Temporal flows refer to the dynamic, continuous progression of time. Instead of time being a static background (as in classical mechanics), these flows represent how time evolves, interacts, and fluctuates in different contexts, such as near masses or in regions of high energy.
Temporal flows behave similarly to fluid dynamics, where time can move at different rates in different regions, influenced by factors such as mass, energy, and velocity. Time exhibits wave-like behavior, meaning it can have oscillations, phases, and amplitudes. Temporal flows are generally smooth and symmetric under normal conditions, but they can become asymmetric due to external factors like mass or energy. Asymmetry in these flows causes time to "slow down" or "speed up" in certain regions, leading to localized distortions.
Temporal Flow Function:
τ(t, s) = F(t) * &(s)
Where:
τ(t, s) is the temporal flow at time t and scale s
F(t) represents the continuous progression of time, capturing its wave-like behavior
&(s) represents the scale-dependent component
Scale Invariance Property:
τ(t, λs) = H(λ) * τ(t, s)
Where:
λ is a scaling factor
H(λ) represents the integral structure: H(λ) = ∫ τ(t, λs) dt
Emergence of Spatial Dimensions:
D(s) = H(s) = ∫ τ(t, s) dt
This equation now directly links the emergence of spatial dimensions to the scale transformation function H(λ).
Wave-like Behavior of Time:
F(t) = A * sin(ωt + φ)
Where:
A is the amplitude of the temporal wave
ω is the angular frequency
φ is the phase
E = ℏω
This is analogous to the photon energy equation, linking the temporal wave frequency to energy.
Quantum-Classical Transition (unchanged):
P(quantum | s) = e^(-s/s_c)
P(classical | s) = 1 - e^(-s/s_c)
Refined Quantum-Classical Transition:
P(quantum | A) = e^(-A/A_c)
P(classical | A) = 1 - e^(-A/A_c)
Where A_c is a critical amplitude related to the quantum-classical transition.
Space Emergence from Time:
Space is not an independent entity but an emergent property of temporal flows. In the same way that waves spread out across the surface of water, temporal waves give rise to space as time progresses. Mathematically, the space that emerges from time is described as:
D_i(τ) = α_i ∫ τ(t) dt
Space Emergece;
[x(t), y(t), z(t)] = E(T(t), T(t+Δt), T(t+2Δt), dT/dt|t, dT/dt|t+Δt, dT/dt|t+2Δt)
The first equation shows that the ith spatial dimension is generated from the integral of temporal flows, weighted by a factor α_i, which accounts for how these temporal flows interact to produce space.
T(t), T(t+Δt), T(t+2Δt): These represent different values of time at specific intervals (t, t + Δt, and t + 2Δt). They indicate how time evolves at various points.
dT/dt: These terms refer to the derivatives of time at those intervals, describing the rate of change of time, or how fast time flows at each point.
E: This function encapsulates the process by which space emerges from time. It takes the various time values and their rates of change as inputs to generate the spatial coordinates (x, y, z).
Curvature from Temporal Density:
Spacetime curvature, a central idea in relativity, is directly linked to the curvature of temporal flows in my model. When time flows smoothly and symmetrically, space remains flat. However, when time becomes asymmetric due to energy or mass, this leads to curvature. The curvature of spacetime, or space, is thus a consequence of how dense and uneven the flow of time is.
C(t) = (∂²τ(t))/(∂t²) = αt²
Here, C(t) represents the curvature caused by temporal density or asymmetry, where α is a constant reflecting how sensitive spacetime is to changes in the temporal flow.
Wave-Like Behavior of Time:
Time behaves in a wave-like manner, naturally explaining the wave-particle duality observed in quantum mechanics. Temporal flows oscillate, and these oscillations are expressed in the wave function:
Ψ(t, x) = A(t) ⋅ e^(i ⋅ φ(t, x))
Here, A(t) represents the amplitude of the temporal flow, and φ(t, x) is the phase of the wave. This wave-like behavior underlies the quantum mechanical description of particles and their probabilistic behavior.
When the temporal wave is disturbed by an energy fluctuation or interaction, the wave localizes, manifesting as a particle. This wave-particle duality is simply a reflection of how time behaves under different conditions.
Asymmetry Leading to Curvature:
Asymmetry in the flow of time leads directly to curvature in spacetime. When temporal flows become uneven or distorted, such as near a massive object or at relativistic speeds, this distortion is felt as curvature in space. Mathematically:
C(t) = (∂²τ(t))/(∂t²) = αt²
In this case, curvature (C) arises from second-order derivatives of the temporal flow function τ(t), with α representing the degree of asymmetry. This curvature gives rise to gravitational effects, as described in general relativity, but is fundamentally caused by time, not space.
Unified View of Space, Time, and Quantum Mechanics:
In quantum mechanics, particles behave as waves until measured or disturbed, where they collapse into a defined state. In my model, this collapse happens when temporal flows become asymmetric:
ΔΨ(t) ∼ α ⋅ t²
Here, ΔΨ(t) represents the localization of the wave function, with α describing the degree of asymmetry in the temporal flow. The more asymmetric the flow, the more likely the wave function will collapse into a particle. This mechanism underpins particle formation and quantum uncertainty.
At high velocities or in the presence of massive objects, the flow of time becomes increasingly asymmetric. This is analogous to time dilation described in relativity:
τ(t) = τ₀ / √(1 − v²/c²)
In my model, time dilation is a direct result of temporal flow asymmetry, with the Lorentz factor γ being a manifestation of how these flows change near the speed of light.
When mass is introduced, the function E must account for the effects of mass on the temporal flow. This leads to changes in how time evolves, particularly in the derivatives of time (dT/dt), as mass affects the rate at which time flows.
[x(t), y(t), z(t)] = E(T(t), T(t+Δt), T(t+2Δt), dT/dt|t, dT/dt|t+Δt, dT/dt|t+2Δt)
x(t), y(t), z(t) = E(T(t), dT/dt, m(t))
The distortion in the temporal flow caused by mass is mathematically represented by the curvature of space.
C(t) = ∇²τ(t)
Where C(t) represents the curvature, and τ(t) is the temporal flow affected by mass.
The relationship m(t) ∼ C(t) can be expressed as:
m(t) ∼ ∇²τ(t)
m(t) is the mass as a function of time, which emerges from the curvature.
∇²τ(t) represents the curvature derived from the second derivatives of the temporal flow τ(t)
Alternatively, express it in terms of the asymmetry in the temporal flow:
m(t) ∼ α * t²
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