|art theory 101~Dark-Dark-Light: Dark Matter = Dark Energy (the inverse of)|
Dark Matter = Dark Energy
(the inverse of):
The Conservation of Spacetime
by The Conservation of Force
© 2003, Reginald Brooks. All rights reserved.
How did it start? And how will it end? We look out at our universe to see and understand the past, using tools of the present, to try to predict the future. The essence of science…and yet Einstein said that the distinction between the past, present and future is merely an illusion, as simultaneity, that is an agreed upon absolute "now", is really personal, i.e. relevant, to one's local position in the vast spacetime continuum. Different energies mask the "now" for different observers. There is no preferred, or absolute, "inertial frame of reference" that is valid for all observers in all spaces and times. Thus there is no absolute past, present and future.
Cosmologies' pursuit of the beginning and the end has lead to discoveries about our universe some of which are incongruent. Chief among these is dark matter and dark energy.
It appears that in looking at the past from our personal spacetime reference in this portion of the Milky Way, that some form of dark matter, i.e. some unknown form of heretofore undetectable, but gravitationally active matter, has provided more than 90% of the gravitational mass required to accurately account for the disposition of all the heavenly bodies that we can actually detect, and often see. The present cannot account for the past, here.
The present also cannot account for the future. If we measure the distance between matter today, and the same again tomorrow, we find it has grown. And if we measure it again it will have grown even more than the first time. The universe is expanding and doing so at an accelerating rate like some form of vacuum or anti-gravity, or negative energy of the vacuum, the cosmological constant (another of Einstein's contributions) of repulsion…or as simply the dark energy.
A focus on the fundamental laws of physics, especially the
"Conservation Laws", directed at the spacetime continuum, of which all matter and all fields, and thus all energy is contained within, points to the equivalence of dark matter and dark energy. The one is the inverse of the other and both are a natural consequence of the Conservation of Force (Part I.) as described by "The LUFE Matrix (Part II).
Total energy, E, is conserved…neither created nor destroyed…and is represented by Rectangle "A" with the area, A (Let A = 25 units2).
Because E can only come in Planck constant, h, quantum units, and because
E = hν (where ν = frequency in cycles/second),
the total conserved energy, E = the total of all the hν 's. And because h = constant, the only variable is ν , the frequency or time unit.
Conservation of E means that energy is symmetrical to or in translations of time ( meaning that over suitable, minimal time periods all E accounting will show zero net gain or loss).
The Heisenberg Uncertainty relation allows
Δ EΔ t = h
E = h/Δ t = h/Δ sec = hν
as the Conservation of Energy (where Δ = change, t = time in seconds), or as
Δ xΔ p = h
E/c · x = h
E = hc/x = hν
x = λ
c/λ = ν
as the Conservation of Momentum (where x = spatial displacement, p = momentum, c = the velocity of light, and λ = the wavelength). The Conservation of Momentum shows itself to be the Conservation of Energy restated in translations of spacetime. Substituting in the above we have
Δ λ Δ p = h
E/c · λ = h
E = hc/λ = hν
p = E/c = h/λ
E = pc .
It is but a small leap to show that the Conservation of Angular Momentum is a restatement of the Conservation of Momentum as rotational translations of space about the radius,r, as
L = px = pr =
(where L = angular momentum,
h = h/2π
λ = 2π r
pλ = p2π r = h
pr = h/2π
h = L
h/λ = p = h/c · ν
E = hc/λ = pc = hν
and we are back out to the Conservation of Energy. The Conservation of Angular Momentum being its restatement in terms of translations in time. More on this later.
Planck's constant, h, is often expressed in even more fundamental and natural
E = hν
(where ω = 2π ν ).
is a natural unit of relation in geometry, it has no physical units and therefore it absence
or presence does not affect the intrinsic parameter or concept described.
An even smaller, and perhaps the truly fundamental unit of action is the intrinsic spin
angular momentum which comes in units of 1/2
If the area, A, of Rectangle "A" = 25 units2 at beginning time, t0, it will always equal 25 units2 at time t1, t2 , t3…tn. Because the total area, AT, will equal the sum of all the component areas, A1 + A2 + A3… + A n. Therefore, all the various frequencies that all the constant h units possess at any time must add up to form the same total energy, ET.
Thus E = hν 1 + hν 2 + hν 3…+ hvn. (If there is a ^ in ν somewhere, there must be a ¯ in ν somewhere else.)
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Let Rectangle "A" be composed of 25 equal h units @ ν = 1 cycle/sec (Figure 1.). If we let the constant h = 1 unit, then 25 · 1 · 1 = 25 unit2 = A =area of Rectangle "A" = ET.
Let us graphically represent the ideal, perhaps primordial state, in which spacetime is isotropic and homogeneous in all directions. In fact, let us make it 25 equal square rectangles which we will now call Rectangle "B"…the ideal.
All the energy in the universe is represented by 25 equal squares, each of which represent 1 unit of Planck Action per 1 unit of time (frequency, ν ).
Simultaneously introduced here, is the notion that the Planck Unit of Action, represented by the Planck constant, h, is, by definition inherent in E = hν or h =E/ν , a cyclic…rhythmic…pulsing unit of action. Energy comes in quantum packets. Quantum packets pulse into…and out of… existence at a frequency of ν , the product of which defines the specific energy…whether the energy is of matter or field, or the total energy (kinetic and potential).
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Figure 2., Rectangle "B" shows the ideal square rectangle composed of 25 equal 1 · 1 squares of h pulsing in and out of existence at a frequency of 1 unit (cycle/sec.).
Mass, or even mass-energy, has not yet been introduced, yet energy all by itself, is gravitationally active. Let the gravitational attraction (acceleration) of any one of the h units in Rectangle "B" be equal and thus neutralizing to any of the other same h units. (You can envision the edges of Rectangle "B" to be toughing each other, if you like, forming the surface of a sphere.)
