| Topic: |
Science > Physics |
| User: |
"" |
| Date: |
07 Oct 2005 07:42:01 AM |
| Object: |
Fractal String Theory - The saga continues ;-) |
The following are some notes and observations
on my post at:
http://groups.google.com/group/sci.physics/browse_frm/thread/d13ba2ca15039444/4bd9addbffae6745#4bd9addbffae6745
Gravity is then simply a manifestation of the tendency
of these strings to minimize their "energy" by aligning
in parallel layers.
A change in the relative orientation of two strings
changes that of their constituent strings relative to
neighboring strings at the same smaller scale, and a
cascade of orientation changes fans out through the
latter (and _their_ constituent strings ad infinitum)
to minimize _their_ energy.
This is somewhat analogous to the group velocity of two
out-of-phase waves increasing as the phases approach
equality.
For convenience I use the word "energy" in this context
throughout; but whatever is "shed" by strings becoming
more parallel may not correspond exactly to energy and
perhaps this word should be considered simply a label
to indicate what is going on.
Whatever is shed must be subject to "compressibility"
constraints of some kind, on account of the ubiquity
of strings at all scales and positions (so that no
pair of strings can ever be considered in isolation),
and maybe simply formalizing this constraint would
be enough to pin down the exact laws governing their
interactions.
I've since learned that this parallelism notion, or at
least its limiting case on manifolds with nowhere-zero
parallel "combed" vector fields, e.g. torus-shaped
singularities and fundamental fermions, relates to
the idea of "connections" and "parallel transport",
used in GR.
Associated with this, in supersymmetry theories, is the
idea of a constant scalar field called a moduli space.
Hmm, so presumably that moduli space would correspond
to the overall uniform distribution of "group energy"
as it is referred to in my previous post.
So concepts that naturally stem from the idea of fractal
string theory do seem broadly consistent with established
principles.
http://en.wikipedia.org/wiki/Connection_%28mathematics%29
lists several possible approaches to the "connection"
concept, including:
"The most abstract approach may be that suggested by
Alexander Grothendieck, where a connection is seen
as _descent_ data from infinitesimal neighbourhoods
of the diagonal"
in which the word "descent" is in turn a link to
http://en.wikipedia.org/wiki/Descent_%28category_theory%29
which describes the construction of vector bundles in
topological spaces by means of fibers.
I'm not so naive as to believe that words like "descent"
and "fiber" are likely to relate directly to a recursive
string model, as the mental images they evoke might
suggest. But it is tantalizing all the same!
[Description of torus-shaped free fermion falling towards
black hole singularity]
At both ends of the particle, as a result of elongation
of the torus a circular ridge has started to form.
perpendicular to the predominant substring direction,
i.e. to the direction in which the fermion is stretching
(should be obvious to anyone visualizing this, but worth
mentioning)
Assuming the constituent strings of the torus form
closed loops with at least one twist, they cannot
maintain exact parallelism at the top of this ridge,
and they thus become locally "skewed" across it.
So to minimize overall energy, sub-strings of comparable
frequency from the surrounding space must start being
deposited on the ridges, and the particle grows at the
ends like a crystal!
I've since learned that string theorists talk about
string "gas" in the vicinity of strings and branes,
which can affect their properties. In fractal string
theory this corresponds to substrings, or in fact
"subfermions" in the form of stubby toruses.
I must admit it's not as clear as I thought exactly how
this deposition works, because one naturally thinks of
the process as "local", occurring only at the circular
ridges at the ends of the stretching fermion torus; but
the strings comprising the torus, and the substrings
comprising each such string, etc ad infinitum, are all
wrapped round the entire circumference of the torus
they comprise, and hence are all wrapped round the
original fermion torus.
Possibly a circular fold causes an entire "virtual"
fermion to take shape above it, to minimize overall
energy, made up of substrings coalescing out of the
"gas" substring background.
Since that fermion must then also be stretched in
the predominant substring direction, and thus itself
form circular folds at its ends, one assumes that an
entire row of virtual fermions coalesces in the same
way, possibly in various stages of "development" the
further from the original fermion one goes.
When these two rows (each of course lined up along
the predominant substring direction) meet then to
maximize overall parallelism they are obliged to
"stitch themselves together", at all substring
levels simultaneously, at neighbouring circular
ridges (which are parallel).
That might also better explain how the fermion can
finally manage to wrap itself round the singularity
as a _pair_ of toroidal tubes (with substrings banded
in opposite directions, to preserve the pattern of
alternately-banded strings comprising the singularity).
(This is analogous to the phenomenon of "mass inflation",
whereby vast amounts of mass/energy can be created inside
black holes by crossing shells of light causing a spacetime
fold. See http://en.wikipedia.org/wiki/Werner_Israel )
For convenience I refer to the above process of fermion
deformation and augmentation as "micro mass inflation";
but the established mass inflation phenomenon may have
the same underlying mechanism.
In a sense both are plucking mass/energy out of "nowhere",
which can then persist moreorless stably in a sufficiently
highly "polarized" spacetime.
