Why There Are Three Spatial
Dimensions
John A. Gowan
Aug., 2013
email:
jag8@cornell.edu
johngowan@earthlink.net
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Fundamentally, the dimensionality of spacetime
is a matter of energy conservation: three dimensions are
sufficient to establish an entropic domain in which the basic
thermodynamic requirements necessary to conserve the energy of
free forms of electromagnetic energy (light, EM radiation, etc.)
are present; likewise, four dimensions are necessary to meet the
conservation requirements of bound forms of electromagnetic
energy (mass/matter).
Light is a 2-D transverse wave, with no time
dimension and no space dimension in the direction of motion
(clocks stop and meter sticks shrink to nothing at velocity c -
as per Einstein). Light requires two dimensions to accommodate
its alternating electric and magnetic fields, which induce each
other at right angles. The energy of light is encoded in its
frequency (E = hv) with its implied (but suppressed)
time dimension. The intrinsic motion of light ("velocity c")
"sweeps out" a third spatial dimension, creating, expanding, and
cooling a 3-D spatial volume. The energy component of light is
therefore 2-dimensional, while the entropy component corresponds
to the 3rd spatial dimension. The entropy "drive" of light (free
electromagnetic radiation) is the "intrinsic motion" of light,
as gauged by the universal electromagnetic constant "c".
We see that three dimensions are sufficient for
2-D light to establish an entropy domain for its own
conservation needs, and therefore light has no need to explore
additional dimensional possibilities. Similarly, in the case of
3-D bound energy forms of electromagnetic energy (massive atomic
"solids"), one further dimension (time) must be added to
establish the entropy domain for matter (history), in which the
"intrinsic motion" of time produces aging and decay (since atoms
have no spatial form of intrinsic motion they must resort to
time - which also suggests that the 3rd spatial dimension is the
only possible higher-dimensional entropic option for light - if
it is to remain in its free form). Gravity combines these two
electromagnetic entropy domains into our familiar spacetime, the
composite entropy domain of our universe of free and bound forms
of electromagnetic energy. (See: "The
Conversion of Space to Time" .)
In the "black hole", the electromagnetic metric
of light and space (as gauged by the universal electromagnetic
constant "c") is completely overwhelmed and replaced by the
gravitational metric of matter and time (as gauged by the
universal gravitational constant "G"). The energy of the black
hole is encoded in its mass (hv = mcc), while the entropy
is encoded in the two-dimensional "event horizon" (as per
Bekenstein and Hawking - see: Scientific American Aug.
2003 pp. 58 - 65.) The entropy drive of matter and the black
hole is the "intrinsic motion" of matter's time dimension, which
creates the spatial flow of matter's gravitational field. A
gravitational field is the spatial consequence of the
intrinsic motion of time. The expansion of the black
hole's "event horizon" is required (when energy is added to the
hole) since the gravitational intensity and material density of
the hole is already at a maximum (g = c); therefore the only way
to increase the gravitational flow (which is necessary to
increase the temporal entropy encoding for the added energy) is
to increase the size of the gravitating mass, in other
words, increase the boundary or surface area of the event
horizon, which is the only part of the hole in active/actual
contact with the outside spatial universe. If the black hole has
a 3-dimensional "volume" at all, it is permanently hidden behind
the event horizon, which is in fact a temporal entropy surface
(see: "A
Description of Gravity"). Hence the extreme
temporal/gravitational/material metric suppresses space just as
the extreme spatial/electromagnetic/light metric suppresses
time.
Information is encoded in our
ordinary universe in all four dimensions. Information requires
the one-way 4th dimension (time) for its entropy drive and for
its historical conservation domain, due to the causal
characteristic of information. Because the black hole either
destroys, suppresses, or hides both the third and 4th
dimensions, (time stands still at the event horizon and meter
sticks shrink to nothing), the black hole contains almost no
information, or as John Wheeler says: "A black hole has no
hair". Information may live forever in the historical domain,
but not in the black hole. Hawking should have stuck to his
guns. (See: Leonard Susskind: "The Black Hole War"; Back
Bay Books, Little, Brown and Co., 2008.)
