[tt] New Scientist: Time gains an extra dimension

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Time gains an extra dimension
http://www.newscientist.com/article.ns?id=mg19626251.400&print=true
7.10.13

[Don't give up on negative probabilities yet! My friend Roy Dent, a 
retired physicist in Boulder, who worked at IBM, Loral, and Lockheed 
Martin, was working on a problem in which he developed probability 
transition matrices that had complex numbers in their cells, not so 
unfamiliar from first year physics that uses complex numbers in 
alternating circuits. I instantly saw the implications, though I certainly 
couldn't do the physics! The constraint was the sum total of everything in 
the table must necessarily be zero, which of course is true of the mundane 
transition matrices that use only non-negative real numbers that we all 
know about. His immediate job completed, he went on to other assignments, 
thus never getting around to revolutionizing physics. I can tell you how 
to contact him, if anyone is up to the physics and is interested.

[The Physical Reviews Letter article follows. I used the generally 
terrific ABBYY transformer, but it handles equations poorly. Just glance 
over the English to get a general picture to the extent you are capable. 
e-mail me for the PDF itself!]

TIME ain't what it used to be. A hundred years or so ago, we thought
that the seconds ticked away predictably. Tick followed tock,
followed tick. And clocks ran... well, like clockwork. Then along
came Einstein and everything changed.

His theories of relativity dealt a blow to our naive ideas about
time. Hitch a ride on a rocket travelling close to the speed of
light, and time slows to a virtual standstill. The same happens if
you park near a black hole and feel its awesome gravity. Even worse,
space-time becomes so warped inside a black hole that space and time
actually switch places.

Now just as we're getting to grips with time's weirdness, one daring
physicist has dropped another bombshell. "There isn't just one
dimension of time," says Itzhak Bars of the University of Southern
California in Los Angeles. "There are two. One whole dimension has
until now gone entirely unnoticed by us."

Does this mean we can look forward to extra hours and seconds? Or
will time's second dimension play havoc with our notions of the
past, present and future? Or is Bars, in fact, a few quarks short of
a proton? One thing Bars's extra time dimension does appear to
reveal is the existence of deep and unexpected connections between
disparate systems, such as atoms and the expanding universe. Such
connections could point the way to a "theory of everything" that
unites all the physical laws of the universe into one. Even better,
Bars claims his theory has true predictive power and can be tested
in upcoming particle physics experiments.

Physicists are no strangers to extra dimensions. For decades,
theorists attempting to unify the forces of nature have been adding
extra dimensions of space to their equations. As early as the 1920s,
mathematicians found that moving up to four dimensions of space,
instead of the three we experience, helped in their quest to
reconcile electromagnetism and gravity. Later, in the 1980s, came
various [15]superstring theories, which describe the universe in
terms of tiny one-dimensional strings vibrating against a backdrop
of nine space dimensions, six of which are curled up so tightly we
cannot see them. A decade or so on, theorists recognised the
assorted string theories as different facets of a single idea called
M-theory that adds yet another dimension, taking the total to 11: 10
of space and one of time.

Double time

Meddling with space, at least, is fair game. So how come so few have
dared to tinker with time? There are two good reasons why adding
extra time dimensions makes theorists queasy. For a start, when you
insert time into your equations it tends to come with a negative
rather than a positive sign. A second time dimension only makes this
problem more severe and leads to events happening with a negative
probability, a concept which is meaningless, says Bars.

Worse, it gives the green light to the idea of time travel. If time
is one-dimensional, like a straight line, the route linking the
past, present and future is clearly defined. Adding another
dimension transforms time into a two-dimensional plane, like a flat
sheet of paper. On such a plane, the path between the past and
future would loop back on itself, allowing you to travel back and
forwards in time (see Diagram). That would permit all kinds of
absurd situations, such as the famous grandfather paradox. In this
scenario, you could go back and kill your grandfather before your
mother was a twinkle in his eye, thereby preventing your own birth.

Two-dimensional time gives every appearance of being a non-starter.
Yet when Bars found hints of an extra time dimension in M-theory in
1995, he was determined to take a closer look. When he did, Bars
found that a key mathematical structure common to all 11 dimensions
remained intact when he added an extra dimension. "On one
condition," says Bars. "The extra dimension had to be time-like."

