The Least Multiplication Principle in Temporal Physics

The Least Multiplication Principle in My Model of Temporal Physics

In the exploration of my model of temporal physics, one of the key aspects I've focused on is how flows within time and space interact to create the structures we observe—especially particles and emergent phenomena like the Cosmic Microwave Background Radiation (CMBR). The underlying framework of my model suggests that interactions between these flows, particularly those governed by phase and amplitude, are governed by a principle of minimalism: the least multiplication principle. This principle, grounded in the idea of minimizing unnecessary computations or interactions, naturally arises when looking at how space and particles emerge.

Temporal Waves and the Emergence of Space

In my model, space isn’t a pre-existing backdrop or static construct. Instead, it emerges from the interaction of temporal flows. These flows are dynamic fields of temporal waves, where each flow is linked to a field $\varphi$ and its gradient $\nabla \varphi$. This gradient is critical because it determines how the temporal waves interact, giving rise to the fabric of space itself.

Mathematically, space is defined by:

$$x = f(\varphi, \nabla \varphi)$$

This equation expresses how space emerges from the interaction of fields and gradients of those fields. These flows, when interacting with each other, lead to the formation of stable structures—particles, in our case. However, not all interactions are fruitful. Only those that meet specific conditions, such as phase alignment and amplitude thresholds, lead to the formation of stable structures. If these conditions aren’t met, the interaction dissolves or remains part of the background flow, contributing nothing significant.

This is where the least multiplication principle plays a role. Instead of considering all potential interactions between flows, only those that meet the threshold and lead to constructive interference are considered relevant. This minimizes the computational load or the “multiplications” involved in understanding how space and particles emerge.

The Shift to the Principle of Minimal Interactions

At a deeper level, interactions between flows in my model are governed by thresholds. These thresholds define the minimum conditions necessary for stable structures to form. For example, when multiple flows interact, they must accumulate in specific ways to exceed the threshold required for particle formation. This is akin to the idea of tensor decomposition in mathematics, where a large, complex interaction is broken down into minimal components that still convey the necessary information.

Mathematically, we can express the principle of minimal interaction as:

$$\Delta x = \sum_{i=1}^{r} A_i \otimes B_i \otimes C_i$$

In this equation:

• $A_i$, $B_i$, and $C_i$ represent fundamental flow components.
• $\otimes$ indicates structured interactions rather than simple additions.
• The rank $r$ represents the minimal number of interactions necessary to form a stable structure.

This tensor decomposition mirrors the process of space emerging from temporal flows. Each component $A_i$, $B_i$, and $C_i$ represents different elements of the flow—such as field values, gradients, and phase components—that, when combined, create the stable structure of space or a particle. The rank $r$ shows us that there’s a minimal set of interactions needed to explain the entire system.

Phase Interactions and Structured Flow

One of the most intriguing aspects of my model is the way phase shifts influence the formation of structures. As temporal waves interact, they do so with phase shifts. This is not a random occurrence—these shifts are structured and contribute to the overall flow dynamics. The phase shifts are represented by the term $e^{i\theta}$, which describes how a flow changes its phase as it evolves in time.

In my model, the equation:

$$x' = x + \Delta x e^{i \theta}$$

shows how space evolves due to phase shifts. The shift in space $\Delta x$ is not random; it's structured by the phase $e^{i \theta}$. This phase structure ensures that only certain interactions lead to significant changes, much like how tensor components combine in a structured manner. In other words, the interactions between temporal waves follow a rule of coherence—only those interactions that respect the underlying structure of the flow contribute to the formation of stable systems.

The Minimal Number of Essential Interactions

What sets my model apart is the idea that only the minimal number of flows are needed to form stable structures. This is a direct application of the least multiplication principle, where unnecessary interactions are ignored. In other words, we don’t need to compute every possible interaction between flows. Instead, only those flows that respect the fundamental rules of phase alignment, threshold crossing, and coherence are considered.

Mathematically, this is expressed by:

$$C(t) = \sum_{i} w_i f_i(t)$$

where $w_i$ are weights that determine the significance of each flow in the interaction, and $C(t)$ represents the accumulated coherent flow that leads to a stable structure. If the accumulated flow exceeds a certain threshold, it results in a stable structure like a particle.

Thus, the flow that accumulates coherently to form a stable structure is minimal in its interactions, ensuring that only the essential flows are included. The result is an efficient system—similar to how tensor decomposition finds the lowest-rank decomposition to explain complex structures with minimal components.

Conclusion: The Optimization of Interaction

In summary, my model of temporal physics inherently follows the least multiplication principle by focusing on minimal, coherent interactions that lead to the emergence of space and particles. Rather than considering all possible interactions between temporal waves, only those that meet specific phase, amplitude, and threshold conditions contribute to the formation of stable structures. This mirrors concepts like tensor decomposition and Strassen's algorithm, which aim to reduce complexity while maintaining structural integrity.

In essence, my model applies this optimization principle not just to the formation of particles, but to the very fabric of space itself—creating a dynamic, efficient system that minimizes unnecessary interactions while still giving rise to complex, stable phenomena.