1. Introduction
---------------
In this post I describe a simple recursive model for how
strings and branes interact and maintain their stability,
based on a surprisingly commonplace principle. This leads
to a compelling, and equally simple, way of thinking about
gravity and mass.
As a first striking example of the model in operation,
we describe, in section 4, the detailed structure of a
black hole singularity and how it maintains this and
grows as the hole accretes mass/energy.
(If the prospect of reading this entire post is too much,
as I can well understand it may be, or if you dear reader
spot what seems like an amateurish turn of phrase or even
kook warning sign, please at least read section 4, and ever
afterward laugh at the crudity of black hole singularies
being described as "points" and of "infinite density" !)
The model can be applied equally to (fundamental) fermions
and in conjunction with SR suggests how rest mass could be
relativistic mass induced by intrinsic motion within the
fermion, and so on at lower scales, so that "true" rest
mass becomes evanescent, even if a useful fiction.
At the opposite end of the scale, the model suggests that
the expansion of our entire Universe (understood to mean
the "visible" Universe, outside black holes, and all the
observer-connected regions beyond our causal horizon)
is an inevitable consequence of gravity acting over
long distances and will accelerate.
Furthermore, it indicates that our Universe started life
as a singularity in a black hole which evaporated as the
Universe (with the same fundamental physical laws as ours)
containing it expanded past a certain rate, and that the
evolution of our Universe is, in broad brushstrokes and
in terms of 2D surfaces as a vague indication of higher-
dimensional equivalents, from a torus to a sphere, just
as in M Theory a single toroidal brane can decay to a
sphere [see "The Elegant Universe" by Brian Greene,
Fig 13.3 on page 327].
Reading Greene's book all through for the first time last
week, I learned that the idea of the Big Bang originating
in a black hole singularity was suggested by Lee Smolin,
who also ingeniously and plausibly elaborated it into a
form of inanimate natural selection of universes whose
physical laws favour the formation of black holes. See:
http://www.edge.org/3rd_culture/smolin_susskind04/smolin_susskind.html
Probably most ideas in this post, such as rest mass being
relativistic mass due to internal motion, have been put
forward by others before (and I'd be very interested if
these are pointed out); but I'm not aware of the idea of
parallelism having been applied to them all as an uniting,
underlying theme.
2. Note to the Reader
---------------------
Let me assure readers worried at the outset by that
phrase "commonplace principle" that my model does
not in any way seek to contradict established
and generally accepted theories such as QM and GR,
quite the reverse.
Even if it is right on the button and allows one
to think about and describe (and hopefully in due
course formalize) sub-microscopic phenomena in
deterministic terms, we as observers are made of
and surrounded by strings and branes and thus the
inescapable probabilistic nature of QM still applies
to us, just the same as the literally inescapable
nature to us of a black hole!
As an aid to understanding and intuition, the descriptions
of strings and branes below are expressed in terms of 3D
space. But as formal string theories operate in 11 or more
dimensions, this is likely to be an oversimplification.
However I trust the reader will not reject it out of hand
on that basis alone.
Also, the reader will have noticed the absence of any
equations, which to many is another worrying sign. I
think the ideas are almost specific enough now for a
crack at the Maxwell equations and SR; but I'll admit
I'm not quite there yet.
I'm also all too aware of "gray areas", the most prominent
being how exactly the "group waves", cavalierly referred
to throughout, tie in with familiar concepts.
3. What is Gravity and How do Strings and Branes Relate?
--------------------------------------------------------
My proposed answer to the first suggests a consistent
answer to the second, and to other fundamental questions,
provided we assume that branes form an infinite heirarchy,
in which a brane is itself composed of elongated branes
or "strings" at lower levels in the heirarchy.
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.
Flat and empty spacetime can be pictured in the familiar
way as a sea of branes, at all scales below a given one,
with a symmetric distribution of orientations.
A gravitational field or, equivalently, curvature of
this spacetime is then a skew in this distribution
towards (locally) one direction.
Mass can then be identified as originating in optimal
or limiting everywhere-parallel string alignment, for
example a torus comprising strings wrapped in parallel
bands with at least one "twist".
(Section 4 explains why strings can only align in branes
rather than solid "bundles".)
Between this limiting brane and a distant symmetric
"random" distribution of orientations is a continuous
gradation of "parallelness", and if two limiting branes
approach then they can obviously increase the overall
"parallelness" of their combined consituent strings and
those in the vicinity by approaching nearer still and of
course changing their orientation to become more parallel.
In M theory, strings and branes have a "frequency". But
in my model, detailed in Section 4, a brane comprises
parallel bands of strings (which are themselves elongated
reconnected branes) and its natural "banded" structure can
perhaps be interpreted as a frequency, the more so as the
banded structure of each string (on account of _its_
constituent substrings) must cause the strings to
"rotate in place". Don't worry - all will become
clear in a few lines ...
The next section gives an example of a brane, describing
in detail how it is constructed from smaller branes, and
exactly how branes interact and combine.
4. Black Hole Singularities
---------------------------
Since the surface of a sphere cannot be "combed", i.e.
contain an everywhere parallel vector field, which our
model assumes mass is, in the limit, and a black hole
is an example par excellence of mass, it is natural
to assume that the singularity at its centre is a
torus and see where this leads.
In practice, we can rule out the ridiculous idea of a
"point of infinite density". I'm sure every physicist
must realize this is an idealization, whatever the
popular science books may claim.
(Curiously, a rapidly spinning black hole develops
outside the main event horizon a disjoint wedding-ring
shaped region called an ergosphere, which is vaguely
suggesive evidence that the assumption of a toroidal
singularity is not so far-fetched, and there's more
evidence to come..)
Before examining the structure of the singularity itself
in detail, consider what happens when a single fundamental
fermion ("particle with mass") falls into the black hole.
As this particle contains mass, we assume in keeping with
our model that it is also at heart torus shaped. In flat
spacetime, barring sub-atomic interactions and so forth,
this torus is "round" in the way one normally pictures
a torus.
But consider what happens as it approaches the singularity,
where the smaller-scale strings comprising spacetime are
increasingly parallel - To maximize its alignment, and
the symmetry of this alignment over its entire surface,
the particle must start elongating and aligning lengthwise
with the predominant sub-string direction until it starts
to resemble a primitive worm, and then something even
stranger starts happening ..
At both ends of the particle, as a result of elongation
of the torus a circular ridge has started to form.
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!
(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 )
That's not all though - Recall that the particle, or string
as is now fast becoming, is increasingly "held in place"
by the increasingly everywhere parallel sub-strings comprising
the spacetime background as it approaches the singularity.
So this parallel field actually guides the "crystal growth"
of the string as if on rails until the two ends meet and
seemlessly join!
In short, the particle has been transformed from a stubby
torus to
...
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