Of course, Bars knew all about the horrors that emerge when you
start to mess around with time. Undeterred, he wondered if negative
probability and time travel would disappear if movement in the new
space-time was severely constrained. But what kind of constraint?
Bars guessed it had to be a hitherto unsuspected symmetry of nature.

Symmetry concerns the properties of objects that stay the same even
when you do something to them - a cube looks the same no matter
which face you view. And symmetry applies to the laws of physics
too. So if you conduct an experiment it makes no difference to the
results whether your laboratory is standing still, being carried
along in the train or being whirled round on a fairground ride.

This connection between physics and symmetry was first recognised by
the German mathematician Emmy Noether. In a remarkable paper
published in 1918, she showed that many of the fundamental
conservation laws of physics are nothing more than consequences of
underlying symmetries. For instance, the law of conservation of
energy - that energy cannot be created or destroyed, merely
transformed from one form into another - is a consequence of "time
translational symmetry", the fact that if you do an experiment today
or tomorrow or next month, you will get the same result, all things
being equal. Both general relativity and the [16]standard model of
particle physics are based on symmetries that hold independently at
every point of space and time, so-called "gauge symmetries".

Noether's powerful insight was a powerful driving force behind
modern fundamental physics, which is constantly looking for the deep
and simple symmetries that spawn the complex phenomena we observe in
the universe. Bars wondered whether an unsuspected gauge symmetry
would make sense of an extra time dimension. And, in 1995, he began
looking for one.

The clue came from quantum theory. Quantum uncertainty limits how
well you can ever know certain properties of a physical system. Pin
down the position of an atom and you can never measure its momentum,
and vice versa. Bars wondered whether this result hints of a deeper
relationship between position and momentum. Could there be an
underlying symmetry between the two?

Living in a shadow

Two things happened when Bars tried to enforce such a gauge
symmetry. First, he discovered that it didn't work unless there were
two extra dimensions, one of space and one of time. According to his
theory, then, we live in a world with six dimensions. (Or, if you
extend M-theory, 13 dimensions.)

On the face of it, this does not solve the time-travel problem.
However, Bars found that gauge symmetry is a very tight straitjacket
indeed. "Phenomena in the six-dimensional world have very little
room to manoeuvre," he says. This restriction on motion in six
dimensions makes it impossible to climb into time's second dimension
and travel through it back to the past. It also irons out those
messy negative probabilities. "To all intents and purposes, the
six-dimensional world behaves like a far more restricted world, one
with only four dimensions," says Bars.

Except that it's not exactly like the four-dimensional world we
inhabit, or there would be nothing new to write home about. It is
here, Bars points out, that the big pay-off lies. "The severely
restricted motions in higher-dimensional space-time reproduce the
usual laws of motion in familiar space-time," says Bars, "but they
also reveal new and unexpected relationships."

According to Bars, the world we see around us is merely a "shadow"
of a six-dimensional world. Think of a 3D object like your hand and
the 2D shadow it makes on a wall. Just as there are many different
possible shadows of your hand depending on where the light source is
located, there are many possible four-dimensional shadows of the
six-dimensional world. "Each gives rise to a different set of
phenomena in our world," he says.

Bars began exploring the simplest possible system in six dimensions,
a particle moving in a straight line with no forces acting on it.
Remarkably, he found that the system has at least two more complex
shadows in four dimensions. One corresponds to an electron orbiting
in an atom; the other is a particle in an expanding universe.
"Although these phenomena seem unconnected, my picture unifies
them," says Bars. "They are both shadows of the same six-dimensional
reality."

Because "two-time" physics, as Bars likes to call it, unites
seemingly unconnected phenomena, might it be able to reconcile the
two mighty pillars of 20th-century physics, quantum mechanics and
relativity?

Bars realised that his economical descriptions of hitherto
unconnected phenomena are worth nothing unless they predict
something new. Recently, he has been incorporating two-time physics
into quantum field theory, which explains all the fundamental forces
of nature within the framework of the standard model - except for
that tricky beast gravity.