Note that mass inflation in a rotating black hole can
produce an "extended" singularity at the Cauchy horizon,
which can dredge up the original singularity from the
depths, so to speak, and absorb it.
In fact some have speculated that a "mature" black
hole, with a Cauchy horizon, would be safe to enter
(even if it would be a one way trip), which brings
us to:
[speculation on how relativistic mass appears
to accumulate in a toroidal fermion in motion
relative to the observer ..]
This effect is most pronounced, or at least can be
expected to have the most effect, nearest to the
Fermion, where the surrounding substrings are the
most parallel, and increases the probability of
the substrings spontaneously crystalizing into
a string that merges into the torus comprising
the fermion, in the same way as described for
the singularity in Section 4, thus increasing
its apparent mass to the observer.
But now we have the baffling scenario in which
the number of strings comprising a brane depends
on the relative motion of the observer!
A week or two ago in sci.physics someone asked what
would happen if one encountered a string, or passed
through an extended brane, e.g. Cauchy singularity.
It was based on the above speculation that my reply
suggested the effect might depend on one's motion
relative to the object:
In free fall it might be scarcely noticeable; but
if you tried to accelerate away, or even towards it,
the result would very likely be a severe mauling!
So far we have focused on the local effects of
string parallelism. But there is also a global
aspect, because a torus is not the only low-
dimensional shape that supports a limiting
everywhere-parallel vector field:
i.e. a nowhere-zero, parallel "combed" vector field
(After asking a related question on sci.math, I was
astonished to find everyone seemed utterly bamboozled
by that phrase "everywhere-parallel" until I clarified
it - an example of the "open sesame" problem, whereby
often most of the difficulty in getting an answer is
phrasing the question in a standard form the experts
can understand! I've often been on the other end
of this in sci.math, answering non-mathematicians'
questions, and can't avoid the suspicion that in
failing to guess peoples' intended meaning some
experts can be wilfully obtuse!)
[..] a torus brane can flip into a larger
sphere in which the constituent strings all point
radially outward, vaguely reminiscent of a popcorn
grain going pop and evolving from a compact object
to a larger fluffy form.
I found an interesting mainstream (read "non-kook"!)
site called "Multiversal Journeys" at:
http://www.multiversaljourneys.com/html/seminar-outline.htm
On that page an abstract of a talk by Prof Raphael Bousso
includes:
"Professor Bousso will emphasize in particular the
counterintuitive nature of these limits: they imply
that in a sense, the universe is only pretending to
have 3 spatial dimensions, like a two-dimensional
hologram on a credit card."
Well a universe that started out as a torus and is on
its way to becoming a "fluffy" extended sphere could
in a sense be said to be only masquerading as 3D!
Cheers
John R Ramsden (jhnrmsdn@yahoo.com.uk)
* remove m from com to reply
* "From" address is defunct, as a spam black hole
.
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| User: "" |
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| Title: Re: Fractal String Theory - The saga continues ;-) |
07 Oct 2005 02:13:06 PM |
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wrote:
[...]
So concepts that naturally stem from the idea of fractal
string theory do seem broadly consistent with established
principles.
http://en.wikipedia.org/wiki/Connection_%28mathematics%29
lists several possible approaches to the "connection"
concept, including:
"The most abstract approach may be that suggested by
Alexander Grothendieck, where a connection is seen
as _descent_ data from infinitesimal neighbourhoods
of the diagonal"
in which the word "descent" is in turn a link to
http://en.wikipedia.org/wiki/Descent_%28category_theory%29
which describes the construction of vector bundles in
topological spaces by means of fibers.
I'm not so naive as to believe that words like "descent"
and "fiber" are likely to relate directly to a recursive
string model, as the mental images they evoke might
suggest. But it is tantalizing all the same!
Here's an extract from the latter page. Squinting hard
enough, one could half imagine they were talking about
a torus brane comprising congruent bands, each itself an
elongated torus comprising twisted bands of substrings etc,
ad infinitum:
"The case of the construction of vector bundles from data on
a disjoint union of topological spaces is a straightforward
place to start. We suppose given a space X, an open cover
Xi of X and set Y to be the disjoint union of the Xi, so
that a natural mapping p:Y -> X is given too. We think of
Y as 'above' X, with the Xi projection 'down' onto X. With
this language, descent implies a vector bundle on Y (so, a
bundle given on each Xi), and our concern is to 'glue' those
bundles Vi, to make a single bundle V on X. What we mean is
that V should, when restricted to Xi, give back Vi, up to a
bundle isomorphism.
The data needed is then this: on each overlap Xij, intersection
of Xi and Xj, we'll require mappings fij to use to identify Vi
and Vj there, fiber by fiber. Further the fij must satisfy
conditions based on the reflexive, symmetric and transitive
properties of an equivalence relation (gluing conditions).
For example f\ij o f\jk = f\ik for transitivity (and choosing
apt notation). The f\ii should be identity maps and hence the
symmetry becomes invertibility of f\ij (so that it is fiberwise
an isomorphism)."
and recall, this whole theory of moduli on vector bundles
is AIUI intended to generalize the concept of connections
and "parallel transport" used in GR.