The value of hν is represented by area = 1.
The total value of hν 1 + hν 2 + hν 3… + hν 25 = E is represented by the area, A = 25 units2. This value must remain conserved for any time period exceeding the Heisenberg Uncertainty relation of Δ E = Δ hΔ t in total, whereas virtually for shorter periods of time there may be any number of temporary transgressions.
If a square of 1 · 1 = 1 unit2 represents boring ideal spacetime, what happens when spacetime becomes exciting (Symmetry breaking: Higgs boson symmetry is broken, forming photon pairs, some of which "spontaneously" generate mass-energy and the expression of mass, charge and spin…all of which rely on combinations of asymmetry and symmetry of their component substructure to generate the various net expressions of mass, charge and spin). Exciting spacetime results in transformations of the 25 identical 1 · 1 =1 unit2 square energy units into different size units…some larger and some smaller…whose sum total must always be equal to 25 units2. No exceptions.
In Rectangle "C" (Figure 3.), a hypothetical mass-energy unit has been introduced (towards the lower left quadrant), skewing the squares within the original Rectangle "B".
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Rectangle "D" (Figure 4.), shows the whole rectangle being skewed, while maintaining E = 25 units2, as an alternative way of viewing Rectangle "C", which is sometimes easier to visualize and describe the effects of such skewing.
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Similar to the real world irony, here too, smaller size (area) represents a greater focus of energy. Thus the smaller the λ = the greater the energy, as shown earlier,
E = pc = hc/λ .
Therefore, smaller areas in the rectangle represent greater concentration of energy. And because all energy is gravitationally active, in that higher energy area (higher than boring spacetime energy of 1 · 1 units) the gravitational acceleration is relatively enhanced. Opposite to this are the lower energy areas (again lower than the ideal, boring spacetime energy), where the spacetime energy density is so relatively unattractive that it appears to be repulsive when viewed from the higher energy position. Those smaller rectangles will be progressively more attractive the smaller they get and vice versa.
Effectively, this describes a force in general, and here, the gravitational force in particular. Geometrically, the higher spacetime curvature of the higher mass-energy density gravitationally attracts all other energy to itself. The concentration of h units here, at higher frequencies than their surrounding spacetime, ST, leads to a net attractive force here.
Because dividing up the symmetrical 25 unit2 Total Energy, ET, Rectangle "B" (or "A") into an asymmetrical, weighted Rectangle "C", still at E T = 25 units2, the lighter, airy portion in the upper right of Rectangle "C" is equal and opposite to the heavy, denser portion in the lower left.
Equal and opposite to what? Equal and opposite in force, F. Conservation of Force. The degree, or amount of F that is gravitationally attractive, relative to boring old ideal ST of 1 · 1 = 1 unit2, is equal, and opposite, to the amount of F that is less attractive (i.e. repulsive) relative to that same boring ST.
Fattraction = Frepulsion (Conservation of Force)
Picture a cross-section through the ST continuum where the curvature of ST is represented by vertical lines. In the middle, which also would represent ideal, boring ST the lines would be perfectly vertical and evenly spaced. Towards the increasing mass-energy density on our left, the lines would increasingly curve towards the left as the spacing between the lines also decreases in progression, depicting what effectively becomes the gravitationally positive "missing mass", or dark matter. Towards the right where the mass-energy density progressively thins out, the vertical lines become spaced further and further apart, and, become increasingly curved to the right, depicting what effectively becomes the negative or antigravity of the dark energy. The image is not far removed from the common image of iron filings in the presence of the opposite poles of a magnet, i.e. a magnetic field.
Expansion and contraction are relative concepts…because of the relativity of ST. If ST consists of all the Planck h units and all the Planck h units times all their frequencies of presentation equals a constant Total Energy, ET, then there can be no net expansion or contraction of the universe…only that of one occurs at the expense of the other. The more contraction force is expressed here, the more the expansion force is expressed there. E = hν will not allow it any other way. The universe…and ST…is expanding at an accelerated rate if viewed from a relatively high ST contraction position.
It is very helpful to think of ST as space/time, or simply as distance (displacement) per unit of time (or frequency):
λ /t = λ ν .
All ST manifests itself as mass or mass-energy (matter or fields). All ST exists as pulses, at a given frequency related to their energy, of Planck's unit of h, and the energy of any such ST existence is
E = hν .
Mass, as matter, represents an asymmetry in a given ST parameter (an attribute which generally limits its mobility, but also provides for net expressions of the charge vector, whether +, -, or 0; and, the spin, or intrinsic angular momentum, vector).
Mass-energy, as a field, represents the relatively symmetrical expression of the ST (an attribute which allows for its lack of mass, lightspeed mobility, neutrality of the charge vector, and gauge boson behavior, i.e. the spin vector is always paired, resulting in only net integral spins of 0, 1 or 2). It is relatively symmetrical, and not absolutely symmetrical. The Higgs Boson represents the absolute symmetry, the progenitor of the ST field. Breaking the symmetry of the Higgs Boson generates the relatively symmetrical ST field mentioned above, which can itself form, through further symmetry breaking, the matter field, a.k.a. the mass expression.
This relatively symmetrical ST field mimics in every way the massless, chargeless, spin = 1 photon, whose λ and ν are always reciprocally related to insure that
c = λ ν ,
the velocity of light, equals the fundamental constant of nature.
*fundamental difference to Standard Theory is duly noted
**mass of the neutrino family of leptons is still unknown
Table I. Comparing the mass, charge and spin of lepton/quark fermion matter to that of its surrounding, non-nuclear field gauge bosons.
Two photons (spin = 1) interfere to form the graviton (spin = 2).
Photons consist of two spin 1/2 (fermion) units aligned such that their mass and charge vectors are equal and opposite, whereas the spin angular momentum vectors point in the same circular direction and thus are additive, as 1/2 + 1/2 = 1.