Last year, he published a paper in [17]Physical Review D (vol 74, p
085019) showing that the standard model is in fact just one shadow
of his six-dimensional theory. According to Bars, there are other
shadows that include gravity, finally uniting it with the standard
model.

So far, few physicists have pursued Bars's idea because previous
attempts by others to introduce extra time dimensions have raised
more questions than they have solved. Among them is the physical
reality of the new dimension: is it on the same footing as time as
we know it? Many physicists are comfortable with an extra time
dimension as a mathematical concept but not as a real physical
entity. "Stephen Hawking and others have used 'imaginary time' in
calculations involving Einstein's general theory of relativity,"
says John Cramer of the University of Washington at Seattle. "I
believe this is just a calculational device for sweeping certain
things under the rug."

Bars insists his extra dimensions are more than mathematical sleight
of hand. "Absolutely not," he says. "These extra dimensions are out
there, as real as the three dimensions of space and one of time we
experience directly."

Sadly, we will never experience a second time dimension in the way
we experience ordinary time. For instance, we'll never be able to
build a clock that records this second time, or enjoy an extra few
hours in bed courtesy of two-time physics. This is because the
ordinary time we experience is just a shadow of a six-dimensional
reality we cannot touch.

That's not to say the effects of an extra time dimension are
invisible. Bars admits they will be subtle, but he believes we may
already have found evidence for two-time physics. "It appears to
solve a problem with the standard model," he says.

Included within the standard model is a theory called quantum
chromodynamics (QCD) that describes the strong nuclear force. It
accounts for the behaviour of quarks inside protons and neutrons,
and of the gluons that stick them together. Yet there is a problem.
According to QCD's equations, the strong force should be lopsided
and favour certain reactions, but this preference has never been
observed in experiments. Pressed to fix QCD, physicists found a
theoretical patch that evens up the strong force and happens to
   and those that determine throw up a hypothetical particle called the 
axion.

So far so good. Experiments, however, have failed to find the
particle. While some experiments report effects that might be down
to axions, their existence is far from conclusive. Bars thinks he
knows why. "The axion does not exist," he says. Project the
six-dimensional world onto four dimensions and the shadow standard
model appears slightly different from the regular version. The
lopsidedness disappears and there simply is no need for the axion in
two-time physics. Search as they might, experimentalists will never
find it, he claims.

The axion's no-show is not enough to verify two-time physics. "The
real test of such a theory is whether it makes experimentally
testable predictions," says Cramer.

Bars's latest work does exactly this. He has applied two-time
physics to supersymmetry, a model that says every particle in the
standard model has a heavier, hitherto unseen "superpartner".
Supersymmetric particles are expected to be produced in collisions
at CERN's Large Hadron Collider near Geneva, Switzerland, which is
due to start up next year. "Bars suggests his approach will place
different constraints on the supersymmetric particles than will
other theories," says Cramer.

Bars, however, is confident that now that he has embedded
six-dimensional physics in quantum field theory he will find many
other places where it differs in its predictions from
four-dimensional physics. "This is only the beginning," he says. "I
expect to get a lot more interest from other physicists soon."

It's a cliché, but time really will tell if he is right.

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Weblinks

Itzhak Bars's homepage
http://physics.usc.edu/~bars/

The standard model of particles and forces in 2-T physics
http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PRVDAQ000074000008085019000001&idtype=cvips&gifs=yes

Supersymmetric field theory in 2-T physics
http://arxiv.org/abs/hep-th/0703002

Large Hadron Collider at CERN
http://public.web.cern.ch/Public/Content/Chapters/AboutCERN/CERNFuture/WhatLHC/WhatLHC-en.html
   in the higher space-time. Therefore, there are many 1T systems that 
emerge in (d --  1) + 1 dimensions as solutions of the constraints with 
various gauge choices. Some examples are given in Fig. 1.

In these emergent spacetimes the Hamiltonian for each 1T system is 
different, hence the dynamics appears different from the point of view of 
1T physics. However, each 1T system holographically represents the 
original 2T system in d + 2 dimensions. Of course, due to the original 
gauge symmetry, the various 1T systems are in some sense equivalent. This 
equivalence corresponds to dualities among the various 1T systems [7-11].

