Article: Mathematician suggests extra dimensions are time-like

Mathematician suggests extra dimensions are time-like

In a recent study, mathematician George Sparling of the University of
Pittsburgh examines a fundamental question pondered since the time of
Pythagoras, and still vexing scientists today: what is the nature of space
and time? After analyzing different perspectives, Sparling offers an
alternative idea: space-time may have six dimensions, with the extra two
being time-like.

Sparling's paper, which was published in the Proceedings of the Royal
Society A, lays the groundwork for his theory. He explains how spatial
dimensions contain positive signs (e.g., Pythagoras' 3D space is expressed
as the sum of the squares of the intervals in three directions, x, y, and
z). Minkowski's time-like dimension, on the other hand, combines these three
dimensions with the square of time displacement, which contains an overall
negative sign.

"In three dimensions, the formula reads s2 = x2 + y2 + z2," Sparling
explained to PhysOrg.com. "Our standard spacetime has four dimensions, but
the formula has a critical minus sign: s2 = x2 + y2 + z2 - t2. The
Lithuanian Hermann Minkowski invented this idea, which was published just
six weeks before he died. Indeed, [Sir Roger] Penrose, for one, says that
special relativity was not a finished theory until Minkowski's famous Raum
und Zeit ['Space and Time'] paper."

Up until now, Sparling explains, most theories concerning extra dimensions
have dealt with space-like rather than time-like dimensions, which results
in a "hyperbolic" rather than an "ultra-hyperbolic" geometry. However,
Sparling notes that there are no a priori arguments for a hyperbolic
geometry, and he looks into the possibility of a "spinorial" theory of
physics, where six dimensions of space-time arise naturally.

"In general dimensions, we say that the space-time is hyperbolic if there is
only one minus sign in the formula for s2," he said. "So, for example, in
the ten dimensions of superstring theory, there are nine spatial dimensions
with plus signs and one minus sign. Only in that situation is there a
clear-cut distinction between the future and the past."

"In my case, I am led to the conclusion that the ordinary four dimensional
space-time extends naturally into six dimensions: the four dimensional space
is hyperbolic as usual, but in the surrounding space there are equal numbers
(3 each) of space and time dimensions, so the formula for s2 reads something
like s2 = x2 + y2 + z2 - t2 - u2 - v2, where u and v represent the new time
variables. I call this structure a (3, 3)-structure (mathematicians call it
ultra-hyperbolic)."

Space-Time is Spinorial

Sparling's spinorial theory is based on Einstein's general relativity and
Elie Cartan's triality concept, which can link space-time with two twistor
spaces. Twistor spaces are mathematical spaces used to understand
geometrical objects in space-time landscapes. Sparling explains spinors in
the following way:

"In physics, the idea of a spinor stems from the finding that spectral lines
of atoms seem to behave as if the angular momentum of the particles
radiating photons was in half-integral units of the quantized spin (whose
size is determined by Planck's constant). This was fully explained by
Dirac's famous theory of the electron, which led him to successfully predict
the existence of the positron."

Some spinorial particles include the electron, muon, tau, proton, neutron,
quarks, neutrinos, and all their anti-particles, which are called fermions
and have half-integer spins. There are also non-spinorial particles, called
bosons, such as the photon, graviton, pion, mesons, the W and Z bosons, the
Higgs, (if it exists) and so on, which have an integer spin, Sparling
explains.

"The key difference between spinors and non-spinors is their behavior under
rotations: typically, non-spinorial (integer-spin) particles return to their
initial value under a 360-degree (or 2?-radian) rotation; however, the
spinorial (half-integer-spin) fermions actually change sign under a
360-degree rotation, requiring a full 720-degree rotation to get back to
their initial values. This is completely foreign to our naive idea of how
rotations work, and yet it is a basic part of reality.

"Consider this analogy: if you take a plate and hold it in one hand
horizontally whilst twisting it under your arm backwards through 360
degrees, your arm ends up in the air after one rotation, and it needs
another 360 degree rotation to get it back to the beginning," he said.

Twistors, then, are a special kind of spinor first introduced by Penrose
(Sparling was a PhD student of Penrose). In Sparling's theory, the two
twistor spaces are each six-dimensional, forcing space-time to also have six
dimensions, in accordance with Cartan's unifying triality. Because the
twistor spaces' geometry is ultra-hyperbolic, the extra dimensions are
time-like.