The energy and entropy of information are encoded
in the black hole's mass and the surface area of its event
horizon. The causal component of information ceases to form new
linkages upon entering the black hole and inside the event
horizon distinguishable atoms are converted to "anonymous"
photons. Causal linkages created by information outside the
black hole, however, continue to propagate forever in historic
spacetime. Entangled elements swallowed by the black hole are
moot, since they remain hidden forever, suspended or "frozen" in
time at the event horizon.
Information is one-way (asymmetric) due to
causality, as well as due to the absence of antimatter
("anti-information");
Gravity is one-way and asymmetric;
Time is one-way and asymmetric;
Entropy is one-way and asymmetric;
Matter is asymmetric - due to its time dimension, gravitational
field, lack of intrinsic motion, mass, and lack of an antimatter
complement.
The black hole is the extreme case of the gravitational metric, as
gauged by the universal gravitational constant "G". The black hole
is the ultimate contrast to a universe of light with no matter at
all, the extreme case of the electromagnetic metric, as gauged by
the universal electromagnetic constant "c". In the light universe,
all forms of energy move at velocity "c', time does not exist, nor
does space (in the direction of a photon's motion). In the black
hole also, all forms of energy move at velocity c, and space and
time are absent. In this comparison, we see "velocity c" acting in
both cases as the "gauge" of a symmetric energy state -
specifically, a state of non-locality either outside or inside the
black hole. In the light universe, photons and their energy
content are distributed equitably everywhere, simultaneously -
since there is no time parameter and no distance parameter (clocks
stop and meter sticks shrink to nothing in the direction of motion
at "velocity c"). This same "non-local" symmetric state with
regard to the distribution of energy is achieved by the black hole
within the boundary of its "event horizon" - again because
all forms of energy move at velocity c, time has stopped and space
has vanished, due to the action of a gravitational field whose
strength is locally equivalent to the electromagnetic constant "c"
(g = c). Clocks stop and meter sticks shrink to nothing at the
"event horizon" of a black hole.
This discussion suggests that the conservation
role of gravity is to pay the "location" symmetry debt of
matter. The "location" symmetry debt/charge arises in
consideration of the spatially undistributed (hence asymmetric)
local concentration of immobile bound energy (matter), VS the
spatially symmetric "non-local" distribution of light's energy
(due to light's intrinsic motion "c"). Because matter is
originally formed from light (bound electromagnetic energy is
originally formed from free electromagnetic energy), matter
carries a gravitational "location" charge, among other symmetry
debts in the form of charges and spin, due to matter's formation
from all-symmetric light. (See: "Symmetry
Principles of the Unified Field Theory".) The gravitational
"location" charge is unique in that it represents an entropy debt
as well as a symmetry debt. Because the intrinsic motion of light
is both the entropy drive of light and the cause of light's
non-local distributional symmetry, the gravitational "location"
charge must conserve both functions if it conserves either one.
(See: "The
Double Conservation Role of Gravitation".) Gravity pays
matter's "location" symmetry debt by creating black holes, in
which "Hawking Radiation" converts (eventually) the entire bound
energy (mass) of the black hole back to free energy (light).
Along the gravitational pathway leading to the creation of black
holes, bound energy is also converted to free energy via the
nucleosynthetic pathway of stars, and by the even more efficient
conversion of gravitational energy and mass to light in other
astrophysical processes such as supernovas and quasars. But once
the black hole condition is reached, conversions of bound to free
energy (in any appreciable quantity) essentially stop (so far as
we know), if only because gravity prevents the escape of any light
produced by such processes, should any occur. In the event
horizon, gravity creates a temporal metric for matter which is the
symmetric equivalent of the spatial metric of light - a metric in
which all forms of energy move with intrinsic motion c. What
happens in the interior of the black hole is moot, since we can
never know. I suspect, however, that proton decay occurs at the
singularity, and hence the black hole is filled only with light -
another way in which the gravitational "location" symmetry debt is
paid, also solving the problem of the infinite compressibility of
matter. But nothing else matters once the event horizon is formed
(at g = c); a symmetric temporal metric has been constructed in
which all energy forms travel at c, and it would appear that no
further conservation concerns need be addressed. But is this
really the final word?
