Anthony Nigel Dean

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Universal Field TheoryTheory of everything, unifying all forces, matter & spacetime.

Assumptions

Einstein Notation & Spacetime

We use lower indices for covectors (rows) & upper indices for contravariant vectors (columns) as per Einstein index notation. Einstein index notation is fully explained on Wikipedia - Einstein Notation page.

  1. Inner Product:

    \displaystyle \begin{aligned} \langle A | B \rangle &= \begin{bmatrix} a & b \end{bmatrix} \begin{bmatrix} c \\ d \end{bmatrix} = ac + bd \\ &= A \cdot B = \overline{B \cdot A} \\ &= {A}^\dagger{B} = {B}^\dagger{A} \\ &= A_{\mu} B^{\nu} = B_{\mu} A^{\nu} \end{aligned}
  2. Outer Product:

    \displaystyle \begin{aligned} | A \rangle \langle B | &= \begin{bmatrix} a \\ b \end{bmatrix} \begin{bmatrix} c & d \end{bmatrix} = \begin{bmatrix} ac & ad \\ bc & bd \end{bmatrix} \\ &= A \otimes B = -B \otimes A \\ &= {A}{B}^\dagger = -{B}{A}^\dagger \\ &= A^{\mu} B_{\nu} = -B^{\mu} A_{\nu} \end{aligned}
  3. Hadamard Product:

    \displaystyle \begin{aligned} | A \rangle | B \rangle &= \begin{bmatrix} a \\ b \end{bmatrix} \begin{bmatrix} c \\ d \end{bmatrix} = \begin{bmatrix} ac \\ bd \end{bmatrix} \\ &= A^{\mu} B^{\nu} = B^{\mu} A^{\nu} \end{aligned}


    \displaystyle \begin{aligned} \langle A | \langle B | &= \begin{bmatrix} a & b \end{bmatrix} \begin{bmatrix} c & d \end{bmatrix} = \begin{bmatrix} ac & bd \end{bmatrix} \\ &= A_{\mu} B_{\nu} = B_{\mu} A_{\nu} \end{aligned}
  1. Spacelike: dimensions are mediated by virtual bosons (or mesons).
  2. Timelike: dimensions are mediated by real bosons (or mesons), aka known force carriers.

This gives us spacetime in a wavelike nature, & spacetime is defined as the middle point between two opposing forms of energy, so a depression in spacetime will be created by a sink of enegy on one side, & a source on the other. The difference between the two being what defines the spacetime curvature.

The most important part of this is time is the dual of space, i.e T = S, so if space can be complex, so must time.

Space & Time Dimension Differences

Time must always be orthogonal to space, represented by indices & conjugate state. This further defines energy to always be orthogonal to momentum, & gravity to be the cross product of momentum and energy (orthogonal to both space and time & momentum and energy). As we are taking the cross product between a real and imaginary values, the result is also imaginary, ergo gravity is a timelike property.

  1. Tμ is to Sν: time is a column to space row.
  2. Tμ is to Sν: time is a row to space column.
  1. This is to differenciate time & space dimensions, while both are fundamentally the same thing.
  2. The conjugate difference is to show difference in direction, space folds time unfolds.
  3. The additional factor of ± ℑ & ℜ defines the following:

    1. + ℜ: spacelike & defines positive event size (real mass).
    2. − ℜ: spacelike & defines negative event size (imaginary mass).
    3. + ℑ: timelike & defines spin outward from the event (aka fermions & photons).
    4. − ℑ: timelike & defines spin inward from the event (aka quarks & gluons).

Without this, the tensor would make no differenciation between time & space components or various products of the two. Now we have two forms of space, the + ℜ is Euclidean space we know, − ℜ is now what represents vacuum energy. With time we have + ℑ for photons, & − ℑ for gluons, causality is now defined by the difference between the two, e.g. time moves forward because there is more energy stored in photons than gluons overall. We see gravity as there is more energy locally in gluons than photons. This gives us the effect that light expands space between objects, but clumps objects locally, it also gives photons much greater range than gluons.

