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(The designations Part 1, 2, 3 etc. are schematic to the order documents are converted to html format and put online, not to their relationship to the theory itself. Eventually another 100+ pages will be converted by OCR from dot matrix on paper to HTML format.)

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*Jan.22/1999*

*For the reader with limited time, the strongest persuasions for
the Author's view are marked with asterisks*. *

*One of the prime objectives of this project is to interest as many
skilled mathematicians as possible in converting the standard "Static
Space" models of physics into the "Expanding Matrix" model
presented here. One of the best candidates in the author's view is "String
Theory" as it already uses a framework based on the concept of spatial
transformations to build reality. The idea that our geometric laws are a
function of dynamic energy transformations is the foremost tenet of the
"Expanding Matrix" model. *

*In older papers, this theory is referred to as "Dynamic Asymmetry".
Great pains were gone to, to explain the origin of the "symmetries"
from such. However to avoid confusion, the term is seldom used anymore.
At the time I was delighted that it clarified a single dynamic identity
for energy and the arrow of time.*

*Anyone who feels compelled to work on this project is encouraged
to do so. More documents will be available as they are put online. The only
thing asked is that you accord due credit to reference material and authorship
of the ideas presented here in any works you may submit for publication.
You may solicit more answers by e-mail as you need them. Eventually a Bulletin
Board will be initiated for more open discourse on the subject. *

*It is anticipated that in the future, funding will be available
to encourage some participants in their research. The larger the pool of
particapants, the sooner this will be accomplished, so please keep me informed
of your progress.*

*F. Pedley*

Expanding Matrix theory as it exists at this time is primarily a model
of *spatial dynamics. *However as such it must necessarily touch on
other aspects of physical phenomenon *especially gravitation*. When
gravitation is considered within the context of these dynamics I believe
the conflict between quantum gravity and the gravity of general relativity
becomes solvable.

Much of quantum theory's effectiveness stems from its successful manipulation of Heisenberg's Uncertainty Principal, which postulates every point in space to be a point of energy. This poses problems within the context of general relativity which postulates gravitation as an attracting force that increases with mass, such that as the escape velocity of light is reached, not even light can escape its attraction. When attempts are made to combine the two theories based on these criteria, the Uncertainty Principal predicts so much energy in the universe, that according to the equivalence postulated for matter and energy by E=mc², the gravitational attraction inferred by general relativity would have collapsed the entire universe into a "black hole" long ago.

As one also considers the *"graviton exchange"* model
used for quantum gravity it is seen that it is essentially a non-attracting
particle that produces attraction through propulsion...much like a rocket.
With the exception of general relativity, there is no viable physics theory,
that accepts the concept of *attraction at a distance* as a natural
logical conclusion. Even Sir Isaac Newton although formulating gravitational
theory, found the concept illogical.

If one accepts the view that *attraction at a distance *is a flawed
concept and opts for an *electron-charge-like *model; a new criterion
is imposed upon him. With this model, (which is probably right), one is
essentially opting for *repulsion* as the *primal identity* for
energy*.* If there are *no true attracting forces* but only localized
field circulations which mimic such, the natural inference is *that the
net charge in the universe is repulsing.* This being so, than then the
only conclusion to be drawn…is that ** all point-energy in the universe
is expanding. **This has in fact been the quantum dilemma when treating
the electron. Unless it is mathematically "tricked" by attributing
it

At this point, that *purely logical view* might seem flawed. However
when one considers that in general relativity, the gravitational field is
considered to be "*Spacetime"*. That in quantum physics the
properties of empty space cannot be divorced from physical properties therein.
That even String Theory demands that there be ten dimensions attached to
our physical universe. One should get the idea that maybe there’s something
about our concept of *space and time* that needs refining.

The fact is all three views can be seamlessly combined if one accepts
*one strange identity* for what *space* really is. The most surprising
conclusion from the model to be presented is that even *the emptiness
of space* proves to be the result of *field transformations*.

