-theory (other signatures), etc. It took ½ century to learn how to overcome such disasters for the first time dimension. More time dimensions make it much worse !! How will such issues be solved with more T’s? 1998: The solution to the disasters is a new gauge symmetry  2T-physics.

15. 15 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

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17. The cartoonist, John Leech, is making a social statement by depicting “substance” as poor people, admiring the “shadow” as rich people. 17 Substance is what is in the room Shadow is what is on the walls analogy room: 2T-physics in higher space-time with 1 extra time plus 1 extra space. New extra dims are large, not curled up. walls: 1T-physics in ordinary space-time 1 time + 3 space plus possible curled up dims. (string theory) Demo: hand and its shadows

18. 18 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 more no less than 2 times 4)Straightjacket in 4+2 makes allowed motions effectively 3+1 motions (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 more no less than 2 times 4)Straightjacket in 4+2 makes allowed motions effectively 3+1 motions (on walls). Non-trivial: 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: 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? “Walls” many perspectives. Many 3+1 (x,p) embeddings in one 4+2 (X,P) “Walls” many perspectives. Many 3+1 (x,p) embeddings in one 4+2 (X,P) t’ x’ t,x,y,z, … (Position & Time) (Momentum & Energy) Indistinguishable at any instant

19. 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. 19 Shadows in 3+1 capture different perspectives of 4+2. Like many takes of a movie scene from different perspectives. Temple/Perspectives Shadows in 3+1 capture different perspectives of 4+2. Like many takes of a movie scene from different perspectives. Temple/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

20. 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) 20 Emergent spacetimes and dynamics, hidden symmetries & dualities from gauge fixing the 2T theory 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. Analogy: multiple shadows on walls. Free or interacting systems, with or without mass, in flat or curved 3+1 spacetimes. Analogy: multiple shadows on walls. 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

21. Energy (n) 0 1 2 3 Angular momentum (L) “Seeing” 4+2 dimensions through the H-atom 21 (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:

22. “Seeing” the 4 th dimension in celestial mechanics 22 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:

23. 23 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 and their anti-particles (anti-matter) Matter particles spin ½, fermions 6 quarks (in 3 colors) 6 leptons 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” ?).

24. 24 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 improvement. There are more shadows  duals This SM emerges as a “shadow” of a 4+2 field theory, with improvement. There are more shadows  duals

25. 25 Unsolved Mysteries: CP (time reversal) violation problem in the strong interactions (but axion not seen?)  2T-physics appears to solve this (a property of 4+2 dims.) – no need for axion! Why these degrees of freedom (quarks&leptons,etc)? 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 in disagreement with 1T-Physics?? Yes, only in hitherto unknown realms.

26. 26 In conclusion … These old Greeks eventually discovered the concept of the atom. The hidden info is predicted by 2T-physics. This is a new 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 cannot capture certain hidden symmetries and dualities, which actually exist. 1T is OK only with additional guidance.

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28. Time dilation Consider the path of a beam of light as shown in the picture as observed from inside or outside the spaceship  TIME (seen from ship) = DISTANCE (seen from ship) / VELOCITY (seen from ship)  TIME (seen from Earth) = DISTANCE (seen from Earth) / VELOCITY (seen from Earth) Light is observed at the same speed c=300,000 m/s in either frame. A property of Nature! same c, different distance, so different time They measure a DIFFERENT time lapse for the same event (emission - reception). Conclusion: Moving clock is slower as seen from Earth. Traveling twin is younger at the end of the trip. Earthbound observers experience a time dilation compared to his time. Experiment with muons in an accelerator confirms this. 28

29. Emergent spacetimes, dynamics and parameters, hidden symmetries, dualities, unification. Emergent parameters mass, couplings, curvature, etc. Holographs one to many (4,2)  (3,1) “room”  “walls” Holographs one to many (4,2)  (3,1) “room”  “walls” Unification of forces & dynamics Unification of forces & dynamics 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 29 Dualities space-time histories in “room” or “walls” are obviously related. Dualities space-time histories in “room” or “walls” are obviously related.

30. 30 MATTER "If, in some cataclysm, all of scientific knowledge were to be destroyed, and only one sentence passed on to the next generations of creatures, what statement would contain the most information in the fewest words? I believe it is that ….... all things are made of atoms." -Richard P. Feynman.

31. 31 Matter particles (fermions – spin 1/2): 6 leptons, 6 quarks (in 3 colors), and their anti-particles Force carrier particles (bosons – spins 1, 0): graviton, 8 gluons, photon, W +,W -,Z 0 and Higgs (not confirmed yet) Four interactions or forces govern all known phenomena in the Universe. A Quantum Field Theory (computational framework) The Standard Model of Particles and Forces Exquisite agreement with experiment. Describes Nature down to 10 -18 m. This SM emerges as a shadow of a 4+2 field theory, with an improvement !! Deeper into matter: 2T-physics and Field Theory (2006)

32. 32 Two-Time Physics The Unified View From Higher Dimensional Space and Time Itzhak Bars, USC Symmetry: order, leads to predictions Perspective: different views of the same thing substance versus shadows Subtle phenomena: hard to notice, surprises tests to confirm or reject theories The ordinary formulation of Physics in 3+1dimensions is insufficient. One extra time plus one extra space dimensions are needed to provide a more complete view of Nature.

33. 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 33 x y z t x,y,z t

34. 34 The laws of Physics are independent of the observer’s space and time perspective Equivalence Principle !! (Einstein) The principle 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.

35. 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 35 1T-physics misses the relations among the “shadows”. 2T-physics predicts them. 1T-physics misses the relations among the “shadows”. 2T-physics predicts them. These are only some examples of much broader phenomena. Free or interacting systems, with or without mass, in flat 3+1 spacetime interacting systems, in various curved spacetimes in 3+1

36. Nobody discusses more time-like dimensions – why? 36 BBecause physicists are scared of them. TTwo kinds of disasters: 1) Ghosts! = negative probability 2) Causality violation (time machines) Can kill your grandmother before you are born ! BBoth are nonsensical, and kept physicists away from contemplating more time-like dimensions.

37. 37 Easy! A new symmetry that makes (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 ! Here it is …