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The Expanding Matrix

(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.)


2 N/A 3 N/A 4 N/A   5 N/A  6 N/A 7 N/A  8 N/A  9 N/A  10 N/A
(N/A = Not Available at this time )



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

Part 1

Table of Contents

  • Abstract*
  • Introduction*
  • Simplify*
  • States of Matter*
  • Assimilating an Expanding Matrix with Present Models
  • Visual and Real Perspective*
  • Perspective From Field Transformations*
  • Dissipation and Conservation of Energy
    1. Pre-Potential*
    2. Wave*
    3. Particle*
  • Origin of the Wave Function
  • Footnotes
  • Other

  • Abstract

    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 zero volume it expands to infinity in a photon flash.

    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.

    Unification of Dynamics

    ©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.


    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 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 19871 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 (Ln) in each moment of expansion.

    As the expansion proceeds absolute length = 2tL0...2tL1...2tL2...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 Matter3

    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 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 n0...n1...n2...n3...n4...n5, 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 Perspective4

    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


    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 Transformations5

    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 (P) which is a function of the time it took the light-image to reach our eyes (t) proportional to a present6 (nearer) gauged length (L) which is also gauged as a function of time:

    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:

    1. Pre-Potential...a state of relative equilibrium where there are no local disruptions in the smoothness of energy distribution i.e., space like.

    2. intermediate 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

    3. Particle...The result of an interaction of the above 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 were able to see all 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)


     ©Francis Pedley 1999
    COPYRIGHTS- This material is protected by copyrights under international law. The material presented here may be reproduced for noncommercial purposes when attribution is given the author.
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