Calculated Tensor

Tensor Table

4D
7D
9D
17D
35D
+ ℑ
− ℜ
− ℑ
+ ℜ
+ ℑ
− ℜ
− ℑ
Dark Matter
Matter
Dark Energy

Factor Table

4D
7D
9D
17D
35D
+ ℑ
− ℜ
− ℑ
+ ℜ
+ ℑ
− ℜ
− ℑ
Dark Matter
Matter
Dark Energy

Realisations

Real Energy (Momentum, Time Component)

Defines the energy of the system (distance from event horizon), when you have an outer product of time (E.g. TμTν). In 3D space, the event horizon is the 2D surface area that defines the boundry between fermions and quarks.

\displaystyle \hat{E} = i \hbar c \gamma^{0} \partial_{0}


  1. Blue: Electromagnetic Force (Photon, γ).
    \displaystyle \gamma^{j} \partial_{j} - \gamma^{0} \partial_{0} = 0
  2. Red: Strong Force (Gluon, g).
    \displaystyle \gamma^{j} \partial_{j} + \gamma^{0} \partial_{0} = 0
  3. Purple: Weak Force (W±, Z0).
  1. Weak force can break CP symmetry due to being made of two seperate antisymmetric blocks.
  2. Think of weak bosons being closer to proton (W±, uud) or neutron (Z0, ddu) than a photon or gluon.
  3. Electromagnetic & strong forces can't break CP symmetry as they exist in singular symmetric blocks.
  4. There is no direct connection between the electromagnetic & strong forces (except via weak force).
  5. Reason for outer product is due to the contravector nature of time to covector space.
  6. Think of this energy as pulling away from an event horizon.
  7. The greater this energy, the less chance of event interaction, aka faster target is harder to hit.
  8. For positive real mass, this must be the smaller of the two energy types.

Think of this energy as defining the margin of error, the greater the margin of error, the less chance you will interact with the particle. The most likely position of the particle, is now defined by a poisson distribution curve with energy level being defined by the greatest probability. The weak force, having mass should be thought of as a way to increase or decrease the event size.

Virtual Energy (Momentum, Space Component)

Defines the momentum of the system (size of event horizon), when you have an inner product of space (E.g. SμSν). In 3D space, the event horizon is the 2D surface area that defines the boundry between fermions and quarks.

\displaystyle i c \hat{p} = \hbar c \gamma^j \partial_j


  1. Orange: Euclidean Space (Virtual Photon γ).
    \displaystyle \gamma^{j} \partial_{j} - \gamma^{0} \partial_{0} = 0
  2. Yellow: Higgs Space (Virtual Gluon g).
    \displaystyle \gamma^{j} \partial_{j} + \gamma^{0} \partial_{0} = 0
  3. Grey: Vacuum Space (Virtual W±, Z0).
  1. Vacuum space can break CP symmetry due to being made of two seperate antisymmetric blocks.
  2. Think of vacuum space being closer to proton (W±, uud) or neutron (Z0, ddu) than a photon or gluon.
  3. Higgs & Euclidean Spaces can't break CP symmetry as they exist in singular symmetric blocks.
  4. There is no direct connection between the Higgs & Euclidean Spaces (except via Vacuum Space).
  5. Reason for inner product is due to the covector nature of space to contravector time.
  6. Think of this as defining the size of the event horizon.
  7. The greater this energy, the more likely of event interaction, aka bigger target is easier to hit.
  8. For positive real mass, this must be the larger of the two energy types.

Think of this energy as defining the event size, so the larger this is the more chance you have of interacting with the particle. Furthermore the center of mass, and point source of the particle is defined as the center of this energy. Similar to the weak force, vacuum space is a way to transfer mass, so also a way to increase or decrease the size of an event.

Charge (Momentum, Spacetime Component)

Defines location & direction of charge, when you have a hadamard product of spacetime (E.g. SμTν, TμSν).

  1. Surrounded by two timelike (real energy) fields (electromagnetic + weak, or weak + strong).
  2. Surrounded by two spacelike (virtual energy) fields (euclidean + vacuum, or higgs + vacuum).
  3. Because of the hadamard product, charge must always be either a covector or contravariant vector.

As charges are a combination of real & virtual energies above, it can either have specific momentum (space) & unknown energy (time) giving particle-like as you are focusing on the event size and its respective center, or known energy (time) & unknown momentum (space) giving wave-like, as you would be focusing on the error margin so the location becomes fuzzy. This is purely changing how you view the charge, not it changing its properties. This is the basis for Heisenberg's uncertainty principle & wave, particle duality. E.g. you either look at the spatial portion as real, or the temporal portion, you can't view both parts as real at the same time.