Hence 2T physics may be recognized as a unifying structure for many 1T 
systems. The unification occurs through the presence of the higher 
dimensions, but in a way that is very different than the Kaluza-Klein 
mechanism since there are no Kaluza-Klein excitations but instead there 
are hidden symmetries that reflect d + 2 dimensions, and also a web of 
dualities among 1T systems that are holographic images of the 2T parent 
theory in d + 2 dimensions.

As shown in Fig. 1, simple examples of such 1T systems in (d --  1) + 1 
dimensions, that are known to be unified by the free 2T particle in flat d 
+ 2 dimensions, and have nonlinear realizations of SO(d, 2) symmetry with 
the same Casimir eigenvalues, include the following systems for spinless 
particles: free massless relativistic particle [1], free massive 
relativistic particle [7], free massive nonrela-tivistic particle [7], 
hydrogen atom (particle in 1/r potential in d --  1 space dimensions) [7], 
harmonic oscillator in d --  2 space dimensions [7], particle on a sphere 
Sd~l X R [11], particle on AdS^_j- X S* for k = 0, 1, "  "  " , (d --  2) 
[7], particle on maximally symmetric curved spaces in d dimensions [8], 
particle on Banados-Teitelboim-Zanelli black hole (special for d = 3 only) 
[9], and twistor equivalents [10,11] of all of these in d dimensions. 
There are also generalizations of these for particles with spin [2], with 
supersymmetry [4], with various background fields [3], and the twistor 
superstring [5], although details and interpretation of the 1T physics for 
gauges other than the massless particle gauge remain to be developed for 
most of the generalizations.

FIG. 1 (color online).    Some 1T physics systems that emerge from the 
solutions of Qtj = 0.

The established existence of the hidden symmetries and the duality 
relationships among such well-known simple systems at the classical and 
quantum levels provide part of the evidence for the existence of the 
higher dimensions. This already validates 2T physics as the theory that 
predicted them and provided the description of the underlying deeper 
structure that explain these phenomena.

Next comes the question of how to express these properties of 2T physics 
in the language of field theory, and how to include interactions. This was 
partially understood [12] in the form of field equations, including 
interactions, as reviewed in Sec. II. But this treatment missed an action 
principle from which all the equations of motion should be derived. The 
field equations were classified as those that determine ematics 
From issue 2625 of New Scientist magazine, 13 October 2007, page 36-39

References

   15. http://superstringtheory.com/
   16. http://particleadventure.org/frameless/standard_model.html
   17. http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=PRVDAQ000074000008085019000001&idtype=cvips&gifs=yes
   18. http://www.newscientistspace.com/channel/astronomy/cosmology
   19. http://www.newscientist.com/article.ns?id=mg19526134.100

+++++++++++++++++++

PHYSICAL REVIEW D 74, 085019 (2006)

Standard model of particles and forces in the framework of two-time 
physics

Itzhak Bars

Department of Physics and Astronomy, University of Southern California, 
Los Angeles, California 90089-2535 USA

(Received 16 June 2006; published 20 October 2006)

In this paper it will be shown that the standard model in 3 + 1 dimensions 
is a gauge fixed version of a 2T physics field theory in 4 + 2 dimensions, 
thus establishing that 2T physics provides a correct description of nature 
from the point of view of 4 + 2 dimensions. The 2T formulation leads to 
phenomenological consequences of considerable significance. In particular, 
the higher structure in 4 + 2 dimensions prevents the problematic F * F 
term in QCD. This resolves the strong CP problem without a need for the 
Peccei-Quinn symmetry or the corresponding elusive axion. Mass generation 
with the Higgs mechanism is less straightforward in the new formulation of 
the standard model, but its resolution leads to an appealing deeper 
physical basis for mass, coupled with phenomena that could be measurable. 
In addition, there are some brand new mechanisms of mass generation 
related to the higher dimensions that deserve further study. The technical 
progress is based on the construction of a new field theoretic version of 
2T physics including interactions in an action formalism in d + 2 
dimensions. The action is invariant under a new type of gauge symmetry 
which we call 2T-gauge symmetry in field theory. This opens the way for 
investigations of the standard model directly in 4 + 2 dimensions, or from 
the point of view of various embeddings of 3 + 1 dimensions, by using the 
duality, holography, symmetry, and unifying features of 2T physics.