"My work has three six-dimensional spaces which at one level are on an equal
footing and which are bound together by a new transform, which I call the
Xi-transform," Sparling said. "Two of these spaces can be understood at the
space-time level as twisters. Then the third space can be given a space-time
interpretation, but only if we have two extra dimensions: so it is the
requirement of symmetry between the spinor spaces and the space-time that
dictates that the extra dimensions be there."

A Harmonious Concinnity

While the concepts of twistor theory and spinors have been previously
investigated as an alternative to space-time, Sparling explains how his new
proposal is slightly different because it's not a complete replacement of
space-time. Rather, the guiding principle of his idea is that of a
harmonious combination of three entities, or a "trinity." Each part of the
theory reinforces the other parts.

"If one accepts that there are these three spaces [space-time and two
twistor spaces] that are central to my theory, one looks for a theory which
unifies them; this would be the 'concinnity'," he explained. "An indicator
that there might be such a theory comes from the theory of Jordan algebras,
which naturally unifies the three spaces into a twenty-seven dimensional
whole, called an exceptional Jordan algebra." Sparling's student Philip
Tillman and ex-students Dana Mihai, Devendra Kapadia and Suresh Maran also
played a significant role related to this work.

"A second indicator is that there are two radically different descriptions
of massless particles, such as the photon: the standard one uses Fourier
analysis in space-time and another uses twistor theory and sheaf
cohomology," he added. "The mathematical formalisms used in these two
different descriptions are so different that it is simply amazing that they
are describing the same basic physics. The concinnity would provide an
explanation for this. This would then unify twistor theory, space-time
theory and string theory-this is very tentative, however.

"A very interesting aspect is that Newton fought strongly against the idea
of the trinity (in a religious context)," Sparling noted. "It is ironic that
I am invoking that very same idea in the context of gravity: perhaps Newton
saw that the concept could be used in physics, but because he could not
think of such a use he rebelled strongly against it (of course, I have no
evidence for this!)."

Although the theory is not definitive, Sparling explains that several major
ideas in current physics would likely play a role (such as condensed matter
physics, category theory, non-commutative geometry, string theory, and the
structure of superfluids). Such connections might also point the direction
to a unified theory, though currently speculative.

"My work can be seen as a strong antidote to the present air of pessimism
surrounding modern fundamental physics," Sparling said. "As is well-known,
string theory has been roundly criticized for its lack of predictive power.
String theorists have been reduced to an absurd reliance on the anthropic
principle, for example. Here I have a clear-cut prediction, which goes
against the common wisdom, which gives experimenters a target to go for:
first find the extra dimensions, then decide their signature (a very tough
homework assignment!). Of course I could be proved wrong, but the effort to
decide is surely worthwhile.

"Actually, in the area of philosophy, I am in opposition to string theory,"
he said. "It is a top down theory: dream up something that works in some
high dimension and then try to finagle some way of reducing to fit in with
the lower-dimensional theory. My approach is bottom up: take the existing
four-dimensional theory seriously and try to build up from it. This is very
tough to do. Hopefully my ideas work. Note that my work only constitutes a
possible beginning at a more inclusive theory."

Sparling continues to explore the ideas of this 6-D time-like spinorial
theory of space-time, with support from a workshop at the BIRS Institute in
Banff, Canada, and ideas from philosophers including Alexander Afriat, Steve
Awodey, Jonathan Bain and Rita Marija Malikonyte-Mockus. He predicts that
experimental investigations in the near future-such as the Large Hadron
Collider-might uncover the extra dimensions.

Citation: Sparling, George A. J. "Germ of a synthesis: space-time is
spinorial, extra dimensions are time-like." Proc. R. Soc. A.
doi:10.1098/rspa.2007.1839.

Copyright 2007 PhysOrg.com.
All rights reserved. This material may not be published, broadcast,
rewritten or redistributed in whole or part without the express written
permission of PhysOrg.com.

http://www.physorg.com/news96027669.html

Posted by
Robert Karl Stonjek

On 18 apr, 02:07, "Robert Karl Stonjek"
wrote:

"In physics, the idea of aspinorstems from the finding that spectral lines
of atoms seem to behave as if the angular momentum of the particles
radiating photons was in half-integral units of the quantized spin (whose
size is determined by Planck's constant). This was fully explained by
Dirac's famous theory of the electron, which led him to successfully predict
the existence of the positron."

