Will Brown
January 20, 2025
The Theory of Causal Relativity is a theory interpreted from Causal Relativity Equations a series of equation transformations for Classical Mechanics, Special Relativity, Thermodynamics, Electrodynamics and Quantum Mechanics.
- Space and time are absolute and separate.
- Gravity acts instantaneously.
- Light speed varies with observers.
- Physics laws are consistent across inertial frames.
- Light speed is constant.
- Space and time form a 4D spacetime.
- Laws of physics are the same independent of time.
- Frames are relative to all other frames.
- Frames are relative to themselves.
The Causal Relativity framework is developed on the theory that all frames are relative, not just to other frames but also to themselves, independent of time.
Starting with an n=1 Universe:
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Traditional Relativistic Assumption: In an n=1 universe, the assumption is that a single mass is at rest with no external forces acting upon it, hence at rest relative to all inertial frames, including its own. The mass is considered to flow through a temporal dimension but does not move in space relative to itself in this scenario.
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Causal Geometry's Challenge: Causal Geometry challenges this by proposing that no mass is ever truly at rest or inertial relative to itself. Here's how this plays out:
Space Curvature by Mass:
- Assumption: The mass curves space around itself, creating a gravitational field that extends indefinitely. This curvature is relative to the location of the mass, stronger near the mass and diminishing with distance.
Propagation of Curvature:
- Assumption: This curvature's influence propagates outward at the speed of light, establishing an intrinsic gravitational coordinate system where the mass is the origin.
Quantum Mechanics and Energy Emission:
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Assumption: Within the mass, relative to the space curvature it creates, quantum particles are never truly at rest due to quantum fluctuations and the Heisenberg Uncertainty Principle. These dynamics lead to:
- Photon Emission: Photons, carrying energy and information about the mass's quantum state, are emitted. These photons propagate through the curved space at light speed, their paths influenced by the mass's gravitational field.
Photons as Information Carriers:
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Assumption: Even without another mass to interact with, these photons carry information about the emitting mass. Their properties reflect the gravitational influence:
- Coordinate in Space: Each photon acts as a spatial coordinate relative to the mass, providing information about its state as it travels further into space.
Energy Loss and Mass Change:
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Assumption: Photon emission leads to energy loss, potentially altering:
- Mass Density: A decrease in mass density over time if energy loss is significant.
- Size: Changes in size, particularly for star-like masses where energy affects structure.
Feedback on Space Curvature:
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Assumption: As the mass's energy changes, so does its gravitational curvature:
- Shifting Curvature: The curvature adjusts, reflecting the mass's new state, continuously influencing space relative to its position.
Intrinsic Coordinate System:
- Assumption: The mass and its photon emissions create an intrinsic coordinate system, mapping the mass's gravitational influence dynamically.
Conclusion:
- Mass, through its quantum particles, is in continuous motion in space relative to itself, even in an n=1 universe. This scenario suggests a self-referential system where gravity and light define mass's coordinates.
The equations are derived on the principle that all physics can be described in a time-independent manner, maintaining consistency with traditional equations but reinterpreting them spatially.
