Transcript Two Times - University of Southern California

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!!)
1
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
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.
2
space-time
(where and when)
Perspective: static observer free of forces, and emphasizing POSITION space


z
What is position in ordinary space ?
What is time ?
y
x
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
x,y,z
t
This point of departure is a perspective not symmetric in momentum vs position
x,y,z
Importance of perspective
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 !!
4
Today we believe in an expanding
Universe that has no center!!
Expansion not uniform, slightly accelerating (DE).
space-time perspectives (relativity)
Watch on ship 1hr,
Watch on Earth
320 yrs.
Measured time
depends on speed
of observer.
Perfect
identical
watches may
not measure
identical
time intervals.
5
Time Dilation
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.
You guessed it – it depends on the speed of the observer !
Space and Time are not absolute
they are relative to the observer
t
Even more weird things happen close to the extremes.
x,y,z
Such effects
arise because
observers are
in relative
motion,
or under the
influence of
gravitational
forces.
7
The observers’
Close to the speed of light, coordinate
or in very strong gravity, systems get
distorted relative
the other observer’s watch to each other.
appears to almost stop.
Inside a black hole,
time & space switch roles.
t
x
x,y,z
t,y,z
The Equivalence
Principle shows how
to relate them. Then
each observer sees
the same Laws of
Physics in their own
coordinate systems.
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”
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One temple,
many
perspectives
relations
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 Principle.
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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 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
subtle effect
Where is the Extra Space?
t
t
x,y,z, …. 7 more