Some spinorial particles include the electron, muon, tau, proton, neutron,
quarks, neutrinos, and all their anti-particles, which are called fermions
and have half-integer spins. There are also non-spinorial particles, called
bosons, such as the photon, graviton, pion, mesons, the W and Z bosons, the
Higgs, (if it exists) and so on, which have an integer spin, Sparling
explains.

"The key difference between spinors and non-spinors is their behavior under
rotations: typically, non-spinorial (integer-spin) particles return to their
initial value under a 360-degree (or 2?-radian) rotation; however, the
spinorial (half-integer-spin) fermions actually change sign under a
360-degree rotation, requiring a full 720-degree rotation to get back to
their initial values. This is completely foreign to our naive idea of how
rotations work, and yet it is a basic part of reality.

"Consider this analogy: if you take a plate and hold it in one hand
horizontally whilst twisting it under your arm backwards through 360
degrees, your arm ends up in the air after one rotation, and it needs
another 360 degree rotation to get it back to the beginning," he said.

It seems to me, that you can easily imagine an object that reflects
the
same way only after X times 360 degrees rotation.
Look at the sun earth system.
You can rotate the system, but earth orbits around sun once a year,
while the sunspots, say the rotation of the sun, is different.
So after one year it would _not_ look the same.
Only after X rotations would it look the same (assuming sunspots
unchanged).
So a 'particle' that needs 720 degrees to appear the same (in spectral
lines)
could well exist of some particle orbited by an other.
When put in rotation by an external force (light shining on it) it
would act as a gear.
No ++++ dimensions needed.
Just 3D and time.
My 2 Euro cents worth.

wrote:
It seems to me, that you can easily imagine an object that reflects
the
same way only after X times 360 degrees rotation.

Imagination is not sufficient, you need a group that has this property.
Spinors are a class of groups that have two types of rotational
symmetry: those unchanged by a 2pi rotation, and those unchanged by a
4pi rotation. The first are characterized by a spin of N (N integer) and
we call particles with such a representation "Bosons"; the latter are
characterized by a spin of N+1/2 and we call particles with such a
representation "fermions". Groups with other spin characteristics have
not been found, and I believe it is known they don't exist; certainly no
known particles require such spin representations.


Tom Roberts

On Apr 17, 7:07 pm, "Robert Karl Stonjek"
wrote:
Mathematician suggests extra dimensions are time-like

In a recent study, mathematician George Sparling of the University of
Pittsburgh examines a fundamental question pondered since the time of
Pythagoras, and still vexing scientists today: what is the nature of space
and time? After analyzing different perspectives, Sparling offers an
alternative idea: space-time may have six dimensions, with the extra two
being time-like.

Sparling's paper, which was published in the Proceedings of the Royal
Society A, lays the groundwork for his theory. He explains how spatial
dimensions contain positive signs (e.g., Pythagoras' 3D space is expressed
as the sum of the squares of the intervals in three directions, x, y, and
z). Minkowski's time-like dimension, on the other hand, combines these three
dimensions with the square of time displacement, which contains an overall
negative sign.

"In three dimensions, the formula reads s2 = x2 + y2 + z2," Sparling
explained to PhysOrg.com. "Our standard spacetime has four dimensions, but
the formula has a critical minus sign: s2 = x2 + y2 + z2 - t2. The
Lithuanian Hermann Minkowski invented this idea, which was published just
six weeks before he died. Indeed, [Sir Roger] Penrose, for one, says that
special relativity was not a finished theory until Minkowski's famous Raum
und Zeit ['Space and Time'] paper."

Up until now, Sparling explains, most theories concerning extra dimensions
have dealt with space-like rather than time-like dimensions, which results
in a "hyperbolic" rather than an "ultra-hyperbolic" geometry. However,
Sparling notes that there are no a priori arguments for a hyperbolic
geometry, and he looks into the possibility of a "spinorial" theory of
physics, where six dimensions of space-time arise naturally.