**Visual and Real Perspective**

One of the curiosities that inspired this quest was
a *thought experiment* of standing in a very long hallway with horizontal
lines painted all the way down one wall. Facing this wall we see the horizontal
lines as they are actually painted (Fig.1b) …*parallel and horizontal.
*Then as one looks in both directions down the hallway they see mirror
images (Figs. 1a,1c) of these lines converging towards their vanishing points.

In order to get an *unbroken* two-dimensional picture of these three
views; we need either a *very* wide-angle camera or a camera that takes
a continuous, incrementally digitized, sweep-picture of all three views
much the way an audio sine wave is digitized. The latter would give *the
best assimilation possible,* of all three views. Both though would produce
*curved lines from straight lines*, cresting where the wall meets ceiling
and floor, closest to the observer (Fig.2b). Although a line at eye

level would appear to be straight, other lines would
curve increasingly away from eye level. It struck me how similar these lines
were to *field lines*. My reaction though was that the observer alone
was causing this result, so I abandoned the idea. Years later in testing
logic of the *Expanding Matrix* model, I reexamined it to see if the
effect could be explained therein…and remarkably it gave a flawless
explanation. That explanation is the basis of the *Expanding Matrix Theory.*

By converting the entire spatial matrix including the gravitational elements
of general relativity into an expanding field with a value of the constant
C representing the velocity of light, I believe the conflict between general
relativity and the uncertainty principal can be resolved. At the same time,
a dynamic picture of what *space* really is emerges.

^{}

*©**Francis Pedley 1998*

In trying to resolve the incompatibility between quantum gravity and
relativity, the methodology as near as I understand it has been to assume
*both* to be correct models in their own domain and to try bridging
the two with a mutually compatible theory. Another option has been to start
from a more fundamental set of assumptions and try to encompass the non-integrating
elements.

In this instance, by following a new series of *a priori* assumptions
a model has been created which I hope may aid in resolving the most divergent
elements between* general relativity and quantum gravity*. In view
of* their* respective treatments of space perhaps the most surprising
conclusion from this new model is that even *the emptiness of space*
would prove to be the result of *field transformations*.

**Simplify**

Because the study of *Physics* is** **by its
nature a study of *dynamics*, it seemed wise to take a second look
at this quality. In classical physics the reaction between any two entities
is interpreted through *acceleration* as a result of *force*.
There are understood to be two fundamental causes for this reaction, *attraction*
and *repulsion. *It is difficult to articulate but I had the feeling
that the chances of *both these *qualities existing simultaneously
as the *primal natures* of energy was probably *zero. *The opinion
was that if it could be correctly concluded which was the only true force-like
identity of energy, then the *opposing quality* could be explained
within *that context.*

If asked which force would be uniquely imperative
to creating a universe, most intuitively opt for an *attracting force.*
After all what holds things together? But when one extrapolates attraction
as an *only* force, the universe quickly disappears, for every particle
in that universe tends to collapse towards the same point. Additionally
with no repulsing force to form the *surface* of solids...no objects
would form. This left one looking at a *repulsing force *to see if
a universe not unlike our own could be constructed from such, and surprisingly
one could. To be convincing
the model had to be capable of duplicating gravity as we know it. The following
excerpt derived from an essay written in 1987^{1} illustrates the point.

Imagine yourself placed at a location in space far
from any obvious gravitational effects. You are floating almost in contact
with a hollow orb 10 meters in diameter. 100 meters away are two .crochet
balls about 50 meters apart. At a given instant you,* the orb and the
crochet balls* will all start expanding at a rate of let us say 2 times
per second (**t**) of linear value, expressed (**L _{n}**)
in each moment of expansion.

