Considering Counting Triangles to Unveiling Temporal Waves

-
  Considering Counting Triangles to Unveiling Temporal Waves By: John Gavel For years, my work in Temporal Flow Physics (TFP) has pursued a radical idea: what if spacetime itself —with all its gravitational curves and quantum fluctuations—isn't fundamental at all? What if it emerges from a deeper reality: a network of one-dimensional temporal flows , weaving the universe together moment by moment? It’s bold, yes—but I believe this view holds the key to a truly unified theory of physics , one that roots both quantum mechanics and gravity in the same temporal fabric. From Counting Triangles to Counting Time My earliest simulations: I counted triangles. More specifically, I measured how triangular motifs in temporal flow networks dissipated under coarse-graining. The decay rate of these patterns—captured by a parameter I called A₃ —served as a stand-in for emergent gravitational effects. If motifs faded predictably with scale, it suggested that macroscopic structure (like sp...
Post a Comment

Clarification of Temporal Wave Equation

-

Temporal Wave Equation


Variable List:


Ψ(t): Temporal wave function at time t

ψ_i(t): Individual wave components at time t

Definitions and Units:


Ψ(t): Represents the aggregate temporal wave profile, with units dependent on the specific physical interpretation of the wave phenomenon.

ψ_i(t): Dimensionless quantities representing the relative magnitudes or "flow values" of the individual wave components at each time point t.

Physical Interpretation:


The temporal wave function Ψ(t) is expressed as the summation of individual wave components ψ_i(t):


Ψ(t) = Summation over i of ψ_i(t)


This formulation captures the concept of "Temporally-Extended Linearity", where the temporal wave dynamics exhibit the following characteristics:


Linearity within Time Indices:


Each ψ_i(t) term has a linear relationship between its magnitude value and the localized influence or impact at the corresponding time point t.

Changes in the value of ψ_i(t) directly correspond to proportional changes in its effect within the same time frame.

Nonlinearity across Time Indices:


The extent or "reach" of each ψ_i(t) term across adjacent time indices is nonlinear, determined by the magnitude value associated with that component.

Wave components with higher magnitude values will have a broader temporal influence, propagating their effects over a larger number of consecutive time points.

Confined Temporal Interactions:


The interactions and propagation of influence between the ψ_i(t) terms are confined within the temporal domain unless there is an explicit exchange of amplitude or value between time indices.

The effects of each ψ_i(t) term remain localized, with limited direct interactions with distant or unrelated time points.

Derivation:


The Temporal Wave Equation emerges from the recognition that temporal phenomena can be represented as a superposition of multiple underlying wave components, each with its own characteristic magnitude and temporal influence.

(In detail:
 Multiple Wave Components: The term "underlying wave components" refers to individual elements or factors contributing to the overall temporal wave function. These components may represent various physical or abstract entities that exhibit wave-like behavior over time.

Characteristic Magnitude: Each wave component, denoted by ψ_i(t), possesses its own magnitude or strength at each time point t. This magnitude determines the amplitude or intensity of the wave component's influence at that specific time.

Temporal Influence: The influence of each wave component is not static but varies over time. This temporal variation is captured by the function ψ_i(t), which represents how the magnitude of the wave component evolves or changes at different time points.

Superposition: The Temporal Wave Equation asserts that the overall temporal phenomenon, represented by Ψ(t), results from the sum (or superposition) of all individual wave components. Mathematically, this is expressed as:

Ψ(t) = ∑ ψ_i(t)

Here, Ψ(t) represents the aggregate or total effect at time t, obtained by adding together the contributions of all individual wave components ψ_i(t).

Effect of Superposition: Superposition implies that the value of Ψ(t) at any given time point is determined by the combined influence of all underlying wave components at that time. Each ψ_i(t) contributes to the overall waveform, and their interactions (summed together) result in the observed temporal phenomenon.)


By summing the individual wave components ψ_i(t), the equation captures the collective wave profile Ψ(t), reflecting the combined impact of these temporally-extended linear and nonlinear interactions.


Dimensional Considerations:


The individual wave components ψ_i(t) are dimensionless quantities, representing the relative magnitudes or "flow values" at each time point. However, the summation into the temporal wave function Ψ(t) may result in a quantity with specific physical dimensions, depending on the nature of the underlying wave phenomena.