| Causal Geometry | Phenomenon | Theory | Original Equations | Causal Relativity Equation | Derivation Paper |
|---|---|---|---|---|---|
| Mass | Newton's Gravitational Force | Classical Mechanics | ( F = \frac{Gm_1 m_2}{r^2} ) | ( K = \frac{GM}{r^2} ) | Newton's Gravitational Force Derivation |
| Mass | Gravitational Curvature (GR) | General Relativity | ( R_{\mu\nu} - \frac{1}{2}g_{\mu\nu}R = \frac{8 \pi G}{c^4}T_{\mu\nu} ) | ( K = \frac{GM}{r^2} ) | Gravitational Curvature in General Relativity Derivation |
| Causal Geometry | Phenomenon | Theory | Original Equations | Causal Relativity Equation | Derivation Paper |
|---|---|---|---|---|---|
| Light | Electromagnetic Wave Propagation | Classical Electromagnetism | ∇×E = -∂B/∂t | ∇×E = -κ ∇⋅B | Electromagnetic Wave Propagation Derivation |
| Light | Electromagnetic Induction | Classical Electromagnetism | ∇×B = μ₀J + μ₀ϵ₀ ∂E/∂t | ∇×B = μ₀J + μ₀ϵ₀κ ∇⋅E | Electromagnetic Induction Derivation |
| Light | Light Wave Equation in Vacuum | Classical Electromagnetism | ∇²E - (1/c²) ∂²E/∂t² = 0 | (1 - κ²) ∇²E = 0 | Light Wave Equation in Vacuum Derivation |
| Causal Geometry | Phenomenon | Theory | Original Equations | Causal Relativity Equation | Derivation Paper |
|---|---|---|---|---|---|
| Gravity | Spacetime Curvature | General Relativity | ds² = -c² dt² + dx² + dy² + dz² | ds² = gᵢⱼ dxⁱ dxʲ | Newton's Gravitational Force Derivation |
| Causal Geometry | Phenomenon | Theory | Original Equations | Causal Relativity Equation | Derivation Paper |
|---|---|---|---|---|---|
| Light + Gravity | Length Contraction | Special Relativity | L = L₀ √(1 - v²/c²) | L' = L √(1 - v²/c²) | Length Contraction Derivation |
| Light + Gravity | Time Dilation | Special Relativity | Δt' = γ Δt | ΔL' = ΔL √(1 - v²/c²) | Time Dilation Derivation |
| Light + Gravity | Stretching (Cosmological) | General Relativity | ( ds^2 = -c^2 dt^2 + a(t)^2 \left( \frac{dr^2}{1 - k r^2} + r^2 (d\theta^2 + \sin^2\theta d\phi^2) \right) ) | ( ds^2 = g_{ij} dx^i dx^j ) where ( g_{ij} ) is derived from ( a(r)^2 \left( \frac{dr^2}{1 - k r^2} + r^2 (d\theta^2 + \sin^2\theta d\phi^2) \right) ) | Cosmological Stretching Derivation |
| Light + Gravity | Relativity of Simultaneity | Special Relativity | x' = γ (x - vΔx / c²) | ( C(r) = \frac{E}{4 \pi r^2} ) where ( C_A(r) = C_B(r) ) defines simultaneity | Relativity of Simultaneity Derivation |
| Light + Gravity | Gravitational Time Dilation | General Relativity | dτ = √(1 - 2GM/c²r) , dt | ΔL' = ΔL √(1 - 2GM/c²r) | [Gravitational Time Dilation Derivation](link needed) |
| Light + Gravity | Gravitational Redshift | General Relativity | z = (1 / √(1 - 2GM/c²r)) - 1 | ΔL' = ΔL (1 / √(1 - 2GM/c²r)) | Gravitational Redshift Derivation |
| Causal Geometry | Phenomenon | Theory | Original Equations | Causal Relativity Equation | Derivation Paper |
|---|---|---|---|---|---|
| Mass + Light | Precession | General Relativity | Δφ = (6πGM) / (c²a(1 - e²)) | Δφ = (6πGM) / (c²a(1 - e²)) | Precession Derivation |