  I. THE SP(2, R) GAUGE SYMMETRY

The essential ingredient in two-time physics (2T physics) is the basic 
gauge symmetry Sp(2, R) acting on phase space XM, PM [1], or its 
extensions with spin [2,3] and/or supersymmetry [4-6]. Under this gauge 
symmetry, momentum and position are locally indistinguishable at any 
instant. This principle inevitably leads to deep consequences, one of 
which is the two-time structure of spacetime in which ordinary one-time 
(1T) spacetime is embedded. Some of the 1T physics phenomena that emerge 
from 2T physics include certain types of dualities, holography, emergent 
spacetimes, and a unification of certain 1T physics systems into a single 
parent theory in 2T physics.

In the present paper a field theoretic formulation of 2T physics is given 
in d + 2 dimensions. To construct the 2T field theory, first the free 
field equations are determined from the covariant quantization of the 2T 
particle on the worldline, subject to the Sp(2, R) gauge symmetry and its 
extensions with spin. Next, an action is constructed from which the 2T 
free field equations are derived, and then interactions are included 
consistently with certain new symmetries of the action. The resulting 
action principle for 2T physics in d + 2 dimensions is then applied to 
construct the 2T standard model in 4 + 2 dimensions. It is shown that the 
usual standard model in 3 + 1 dimensions is a holographic image of this 4 
+ 2-dimensional theory. The underlying 4 + 2 structure provides some 
additional restrictions on the standard model, with significant 
phenomenological consequences, as outlined in the abstract. The 4 + 
2-dimensional theory suggests new nonperturba-tive approaches for 
investigating 3 + 1-dimensional field theories, including QCD.

Prior to this development, 2T physics had been best understood for 
particles in the worldline formalism interacting with all background 
fields [3], including gauge fields, gravitational field and all high spin 
fields, and subject to the Sp(2, R) gauge symmetry, or its extensions with 
spin. For the spinless particle, the three Sp(2, R) gauge symmetry 
generators Qtj(X,P), i, j = 1,2, are functions of phase space and depend 
on background fields (f>Mi-M2"'M'(X) of any integer spin s. The simplest 
case of 2T physics corresponds to a spinless particle moving in the 
trivial constant background field rjMN that corresponds to the metric in a 
flat spacetime. In this case the Sp(2, R) gauge symmetry is generated by 
the operators

(1.1)
<2n = ^x "  x,      Q22 = \p ' p>
<2i2 = G21 = tyx' p + p ' x),

where the dot product involves the flat metric rjMN. Similarly, for 
spinning particles of spin s, phase space (jf, XM, PM), includes the 
fermions /f, i = 1,2, "  "  "  ,2s, so the gauge symmetry is enlarged to 
the worldline supersymmetry OSp(2s|2) which includes Sp(2, R). In flat 
spacetime, the generators of the gauge symmetry correspond to all the 
spacetime dot products among the /f, XM, PM. These generators are first 
class constraints that vanish, thus restricting the phase space (/f1, XM, 
PM) to a OSp(2s|2) gauge invariant subspace.

To have nontrivial solutions for the constraints Qtj = 0, etc., the flat 
metric rjMN, which is used to form the dot products in the constraints, 
must have a two-time signature. So, in the absence of backgrounds, the 2T 
particle action is automatically invariant under a global SO(d, 2) 
symmetry in d + 2 dimensions, where the 2T signature emerges from the 
requirement of the local gauge invariance of the physical sector. In the 
presence of backgrounds, the 2T signature in d + 2 dimensions is still 
required by the gauge symmetry. However, the nature of the spacetime 
global symmetry, if any, is determined by the Killing vectors of the 
background in d + 2 dimensions, and it may be smaller or larger than SO(d, 
2).

It is well understood [1-7] that the gauge symmetry compensates for extra 
dimensions in phase space (XM, PM, /f) and effectively reduces the d + 
2-dimensional space by one-time and one-space dimensions, thus 
establishing causality and guaranteeing a ghost free 2T physics theory. 
The subtlety is that there are many ways of embedding the remaining d ian