Gravitons consist of two or more photons at the point of constructive interference(s), i.e. the spin 1 of each photon is in the same direction and thus additive, to give spin = 2.
Higgs Boson consists of two photons with absolute symmetry in that their mass, charge and spin vectors are all equal and opposite and thus net spin = + 1/2 + -1/2 = 0; charge = +1 + -1 = 0; and, mass spin = 0. Two opposite spin interfering photons will thus form a Higgs Boson, as will two opposite spin gravitons.
The high curvature of ST in the presence of mass/mass-energy is then a relative curvature, borrowing from a fixed, constant pool of Total Energy, ET, thus assuring that the velocity of light remains constant. The Conservation of ST Curvature = the Conservation of Force = the Conservation of the Velocity of Light = the Conservation of Momentum (Linear and Angular) = the Conservation of Energy. Each conservation exists, not as independently conserved parameters, but rather as the interconnectedness of ST from simple to multiple dimensions. The interplay between the rate of Planck pulse unit of h, and the symmetry/asymmetry orientation of its component vectors, defines the net expression of charge, mass, spin and the resultant mobility of the entire ST field, whether of mass or massless energy. The fundamental building block of that interplay is that of the simplest expression of ST, c, the velocity of light, as
λ ν .
There are two polemics that, while differing in the number of dimensions they encompass, and thus required to describe them, nevertheless in actuality, describe the same conservation process at work.
One polemic, the simplest and in only two defining dimensions, is ST. Conservation of ST assures nature's accounting system in which electric charge units are always presented in whole integer units and the speed of light is both a constant and defines the very fundamental building block of nature as displacement per unit of time elapsed. Thus space/time, or
λ /t = λ ν =c ,
relates the two as the photon travels at c as a constant and defines (communicates) the electromagnetic interaction, which is based on the constant integral charge expression (charge also being one of the fundamental conserved properties of nature, as the Conservation of Charge).
At the other polemic, we have energy (Conservation of Energy), which is defined in 10 dimensions (5 spatial + 5 temporal which we designate as SV/TV) when expressed as power, P, or the total amount of energy per unit of time.
More commonly, energy is expressed in absolute terms, without the temporal element, as E (5 spatial + 4 temporal which we designate as SV/TIV).
If you further express the energy as relative to the speed of light,
E/c = p ,
You get the expression of momentum (another fundamentally conserve property, the Conservation of Momentum). Notice that E @ SV/TIV divided by c @ SI/TI = p @ SIV/TIII, again
E/c = SV/TIV ¸ SI/TI = p
p = SIV/TIII
Do notice that S/T parameters follow the rules for multiplication and division of exponentials, i.e. they are added and subtracted, respectively.
The assignment of space and time dimensions is fully explored in the LUFE Matrix …an introduction lies ahead.
The full LUFE Matrix, developed and published by the author in 1985 in L.U.F.E (The Laymans Unified Field Expose¢ ), and again several times thereafter as shown on the list below.
Writings based on visual art, math, music and physics
2001-Part II below, from 2000, was rewritten and recast for online publication as a three part series:
Part 1: "PIN: Pattern in Number...from primes to DNA" A brief primer on visual patterns found in simple, well known number systems leading into the remarkable number magic and esthetic beauty of the DNA double helix (axial view) found in Part 2.GoDNA and continued in Part 3.SCoDNA.
Part 2: "GoDNA: the Geometry of DNA (axial view) revealed"
Which came first? The self replicating underlying geometry or the form itself with its dependence on enzymes, hydrogen bonding and a matching code of bases?
Part 3: "SCoDNA: the Structure and Chemistry of DNA (axial view)"
Extending GoDNA into the realm of structural detail and chemistry forming the composite design.
2000-"The Geometry of Music, Art and Structure…linking science, art and esthetics, Part II" self-published. The original material for this paper was presented (self-published) at the 1997 solo exhibition at the Montage Gallery, Portland, OR under the title "Patterns In Numbers: From Prime Numbers to DNA".
1998-"The Geometry of Music, Art and Structure…linking science, art and esthetics, Part I" presented at the Eighth International Conference on Engineering Computer Graphics and Descriptive Geometry inAustin, TX, sponsored and published by the International Society of Geometry and Graphics. The original material for this was presented at the 1996 solo exhibition at the Montage Gallery, Portland, OR.
1991-"The LUFE Matrix: the distillation of SI units into more fundamentally base units of space and time dimension (Short Title: The Multi-dimensional LUFE Matrix) " with supplement, paper, self-published
1987-"Fundamental Constants of Nature: Mass", paper, self-published
1987-"Fundamental Constants of Nature: Ratios", paper, self-published
1987-"Fundamental Constants of Nature: Charge", paper, self-published
1987-"Fundamental Constants of Nature: The LUFE Matrix", paper, self-published
1986-"Mass Variation in the Electron by Photon Absorption & The Inverse Square Law", paper, self-published
1986-"Expose on Music, Color and the Inverse Square Law", paper, self-published
1985-"L.U.F.E.: The Layman’s Unified Field Expose" (a visual guide), textbook-manuscript, self-published
Again, dividing the conserved property E by another conserved property c, gives a third conserved property, p.
(Also note that the dividing the conserved property p by the conserved property c equals the conserved properties of mass, m, as p/c = m, or as charge, q, as p/c = q.)
Another example is
E/c2 = q
(where q = charge, the Conservation of Charge)
and of course
E/c2 = m
(where m = mass, the Conservation of Mass, as mass-energy).
Mass and charge, both having 3 spatial and 2 temporal dimensions, appear as almost equal properties, but are really different manifestations of the underlying asymmetry of the vector component substructure.
