TwoTime Physics The Unified View From Higher Dimensional

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. 1 • String theory: consistent Quantum Mechanics + Gravity

Themes in this lecture: 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 2 Surprising and far reaching preliminary conclusion:

space-time (where and when) Perspective: static observer free of forces, and emphasizing POSITION space What is position in ordinary space ? What is time ? t 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 This point of departure is a perspective not symmetric in momentum x, y, z

Importance of perspective Left alone, over time, Isaac will develop the notion that the Sun goes around the Earth. 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 !! A matter of perspective !! 4 Today we believe in an expanding Universe that has no center!! Expansion not uniform, slightly accelerating (DE).

space-time perspectives Watch on ship 1 hr, Watch on Earth 320 yrs. Measured time depends on speed of Perfect observer. identical watches may not measure Time identical 5 Dilation time (relativity) 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.

More Perspectives: Space Contraction 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. 6 AT Identical rulers may measure differently the same space interval.

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

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: 8

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

Local Symmetry The Equivalence Principle explains it all as different perspectives in space-time Consequence of this symmetry: Gravity must exist, and must be described by General Relativity!! 10 Predictions & subtle effects : E=mc 2, Big Bang, Black Holes, Expanding Universe, etc.

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

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.

subtle effect Where is the Extra Space? t x, y, z 7 more 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

Not much discussion of more time-like dimensions – why? Because the road to 2 T 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 ! 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 But there are some clues for more T’s in the search of the mysterious more T’s? 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), 1998: The solution to the disasters etc. is a new gauge symmetry 2 Tphysics.

The new fundamental principle: A broader equivalence principle. A new gauge symmetry of the Laws of Mechanics Applied to all motion 15 Gauge symmetries are so powerful that they highly constrain the equations that can be written down, sometimes fully determining All known them. 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 Model Particles Forces To have the. Standard symmetry, theof force mustand exist, its (strong, weak, and electro-magnetic)

How does 2 T-physics solve the problems of 2 times? 16 I prefer formulas, but I will use some analogies, instead!

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

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: How does it work? t’ t, x, y, z, … x’ “Walls” many perspectives. Many 3+1 (x, p) embeddings in one 4+2 (X, P) many 3+1 shadows emerge for same 4+2 spacetime 18 history. Each shadow contains only one timeline (a

19 One higher dimensional reality gives rise to many related lower dimensional Demos: hand, Physicists who shadows 1 loop, sphere. 2 live only on the Shadows in 3+1 capture different perspectives of 4+2. Like many takes of a movie scene from different perspectives. 7 8 Event s in higher dims. 5 6 3 4 “wall” in 3+1 dims. can experiment only on the “wall”. The shadows appear to be independent phenomena to such observers. From relations among many shadows could reconstruct Temple/Perspective in 4+2. s. See similarities to Plato’s Allegory ofinfo the Cave. But Plato does not have many full shadows or their relations that are crucial in making the connections between 1 T and

Emergent spacetimes and dynamics, hidden symmetries & dualities Massle Particle in Roberstso from gauge fixing the 2 T theory ss Hidden Free or interacting systems, with or without mass, in flat or curved 3+1 spacetimes. n-Walker relativistic expandin particle (pmg )2=0 Symm. SO(4, 2) C 2=1 -d 2/4= -3 conformal Universe sy Dirac Twistor Harmonic s oscillator SU(2, 2)=SO(4, 2 space 2) twistor dims mass = 3 dim transform Analogy: SO(2, 2)x. SO( for all multiple 2) these shadows on 2 T-physics walls. predicts hidden symmetries and dualities (with parameters) among the “shadows”. 1 T 20 physics misses these phenomena. rd 2 T-physics Sp(2, R) . X 2=P 2=X∙P=0 singleton Particle in Massive. Background flat 6=4+2 dims SO(4, 2) symmetry Particle in any H-atom any relativistic Maximally 2 2 (p. Symmetric m) +m =0 Space, Non- e. g. Ad. S 4 relativistic 2/2 m n H=p nx. S Conformall 3 space y flat dims Space H=p 2/2 m -a/r singular SO(4)x. SO(2) OK, some SO(3)x. SO(1, 2) Black These emerge in. Holes 2 T-field theory as Emergent parameter s mass, couplings, curvature, etc. • Holography: These emergent holographic images are only some examples of much broader

“Seeing” 4+2 dimensions through the Hatom Subtle effects: Shadow of free motion in 4+2 subject to : 21 H-atom orbitals Energy (n) 0 … 1 2 … … 3 … Angular momentum (L) 4 states at the same energy. Seeing 1 space (the 4 th), and 2 times : At fixed angular momentum (3 space) the energy towers are patterns of 1 at L=0 3 at L=1, etc Why L=0, 1 same th Demo : the 4 dimension energy? shadow of rotating system

Subtle effects: “Seeing” the 4 th dimension in celestial mechanics One of the shadows in 3+1 of free motion in 4+2, subject to symmetry 22 Angular momentum (defines plane) constant of motion (same at any point in orbit) because of rotation symmetry in 3 Laplace-Runge-Lenz vector dims. Unchanging ellipses – No (axis of ellipse // to A) precession. constant at any point in orbit. WHY? It determines the eccentricity and An accidental symmetry – the orientation of the ellipse in the meaning? plane. 2 T-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 Demo with rotation shadows: eccentricity and in orientation of symmetry 4 dims. ellipse arises from orientation of orbit in 4 space

Deeper into matter: 2 T-physics and Field Theory What are the true constituents of matter? Macroscopic matter molecules atoms nuclei (many isotopes) (protons + neutrons +…) quarks + leptons Matter particles spin ½, fermions 6 quarks (in 3 colors) 6 leptons and their anti-particles (anti-matter) All known matter is made up of quarks, leptons and “force 23 particles” that hold them together. Currently we don’t know their sizes, and what, if anything, is inside quarks, leptons or force particles (maybe “superstrings” ? ).