| Mass + Light | Gravitational Lensing | General Relativity | θ = (4GM) / (c²R) | θ = (4GM) / (c²R) | Gravitational Lensing Derivation |
| Mass + Light | Spacetime Curvature & Geodesics | General Relativity | Geodesic equation: (d²xᵢ / ds²) + Γᵢʲₖ (dxʲ / ds) (dxᵏ / ds) = 0 | (d²xᵢ / ds²) + Γᵢʲₖ (dxʲ / ds) (dxᵏ / ds) = 0 | Spacetime Curvature & Geodesics Derivation |
| Causal Geometry | Phenomenon | Theory | Original Equations | Causal Relativity Equation | Derivation Paper |
|---|---|---|---|---|---|
| Mass + Gravity | Mass-Energy Equivalence | Special Relativity | E = mc² | E = mc² | Mass-Energy Equivalence Derivation |
| Mass + Gravity | Relativistic Mass | Special Relativity | m' = m / √(1 - v²/c²) | m' = m / √(1 - v²/c²) | Relativistic Mass Derivation |
| Mass + Gravity | Energy of Light in Gravitational Field | General Relativity | Eₒᵤᵗ = Eᵢⁿ (rₛ / r) | Eₒᵤᵗ = Eᵢⁿ (rₛ / r) | Energy of Light in Gravitational Field Derivation |
| Causal Geometry | Phenomenon | Theory | Original Equations | Causal Relativity Equation | Derivation Paper |
|---|---|---|---|---|---|
| Electro Causal Sphere | Electromagnetic Wave Propagation | Electrodynamics | ( \nabla \times \mathbf{E} = -\frac{\partial \mathbf{B}}{\partial t} ) | ( \nabla \times \mathbf{E} = -\kappa \nabla \cdot \mathbf{B} ) | Electromagnetic Induction in Gravitational Fields Derivation |
| Electro Causal Sphere | Electromagnetic Induction | Electrodynamics | ( \nabla \times \mathbf{B} = \mu_0 \mathbf{J} + \mu_0 \epsilon_0 \frac{\partial \mathbf{E}}{\partial t} ) | ( \nabla \times \mathbf{B} = \mu_0 \mathbf{J} + \mu_0 \epsilon_0 \kappa \nabla \cdot \mathbf{E} ) | Electromagnetic Induction in Gravitational Fields Derivation |
| Electro Causal Sphere | Light Wave Equation in Vacuum | Electrodynamics | ( \nabla^2 \mathbf{E} - \frac{1}{c^2} \frac{\partial^2 \mathbf{E}}{\partial t^2} = 0 ) | ( (1 - \kappa^2) \nabla^2 \mathbf{E} = 0 ) | Light Wave Equation in Vacuum Derivation |
| Electro Causal Sphere | Jefimenko's Equations | Electrodynamics | Complex and dependent on charge and current distribution | Spatial causality terms replacing temporal derivatives; exact form needs further derivation | Skip cell |
| Thermo Causal Spheres | Conservation of Energy | Thermodynamics | ( \Delta U = Q - W ) | ( \Delta U = \Delta Q_{\text{space}} - \Delta W_{\text{space}} ) | Conservation of Energy in Causal Relativity Derivation |
| Thermo Causal Spheres | Increase in Entropy | Thermodynamics | ( dS = \frac{dQ}{T} ) | ( dS = \Delta S_{\text{space}} ) | Increase in Entropy Derivation |
| Thermo Causal Spheres | Minimum Entropy at 0K | Thermodynamics | ( S \rightarrow 0 ) as ( T \rightarrow 0 ) | ( S_{\text{space}} \rightarrow S_{\text{min}} ) as spatial activity ( \rightarrow 0 ) | Minimum Entropy at 0K Derivation |
| Quantum Causal Spheres | Quantum State Evolution | Quantum Mechanics | ( i \hbar \frac{\partial \psi(\mathbf{r}, t)}{\partial t} = \hat{H} \psi(\mathbf{r}, t) ) | ( \hat{H}{\text{causal}} \psi(\mathbf{r}) = E{\text{causal}} \psi(\mathbf{r}) ) | Quantum State Evolution Derivation |