Now, instead of dividing E by c (c of which equals λ ν or λ /t), what if we were to split up c into its components and divide these into E separately as in
E/ν = h (SV/TIV¸ 1/TI=SV/TIII)
or Planck's constant, another fundamental constant of nature. We know that momentum, p, as in
pλ = h (SIV/TIII· SI=SV/TIII)
h/λ = p = h ¸ c/ν (SV/TIII¸ SI=SIV/TIII=SV/TIII ¸ [SI/TI¸ TI])
pc = hν = E (SIV/TIII· SI/TI=SV/TIII· 1/TI=SV/TIV)
p · 2π r = h (SIV/TIII· SI=SV/TIII)
*λ = 2π r (SI=SI), *see side bar 3
pr = h/2π
h = L (SIV/TIII·
the angular momentum, another conserved property, as in the Conservation of Angular Momentum.
Another difference to note from the Standard Theory is the fundamental conceptual difference in the definition of λ which is actually embedded in the basic mathematical descriptions of Einstein, Bohr, Heisenberg, deBroglie and others in their descriptions of the waveform of light and matter energy as the basis of Special Relativity and Quantum Mechanics. See especially Bohr's quantization of the hydrogen atom and deBroglie's description of matter waves.
Next, take E and divide by the spatial element of c and get
F = E/λ (SIV/TIV=SV/TIV¸ SI).
The division of a conserved property, like E, by another conserved property, like c, or by its separately conserved components of λ or ν , generates a conserved property, i.e. the Conservation of Force. Let's explore this further.
(click to enlarge image)
In Figure 5., an overview of the layout of the LUFE Matrix is shown. Spatial dimensions S I, SII, SIII, SIV, and SV… run along the horizontal x-axis as λ 1, λ 2, λ 3, λ 4 and λ 5, respectively. Temporal dimensions 1/TI, 1/TII, 1/T III, 1/TIV and 1/TV…run down the vertical y-axis as ν 1, ν 2, ν 3, ν 4 and ν 5, respectively. The perfectly symmetrical c1, c 2, c3, c4, and c5 occupy 2, 4, 6, 8 and 10 ST dimensions, respectively. They are designated as SI/T I, SII/TII, SIII/TIII, SIV /TIV and SV/TV.
(click to enlarge image)
Figure 6. Interrelationships in the Conservation of Mass, Charge, Momentum, Angular Momentum, Energy, and the Conservation of Force. Note that the fundamental and conserved unit of ST, the velocity of light, c, can reveal each of these conserved physical parameters.
(click to enlarge image)
It is not a great leap to bring together Figures 5. and 6. to form Figure 7. One becomes immediately aware that between the beginning of ST at c and the full 10-dimensional expression of ST as energy/time, or power, at c5, that all physical expressions in between appear as little more than simple transformations of the building blocks of ST energy. As such, given the proper boundaries and constraints when one is considering these in between entities, they must all collectively add up to the conserved ST energy itself. Those which are on the diagonal line of symmetry or situated off-center by a factor of c (or its λ or ν components) are themselves conserved as well.
If the Conservation of Charge, q, equals the total number of negative charge equals the total number of positive charge, that is together they always equal zero, then
qν = I = F/c
then the total coulombs/sec (qν = I)is also conserved. A potential difference is generated whenever positive and negative charges are separated from each other. If the total number of positive charges equals the total number of negative charges, it follows that the total net potential difference must also always be conserved. It follows as night follows day, that there is a Conservation of Force joining the ranks of conserved properties.
As we can see in Figure 7., the symmetrical properties of the velocity of light, c; the potential difference, V; the current, I; force, F; and, power or energy per second, P, are naturally conserved properties.
From these, the asymmetrical entities of mass, m; charge, q; momentum,
p; angular momentum, L (or spin angular momentum, J),…a category which
includes the ultimate quantum unit, h (or
h), Planck's constant; and energy, E, are the traditionally conserved properties
which may in fact owe such conservation to being directly linked to the symmetrically conserved
properties, and to each other, by velocity of light, c, or one of its components,
as space or ν
Why are certain entities conserved? Is it not really conservation of ST dimensions? Energy, E (as Sv/TIV), or in its full power form, P (as Sv/TV), represents the ultimate fully realized fundamental quantum unit of manifest existence. It is higher order dimensions (5 space + 5 time) from which all lower order entities are but derivatives, or subunits of.
Finally, a comment concerning entropy. Entropy, S, occupies the same dimensional
construct (Sv/TIII) as does Planck's constant, h. Entropy, as the measure of
disorder, appears not to be a conserved property. In fact, it is not even an entity but rather
a statistical construct relating the amount of information, as based on the number and ordering
of h units, i.e. their pattern distribution. However, h units, especially when
h, or angular momentum units, are a conserved entity…being the building block
dimensionally of E, as E = hν
. If E represents the maximum ST dimensional order and is always conserved…in that
all accounting must add up to the same amount of SV/TV at the end of the
day…then any deconstruction into subunits must necessarily be composed of dimensionally
entities, i.e. mcc, qcc, pc, and so on. So unlike energy, or its derivative h,
entropy is not conserved, is not directly related by c to the other mainstream conserved
entities, and really is the pattern of order vs. disorder. The second law of thermodynamics can
be stated as the natural flow of heat downhill, but never in reverse, or equivalently, as the
natural flow from order to disorder and the resultant increase in entropy. If we ever could get
our minds around a universe in which the amount of order was conserved we would be that much
closer to understanding the true nature of creation.
A case may be made, therefore, that because conservation of p, L, F, q, and m are dependent on and reflect the all encompassing conservation of E, all parameters which are dimensional subunits of E can, with proper accounting, be shown to be conserved as well. This becomes ever more apparent when one fully realizes that lowest dynamic (contains both space and time dimensions) dimensional parameter is c, the velocity of light. With one unit of space (in this case spatial displacement as the wavelength, λ ) per one unit of time (in this case the temporal displacement as cycles per second, or frequency, ν ), the product of which equals the velocity of light, c, a universal constant and conserved parameter of nature. In other words, fundamentally, spacetime is itself made up of, delivered and expressed by, and ultimately conserved as c, the speed of light.