Boson & Meson Mediated Universes

Spacetime can either be boson mediated (spin 1), or meson mediated (2 x spin ½)

  1. If you zoom the tensor diagrams to 17D or above, two universes that are bosonic & two mesonic.
  2. The two parallel boson universes are for matter and antimatter, and are mirror images of each other.
  3. The Higgs field is now the unitary spacelike field that connects all four universe subtypes.
  4. Dark matter and energy would be similar tensors, but rotated 180o either into or out of the page (spin 2 seperation). Again the ± ℑ would come into play here, + ℑ would be the Tachyon (similar to Photon), − ℑ would be the Graviton (similar to Gluon). Likewise there would also be W± and Z0 like bosons that would mediate mass and event size.
  5. The two parallel meson universes link between matter and antimatter universes.
  6. This tensor is based on waveform that is stretching along the x/y axis, 1, 3, 5, etc. Based on water drop into larger body of water, with central peek (Higgs space) as the highest, but also smallest width (1D), then peaks getting smaller but also further spread out.
  7. We should also have waveform stretching along the z axis, but to keep calculation simple it is kept constant.

Types Of Matter

Mass & Energy Equivalence

The 45o light blue lines now shows massless bosons (photon & gluon), specifically how they differ with temporal gradients. Similarly 45o in or out the page shows accelerated bosons (tachyon and graviton) spacetime cross product.

Klein-Gordon Equation

\displaystyle \nabla ^2 \psi - \frac{1}{c^2} \frac{\partial^2}{\partial t^2} \psi = (\frac{mc}{\hbar})^2 \psi

Einstein Equation

\displaystyle (i \hat{p} c)^2 + \hat{E}^2 = (mc^2)^2

Dirac Equation

\displaystyle (i \hbar c \gamma^{\mu} \partial_{\mu} - mc^2) \psi = 0

Important thing to note is that curvature is now defined as the exterior product of energy & momentum, mass is now the radius of the 3D sphere. However as it is also imaginary, it will appear to be similar to energy, so timelike in nature. This is why we can make direct comparison between the photon & gluon to the tachyon & graviton. Likewise we will have an equivilent set of W and Z bosons to manipulate the momentum event size & mass.

This way we can define momentum, energy & curvature as a 1D string, for which mass is the radius. Thus unifying special & general relativity, with three planes. First defining the relationship between momentum & gravity, second between gravity & energy, third being the relationship between energy & momentum. It also shows how timelike quarks can communicate with spacelike fermions, the tunnel like events as described previously.

Tensor Overview

Showing how each universe must be complete by having two mediated by bosons (which represent matter and antimatter, ± ℑ Time), and two mediated by mesons (which also represent matter and antimatter, but ± ℜ Time).

Now you can see the bosonic universes are spacelike, mesonic universes are timelike. Also the RL meson universe is strongly attractive to spacelike quarks and anti-fermions, so could be a good candidate for the reason quarks are very strongly bound in the nucleus, whilst also the mesonic timelike portions self repel (as fermion and anti-quark have same charge). However the LR timelike area acts to hold the fermions and anti-quarks steady making them losely bound.

This makes the timelike mesonic universes repulsive (expanding time, like charges repel), spacelike bosonic universes attractive (compressing space, opposite charges attract). The combination of the two, makes the nucleus heavier than the electrons in our universe, but positrons heavier than anti-quarks in the mirror antimatter bosonic universe.

Now imagine if you can matter acting perpendicular to the plane shown in this image, it can curl to the left, right, top or bottom. If it curls to the bottom it will increase the energy of quarks, if it curls to the top it will increase the energy of electrons, to the left it will increase the momentum of antimatter and to the right, increase the momentum of matter. This is how dark matter and dark energy effect spacetime, while also not being part of of the special relativistic plane. However as matter has both energy and momentum, it also can curve spacetime, defined as the product of energy and momentum. As light has no mass, its energy and momentum are equal and aligned, so the cross product for light (and the gluon) is zero.

Commecting Special & General Relativity

Horizontal plane is special relativistic universe seperating spacelike & timelike events with photon & gluon light cone. Vertical plane is general relativistic universe seperating events with tachyon & graviton light cone instead.