| Quantum Causal Spheres | Particle in Spherical Well | Quantum Mechanics | ( E_n = \frac{\hbar^2}{2m} \left(\frac{n\pi}{R}\right)^2 ) | ( E_{n,\text{causal}} = \frac{\hbar^2}{2m} \left(\frac{n\pi}{R_{\text{causal}}}\right)^2 ), where ( R_{\text{causal}} = R \cdot \left(1 + \frac{\Delta R}{R}\right) ) | Skip cell |
| Quantum Causal Spheres | Time-Dependent Harmonic Oscillator | Quantum Mechanics | ( i\hbar \frac{\partial \psi(x,t)}{\partial t} = \left[ -\frac{\hbar^2}{2m} \frac{\partial^2}{\partial x^2} + \frac{1}{2} m \omega^2 x^2 + \lambda x \cos(\omega_0 t) \right] \psi(x,t) ) | ( \hat{H}{\text{causal}} \psi(\mathbf{r}) = E{\text{causal}} \psi(\mathbf{r}) ), where ( \hat{H} = \frac{-\hbar^2}{2m} \frac{\partial^2}{\partial x^2} + \frac{1}{2} m \omega^2 x^2 + \lambda x \cos(kx) ) | Time-Dependent Harmonic Oscillator Derivation |
| Quantum Causal Spheres | Energy Eigenvalue Problem | Quantum Mechanics | ( \hat{H} \psi(x) = E \psi(x) ) | ( \hat{H}{\text{causal}} \psi(\mathbf{r}) = E{\text{causal}} \psi(\mathbf{r}) ), where ( \hat{H} = \frac{-\hbar^2}{2m} \frac{\partial^2}{\partial x^2} + \frac{1}{2} m \omega^2 x^2 + \lambda x \cos(kx) ) | Energy Eigenvalue Problem Derivation |
| Quantum Causal Spheres | Spatial Oscillatory Potential | Quantum Mechanics | ( \lambda x \cos(\omega_0 t) ) | ( \lambda x \cos(kx) ) | Spatial Oscillatory Potential Derivation |
| Quantum Causal Spheres | Wave Function Evolution | Quantum Mechanics | ( \psi(x,t) ) | ( \psi(\mathbf{r}) ) | Wave Function Evolution Derivation |
| Quantum Causal Spheres | Path Integral Formulation | Quantum Mechanics | ( \psi(x_f, t_f) = \int \mathcal{D}x , \exp\left(\frac{i}{\hbar} S[x]\right) ) | ( \psi(\mathbf{r}_f) = \int \mathcal{D}\mathbf{r} , \exp\left(\frac{i}{\hbar} S[\mathbf{r}]\right) ) | Path Integral Formulation Derivation |
| Quantum Causal Spheres | Dirac Equation | Quantum Mechanics | ( (i\hbar \gamma^\mu \partial_\mu - mc)\psi = 0 ) | ( (i\hbar \gamma^i \partial_i - mc)\psi(\mathbf{r}) = 0 ) | Dirac Equation Derivation |
| Quantum Causal Spheres | Time-Dependent Schrödinger Equation | Quantum Mechanics | ( i\hbar \frac{\partial \psi(x,t)}{\partial t} = \hat{H} \psi(x,t) ) | ( \hat{H}{\text{causal}} \psi(\mathbf{r}) = E{\text{causal}} \psi(\mathbf{r}) ) | Time-Dependent Schrödinger Equation Derivation |
| Quantum Causal Spheres | Time-Independent Schrödinger Equation | Quantum Mechanics | ( \hat{H} \psi(x) = E \psi(x) ) | ( \hat{H}{\text{causal}} \psi(\mathbf{r}) = E{\text{causal}} \psi(\mathbf{r}) ) | Time-Independent Schrödinger Equation Derivation |
| Quantum Causal Spheres | Heisenberg Uncertainty Principle | Quantum Mechanics | ( \Delta x \Delta p \geq \frac{\hbar}{2} ) | ( \Delta x \Delta p \geq \frac{\hbar}{2} ) (Spatial distribution-based uncertainty, same principle applied in space) | Heisenberg Uncertainty Principle Derivation |
| Quantum Causal Spheres | Information Bound | Holographic Principle | ( I \leq \frac{A}{4l_P^2} ) | ( I_{\text{causal}} = \frac{A}{4l_P^2} \left(1 + \frac{\Delta A}{A}\right) ) | Information Bound and the Holographic Principle Derivation |