Thus we have two ends of the spectrum (in this case the LUFE Matrix spectrum) that fundamentally make up, define and exist in perpetuity as conserved, dynamic dimensional parameters of nature…from the one unit of S/T c to the five units of S/T of power, P (E/sec).
Note that dynamic dimension (as space-time, spacetime, ST or space/time, S/T) always incorporate the dynamic between one or more spatial dimensional units and one or more temporal dimensional units. The total dimensions are always the sum of the spatial and temporal dimensions. However, when one refers to the symmetrical, dynamic dimensional building blocks of the LUFE Matrix, we often speak of composite S/T dimensions. One S/T dimension is composed of two dimensions. This may seem obvious, but clarity counts when bouncing between ordinary descriptions of dimensions and dynamic dimensional spacetime dimensions.
The LUFE Matrix consists of four quadrants resulting from the intersection of a x-horizontal axis, representing the spatial dimensions of displacement, SI, SII, S III, SIV, SV,…, or equivalently as λ 1, λ 2, λ 3, λ 4, λ 5,…, respectively, and the y-vertical axis, representing the temporal dimensions. Because most, but not all, of the LUFE Matrix focuses on the lower right quadrant, space/time, S/T, appropriately describes this area of interest. Here the vertical axis of time, being in the quotient, is designated as 1/TI, 1/TII, 1/TIII, 1/T IV, 1/TV,…as per second, or equivalently, as ν 1, ν 2, ν 3, ν 4, ν 5,…, as the frequency in cycles/per second. Thus
c = λ ν = λ /t = S/T
c2 = (λ ν )2 = SII/TII (potential difference, in volts, V)
c3 = (λ ν )3 = SIII/TIII (current, I, in amps, A)
c4 = (λ ν )4 = SIV/TIV (force, F, in Newtons)
c5 = (λ ν )5 = SV/TV (power, P, in watts, W)
TI = 1/ν 1
ν 1 =1/t1 = 1/TI
ν n =1/tn = 1/Tn .
c2 · c3 = c5 = SII/TII · SIII/TIII = SV/TV = volts · amps = watts.
To note is how dynamic dimensions, like working with exponents, are added when multiplied and subtracted when divided. There is no actual addition or subtraction of ST dimension itself. And because the units are dynamic ST dimensions, not SI units, there are no quantities involved. This simplification reveals the interrelationships between the dynamic ST parameters. It speaks to their common dynamic dimensional ST structure and thus reveals the conservation laws in a direct manner.
Symmetrical S/T, that is equal parts of S and T (or λ and ν ), generates the diagonal line of c, c2, c3, c 4, and c5 alluded to earlier (Figure 5.) This really is the highly dynamic corridor of conservation.
Next to it, running parallel, is the slightly asymmetric S/T parameters of magnetic flux;
mass, charge and electric flux; momentum; and energy. Each differing from each other by a factor
of c, and each in turn related back to the symmetrical midline by a factor of either
. And of course, the key to it all is Planck's constant, h (or
h), the defining quantum expression of the energy, as
E = hν
which relates back to the midline parameter of force, F, by a factor of c' (from the upper right quadrant) as
h = Fc' (SV/TIII =SIV/T IV · SITI).
It is conceptually key to note how important the role of asymmetry is in defining the parameters of matter…like charge, mass, momentum and spin (angular momentum), and of course energy, as we can see in the LUFE Matrix. It is a similar asymmetry that structurally gives the vectors of matter, fields and their force moderating bosons, their net expression of such mass, charge and spin, as well as velocity and ultimately their energy signature. At the same time, in other ST entities, the near perfect symmetry of similar vectors results in other particles having zero net expression of mass and charge, while demonstrating only integral (additive vectors of 1/2) expressions of spin (i.e. photons, gluons and gravitons with spins of 1, 1 and 2, respectively). Perfect symmetry being the sole guest of the Higgs boson (massless, chargeless, and spinless in its ideal state, but with the full potential to break its perfect symmetry and form any ST entity, be it matter or field).
(click to enlarge image)
In Figure 8., a simplified LUFE Matrix is laid out with λ and ν axis on the left and with S and 1/T axis on the right.
The physical parameters are laid out in parallel diagonal rows, becoming a little more asymmetrical to space and time dimensions as they become removed from the midline.
Velocity, mass/momentum, charge, and spin become the primary fingerprints, or ID, which fundamentally define the energy signature of any ST matter or particle. These are the same parameters that inform the conservation laws.
All of this is set in the context of the forces of interaction. Conventional wisdom of the Standard Theory accounts for four such forces. Gravity, by far the weakest of the four, is moderated by the graviton, gg , gauge boson while electromagnetism is moderated by the photon, g , gauge boson. The weak force of nuclear decay, or interaction, is moderated by the W and Z gauge bosons, while the strong nuclear force is moderated by a set of color charged gluon gauge bosons. It is becoming abundantly clear that the fifth force is that of the ST field, a.k.a. the Higgs field, which is the ideal, perfect symmetry and multipotential generative field in which all other matter and fields are contained and expressed in. It is moderated by the Higgs boson, H . Ultimately, all force fields are conserved in the same way that all energy is.
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Table II. Comparison of first generation elementary particles with their force carrying gauge and non-gauge bosons (mesons).
In Table II we see that each parameter is the net expression of the individual ST units (lepton or quark fermions or photon-like gauge bosons) which composed it. Each of these is subject to conditions of symmetry or asymmetry within which accounts for that net expression.
The full LUFE Matrix and its Supplement will soon be presented in a digitized form. This will make it very clear and easy to use. The original paper form requires a bit of paper shuffling back and forth to really make easy sense of this powerful new tool. It is also too long to present here.