"In general dimensions, we say that the space-time is hyperbolic if there is
only one minus sign in the formula for s2," he said. "So, for example, in
the ten dimensions of superstring theory, there are nine spatial dimensions
with plus signs and one minus sign. Only in that situation is there a
clear-cut distinction between the future and the past."

"In my case, I am led to the conclusion that the ordinary four dimensional
space-time extends naturally into six dimensions: the four dimensional space
is hyperbolic as usual, but in the surrounding space there are equal numbers
(3 each) of space and time dimensions, so the formula for s2 reads something
like s2 = x2 + y2 + z2 - t2 - u2 - v2, where u and v represent the new time
variables. I call this structure a (3, 3)-structure (mathematicians call it
ultra-hyperbolic)."

This is remarkably similar to what I wrote on spr several months ago,
when I repeatedly stressed that, in such a symmetry with such a
metric, all distances could be made null (lightlike) by a suitable
rotation of coordinates.

Invariance of "proper time" would be an illusion and Delayed Choice
Experiments would not violate causality.

Barry

"Consider this analogy: if you take a plate and hold it in one hand
horizontally whilst twisting it under your arm backwards through 360
degrees, your arm ends up in the air after one rotation, and it needs
another 360 degree rotation to get it back to the beginning," he said.

I wish someone would explain this part. What does he mean by
"under your arm"? And every way I try to "twist" a plate (by which
I suppose he means "rotate" - twisting a plate would break it!)
ends up taking it through 180 degrees: a few degrees more and
my arm would break.

On Wed, 18 Apr 2007 00:07:27 GMT, "Robert Karl Stonjek"
wrote:

Mathematician suggests extra dimensions are time-like

In a recent study, mathematician George Sparling of the University of
Pittsburgh examines a fundamental question pondered since the time of
Pythagoras, and still vexing scientists today: what is the nature of space
and time? After analyzing different perspectives, Sparling offers an
alternative idea: space-time may have six dimensions, with the extra two
being time-like.

Sparling is obviously a crackpot since a time dimension forbids
motion. Don't laugh! This is the reason that Sir Karl Popper calls
Eintein's spacetime a block universe in which nothing happens!
ahahaha... That's right, nothing moves in spacetime, by definition!
So, if one time dimension is crackpottery, what can one say about
three? ahahaha...

Sparling is giving the University of Pittsburgh a bad name, IMO.
That's the problem with mathematicians. They're stupid as **** when it
comes to physics. ahahaha... AHAHAHA... ahahaha...

Nasty Little Truth About Spacetime Physics:
http://rebelscience.org/Crackpots/notorious.htm

Louis Savain

Axel Harvey wrote in news:1177082357.235068.236390
@y5g2000hsa.googlegroups.com:

"Consider this analogy: if you take a plate and hold it in one hand
horizontally whilst twisting it under your arm backwards through 360
degrees, your arm ends up in the air after one rotation, and it needs
another 360 degree rotation to get it back to the beginning," he said.

I wish someone would explain this part. What does he mean by
"under your arm"? And every way I try to "twist" a plate (by which
I suppose he means "rotate" - twisting a plate would break it!)
ends up taking it through 180 degrees: a few degrees more and
my arm would break.


http://www.jqhome.net/taiso/bwx/bwx-twister.html





--
bz

please pardon my infinite ignorance, the set-of-things-I-do-not-know is an
infinite set.

remove ch100-5 to avoid spam trap

On Apr 20, 11:34 am, Traveler wrote:
On Wed, 18 Apr 2007 00:07:27 GMT, "Robert Karl Stonjek"

wrote:
Mathematician suggests extra dimensions are time-like

In a recent study, mathematician George Sparling of the University of
Pittsburgh examines a fundamental question pondered since the time of
Pythagoras, and still vexing scientists today: what is the nature of space
and time? After analyzing different perspectives, Sparling offers an
alternative idea: space-time may have six dimensions, with the extra two
being time-like.

Sparling is obviously a crackpot since a time dimension forbids
motion. Don't laugh! This is the reason that Sir Karl Popper calls
Eintein's spacetime a block universe in which nothing happens!
ahahaha... That's right, nothing moves in spacetime, by definition!
So, if one time dimension is crackpottery, what can one say about
three? ahahaha...