The Standard Model of Particles and Forces Four interactions or forces govern all known phenomena in the Universe. Understood in the framework of Quantum Field Theory (computational framework). plus Higgs unconfirmed Describes Nature down to 10 -18 meters. Exquisite 24 agreement with This SM emerges as a “shadow” of a 4+2 field theory, with

So far 2 T-physics known physics, but in new light with new predictions related to 1+1 dims. Are there predictions in disagreement with 1 T-Physics? ? Yes, only in hitherto unknown realms. Unsolved Mysteries: • CP (time reversal) violation problem in the strong interactions (but axion not seen? ) 2 T-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 !! 2 T-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 2 T-physics ! Tests ! b) 2 T-physics may provide an alternative (conformal symmetry, 6 dims. !!) ? Possible candidates for these exist • What is dark energy? 70% of the energy in the Universe. among the degrees of • How do we solve the Quantum Gravity problem (strings 9+1 dims, M-theory 10+1 freedom above. 25 dims, curled up dimensions) ? This is a framework ! Not a theory yet ! 2 T-physics requires extra 1 -space + 1 -time. M-theory in 11 space + 2 times !! • What is dark matter ? 25% of the matter in the Universe.

In conclusion … These old Greeks eventually discovered the concept of the atom. Similarly, you can’t ignore 2 T-physics. 26 1 T-physics cannot capture certain hidden symmetries and dualities, which actually exist. 1 T is OK only with additional The hidden info guidance. is predicted by 2 T-physics. This is a new unification. A lot more remains to be done with 2 T-physics. New testable predictions at every scale of physics are expected from the hidden dualities and symmetries.

2 T-physics works down to 10 -18 meters at least ! … and through work in progress we hope to extend its domain of validity to solve the remaining mysteries!! 27 The End

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. 28 • Experiment with muons in an accelerator confirms this.

29 Emergent spacetimes, dynamics and parameters, hidden symmetries, dualities, unification. Holographs one to many (4, 2) (3, 1) “room” Dualities “walls” space-time histories in “room” or “walls” are obviously related. Massless Particle in relativistic Roberstso particle n-Walker (pm)2=0 expanding conformal Universe symm. Harmonic Twistors SU(2, 2)=SO(4, oscillator 2 space 2) twistor dims mass = transform 3 rd dim for all SO(2, 2)x. SO(2 these ) 2 T-physics Sp(2, R) . X 2=P 2=X∙P=0. Background flat 6=4+2 dims SO(4, 2) symmetry Particle in Massive any relativistic 2 2 (p. Maximally m) +m =0 Symmetric Non-relativistic Space, e. g. H=p 2/2 m n Particle in any H-atom Conforma ll 3 space y flat 2 dims H=p /2 m Space -a/r singular SO(4)x. SO(2) SO(3)x. SO(1, 2 OK, some ) Black Holes Unification of forces & dynamics Hidden Symm. SO(4, 2) C 2=1 -d 2/4= -3 singleton Ad. S 4 -nx. S Emergent parameter s mass, couplings, curvature, etc.

MATTER 30 "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.

Deeper into matter: 2 T-physics and Field Theory (2006) The Standard Model of Particles and Forces 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) Matter particles (fermions – spin 1/2): 6 leptons, 6 quarks (in 3 colors), and their anti-particles This SM emerges as a shadow of a 31 4+2 field theory, with an improvement !! Exquisite agreement with experiment. Describes Nature down to 10 -18 m.

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 32 The ordinary formulation of Physics in 3+1 dimensions is insufficient. One extra time plus one extra space dimensions are needed to provide a more complete view of Nature.

space-time 33 (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. ) t 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 x, y, z

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 34 The force of gravity exists because of this symmetry. All details of the gravitational force is controlled by this

Emergent spacetimes and dynamics, hidden symmetries & dualities Massle Particle in from gauge fixing the 2 T theory Roberstso ss 35 Free or interactin g systems, with or without mass, in flat 3+1 spacetim e These are only some examples of much broader phenomen a. n-Walker relativistic expandin particle (pmg )2=0 conformal Universe sy Dirac Twistor Harmonic s oscillator SU(2, 2)=SO(4, 2 space 2) twistor dims mass = dim transform SO(2, 2)x. SO( for all 2) 3 rd these 2 T-physics Sp(2, R) . X 2=P 2=X∙P=0. Background flat 6=4+2 dims SO(4, 2) symmetry Particle in any H-atom Conformall 3 space y flat dims Space H=p 2/2 m -a/r singular SO(4)x. SO(2) OK, some SO(3)x. SO(1, 2) Black Holes interactin g systems, in various curved Particle in spacetim Massive any es in 3+1 relativistic Maximally 2 2 (p. Symmetric m) +m =0 Space, Non- e. g. Ad. S 4 relativistic 2/2 m n H=p nx. S 1 T-physics misses the relations among the “shadows”. 2 T-physics predicts

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

How can 2 T-physics advocate 2 times? 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 ! 37 I prefer formulas, but I will use some analogies, Here it is … instead!