| Causal Geometry | Phenomenon | Theory | Original Equations | Causal Relativity | Derivation Paper |
|---|---|---|---|---|---|
| Big Bang Causal Sphere | Big Bang Initial Information | Cosmology | ( I_{\text{universe, initial}} = \frac{A}{4l_P^2} ) | ( I_{\text{universe, initial, causal}} = \frac{A_{\text{initial}}}{4l_P^2} \left(1 + f(K)\right) ), where ( f(K) ) is a function of curvature ( K ) | Big Bang Initial Information Derivation |
| Big Bang Causal Sphere | Dark Matter Density | Cosmology & Relativity | ( \rho_{\text{DM}} = \frac{C H(t)^2}{8 \pi G} ) | ( \rho_{\text{DM, causal}}(t) = \frac{C H(t)^2}{8 \pi G} \left( 1 + \Delta \rho_{\text{DM}} \right) ) | Dark Matter Derivation |
| Big Bang Causal Sphere | Dark Energy | Cosmology & Quantum Mechanics | ( \rho_{\text{DE}}(t) = \frac{\Lambda}{8 \pi G} ) | ( \rho_{\text{DE, causal}}(t) = \frac{\Lambda}{8 \pi G} \left(1 + f(K)\right) ) | Big Bang Initial Information Derivation |
| Causal Geometry | Phenomenon | Theory | Original Equations | Causal Relativity Equation | Derivation Paper |
|---|---|---|---|---|---|
| Black Hole Causal Sphere | Event Horizon Information | General Relativity | ( S_{BH} = \frac{A}{4l_P^2} ) | ( S_{BH,\text{causal}} = \frac{A}{4l_P^2} \left(1 + \frac{\Delta A}{A}\right) ), where ( \Delta A ) accounts for the difference between the inner/outter boundary of curvature. | Black Hole Event Horizon Information |
| Black Hole Causal Sphere | Hawking Radiation | Quantum Gravity | ( \mathcal{L}{\text{HR}} = \frac{1}{4} \frac{g{\mu\nu} \partial^{\mu} \partial^{\nu} \phi}{r_s^2} ) | ( \mathcal{L}{\text{HR, causal}} = \frac{1}{4} \frac{g{\mu\nu} \partial^{\mu} \partial^{\nu} \phi}{r_s^2} \left( 1 + \frac{\Delta A}{A} \right) ) | Hawking Radiation Derivation |
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- Derivations of Equations
- Black Holes: Event Horizons and Singularities in Spatial Terms
- The Big Bang: A Spatial Interpretation in Causal Relativity
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- Time Dilation Reinterpreted as Spatial Dilation
- Length Contraction in a Three-Dimensional Space
- Relativity of Simultaneity Without Temporal Dimension
- Relativistic Mass Increase in Causal Spatial Geometry
- Doppler Effect for Light in a Non-Temporal Framework
- The Twin Paradox: A Spatial Perspective
- Aberration of Light in Causal Relativity
- Mass-Energy Transformation in Causal Relativity: E = mc^2
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- Precession of Mercury's Orbit in Causal Geometry
- Gravitational Lensing Explained Spatially
- Gravitational Time Dilation as Spatial Dilation
- Gravitational Redshift Without Time
- Frame-Dragging in a Time-Less Universe
- Perihelion Shift of Planets and Causal Relativity
- Gravitational Waves: Spatial Propagation in Causal Theory
- Shapiro Time Delay as a Spatial Phenomenon
- Cosmological Redshift: A Spatial Interpretation
Causal Sphere Thought Experiments: Alice and Bob Causal Spheres
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