There are an increasing number of papers discussing the modelling of
the universe as a "3-brane" on a large extra dimension. In every
case, the extra dimension is supposed to be a spatial dimension.
I wish to point out that the whole thing is more sensibly done by
modelling the large extra dimension as a second time dimension, not a
fourth spatial dimension. The time dimension is apropos in that
gravity and time map into eachother under GR, so the second time
dimension can serve as the source of gravity, warped by massive bodies
to where we have the naive impression that the gravity comes from the
mass itself, rather than mass being the conduit.
A new paper "hep-th/0004056" models distortions in the large extra
(spatial) dimension consequential to universal expansion, and suggests
that this is the source of "dark energy". In other words, universal
expansion is begetting a gravitational scalar. This evokes my old
posting that gravity is the result of universal expansion, or more
precisely, the linear drift of a universal parameter which mimics
spatial expansion.
This idea unifies with GR simply by modelling the large extra
dimension as a time dimension, instead of a physical dimension. So
the 5-manifold consists of three spatial dimensions and two time
dimensions, the second one of which bears a migrating universal
parameter which at once yieds gravity and makes the universe seem to
be physically expanding.
Eric Flesch
eric@flesch.org (Eric Flesch) wrote, in part:
>I wish to point out that the whole thing is more sensibly done by
>modelling the large extra dimension as a second time dimension, not a
>fourth spatial dimension.
While this doesn't directly relate to your theory (in relation to
which, I'll note that any extra dimension is normally called a spatial
dimension simply because time is what we all move along at a fixed
rate), I remember coming up with an amusing little 'theory' that,
although it didn't really include a second time dimension, came close.
In order to allow the tachyon to exist while preventing it from
defying causality, I worked things out this way:
- a photon, having no real or imaginary mass, must move through both
space and time at the speed of light
- a matter particle, having no imaginary mass, but some real mass,
must move through time at the speed of light, but must move through
space more slowly
- a tachyon, having no real mass, but some imaginary mass, must move
through space at the speed of light, but must move through time more
slowly (instead of having to move through space faster than the speed
of light, which is sort of equivalent, since velocity is units of
space moved through per unit of time)
But to make 'moving through time more slowly' meaningful, I changed
time to "time", a spatial dimension, while *real* time was causal
time.
So I called this the 'tin can theory of the Universe'. The lid on the
top of the can was the matter Universe. The rim of the top of the can
is the photons from the Big Bang. (So there can be no cosmic
background radiation, hence the theory fails to match up with
observation.)
The can itself, its pipe-like wall, is the tachyon universe.
The bottom of the can is an antimatter universe. (Note another rim of
backwards-moving photons.) So the theory at least accounts for the
lack of antimatter in our universe.
Inside the can is a four-dimensional realm of particles having *both*
real and imaginary mass; this dangerous expanse of complex-mass
particles is where someone would end up who built what he _thought_
was a time machine! (Cute idea for a science-fiction story...)
The direction from the bottom to the top of the can is the spatial
time axis; two axes on the lid of the can represent space, and the can
grows with the passage of time at the speed of light in all
directions. But a particle can move in space and in spatial time both
at the speed of light, or slightly below: in this 4-D realm, if
velocities were calculated in the ordinary way, photons would move at
sqrt(2) times the speed of light.
This is as close as I can get to imagining another time dimension; an
anisotropic spatial dimension that from our perspective as matter
beings instead of tachyon beings is associated with time.
John Savard (jsavard<at>ecn<dot>ab<dot>ca)
http://www.ecn.ab.ca/~jsavard/crypto.htm
In article <38f78797.8331391@news.iconz.co.nz>, eric@flesch.org
(Eric Flesch) wrote:
>There are an increasing number of papers discussing the modelling of
>the universe as a "3-brane" on a large extra dimension. In every
>case, the extra dimension is supposed to be a spatial dimension.