The full LUFE manuscript (1985) was devoted to the visual presentation of the ideas summarized here. The original textbook form, widely distributed, is over 500 pages and contains hundreds of hand drawn figures. It is undoubtedly a highly stylized interpretation. The following is a very brief synopsis of the pertinent concepts that are germane to this presentation.
Think of it this way. The Higgs boson represents the exchange particle defining the Higgs field. It is massless, chargeless and spinless. The ST units that define these three primary fingerprint ID parameters are capable of existing in either symmetrical or asymmetrical sets. Sets are composed of individual vector components such that a set of two equal but opposite (mass, charge or spin) vectors will result in a net symmetrical expression of zero. If the vectors are instead, lined up additively, then the result is a net asymmetrical expression of mass, charge and/or spin. For example, two up quarks with charge +2/3 combined with 1 down quark with charge -1/3 gives a net asymmetrical expression of charge +1 (as in the proton). Likewise, one up +2/3 plus 2 down -1/3 charges for the neutron result in a net symmetrical charge expression of zero.
Thus the Higgs boson represents that state where the mass, charge and spin vectors (contained within the ST units forming it) are each lined up to point in equal but opposite directions to give a net symmetrical expression of 0, 0, and 0, respectively.
Break the symmetry of the spin vector, changing it from equal and opposite, to additive, and you now have the graviton at mass 0, charge 0 and spin 2. The graviton is actually composed of two spin 1 photons that are constructively added together (i.e. positive interference construction). More on this shortly.
The photon, once again, represents the fundamental dynamic dimensional ST particle that has mass 0, charge 0 and spin 1. It is symmetrical in two vectors (mass and charge), but asymmetrical in spin (which, along with zero mass, accounts for its net lightspeed velocity with each ST pulse).
To note is that all spin on any particle can point in one of two opposite directions and therefore you can have net expressions of spin that are equal and opposite, i.e. left-handed and right-handed. Likewise, i.e. the photon, you can have left- and right-handed spin 1 states (or counter-clockwise and clockwise if you're riding the photon).
So going up the particle ladder, we have photons which have asymmetrical spin 1 vectors which can spin additively in one of two directions, say either clockwise, Ck, or counterclockwise, CCk. Now if two Ck photons constructively interfere, they generate (momentarily) a graviton with spin 2 (Ck). Likewise, two CCk photons can generate a graviton with spin 2 (CCk). However, a Ck photon interfering with a CCk photon will generate a spin 0, mass 0, charge 0 Higgs boson.
Because bosons can, unlike spin 1/2 fermions, exist in the same quantum place and time simultaneously, they can and do readily interfere with each other as they radiate out from their source. In so doing they form a true and perfect interference pattern when they are of the same energy (c=l n , E=hn ), or a less perfect pattern when they encounter photons of different energies. It is these spontaneously generated, yet transient, constructive and destructive interferences which generate the elusive graviton and Higgs boson particles. Because the photons pass through each other, the transient pattern at one ST location is repeatedly regenerated in each ST upon which it encounters another photon. The evolving ST field of photons, gravitons and Higgs bosons is thus self-sustaining and indeed actually does define the ST. But there is more.
All energy is gravitationally active. Our photon, graviton, Higgs boson ST field is both self-sustaining and gravitationally active. The greatest energy is located at the points of constructive interference (which we will arbitrarily designate as spin 1 Ck + spin 1 Ck = spin 2 Ck) and destructive interference (therefore, spin 1 CCk + spin 1 CCk = spin 2 CCk). This then presumes the least active gravitational energy at the nodes (i.e. spin 1 Ck + spin 1 CCk = spin 0) …the state of the Higgs boson.
(Here we have to be careful. The spin vector defines the angular momentum of the particle and appears to be the drive energy for its movement. Therefore, gravitons with spin 2 (either Ck or CCk) will move with velocity of spin 1 photons or perhaps faster at 2c, or maybe they are at c2 and act like a potential difference to their surrounding ST. Similarly, perhaps the spin 0 Higgs boson loses its mobility as the spin vector becomes symmetrical. Does it also lose its gravitationally active and associated energy until it decomposes back into its equal but opposite spin 1 photons? On the other hand, the Higgs boson nodal state may remain a relatively static, but gravitationally active ST focal point with all sorts of consequences.
Going down the ladder, photons also can, through further symmetry breaking, decompose, or de-resonate, into any of the particles which we associate with matter, i.e. leptons like the electron and neutrino or the quarks forming the proton, neutron, and meson, to name a few. In each case, whether generating spin 1/2 series fermions or spin 1 series bosons, there is further breakage of the symmetry allowing for different vector sets of mass, charge and spin to transform into the characteristic matter particles.
The photon acts as a gateway particle between matter and fields. The velocity of light, c, is always, in its net expression, constant and is by its nature of defining the fundamental dynamic dimensional ST unit, the conservator of ST itself. Its equal but opposite set of charge vectors guarantees that any charged particles created from its symmetry break will always have a net expression of either 0 or some interval of 1. The photon and the velocity of light are the chief accountants of the universe.
The photon may also generate matter when interfering with the right number of other photons, gravitons and or Higgs bosons. With appropriate energy signatures to allow for a symmetry break from the ST field to ST matter.
If St fields can become matter, can matter phase back into fields? Yes of course, as has already been known for close to a century now. Matter plus antimatter equals photons. But how can matter, plain matter, generate ST fields without annihilating itself in the process? Generating gravitational active ST fields as communicated with the graviton? Let's see how as we summarize all this next.
In Part I, the Conservation of Force was called upon, as it follows naturally from the conservation of energy, momentum, angular momentum, and ultimately, from the conservation of ST itself, to elucidate the expansion of the universe. The dark, negative energy of the vacuum of space (Cosmological Constant) invoked by others to explain a simple geodynamic balance of ST forces. While the search for the mysterious form of dark matter gravitation has literally obscured the other end of that balance. We have instead invoked a fresh approach that connects the dark matter with the inverse of the dark energy (or vice versa).