Actually, Sparling didn't write that time was a dimension, he wrote
that there were three "timelike" dimensions.

"Timelike" is an atrocious word, but Sparling is stuck with using it
since that's the conventional word - it's the simplest way that he
can make himself understood. When in Greece, try to speak Greek.

A "timelike" direction is better thought of as the direction in which
an object moves relative to its comoving three space (the three space
with respect to which an object is "stationary").

"Time" is something else altogether, although it's not possible to
convince those that don't want to be convinced.

How long have you (and I) been trying?

Barry

..

On Apr 21, 8:34 am, Barry wrote:
On Apr 20, 11:34 am, Traveler wrote:



On Wed, 18 Apr 2007 00:07:27 GMT, "Robert Karl Stonjek"

wrote:
Mathematician suggests extra dimensions aretime-like

In a recent study, mathematician George Sparling of the University of
Pittsburgh examines a fundamental question pondered since thetimeof
Pythagoras, and still vexing scientists today: what is the nature of space
andtime? After analyzing different perspectives, Sparling offers an
alternative idea: space-timemay have six dimensions, with the extra two
beingtime-like.

Sparling is obviously a crackpot since atimedimension forbids
motion. Don't laugh! This is the reason that Sir Karl Popper calls
Eintein'sspacetimea block universe in which nothing happens!
ahahaha... That's right, nothing moves inspacetime, by definition!
So, if onetimedimension is crackpottery, what can one say about
three? ahahaha...

Actually, Sparling didn't write thattimewas a dimension, he wrote
that there were three "timelike" dimensions.

"Timelike" is an atrocious word, but Sparling is stuck with using it
since that's the conventional word - it's the simplest way that he
can make himself understood. When in Greece, try to speak Greek.

A "timelike" direction is better thought of as the direction in which
an object moves relative to its comoving three space (the three space
with respect to which an object is "stationary").

"Time" is something else altogether, although it's not possible to
convince those that don't want to be convinced.

How long have you (and I) been trying?

Barry

.

A theory that provides additional dimensions should offer a concise
yield of spacetime as a natural consequence. Otherwise it cannot claim
physical correspondence. The Minkowski spacetime does not address the
unidirectional nature of time. Furthermore it does not address the
observed lack of freedom in the time dimension. These properties can
be constructed arithmetically. By building one-signed numbers
superposition will only yield larger values:
- 1 - 1 = - 2 .
These unidirectional one-signed numbers obey the same laws as the two-
signed real numbers. Following through with this paradigm we should
consider three-signed numbers, etc. Generalized sign leads one to a
symmetrical featu
Sum over s ( s x ) = 0
where s is sign and x is magnitude.
For the two-signed real numbers
- x + x = 0
which you can see is sensible. For three-signed numbers the extension
merely means
- x + x * x = 0 where '*' is a new sign.
General sums no longer cancel to a singular sign and magnitude:
- 1 + 2 * 3
= ( - 1 + 1 * 1 ) + 1 * 2
= + 1 * 2 .
The general sign product (see link) is very natural and exposes the
dimensional relation to signature
D = n - 1 .
Oddly enough the polysign arithmetic approach dictates that one-signed
numbers are zero dimensional while still posessing their
unidirectional arithmetic nature. This is entirely consistent with
time. There are many more suprises to this approach including natural
support for spacetime:
http://bandtechnology.com/PolySigned/PolySigned.html
While most will scoff at generalized sign will they admit that they
constrict themselves to using two signs with multiplicity? That
mathematics has the ability to inherently generate the basis which
physicists assume to exist without explanation suggests that the
polysign approach is of value not only to the mathematician but to the
progressive physicist as well. Spacetime is observed yet the theorists
of the past felt no ability to explain this observation mathematically
beyond the manual construction
R x R x R x R .
The polysign construction suggests the progressive topology
P1 x P2 x P3 ...
with a natural breakpoint beyond P3 (see link). This structured basis
is consistent with brane type theories and is suggestive of Maxwell's
relations. Time is nearly meaningless under the polysign
interpretation, as it should be. As Janis Joplin has said
"It's all the same ****ing day, man."

-Tim