The Expanding Matrix

(N/A = Not Available at this time )(N/A = Not Available at this time )

Jan.22/1999

Preface

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.

When one considers the "graviton exchange" model used for quantum gravity, it is depicted as a non-attracting particle that produces a semblance of attraction through propulsion...much like a rocket.  This model eliminates attraction as integral quality of matter and invokes "little rockets" to propel masses together.  This still acknowledges repulsion as the primal identity for energy with the inference 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.

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, I believe the conflicts preventing unification can be resolved. At the same time, a dynamic new picture of reality emerges.

Unification of Dynamics

©1998 Francis Pedley

INTRODUCTION

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 our perceived space would prove to be the result of energy transformations within a flat absolute space.

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 given the choice of only having one force to build a universe with and asked which force would be uniquely imperative to creating a universe, most people 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 would tend to seek to occupy the same point in the space and hence disappear.  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 is a modified version of an essay written in 1984 and rewritten several times since.  In fact if anyone can improve on the thought experiment it would be welcomed.

Dynamics

The following thought experiment looks at Einstein's principal of equivalence.  That principal states that  the g-force known to be caused by acceleration and deceleration is equivalent or identical to the gravitational force...the "g" standing for gravity.

The thought experiment goes like this; imagine yourself placed at a location in space far from any obvious gravitational effects. You are floating almost in contact with a hollow orb whose radius (R) is 4.9 meters.  50 meters away are two crochet balls about 50 meters apart.  If you touched the orb, it would move away from you as both it and you are weightless.  

The idea is to let the orb start expanding at its starting radius (4.9 m) per each second squared.  But not just the orb will expand but you and the crochet ball will also expand exactly proportional to the orb.  That is to say you will notice no change in scale between yourself the orb and the crochet balls as your expansion proceeds.

The true change in radius of the orb per unit time:  t  would proceed:

t₀=R...t₁=2R...t₂=5R...t₃=10R...t₄=17R...t₅=26R...t₆=37R...etc...

(Each radius appears one larger than R times t squared as the original static radius is added to the total)

We're actually letting the acceleration settle in a 9.8 meters per second squared, which is of course close to g, the acceleration constant used for the earth's gravity.  (A point to take into account is that for the sake of this thought experiment, we're going to deliberately ignore the inertial effects that would be caused by our own bodies and the crochet balls as they expand but we are only acknowledging the acceleration effects of the orb).  

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.  The acceleration would be 1 "g-force", so you could sit on the orb and you would feel weight exactly as on earth.  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 of the orb from its center of mass.  Our scenario has almost perfectly duplicated the gravitational phenomenon without invoking any attractive forces.

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 imagination taken from our real space-time sufficed for our purposes.  The spacetime continuum which appears in EMT are acceleration shells around masses (and actually within masses) that mimic time shells in relativity models.  Also no attempt was made to account for mass in this model but the scenario is simulated purely by use of scale. 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. The rest of this article will be dedicated summarizing details and discoveries which indicate that the essence of an expanding matrix is true.

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 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 n₀...n_1...n_2...n₃...n_4...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.

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 un-broken image of these three views, we need either a very wide angle camera or an as-of-yet un-invented

Fig.1a,b,c.

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) (see Abstract, beginning of document).  If one were to paint a series of horizontal lines on a wall extending the length of the hallway and took such a 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.

Fig 2a,b,c.

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

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

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.   Wave...an 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 geometries as to the way their waves transform.8

3.   Particle...The result of an interaction of any above wave transformation with another wave entity 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 transformations around him and change his frame of reference to selectively match different individual ones...then not only would the relative velocities of all other transformations change, but so would their original locations (assuming one could know exactly where they were supposed to be).

 

Origin of Wave Transformations

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 external universal pressure feeding a internal disequilibrium, which in turn converts to waves or interacts with existing waves. 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, manifests itself as zero potential at 0^° Kelvin. In order to disrupt the flatness, energy is introduced which initiates a wave-geometry. Energy flows both inwards and outwards within the geometry.  If the inward flowing energy is out of phase as approaches and 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 and energy is flowing into the system, 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.

© 1985, 1998, 1999 Francis Pedley

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. Part_1 - 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

To the Top