In Part II, the LUFE Matrix (a brief introduction) was called upon to further elaborate on the nature of spacetime, matter and fields, and the dynamic dimensional ST parameters that it defines. Here we more clearly see the interrelationships between the parameters, especially the key role that symmetry and/or asymmetry plays in the net expression of certain vector-defined ST parameters such as mass, charge and spin. Here one see how the ST field, as defined by the massless, chargeless photons, gravitons and Higgs bosons which make it, becomes the multidimensional fluid out of which condensates of matter are formed. Some of that matter condensate remains as bosons, and as such can co-exist with other bosons in the same state, as well as acting as communication/exchange messengers between the fermions and other bosons. Most of the other known matter condensate is indeed the leptons and quarks. The quarks make up the fermions like the proton and neutron, as well as the lesser bosons like the pion and kaon mesons.
By itself, all such matter condensate only accounts for some 4% of the gravitational influence that surrounds any such matter congregation. Clearly, there is a need to account for the presence of the other 96% gravitational activity. Likewise, in the furthest and oldest reaches of the universe, we find what appears to be the opposite phenomenon…accelerated expansion of ST itself bereft of a causative agent, acting as though space is itself pushing things, matter, away…in effect a negative force, or energy, acting like some form of anti-gravity.
Both phenomena can be explained with a single geodynamic view of ST as the primary structure of the universe that is manifest in real time and in real space. ST is the interface between the vacuum or subspace universe, that which lies below the Planck Event Horizon, and real space and time, that as we know as our universe. As the primary structure between the two universes it plays an absolutely critical and defining role as to the disposition, expression, fate and ultimate conservation of all those elements we can experience in our universe. ST is the gatekeeper of our universe. The matter and fields that are contained within the ST fall short of accounting for our entire universe precisely because they are but a part, and a relatively small part at that, of our entire universe. The true conservation laws of lightspeed, charge, mass, momentum, spin angular momentum, energy that we are so familiar with, are really just parts, subsets, of the overall true conservation...that of the conservation of ST. Conservation of ST leads to and explains all the other conservation laws, and, with the help of the LUFE Matrix, helps us see that there are a number of other conservation laws embedded therein, including the conservation of force. Newton has always had it right when he states that for every action there is an equal and opposite reaction. This is more than a statement about the conservation of momentum and energy. Momentum per second equals force. Energy per distance unit equals force. Power divided by c equals force. The conservation of energy, which is parsed into units of momentum to prove the conservation of momentum, can also be parsed into units of force to reveal its conservation. It is because energy (especially in the form of energy/sec or power) is at the top of the ST dynamic dimensions heap (at 5 units, or 10 conventional space-time units of 5 units of S + 5 units of T) that all other parameters below are indeed conserved. If you skew the matrix, you skew the energy and all the parameters that support it. Yet you cannot screw the matrix. Let's see why.
ST pulses. It pulses into and out of our "ordinary reality". From the vacuum of space, that which is really the continuum on the other side of the Planck Event Horizon, ST as matter and ST as field pulse into and out of existence. Pulsing into existence, ST must always meet certain stringent accounting requirements (which we have discovered to be the conservation laws).
All ST units, matter and field alike, must strictly account to these requirements. This is accomplished by building the ST pulses as sets of ST unit pulses which have simple vector expression polemics (i.e. on-off, clockwise-counterclockwise, up-down, in-out, yin-yang, etc.) built into them so that equal and opposite vector symmetries cancel out and vector asymmetries add up to net expressions. (Quarks, which do not have a net expression by themselves…asymptotic freedom…as they never exist alone, have charge vectors of ± 1/3 and ± 2/3, in a relationship in charge of 1:2. Net expression of ST matter units made of three quarks, as in the proton and neutron baryons, and two quarks, as in the form of a quark plus an anti-quark in the mesons, still have a net composite charge expression limited to whole integers, 0, 1, -1,….)
The vector expression itself is perhaps local to the ST pulse or perhaps it is absolute to the vacuum continuum. Nevertheless, it is modular and functions as a simple pole-anti-pole switch. Together a coherent ST pulse is formed whose energy is a constant and reproducible primary signature of that ST unit. The rest-mass energy for any matter ST unit and the constancy of c for any massless, field ST unit is without variance.
Pulsing from nothing to its full ST pulse expression and back, ST units pulse or vibrate alive in many ways similar to that described in string theory. It is entirely possible that during the pulse generation individual vector components are actually formed at velocities greater than c, but the net expression for c will always be constant for the ST unit itself so formed.
At the full form of the ST pulse all its defining mass, charge and spin parameters are fully realized. Thereafter, part of the ST pulse energy collapses back onto itself and is reabsorbed into the singularity/vacuum port from whence it came, readying itself for the next pulse generation. A small part of that energy is given off as resonant matter waves…what are really boson ST field waves.
It is these critically resonant-matter boson ST waves, mimicking the energy footprint of the matter ST pulse unit which formed them, which now continue outward into the mix of other ST pulses everywhere in the universe. Naturally their density is highest next to their source and so are the odds that they would constructively or deconstructively interfere with their " siblings" to form gravitons nearby, decreasing as the inverse square law dictates. These boson ST pulse waves act in every way like photons, the great gatekeepers of the matter-field ST. They have energy and become even more gravitationally active as they combine to become gravitons and Higgs bosons. Eventually this energy becomes reabsorbed back into the continuum, perhaps through the Higgs boson itself. As a ST nodal structure of perfect symmetry (0 mass, 0 charge, 0 spin), the Higgs boson may indeed by the ultimate gateway and gatekeeper between the vacuum continuum (below the Planck Event Horizon) and ST. This then is the light. The 96% missing, dark matter is really the ST field of photons (both ordinary and resonate-matter), gravitons and Higgs bosons.