The dimensional consistency between Ψ(t) and the physical quantities it represents is crucial for interpreting the wave function and its interactions within the broader temporal physics framework.


Applications and Limitations:


The Temporal Wave Equation is well-suited for modeling a wide range of temporal phenomena, accommodating both linear and nonlinear aspects of wave dynamics. Its ability to capture the "Temporally-Extended Linearity" makes it applicable to scenarios where localized effects and temporally-extended propagation play a significant role.


Potential applications may include, but are not limited to:


Wave propagation in materials

Analysis of temporal data signals

Modeling of quantum mechanical wave functions

Investigation of complex systems with interacting temporal components

Limitations and Boundaries:


The primary limitation of the Temporal Wave Equation's "Temporally-Extended Linearity" concept is set by the speed of light, which establishes a fundamental bandwidth limit on the temporal propagation and interactions of the wave components ψ_i(t).


The speed-of-light boundary marks the limit of the "Temporally-Extended Linearity" concept, beyond which the equation may need modification to account for relativistic effects and higher-order nonlinearities.

Comments

Post a Comment

Popular posts from this blog

A build up of time

-
 Building up time. You could think of time as physical, or much more basic such as meta dynamics of what is physical. Sense you are working with a single dimension that builds up dimensons through interations.  c = j⋅r_i + 2⋅(Δr_i / Δj)⋅r_i Where: c is the result  j is flow (a positive or negitive value) r_i represents a rate (which is a conglomerate of flows) Δr_i and Δj represent changes in rate and flow, respectively given the "speed" of light consider our dimensions are D = fa + fb A dimension (D) emerges as the ratio of two interacting flows (fa and fb). This suggests that dimensions are not absolute, but relative measures arising from the interaction of more fundamental entities, flows. Lets go further and say space emerging from time. A metric for this space as: ds² = Σ(Ri + fi)² * dxi² Where i runs over all dimensions. Include our speed of light in the metric ds² = c² * [dt² - (1/c²) * Σ(ri² * dx0²)] Events with ds² > 0 are timelike separated, ds² = 0 are light...
Read more

Temporal Physics: A New Framework

-
Temporal Physics: A New Framework Table of Contents 1. [Fundamental Framework](#1-fundamental-framework) 2. [Emergence of Space](#2-emergence-of-space) 3. [Fields and Force Dynamics](#3-fields-and-force-dynamics) 4. [Particle Properties](#4-particle-properties) 5. [Quantum Entanglement](#5-quantum-entanglement) 6. [Quantum-Classical Transition](#6-quantum-classical-transition) 7. [Observable Phenomena](#7-observable-phenomena) 8. [Experimental Implications](#8-experimental-implications)  1. Fundamental Framework Time as the Fundamental Entity - Traditional physics treats space as primary; we invert this paradigm. - Core Assertion : Time flows generate spatial dimensions, implying that space is a byproduct of temporal interactions. - The interplay of temporal flows shapes all physical phenomena, creating a dynamic framework that transcends classical interpretations.  Core Principles 1. Time is Primary, Space is Emergent : Space does not exist independently but arises from the c...
Read more

Bridges of Morality: A Philosophy of Autonomy, Suppression, and Social Responsibility

-
 Bridges of Morality: A Philosophy of Autonomy, Suppression, and Social Responsibility I. Introduction — The Fractured Freedom of Being The Fractured Freedom of Being Autonomy is often misunderstood. It's not a privilege granted by society, nor a luxury reserved for those in power. It's something deeper: the raw capacity to choose, to act, to reflect. This capacity—this fundamental freedom—emerges the moment a mind becomes aware of itself and its possibilities. But here's the tension that defines human existence: society doesn't reward unfiltered autonomy. In fact, it punishes it. So we learn to suppress parts of ourselves—not because we're wrong, but because survival inside any social system requires strategic adaptation. This tension exists because of what I call the truth asymmetry—the gap between infinite and finite modes of being, to borrow Spinoza's terminology. If we think of absolute truth as analogous to Spinoza's infinite substance—complete, eterna...
Read more