[discussion on "micro mass inflation" ..]
Possibly a circular fold causes an entire "virtual"
fermion to take shape above it, to minimize overall
energy, made up of substrings coalescing out of the
"gas" substring background.
Since that fermion must then also be stretched in
the predominant substring direction, and thus itself
form circular folds at its ends, one assumes that an
entire row of virtual fermions coalesces in the same
way, possibly in various stages of "development" the
further from the original fermion one goes.
One could picture this vaguely resembling the regular
pattern sometimes seen in the exhaust flame of a jet
engine.
Given the current sci.physics thread about von Neumann
machines (self-replicating ones), it's striking to think
that near enough to a black hole singularity fermions
could be replicating themselves by the bushel, from
background substring "gas", i.e. "projecting" their
fractal curvature structure to a ghostly double
which then becomes a fermion itself and repeats
the process.
By the way, it should go without saying (but apparently
doesn't!) that I welcome any criticism of my musings,
assuming they are not considered as beyond it (in the
"not even wrong" sense). I'd be very pleased to try
and field any questions or hear suggestions.
I must say the feedback so far has been disappointing,
apart from a reply from "xxein" which I interpreted
as broadly approving albeit with his own slant.
Cheers
John R Ramsden (jhnrmsdn@yahoo.com.uk)
* remove m from com to reply
* "From" address is defunct, as a spam black hole
.
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| User: "Happy Hippy" |
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| Title: Re: Fractal String Theory - The saga continues ;-) |
07 Oct 2005 02:40:15 PM |
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wrote:
snippity near enough to a black hole singularity fermions
could be replicating themselves by the bushel, from
background substring "gas", i.e. "projecting" their
fractal curvature structure to a ghostly double
which then becomes a fermion itself and repeats
the process.
Closer and closer to the singularity the
acceleration of the spin increases rapidly.
At some point 'virtual particles' are given
enough spin to become charged plasma. The charged plasma
is shot out along the magnetic field lines and
coalesces into stars. The stars go through their
life, degenerate into neutron stars or whatever, and
eventually fall back into the singularity.
The process repeats.
John
The Galaxy Model for the Atom
http://users.accesscomm.ca/john/
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| User: "" |
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| Title: Re: Fractal String Theory - The saga continues ;-) |
08 Oct 2005 09:12:09 PM |
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Happy Hippy wrote:
john_ramsden@sagitta-ps.com wrote:
near enough to a black hole singularity fermions
could be replicating themselves by the bushel, from
background substring "gas", i.e. "projecting" their
fractal curvature structure to a ghostly double
which then becomes a fermion itself and repeats
the process.
Closer and closer to the singularity the
acceleration of the spin increases rapidly.
At some point 'virtual particles' are given
enough spin to become charged plasma. The
charged plasma is shot out along the magnetic
field lines and coalesces into stars.
The snag is "plasma" can't escape from a black hole,
any more than light can.
Also, the further into a black hole you go the faster
you travel into the future compared to an observer
outside.
My conjectural descriptions may sound like they apply
to events unfolding in space over time. But a string
is a "spacetime shard" (as Brian Greene describes it
in his book "The Elegant Universe", which I recommend),
and string interactions occur in at least 4 dimensions
(possibly many more, e.g. 12 or 26 according to most
string heories).
As a footnote, a toroidal singularity is probably a
whole "sheaf" of nested individual torus surfaces each
with a different number of twists to its constituent
strings, and possibly rotating like fan blades of a
jet engine at varying speeds so they all "look"
indentical in some sense relative to each other.
In 3D a stretched and reconnected fermion could not
merge with the torus of its banding without crossing
other toruses, whereupon all hell would break loose!
But in 4D or higher dimensions it could shrink down
onto its matching torus without touching any others.
The Galaxy Model for the Atom
http://users.accesscomm.ca/john/
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| User: "Happy Hippy" |
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| Title: Re: Fractal String Theory - The saga continues ;-) |
08 Oct 2005 12:16:39 PM |
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Happy Hippy wrote:
john_ramsden@sagitta-ps.com wrote:
snippity near enough to a black hole singularity fermions
could be replicating themselves by the bushel, from
background substring "gas", i.e. "projecting" their
fractal curvature structure to a ghostly double
which then becomes a fermion itself and repeats
the process.
Closer and closer to the singularity the
acceleration of the spin increases rapidly.
At some point 'virtual particles' are given
enough spin to become charged plasma. The charged plasma
is shot out along the magnetic field lines and
coalesces into stars. The stars go through their
life, degenerate into neutron stars or whatever, and
eventually fall back into the singularity.
The process repeats.
John
The Galaxy Model for the Atom
http://users.accesscomm.ca/john/
Radiotelescopes show the magnetic poles projecting
normal to the center in both directions from the
plane of galaxies.
The plasma thrown out one way from *the black hole*
is opposite magnetically from that thrown out the
other way.
Likewise the electron one one side of the orbital
is opposite from that on the other.
John
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