As the expansion proceeds a*bsolute length* =
**2tL _{0}...2tL_{1...}2tL_{2...}etc.**

You should achieve an accelerating expansion which
*appears spatially proportional* so that changes in magnitude are unnoticeable
to you as the participant. The orb will expand with **t**...20m, 40m,
80m, etc*. until it settles in arbitrarily at one "g force"
of acceleration.* Intuition should tell us that the instant the expansion
starts, even though linear proportions remain seemingly constant, the scenario
would come alive with activity. First you would feel the orb nudge you and
experience a gravitating-effect as you mutually expand into each other*.
(When acceleration approached 1 "g", you could sit on the orb).
*The crochet balls would converge on each other and towards you so that
you could catch them. Throwing them away they would always repeat the same
process converging towards you and each other, even appearing to accelerate
as they fell towards you. In your hands they would have *weight* due
to *inertial forces*,
a result of the *acceleration *as the surfaces expand into each other
from their centers of mass. Our scenario has almost perfectly duplicated
the gravitational phenomenon without invoking any attractive forces.^{2}

The preceding is of course just an illustration to
get over the "hump" of accepting a universe with *no absolute*
attracting forces. The actuality would be more complex. For brevity, Part
1 will be dedicated only to summarizing details which support the aforementioned
view.

**States of Matter**^{3}

It is useful to view this topic in terms of the states
of matter (*solid, liquid, gas*) and their relation to a gravitational
field. We know that water for example is *solid* at lower temperatures.
As energy (heat) is added, it becomes *liquid* and as more is added
it turns to *vapor*. These *states* are mirrored in their same
hierarchy in a gravitational field...the more energy, the higher they are
found (in altitude). However according to the traditional view ...after
ascending *1..2..3..* there is a reversion to *..0..* (outer space),
whereas in our expanding matrix the ascending order for *available*
energy is *1..2..3..4..* (solid, liquid, gas, space).

To elucidate...in *air* one can move quite freely,
whereas in *water* less so. The reason though is not because water
is "stronger" than air but because it absorbs more *kinetic*
energy leaving less for movement. Encased in concrete than, one could not
move because the energy-poor solid is absorbing *"all"* kinetic
energy leaving *none* for movement. In vacuum space everything including
light moves with the least resistance, not because there is nothing there,
but because it is a medium of the purest *available* energy and so
absorbs minimally from any system within it. This concept is validated by
the procedure of *"squeezing light" where *a sodium solution
is bombarded with gamma radiation to energize it. Light shone through the
thus *energized* solution traverses it at a higher velocity because
less energy is *robbed* by the energized solution.

Reinforcing this view is the accepted doctrine that
*momentum is energy*. The fact that an object acquires energy by elevating
it in a gravitational field should raise the question as to where that energy
is coming from. To say "from the energy expended to get it there",
is not a valid argument, for drifting in from outer space it would have
fallen just as fast. Neither location has any preeminence as a point of
origin. The argument would be equally valid, that energy added to elevate
something serves to equalize it with the increasing energy at higher elevations.
However the natural geometry of this expanding matrix model shows *an
increase of momentum energy away from any center of mass*. This geometry
could be likened to repulsing beads on a string so that momentum energy
increases outwards from center n_{0}...n_{1...}n_{2...}n_{3}...n_{4...}n_{5},
etc. The momentum energy can be likened to a field around each bead separating
it from the next bead on the string. As the field increases magnitude, so
does the apparent space between beads, *because the field and the space
are one and the same thing*.

**Assimilating an Expanding Matrix with Present Models**

Viewing gravity as *an attracting force able to
curve space-time* seems to have created problems in the light of quantum
theory. However by reversing the gravitational arrow with an expanding matrix
as illustrated above, a *curved space-time* is retained which differs
little from Einstein’s model. Such a space would itself* be* pure
energy and hence allows for *a cosmological constant* which is in closer
agreement with *quantum* predictions while conversely allowing for
the observed expansion of the universe. It also *seems* to point at
a mechanism driving *the uncertainty principal,* although it shows
no way around it.