I call the vertical lines as tunnel events as they are part spacelike and part timelike. This best describes spooky action at a distance entanglement. When two particles are far enough apart that they are considered spacelike events, but still act as if they are causaly connected. This comes about because the time parameters of the tensor are outer products, and as such is not just a real value.

This allows communication between two particles in what appears to be faster than light, however it is a result of the wavelike nature of two events being in sync with each other. The paradox is resolved as entanglement is possible between two spacelike particles, by using a timelike quark as intermediary. Thus not breaking the rules of special relativity.

Connecting Dark Matter & Energy

Showing each special relativistic domain (matter, dark matter, dark energy; shown as double rotations about Z axis above).

Each special relativistic domain is seperated by spin 2, aka matter, dark matter and dark energy only have general relativistic connectivity & are barred from any special relativistic connectivity, so they can never interacte with each other except via gravity & causality.

Causality always moves forward, as we have more dark energy than matter & dark matter (spacetime is curved slightly towards single colour time defined by electromagnetic energy). Dark matter has the effect of holding onto the nucleus more than electrons, which is why the nucleus holds more mass & is harder to seperate protons & neutrons from the nucleus than and electron from its orbit.

Matter & Probability Density

Mass is the net probability density of interacting with something else. Calulated by determining the event size from spatial momentum, minus temporal error margin. For a particle to be spacelike it must have a greater spatial event radius than temporal error margin (e.g. you can locate the particle spatially, but not temporally). A particle is timelike if the error margin is greater than the spatial radius (e.g. you can locate the particle temporally, but not spatially).

  1. Real Timelike: s2 < 0, events are causally spin 1 (momentum) connected.
  2. Imaginary Timelike: s2 < 0, events are causally spin 2 (acceleration) connected.
  3. Real Spacelike: s2 > 0, events are causally spin 1 (momentum) disconnected.
  4. Imaginary Spacelike: s2 > 0, events are causally spin 2 (acceleration) disconnected.
  5. Lightlike: s2 = 0, events interact via light.
  1. Dark matter is an imaginary spacelike event, it brings matter towards causal connection.
  2. Dark energy is an imaginary timelike event, it seperates matter towards causal disconnection.
  3. Dark matter & energy have negative probability of interacting via special relativity.
  4. Dark energy increases tachyonic acceleration, increases entropy, causes fission & expansion of spacetime.
  5. Dark matter increases gravitonic acceleration, causes fusion & compresses mass into galaxies & stars.

Normal Matter

This is when the momentum SμSμ is greater than energy TμTμ.

  1. Electrons: Between euclidean & vacuum Space, electromagnetic & weak forces, only has up/down spin.
  2. Quarks: Between euclidean & vacuum space, strong & weak forces, has colour and up/down spin.
  1. Positive mass refers to positive probability of interaction (attractive).
  2. Imaginary mass refers to negative probability of interaction (repulsive).
  3. Can never go faster than light, or slower than absolute zero temperature.

Dark Matter

This is energy that is imaginary spacelike, it doesn't exist in the same spacetime as matter.

  1. Think of it as being beyond spacetime, so normal matter is beyond its reach to interact with it.
  2. It increases spatial energy and decreases temporal energy which attracts matter.
  3. This is what stabilizes smaller particles and gives us fusion.
  4. In the tensor diagram above, dark matter is accelerationally rotated from matter by 180o to the left.

Dark Energy

This is energy that is imaginary timelike, it doesn't exist in the same spacetime as matter.

  1. Think of it as being beyond spacetime, so normal matter is beyond its reach to interact with.
  2. It increases temporal energy and decreases spatial energy which repels matter.
  3. This is what puts an upper limit to mass and gives us fission & positive entropy.
  4. In the tensor diagram above, dark energy is accelerationally rotated from matter by 180o to the right.

Conclusions

Scale Factors

From the factors table above.

  1. ± 1: SμSμ and TμTμ or diagonal of matrix (rest mass, spin 0, overal size of event).
  2. ± 1: Everything else (momentum, spin 1), mediated by boson force carriers.
  3. − i: Curl inwards (contracts) against time (gluons, gravitons).
  4. + i: Curl outwards (expands) with time (photons, tachyons).

Flow Of Time / Causality

From the comparison of different matter and energy types.

  1. Everything moves forward as we have more dark energy than dark matter & mass, i.e. expansion of spacetime is greater than compression.
  2. Causality, positive entropy & expanding spacetime are all equivilent, resulting from overal curvature.