(click to enlarge image)
In Figure 9., elementary particles and fundamental forces are laid out in a composite ST pulse unit(s) based on the difference of the spin 1/2, 3/2 fermions, which do obey the Pauli Exclusion Principle, and, the spin 0, 1, 2 bosons, which do not.
Bursting from the invisible Planck Event Horizon below, into the ST matrix of the Higgs Boson Field and outward to realize their full ST expression are the fermions and bosons. The fermions form the matter. The bosons, most of which are massless and travel at c (excepting the massive W/Z gauge bosons of the weak force and the mesons, like π that facilitate nucleon transformations), are the main gauge force carrying particle of the strong, electromagnetic (EM) and gravitational forces. The Conservation of Force is mediated by the Higgs Boson ST Field, a force…the fifth force…that is carried by, and thus defined by, the Higgs Boson.
(click to enlarge image)
In Figure 10., the fermion field has been rearranged. It now it sandwiched in between the gauge and Higgs Boson Fields. It is organized now from spin 0 to spin 2.
Spin, which may principally account for net mobility of any ST particle, is shown first at Spin 0, the Higgs Boson emerging from the black hole depths at the Planck Event Horizon. The spin 1/2 vectors forming any boson are cancelled out in their symmetrical arrangement in the Higgs Boson. It most likely does not move. Spin 1/2 (or 3/2 quark composites of three spin 1/2 vectors lined up to point in the same direction) fermions gain increasing mobility as their mass decreases in the third to first generations. Remember, there is no net charge expression without accompanying mass expression, while there can be the opposite, a massive ST unit with zero net charge. Asymmetry of the charge and spin vectors is a requirement for net expression of these parameters. The mass forming vector is not really a separate structural vector in the same sense as the charge and spin vectors. Rather it is manifested as the result of the particular combination(s) of the other two and in the end acts just like a vector in the sense that if those combinations produce a composite asymmetry mass is expressed (like a localized knot in the ST field). When they produce a composite symmetry, like in the Higgs, gluon, photon and graviton bosons, no mass is expressed and whatever asymmetry is present in the spin vectors (like the spin 1 gluons and photons, and the spin 2 gravitons), that spin energy now translates into 100% mobility with each ST pulse. The Higgs Boson, with spin 0 and charge 0, is assigned a mass and mobility of 0 here to be fully consistent with this model. Its perfect symmetry has no net expression mass, charge or spin. Nevertheless it has mass-energy resulting from the equal and opposite individual charge, spin (and mass) vectors. It spins in place acting as the multipotential transformative gateway that all other ST units are derived, and measured, from and return to. Through interference, photons can become gravitons or Higgs Bosons. Interference of gravitons can also regenerate Higgs. The accounting system for the conservation laws has come full circle.
The irony is that the condensate of matter is light and we see it, while the fluid of which it is composed is dark and invisible. While the curvature of ST inwards toward its mass-energy seen should not exactly point to curvature outward where inflation began is the light.For those who are in doubt, yet consider the Conservation of Energy to be inviolable, consider this:
If energy is conserved now, it must have been conserved in the past and in the future as well (that is if the notions of a past, present and future are endeared likewise).
All the energy now is the same, in amount, as all the energy at the Big Bang, both before and after inflation.
Energy disposition, that is its spatial dispersement, must likewise account for the total sum.
If the energy density fluctuates in one area, it must also fluctuate in another area or areas in an opposite manner.
If the energy density rises in one area or areas, then it must fall in another area or areas.
Force is the moderator, or interface resolution, from one energy (be it type, density or location in space or time) to another.
Force is the energy per spatial displacement.
Planck's constant, as a unit of action, is the energy per temporal displacement. It is conserved (as a constant) and as angular momentum.
If energy is conserved, then force must be conserved.
The Conservation of Force serves to uphold the Conservation of Energy.
The Conservation of Energy serves to uphold the Conservation of SpaceTime, of which it is composed of.
The Conservation of SpaceTime is built upon the velocity of light constant, c.
If the spacetime density fluctuates in one area, it must also fluctuate in another area or areas in an opposite manner.
If the spacetime density (gravitational curvature) rises in one area or areas, then it must fall in another area or areas.
If the elevated spacetime density is the Dark Matter and the depleted spacetime density is the Dark Energy then,Dark Matter = Dark Energy (the inverse of).
This paper and all its contents Copyright© 2003, Reginald Brooks. All rights reserved. Permission is hereby granted for single copies to be made for personal, non-commercial use for students and teachers of schools, colleges and universities provided that: either the entire paper, including figures and tables, is kept intact; or, any extracts of the text, or figures or tables (in part or whole), be properly and visibly cited as to authorship and source.
A new graphical supplement to "Dark Matter = Dark Energy (the inverse of): The Conservation of Spacetime by The Conservation of Force" 11/28/04
A short, update supplement to "Dark Matter = Dark Energy (the inverse of): The Conservation of Spacetime by The Conservation of Force" and "The History of the Universe in Scalar Graphics." 09-05-07
Page 5a- Dark-Dark-Light: Dark Matter = Dark Energy
Page 5b- The History of the Universe in Scalar Graphics
Page 5c- The History of the Universe_update: The Big Void
Page 6a- Geometry- Layout
Page 6b- Geometry- Space Or Time Area (SOTA)
Page 6c- Geometry- Space-Time Interactional Dimensions(STID)
Page 6d- Distillation of SI units into ST dimensions
Page 6e- Distillation of SI quantities into ST dimensions
Page 7- The LUFE Matrix Supplement: Examples and Proofs: Introduction-Layout & Rules
Page 7c- The LUFE Matrix Supplement: References
Page 8a- The LUFE Matrix: Infinite Dimensions
Page 9- The LUFE Matrix:E=mc2
Page 10- Quantum Gravity ..by the book
Page 11-Conservation of SpaceTime
Page 12- LUFE: The Layman's Unified Field Expose`