**Visual and Real Perspective**^{4}

As stated earlier, this model implies that *the
emptiness of space* is a result of field transformations. There are many
implications to this but one result which I find engaging is the phenomenon
of visual (and *real*) perspective.

The event that convinced me, (long before I knew what
it meant) that space or the void was the result of field transformations
was a *thought experiment* of standing in a very long hallway. As one
looks in both directions down the hallway they see mirror images of what
can be described as a rectangle with an "X" formed by two diagonals
where the *ceiling, walls* and *floor* meet (Figs.1a,1c). Looking
in front of us we see two parallel lines formed by the ceiling and floor
(Fig.1b). In order to get an

**Fig.1a,b,c.**

*unbroken* image of
these three views, we need either a *very* wide angle camera or an
*as-of-yet uninvented* camera that takes a continuous, incrementally
digitized, sweep-picture of all three views much the way an audio sine wave
is digitized. The latter would give *the best assimilation possible,*
of all three views. Both though would produce *curved lines from straight
lines*, cresting where the wall meets ceiling and floor, closest to the
observer (Fig.2b). If one were to paint a series of horizontal lines (see
Abstract, beginning of document) on a wall extending the length of the hallway
and took such a

**Fig 2a,b,c.**

photograph, lines at eye level would remain straight
but would curve increasingly away from eye level It struck me how similar
these lines would be to *field lines* found for example in magnets.
My reaction though was that the observer alone was causing this result,
so I abandoned the idea. Years later in testing logic of the expanding matrix
*model*, I reexamined the effect.

**Perspective From Field Transformations**^{5}

In this expanding matrix model it is postulated that
every point of energy (or object) in the universe* increases its absolute
size *as it proceeds in time, at a constant which is equivalent* *to
the velocity of light. Conversely this means that every object* was proportionally
smaller in the past than it is in the present (or future)*. In other
words if we could examine a given object in the *past* and compare
it with the same object in the *present*, it should have been smaller...and
the further in the past we look, the *smaller* it should appear to
be. We are doing just this when we examine the phenomenon of *perspective.
*Any image received
from the past would be expected to have an* apparent length*
(

^{}So that _{}
...where **P** is the parameter for *perspective.*

This is a departure from the conventional assumption
that perspective is uniquely a function of *the inverse of distance*.
It describes an *active cause* as opposed to a *passive* one.
To illustrate the difference, assuming everything is expanding**:** if
we had 10 rulers lined up equidistant from us and imagined the light from
one ruler* delayed by twice* the normal time in reaching our eyes,
it would appear half their size. Our assumption would be that it was*
twice the distance* *of* the others away, because we’re receiving
a late message about the ruler’s size relative to the others. This
is why the curvatures in Fig.2b are a real part of nature. If one applies
the function to
each point on any line in real space, the curvatures will appear as illustrated
in Fig.2d.

**Fig.3 **If light were
instantaneous than the viewer would see the objects as we do...all the same
size. As light though has a finite velocity, objects appear progressively
smaller the greater the delay in the light image arriving at the viewer's
eye. This is a result of these images arriving from further in the past
when the actual object itself was smaller (Fig.4).

**Fig.4 ( Solid
Lines have been kept artificially vertical and horizontal for facility.
The blue line would actually stay horizontal and all other
lines would keystone including the base-timeline).**

**Dissipation and Conservation of Energy**

In the absence of the defined *field-space, *a
quality would exist I refer to as "*absolute space"*. This
space unlike field-space should not transmit light or any form of energy.
Although it acts *voluminous *in that it houses our universe, it would
be inaccurate to think of it in the same terms that we understand space.

