Time, Length, Mass, and Acceleration
In the ArXe system, time (\(T\)) is the fundamental dimension from which all others emerge. This approach allows for a unified understanding of physical properties, linking them directly to the nature of temporal flow and consistency. Below, we’ll explore how Length (\(L\)), Mass (\(M\)), and Acceleration (\(a\)) are defined through the “exentations” of time.
Time (\(T\)): The Primordial Flow
Time is the basis of everything in ArXe. It’s associated with exentation \(e_2\), meaning its most direct and fundamental manifestation occurs as \(T^1\).
- Association in ArXe: \(e_2 = T^1\)
- Interpretation: Time (\(T^1\)) is the discernible flow, the foundation of causality and progression. It’s the experience of “something happening,” the inherent pulse that allows for the sequencing of events. It’s the fundamental unit of duration in ArXe.
Length (\(L\)): The Extension of Time
Length, representing spatial extension, isn’t an independent dimension in ArXe; instead, it emerges directly from time. It’s defined through exentation \(e_4\), implying a quadratic relationship with time.
- Association in ArXe: \(e_4 = T^2 \Rightarrow L=T^2\)
- Dimensional Formula (conventional): \(L\)
- In ArXe (derivation): If we consider velocity (\(v = L/T\)) and know that \(v\) is \(T^1\), then \(L = v \cdot T = T^1 \cdot T^1 = T^2\).
- Interpretation: Length (\(T^2\)) is the inherent distance that time “travels” or “encompasses” in its own extension. It represents time’s ability to differentiate itself spatially, creating a “space” that can be measured. It’s the “measure of alterity in the flow.”
Mass (\(M\)): The Consistency of Time
Mass, the measure of inertia and quantity of matter, is also a manifestation of time in ArXe. It’s associated with exentation \(e_6\), indicating a cubic relationship with time.
- Association in ArXe: \(e_6 = T^3 \Rightarrow M=T^3\)
- Dimensional Formula (conventional): \(M\)
- In ArXe (derivation): This relationship is a fundamental postulate in ArXe, directly linking the “quantity of existence” or “consistency” of something to a deeper phase of time.
- Interpretation: Mass (\(T^3\)) is the “saturation” or “density” of time, the temporal flow’s ability to accumulate and sustain a form. It’s the “consistency” that resists phase change, the principle of inertia that gives “body” to reality in ArXe.
Acceleration (\(a\)): The Impulse of Ex-Istence
Unlike the other dimensions, acceleration holds a unique place in ArXe, associating with exentation \(e_1\), which corresponds to \(T^0\).
- Association in ArXe: \(e_1 = T^0\)
- Dimensional Formula (conventional): \(a = L/T^2\)
- In ArXe (derivation): Using the ArXe definitions of \(L\) and \(T\), we get: \(a = L/T^2 = T^2 / T^2 = T^{2-2} = T^0\).
- Interpretation: Acceleration (\(T^0\)) is the fundamental engine of change and distinction. It’s not a quantity that “exists” in time in a direct sense, but rather the primary condition for time and its derived dimensions to manifest. It’s the initial “non-stillness,” the potency of Ex-Istence that allows for alterity without consuming time in its essence. It could be seen as the primary “will” or “impulse” that gives rise to dynamics within the ArXe system, without requiring temporal duration for its own existence.
This ArXe framework offers a fascinating perspective where all fundamental physical properties are intrinsically linked to time and its complex “exentations,” revealing an underlying structure where temporality is not just a measurement, but the very essence of reality itself.
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