Rethinking Physics: Embracing Temporal Dynamics

The Traditional View of Spacetime

In classical physics, spacetime is treated as a 4D vector space with components:

$$x^\mu = (x, y, z, t)$$

where $x, y, z$ represent the spatial dimensions, and $t$ represents time. Forces, velocities, and accelerations are expressed as vectors within this space, and time is typically treated as an independent variable. Newton's laws and Einstein's theory of relativity rely on this framework, which treats space and time as separate entities.

Temporal Flows as the Fundamental Axis

In my model, I propose a shift in perspective: time becomes the fundamental axis, and spatial dimensions emerge as a result of temporal interactions. Physical phenomena are not just events in a spatial vector space but arise from how time flows through space.

We express this by defining temporal flow as the primary driver of physical interactions. The key quantity in this framework is $\tau(t)$, which represents the amount of temporal flow at a given time $t$. This flow influences the spatial dimensions, leading to spatial emergence. Instead of considering motion and forces as occurring within a fixed spatial context, these phenomena arise from the dynamics of time itself.

Temporal Flows vs. Vector Flows

In classical mechanics, motion is described by vectors (position, velocity, and acceleration), and forces are represented as spatial vectors:

$$F = m \cdot a$$

However, in my model, temporal flow replaces the role of spatial vectors. The motion and acceleration of objects are consequences of how temporal flows accumulate and change over time.

To quantify this, we write the temporal flow equation as:

$$\frac{d^n \tau(t)}{dt^n} \quad (\text{higher-order temporal derivatives})$$

This equation captures the rate of change of temporal flow over time, which directly influences how objects move and interact in space. As temporal flows accumulate more rapidly, motion (velocity, acceleration) and gravitational effects become more pronounced.

Same grid in Times Dimension

Mass as Temporal Flow

In classical physics, mass is a measure of inertia and gravitational attraction. In my model, mass is instead a measure of the accumulated temporal flow in a system. The relationship between mass $m$ and temporal flow $\tau(t)$ can be expressed as:

$$m = \int \frac{\tau(t)}{c} \, dt$$

This equation shows that mass is the integral of normalized temporal flow over time. As temporal flow accumulates, it leads to inertia (resistance to acceleration) and gravitational effects. The more temporal flow a system contains, the stronger its gravitational influence and its resistance to acceleration.

Gravity and Spacetime Curvature

In General Relativity, gravity is described as the curvature of spacetime caused by mass-energy. In my model, gravity arises not from mass itself, but from the interaction and accumulation of temporal flows. The curvature of space can be described by the Riemann curvature tensor $R_{\mu\nu}$, which now relates directly to how temporal flows accumulate and change:

$$R_{\mu\nu} = \frac{\partial^2 \tau(t)}{\partial x_\mu \partial x_\nu}$$

Instead of mass being the source of spacetime curvature, temporal flow determines how space curves. Gravity is not a force acting within space, but the effect of temporal flows on the geometry of spacetime. Mass indicates the amount of temporal flow, and its influence on space is governed by the rate at which temporal flow accumulates and changes.

A Unified Concept of Energy and Mass

In my framework, energy and mass are seen as emergent properties of temporal flows. They are tied directly to the rate of temporal flow and its accumulation. The famous equation $E = mc^2$ from Einstein's theory can be adapted to reflect this unified view:

$$E = c^2 \cdot \int \tau(t) \, dt$$

Here, $m$ represents the temporal mass, which is the accumulated temporal flow, and $c^2$ is the conversion factor that connects temporal flow to spatial effects (energy and mass).

Relation to Classical Mechanics

In classical mechanics, the force equation $F = ma$ can be reinterpreted in my model by replacing mass $m$ with the accumulated temporal flow $\tau(t)$. The equation becomes:

$$F = \left( \int \frac{\tau(t)}{c} \, dt \right) \cdot a$$

This equation shows that the force is a result of the accumulated temporal flow, and the acceleration depends on the rate at which this temporal flow is distributed and accumulated over time.

Space as a Construct of Temporal Interaction

In my model, space is not a static container for events, but rather an emergent property of how temporal flows interact with each other. The dynamics of temporal flows define how spatial dimensions arise. As temporal flows accumulate and change, they lead to the emergence of space, rather than space existing independently of the phenomena it contains.

This shift in perspective can be represented by a temporal flow metric that defines the interaction of temporal flows with spatial dimensions:

$$g_{\mu\nu}(t) = \begin{bmatrix} \alpha_1 \cdot \int \frac{\tau(t)}{c} \, dt & 0 & 0 \\ 0 & \alpha_2 \cdot \int \frac{\tau(t)}{c} \, dt & 0 \\ 0 & 0 & \alpha_3 \cdot \int \frac{\tau(t)}{c} \, dt \end{bmatrix}$$

This metric tensor \( g_{\mu\nu}(t) \) describes how temporal flow influences the spatial dimensions. The coefficients \( \alpha_1, \alpha_2, \alpha_3 \) can accommodate potential local anisotropic behavior, indicating that temporal flows might affect space differently along each spatial axis in localized regions. However, the overall influence of the speed of light \( c \) ensures a global isotropy, where space exhibits uniform properties at larger scales.