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 explore
the small dimensions and bring the information to us.
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 !
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?
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.
1998: The solution to the disasters is a new gauge symmetry  2T-physics .
The new fundamental principle: A broader equivalence principle.
XM=(Position & Time)
PM= (Momentum & Energy)
indistinguishable
at any instant.
A new gauge symmetry of the Laws of Mechanics
Applied to all motion
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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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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.
analogy
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walls: 1T-physics in
ordinary space-time
1 time + 3 space
plus possible curled
up dims. (string
theory)
Demo:
hand and 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).
How does it work?
(Position & Time)
(Momentum & Energy)
Indistinguishable
at any instant
t’
t,x,y,z, …
x’
“Walls” many
perspectives.
Many 3+1 (x,p)
embeddings
in one 4+2 (X,P)
Non-trivial:
many 3+1 shadows emerge for same 4+2 spacetime history.
18Each shadow contains only one timeline (a mixture of all 4+2)
One higher dimensional reality gives rise to
many related lower dimensional shadows
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Demos: hand,
loop, sphere.
Shadows in 3+1
capture different
perspectives of
4+2.
Like many takes of a
movie scene from
different perspectives.
Temple/Perspectives
1
7
Events
in
higher
dims.
5
3
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.
From relations among many shadows could reconstruct full info in 4+2.
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.
Emergent spacetimes and dynamics, hidden symmetries & dualities
from gauge fixing the 2T theoryMassless
Free or
interacting
systems, with
or without
mass, in flat or
curved 3+1
spacetimes.
Harmonic
Analogy: multiple
oscillator
shadows on walls.
2 space dims
mass = 3rd dim
SO(2,2)xSO(2)
2T-physics predicts
hidden symmetries
and dualities (with
parameters) among
the “shadows”.
1T-physics misses
these phenomena.
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relativistic
particle
(pm)2=0
Hidden Symm.
SO(4,2)
Dirac
singleton
C2=1-d2/4= -3
conformal sy
2T-physics
Sp(2,R)
Massive
X2=P2=X∙P=0 .
relativistic
(pm)2+m2=0
Non-relativistic
H=p2/2m
Background
flat 6=4+2 dims
SO(4,2)
symmetry
H-atom
3 space dims
H=p2/2m -a/r
SO(4)xSO(2)
SO(3)xSO(1,2)
These emerge in 2T-field theory as well
Emergent
parameters
mass,
couplings,
curvature,
etc.
•Holography:
These emergent
holographic
images are only
some examples
of much
broader
Subtle effects:
“Seeing” 4+2 dimensions through the H-atom
Shadow of free motion in 4+2 subject to :
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Indistinguishable
(Position & Time)
(Momentum & Energy)
at any instant
H-atom orbitals
Energy
(n)
0
1
2
3
Angular
momentum (L)
4 states at the
same energy.
1 at L=0
3 at L=1, etc
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)
Why L=0,1
same energy?
Demo : the 4th dimension
shadow of rotating system
Subtle effects:
“Seeing” the 4th dimension in celestial mechanics
One of the shadows in 3+1 of free motion in 4+2, subject to symmetry
(Position & Time)
(Momentum & Energy)
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Indistinguishable
at any instant.
Angular momentum (defines plane)
constant of motion (same at any point in orbit)
because of rotation symmetry in 3 dims.
Unchanging ellipses – No precession.
WHY?
An accidental symmetry – meaning?
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.
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.
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
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
24agreement with experiment.
This SM emerges as a “shadow” of a
4+2 field theory, with improvement.
There are more shadows  duals
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.
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.
Possible candidates
for these exist
among the degrees
of freedom above.
•How do we solve the Quantum Gravity problem (strings 9+1 dims, M-theory 10+1
25 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 !!
In conclusion …
These old Greeks
eventually
discovered the
concept of the
atom.
Similarly, you
can’t ignore
2T-physics.
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1T-physics cannot
capture certain
hidden symmetries
and dualities, which
actually exist. 1T is
OK only with
additional guidance.
The hidden info is
predicted by
2T-physics. This is
a new unification.
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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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.
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•Experiment with muons in an accelerator confirms this.
Emergent spacetimes, dynamics and parameters,
hidden symmetries, dualities, unification.
29
Holographs
Massless
relativistic
particle
(pm)2=0
conformal
symm.
one to many
(4,2)(3,1)
“room”  “walls”
Dualities
space-time
histories in
“room” or
“walls” are
obviously
related.
Harmonic
oscillator 2
space dims
mass = 3rd dim
SO(2,2)xSO(2)
2T-physics
Sp(2,R)
Massive
X2=P2=X∙P=0 .
relativistic
(pm)2+m2=0
Non-relativistic
H=p2/2m
Background flat
6=4+2 dims
SO(4,2)
symmetry
H-atom
3 space dims
H=p2/2m -a/r
SO(4)xSO(2)
SO(3)xSO(1,2)
Unification
of forces & dynamics
Hidden Symm.
SO(4,2)
C2=1-d2/4= -3
singleton
Emergent
parameters
mass,
couplings,
curvature,
etc.
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 ….
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... all things are made of atoms."
-Richard P. Feynman.
Deeper into matter: 2T-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-,Z0
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+1dimensions is insufficient.
One extra time plus one extra space dimensions are needed
to provide a more complete view of Nature.
space-time
(where and when)
33


z
What is position in ordinary space ?
–3 dimensions (location in space) = where
x
What is time ?
– time on your watch = when
y
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
t
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
The force of gravity exists because of this symmetry.
All details of the gravitational force is controlled by this symmetry.
34
Emergent spacetimes and dynamics, hidden symmetries & dualities
from gauge fixing the 2T theory Massless
35
Free or
interacting
systems,
with or
without
mass, in
flat 3+1
spacetime
relativistic
particle
(pm)2=0
conformal sy
Dirac
Harmonic
oscillator
2 space dims
mass = 3rd dim
SO(2,2)xSO(2)
These are
only some
examples
of much
broader
phenomena.
2T-physics
Sp(2,R)
Massive
X2=P2=X∙P=0 .
relativistic
(pm)2+m2=0
Non-relativistic
H=p2/2m
Background
flat 6=4+2 dims
SO(4,2)
symmetry
H-atom
3 space dims
H=p2/2m -a/r
SO(4)xSO(2)
SO(3)xSO(1,2)
interacting
systems,
in various
curved
spacetimes
in 3+1
1T-physics
misses the
relations
among the
“shadows”.
2T-physics
predicts them.
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.
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 …
37