What then of "Hawking Radiation"? We note, of course, that Hawking
radiation is pitifully small for any large hole, and tellingly, it
gets smaller as the hole grows larger, not an encouraging sign for
the cause of symmetry conservation at least via this route, since
the natural tendency of the black hole is to forever increase in
size, which means this symmetry conservation pathway is
asymptotically suppressed in the natural course of events.
However, if the interior of the black hole is indeed filled only
with light, then some photons may escape the event horizon by
quantum mechanical "tunneling", and this process might increase
with the size of the hole, counteracting the decrease in Hawking
radiation. Whatever the case, the amount of time available for
this process (in a universe that does not collapse) is essentially
unlimited (assuming that other, unknown cosmological processes do
not intervene), so in the end the hole will completely evaporate
its mass to light: bound, asymmetric electromagnetic energy
returns to free, symmetric electromagnetic energy. One rationale
for this scenario is that the temporal entropic metric of the
black hole event horizon is less symmetric (being one-way) than
the "all-way" spatial entropic metric of light, driving the
eventual and final conversion of mass to light in complete
satisfaction of Noether's Theorem. Nevertheless, the time required
for this conversion to go to completion is so immense that it
suggests Natural Law is in fact rather comfortable with this
arrangement - the temporal metric of the black hole is stable,
leaving little to be desired either inside or outside the event
horizon in terms of conservation issues. This is another reason
for suspecting that the interior of the black hole is filled with
nothing but light, rather like a superconducting medium in which
photons have become heavy.
All this notwithstanding, a major conservation issue remains
unresolved, as attested by the continuing presence in the
surrounding universe of the black hole's powerful gravitational
field, even after the event horizon has formed. So long as this
field is present, the symmetry debt it encodes and represents
remains unpaid. One reason that gravity keeps working even after
the formation of the event horizon is that matter's entropy debt
must keep being paid until matter's symmetry debt is completely
paid, and as far as the outside universe is concerned, the black
hole still represents a grossly asymmetric concentration of
undistributed, immobile mass-energy, a severe affront to symmetry
conservation in terms of the equitable dispersion of energy
throughout space - as was originally the case for the light from
which the black hole's matter was produced. The gravitational
entropy debt of matter can be thought of as an "interest" payment
on matter's symmetry debt - just as on planet Earth, the interest
has to be paid until the symmetry debt is retired. But the Earth's
gravitational field is too weak to convert mass to light, so it
never "pays down" the principle on its symmetry debt - that is,
despite the continuous working of Earth's gravitational field, it
never gets weaker because it never converts any of Earth's mass to
light. In our Sun, however, we see gravity actually "paying down"
the symmetry debt of the Sun's mass by converting some of the
Sun's bound energy to light, and hence reducing the Sun's total
mass and its associated gravitational field. Gravity will vanish
completely when its symmetry debt is well and truly paid, like any
other charge (see: "Does
Light Produce a Gravitational Field?"). So the black hole's
gravitational field keeps working until the mass energy of the
hole - whose entropy is represented by the surface area of the
event horizon - completely evaporates away.
Since it is the surface area of the event horizon which is in
contact with the outside universe, it is the surface area which
generates the gravitational field. Hence the connection between
time, gravity, and entropy is especially evident in this example.
A gravitational field is the spatial consequence of the
intrinsic motion of time (see: "The
Conversion of Space to Time"). (See also: "The
Destruction of Information".)
email:
jag8@cornell.edu
johngowan@earthlink.net
home page (page 1)
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