Two Times

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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 20th 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!!)

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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
31 dims. Hard to notice, surprises, tests to
confirm or reject theories Surprising and far
reaching preliminary conclusion The ordinary
formulation of Physics in 31 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.
Related work One corner of 2T-physics makes
contact with work by Dirac, Salam, Adler,
Ferrara, Siegel, Marnelius, Vasiliev, (conformal
symmetry)
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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)
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space-time (where and when)
Perspective static observer free of forces, and
emphasizing POSITION space

• 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

This point of departure is a perspective not
symmetric in momentum vs position
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space-time perspectives (relativity)
Prediction Special Relativity allows time
travel to the future.
Ships watch 1hr, but Earths 320 yrs. , as
observed by astronauts. Time duration seen on a
watch depends on the speed of the observer
relative to that watch.
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.
Time Dilation
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More Perspectives Space Contraction
But, particles in accelerators move at great
speeds, and behave precisely as predicted. e.g.
sphere looks like pancake.
Subtle effects. The effect is too small to notice
in daily phenomena because the speed is too
small.
Identical rulers may measure differently the same
space interval. You guessed it it depends on
the speed of the observer !
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Space and Time are not absolute they are relative
to the observer
Even more weird things happen close to the
extremes.
The observers coordinate systems get distorted
relative to each other. The Equivalence
Principle shows how to relate them. Then
observers see same Law.
Such effects arise because observers are in
relative motion, or under the influence of
gravitational forces.
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.
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Equivalence Principle !! (Einstein) The laws of
Physics are independent of the observers 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.
Predictions subtle effects Emc2, Twin
paradox, Big Bang, Black Holes, Expanding
Universe, etc.
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But there is more to explain
Properties of matter other than history in
space-time?
Electric charge, Non-gravitational forces?
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Space-Time and Higher Dimensions

• Kaluza (1921) and Klein (1926) considered 1 extra
  dimension. Explain charge and EM (Gen Rel in
  41)
• 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.

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Where is the Extra Space?
subtle effect

• 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 31 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.

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Nobody discusses more time-like dimensions why?

• Because physicists are scared of them.
• 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. !
• Both are nonsensical, and kept physicists away
  from contemplating more time-like
  dimensions.

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Then, how can 2T-physics advocate 2 times?

• 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

H
Invariant
2T-physics emerges from demanding that this
global symmetry turn into a local symmetry
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The new fundamental principle A broader
equivalence principle.
A new gauge symmetry of the Laws of
Mechanics Applied to all motion
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)
To have the symmetry, the force must exist, its
details fixed.
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How does it work?

• New symmetry allows only highly symmetric
  motions. ?little room to maneuver.
• With only 1 time the highly symmetric motions
  impossible. ?Collapse to nothing.
• Extra 11 dimensions necessary ? 42 !! No less
  and no more than 2T.
• Straightjacket in 42 makes allowed motions
  effectively 31 motions (like shadows on walls).

Constraints generators vanish !!!
Generalized Sp(2,R) generators Qij(X,P) instead
of the simpler Qij(X,P)(X2,P2,X.P) include ALL
possible background fields.
Non-trivial Gauge fix 42 to 31 (have 3 gauge
parameters) many 31 shadows emerge for same 42
spacetime history. Each shadow contains only one
timeline (a mixture of all 42)
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One higher dimensional reality gives rise to
many related lower dimensional shadows
Demos hand, loop, sphere.
Physicists who live only on the wall in 31
dims. can experiment only on the wall.
The shadows appear to be independent phenomena to
such observers.
Shadows in 31 capture different perspectives of
42 See ALL 42 ! Like many takes of a movie
scene from different perspectives.
From relations among many shadows could
reconstruct full info in 42.
See similarities to Platos 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.
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Emergent spacetimes and dynamics, hidden
symmetries dualities from gauge fixing the 2T
theory
Hidden Symm. SO(4,2) C21-d2/4 -3 singleton
Free or interacting systems, with or without
mass, in flat or curved 31 spacetimes
Emergent parameters mass, couplings, curvature,
etc.
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.
These emerge in 2T-field theory as well
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Seeing 42 dimensions through the H-atom
Subtle effects
Shadow of free motion in 42 subject to
H-atom orbitals
Seeing1 space (the 4th), and 2 times At fixed
angular momentum (3-space) the energy towers are
patterns of space-time symmetry group SO(1,2)
Demo the 4th dimension shadow of rotating system
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Seeing the 4th dimension in celestial mechanics
Subtle effects
One of the shadows in 31 of free motion in 42,
subject to symmetry
Unchanging ellipses No precession. WHY? An
accidental symmetry meaning?
2T-physics says A is just the component of
angular momentum for rotating from ordinary
3-space into the 4th 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.
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Deeper into matter 2T-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 (Including right-handed or
Majorana singlet neutrinos) and their
anti-particles (anti-matter)
All known matter is made up of quarks, leptons
and force particles that hold them together.
Currently we dont know their sizes,
and what, if anything, is inside quarks,
leptons or force particles (maybe
superstrings ?).
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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
agreement with experiment.
This SM emerges as a shadow of a 42 field
theory. With better features. AND there are more
shadows ?? duals
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So far 2T-physics ? known physics, but in new
light with new predictions related to 11 dims.
Are there predictions of disagreements with
1T-Physics?? Yes, only in hitherto unknown realms.
Unsolved Mysteries

• CP (time reversal) violation problem in the
  strong interactions (but axion not seen?)
• ? 2T-physics solves this (a property of 42
  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 91 dims, M-theory 101 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.
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In conclusion
Hidden information is predicted by 2T-physics. A
new idea on unification.
These old Greeks eventually discovered the
concept of the atom.
1T-physics on its own cannot capture these hidden
symmetries and dualities, which actually exist.
1T is OK only with additional guidance.
Similarly, you cant 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.
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2T-physics works down to 10-18 meters at least !
and through work in progress we hope to the
extend its domain of validity to solve the
remaining mysteries!!
The End