Our concept of dissipation must be thought of as *induced
by* and *unique to* the energy system itself, not an* inherent*
quality of an *absolute space*. Hence our universe can expand to infinity
without dissipating or *coming apart. *Parts cannot* break off*
and go their own way as they are ironically *connected* by the expanding
medium. Because total *energy
is finite* and* absolute space is infinite*, the system acts like
a finite system with infinite (*temporal*) potential. That is to say,
the "absolute space" acts like an *infinite sink, *drawing
the* finite energy *outwards forever. If both were* infinite*,
there would be no dynamics.^{7}

The model for the above energy should have three fundamental stages all within an expanding matrix:

...a state of**Pre-Potential***relative equilibrium*where there are no local disruptions in the smoothness of energy distribution i.e.,*space like.*...an intermediate**Wave***phase of disruption*in a localized region of the expanding field that builds up into areas of*high*and*low potential*. The*interactions of these potentials*are the genesis of*reality*. Massless and heavy particles would have distinctly different mechanisms to their wave functions.^{8}...The result of an interaction of the above**Particle***wave-function with another wave function*e.g.*observer.*This is somewhat more complex when viewed in an*expanding matrix*, i.e., if an observer*the different wave functions around him*and change his frame of reference to selectively match different individual functions...then not only would the*relative velocities*of all other functions change, but so would their*original locations*(assuming one could know exactly where they were*supposed*to be).

**Origin of the Wave Function**

A dividend of the *expanding matrix* model is
that it becomes easier to envision why a wave can perpetuate as an enduring
bit of matter. There is a constant universal pressure waiting to convert
to a wave function. In trying to account for the world as we know it, the
following is one of several speculations of how this mechanism might work,
especially in accounting
for gravitational mass.

Envisioning a *flat* expanding matrix, which
although it is dynamic, it manifests itself as zero potential at 0º
Kelvin. In order to disrupt the flatness, energy is introduced which initiates
a wave function. Energy flows both inwards and outwards in the function.
. If the inward flowing energy is out of phase as it crosses at the locus,
mutual cancellation occurs producing an energy "hole" whereas
outward crests amplify forming, individually *a shell*, or in combination
*a lattice*. It should be kept in mind that because there are no "absolute"
attracting forces, even this "hole" is expanding with the matrix. The progression of this wave is
such that as energy transforms outwards there is a particular *wave-shell*
which is the *convergence *of energy *greater* than the matrix
energy (outwards) and *less* than the matrix energy (inwards). This
*shell* interprets at our reality as "*material surface*".
Because *"surface"*^{9}
is where our sense of reality begins, we interpret it
as static with a self-contained inward moving arrow or "*mass*",
even though everything is expanding. The outward moving energy is spacelike
and interprets as spacetime or the gravitational field. Although the perception
of it as *spacetime* is perfectly legitimate, the idea of it as a force
capable of initiating a gravitational *singularity* would be an error
within the proposed context.

*©Francis Pedley
1998 *

*Most recent edit, May 26/1999*

- Footnote 1. "An Imaginary Gravity Simulation...."...the
author 1987. (back)

- Footnote 2. The key
element missing in our experiment is an artificial space-time continuum
which would more accurately complete the picture. This was omitted as our
real space-time sufficed. (back)

- Footnote 3. Abstract
- Dynamic Asymmetry 1988, Francis Pedley. (back)

Footnote 4. Chapter XXII, Dynamic Asymmetry 1988, Francis Pedley. (back)

Footnote 5. Chapter XXIII, Dynamic Asymmetry 1988, Francis Pedley. (back)

Footnote 6. The term present length used here is a misnomer. It is in fact also a gauged length. To be in the viewer's absolute present the measured item would have to rest on his eyeball. (back)

Footnote 7. Author's note - strangely there is a model where this space and energy configuration can be reversed yet produce similar results. (back)

Footnote 8. "Dynamic Nature of a Matter Wave" 1988 Francis Pedley. (back)

Footnote 9. Chapters XLI, XLII, Dynamic Asymmetry 1988, Francis Pedley. (back)

End of Part 1*"The Expanding Matrix Project"*has been solely supported by the author since 1984. To track the author's professional activities please go to Aesthiqe Fine Arts. (Look for the approximately 40 links comprising these locations)