>
>I wish to point out that the whole thing is more sensibly done by
>modelling the large extra dimension as a second time dimension, not a
>fourth spatial dimension. The time dimension is apropos in that
>gravity and time map into eachother under GR, so the second time
>dimension can serve as the source of gravity, warped by massive bodies
>to where we have the naive impression that the gravity comes from the
>mass itself, rather than mass being the conduit.
>
>A new paper "hep-th/0004056" models distortions in the large extra
>(spatial) dimension consequential to universal expansion, and suggests
>that this is the source of "dark energy". In other words, universal
>expansion is begetting a gravitational scalar. This evokes my old
>posting that gravity is the result of universal expansion, or more
>precisely, the linear drift of a universal parameter which mimics
>spatial expansion.
>
>This idea unifies with GR simply by modelling the large extra
>dimension as a time dimension, instead of a physical dimension. So
>the 5-manifold consists of three spatial dimensions and two time
>dimensions, the second one of which bears a migrating universal
>parameter which at once yieds gravity and makes the universe seem to
>be physically expanding.
I came up with my own little theory a few years ago along
these lines. I wrote Maxwell's equations in 3+2 spacetime
and then assumed all the fields were independent of this
second time dimension. We can then divide the Maxwell
antisymmetric tensor into the classical electric field,
the classic magnetic field, a three vector, and a scalar.
Read the rest of this message... (24 more lines)
Just saw this in Physics News Updates. It addresses the matter of an
"expanding universe" bequeathing a gravitational scalar. Just
extrapolate this into a second time dimension and you have an elegant
simplification which removes the need for an expanding universe. The
so-called "accelerating" expansion is then simply mapped into a
linearly-migrating cosmological parameter operating out of that second
time dimension.
Eric
__________ article follows _______________-
DARK ENERGY AND THE MICROWAVE BACKGROUND. The
theory of general relativity introduced the notion that spacetime
could be warped or curved by the presence of matter. Locally, stars
or any object with mass will curve space, but the expansion of the
universe itself may introduce a curvature of its own. This is how
cosmologists summarize things: a static universe with no matter (if
such a thing were possible) would have no curvature. If, however, the
empty universe were expanding it would have negative overall
curvature. Increase the mass density from zero and the curvature
would be less negative. Add still more mass and you might reach a net
zero curvature. The ratio of matter to the critical matter needed for
zero curvature is called omega; the popular version of the big
bang model, featuring a very rapid expansion in an early "inflation"
phase, predicts that omega should equal 1 exactly. A new paper in
Physical Review Letters by Scott Dodelson of Fermilab and Lloyd Knox
of the University of Chicago (773-834-3287) provides the theoretical
underpinning for the higher-precision mappings of the cosmic microwave
background (CMB) reported over the past nine months. The paper was
prepared just as the first of the observational results appeared last
summer: a Princeton-Pennsylvania collaboration taking data from Cerro
Toco in Chile. Their findings (preprint astro-ph/9906421) can be
plotted as the size of the observed fluctuations in the CMB as a
function of the angular size of the fluctuation region (actually
astrophysicists usually transform the data so that it can be plotted
against the size of angular moment, or "l"). These data and those of
the "Boomerang" (preprint 9911444 and 9911445; also see Update
460) and "Viper" (preprint 9910503) groups sit right on top of a
theoretical curve drawn by Dodelson and Knox corresponding to the case
where omega equals 1 and the net curvature of the universe is zero.
With the contribution of matter (luminous and dark) to the density of
the universe expected to be about one-third the critical value (of
omega=1), this presents a stronger-than-ever argument in favor of the
existence of yet another form of energy, often called "dark energy,"
to provide the missing two-thirds of the energy needed to make
omega=1. This dark energy would also provide the "negative pressure"
or repulsiveness needed to make the expansion of the
universe greater than in the past, a development suggested
independently by studies of distant supernovas. (Dodelson and Knox,
Physical Review Letters, 17 April; Select Article.)
 |
©2002 Google