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 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 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.
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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 ?
• 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

This point of departure is a perspective not
symmetric in momentum vs position
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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 !!
Today we believe in an expanding Universe that
has no center!! Expansion not uniform, slightly
accelerating (DE).
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space-time perspectives (relativity)
Watch on ship 1hr, Watch on Earth 320
yrs. Measured time depends on speed of observer.
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.
Perfect identical watches may not measure
identical time intervals.
Time Dilation
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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.
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 each
observer sees the same Laws of Physics in their
own coordinate systems.
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, the other observers 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 for all physical
phenomena Invariance under general coordinate
transformations
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Example of Symmetry and Perspective
One temple, many perspectives ?relations
Local symm. Rotate white tiles individually Globa
l symm. Rotate picture tiles everywhere
Search for subtle effects
Now substitute the temple with Equations that
describe Laws of Physics to grasp the notion of
symmetry and perspective, and Equivalence
Principle.
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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!! Predictions subtle
effects Emc2, 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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Not much discussion of more time-like dimensions
why?

• Because the road to 2T is dangerous and scary
• Ghosts
• Some events can happen with negative
  probability.
• 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 more Ts?
But there are some clues for more Ts in the
search of the mysterious theory Extended SUSY of
M-theory is (102) SUSY (Bars -1995), F-theory
(102 or 111), S-theory (112), U-theory (other
signatures), etc.
1998 The solution to the disasters is a new
gauge symmetry ? 2T-physics .
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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 2T-physics solve the problems of 2 times?
I prefer formulas, but I will use some analogies,
instead!
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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
Substance is what is in the room
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)
analogy
Demo hand and its shadows
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How does it work?

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 11 dimensions necessary ? 42 !! No more
   no less than 2 times
4. Straightjacket in 42 makes allowed motions
   effectively 31 motions (on walls).

Walls many perspectives. Many 31 (x,p)
embeddings in one 42 (X,P)
Non-trivial 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. Like many takes of a movie scene from
different perspectives. Temple/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. Analogy
multiple shadows on walls.
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 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 improvement. 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 in disagreement 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 appears to solve this (a property of
  42 dims.) no need for axion!
• Why these degrees of freedom (quarksleptons,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 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
1T-physics cannot capture certain hidden
symmetries and dualities, which actually exist.
1T is OK only with additional guidance.
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 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
extend its domain of validity to solve the
remaining mysteries!!
The End