On the Intrinsic Mathematical Mechanism of the Common Origin of Space and Time and the Co-Directionality of Length Contraction and Time Dilation

Author: Zhang Suhang, Luoyang, Henan

Abstract

Classical relativity merely provides the calculated results of length contraction and time dilation through the mathematical form of the Lorentz transformation, but it does not reveal the underlying ontological reason why these two effects necessarily co-occur in the same direction. This paper steps beyond the traditional perspective of four-dimensional spacetime symmetry and establishes an asymmetric dependency relation: space and time are fundamentally of common origin and are not mutually independent physical substrates; time is not an independent primordial dimension, but a derived measure generated from changes in spatial configuration. Relative changes in spatial structure necessarily drag along synchronous changes in the time measure attached to that space, thereby explaining, from mathematical foundations, the core mechanism by which length contraction and time dilation are always co-directional, co-occurring, and inseparable.

Keywords: common origin of space and time; space-time dependency relation; Lorentz transformation; length contraction and time dilation; relativistic effects

I. Introduction

Modern physics by default treats four-dimensional spacetime as a symmetric unified whole, in which spatial dimensions and the temporal dimension hold equal status and are mutually symmetric. This paradigm can calculate relativistic effects, yet it cannot answer a core question: why, in all inertial frame transformations, does spatial contraction necessarily accompany temporal expansion, with the two effects strictly co-directional and synchronized, such that neither length contraction alone nor time dilation alone can occur?

Traditional theory can only offer a superficial explanation of "mathematical formula coupling," lacking analysis at the ontological level.

This paper proposes a new cognitive framework:

Without discussing the temporal sequence of cosmic evolution, and establishing core propositions solely from mathematical structure and the logic of measure generation:

1. Space and time share a common origin; both are rooted in the positional relations and state evolution of material particles, with no independently separated ontology;

2. The measure of time is entirely dependent on changes in spatial configuration for its existence, and possesses no independent definition apart from space;

3. Relative distortion of spatial structure necessarily leads to synchronous distortion of the time measure, constituting the sole underlying reason for the co-directional co-occurrence of length contraction and time dilation.

II. The Core Argument for the Common Origin of Space and Time

Space and time are not two sets of mutually independent, pre-existing physical entities.

The origin of all concepts of space and time comes from the existence and relative positions of material particles:

Only with particles and differences in spatial position can there be spatial structure;

Only with the dynamic succession of spatial positions and configurational change can there be sequences of before and after, thereby generating the measure of time.

Therefore, space and time arise from a common origin: both originate jointly from the configurational and evolutionary relations of material systems. There exists no mutually separated, mutually independent physical substrate. This is the principle of the common origin of space and time.

This principle differs from classical views of space and time:

· Newtonian space-time: space is a fixed container, time flows independently and uniformly; space and time are of separate origins;

· Traditional relativistic space-time: the four dimensions of space-time are symmetrically equivalent, with no primary-secondary relation and no dependency;

· The view of space-time in this paper: space and time share a common origin and co-exist, but their structural roles are not equal; space is the substrate carrier, and time is the derived measure.

III. The Dependency of Time on Space (Core Innovation)

This paper explicitly establishes a rigorously self-consistent rule of mathematical dependency:

Space is the substrate configuration; time is the ordered measure of changes in spatial configuration.

Without matter, without particles, without differences in spatial position, there is no definable change whatsoever;

Without dynamic change in spatial configuration, there is no before-and-after of events, no evolutionary sequence, and no definable time.

Time cannot exist independently of space, be measured independently, or evolve independently.

Time does not possess the independence of a primordial dimension; its units, rate of passage, and rules of measurement are all defined and altered depending on the state of spatial structure.

Key clarification:

This paper does not explore the physical chronology of the birth of the universe, nor does it advocate the cosmological origin hypothesis that "space was born first and time afterward."

This paper merely expounds the logic of mathematical measure and structure: in the constructive relation of the space-time system, space is the root and time is the branch; space is the substance and time is the function.

IV. The Underlying Mechanism of the Co-Directionality and Co-Occurrence of Length Contraction and Time Dilation

In the Lorentz transformation, a high-speed inertial frame simultaneously produces contraction of spatial scale and expansion of temporal intervals. These two effects are forever synchronized, co-directional, and vary with the same coefficient. The essence of this phenomenon can be fully explained by the dependency theory of this paper:

1. The essence of reference-frame motion is the relative distortion of spatial configuration.

Relative motion alters the spatial distribution scale of matter within the observational system, producing spatial contraction—this is a change in the substrate structure.

2. Time depends on space for its existence; distortion of the substrate necessarily drags along distortion of the derived measure.

Because time is not an independent dimension, but an auxiliary measure of spatial change.

When the spatial substrate undergoes relative contraction, the rules of temporal passage and the definition of temporal intervals attached to that spatial structure necessarily undergo synchronous deformation.

3. The effects are necessarily co-directional and inseparable.

Space is the carrier; time is the carrier's property reading.

When the carrier changes, the property must change.

It is impossible for "space to contract while time remains unchanged" or for "time to expand while space remains unchanged."

This is the ultimate mathematical reason for the strict co-directionality, co-occurrence, and one-to-one correspondence of length contraction and time dilation.

V. Theoretical Comparison and Advantages

1. Classical relativity

Possesses only the phenomenon of mathematical coupling, with no ontological mechanism; it knows the "how" but not the "why."

2. The space-time dependency theory of this paper

Directly derives the constraint rules of relativistic effects from the common origin of space and time plus the primary-secondary dependency of space and time. It perfectly explains the synchronicity, co-directionality, and inseparability of length contraction and time dilation in all inertial frames, filling the gap in the mechanism of classical theory.

VI. Conclusion

1. Space and time share a common origin and co-exist, rooted in the configurational and evolutionary relations of material systems, with no independently separated ontology;
2. Time is the derived measure of changes in spatial configuration, entirely dependent on the spatial substrate, and does not possess the attribute of an independent physical substrate;
3. The co-directional co-occurrence of length contraction and time dilation is not a mathematical coincidence, but the necessary mathematical result of the dominance of the spatial substrate and the dependency of the temporal measure.

The asymmetric dependency framework of space and time established in this paper corrects the inherent cognition of the complete symmetry of four-dimensional space-time, and provides a new ontological explanatory system for relativistic effects.