5.Local time , the proper time and relative time in Relativity
5.1 local time. As previously established, global time is defined by the transformations of the universe. This work introduces local time as an operational concept that: (1) provides correspondence with special relativistic time notions; and (2) enables precise specification of time scales for localized physical processes. Crucially, any measurable time parameter in physical calculations necessarily corresponds to transformations within a specific local space. This operational concept is designated as local time.
The local space scope must be unambiguously specified: either as the SEQ network along the physical process path or the connected region within the observer's light cone. This distinction mirrors the complementarity between Feynman's path-integral formulation and relativistic theory, avoiding conceptual confusion in prior works.
Local time: it can specify the time set corresponding to the transformations within a specific spatial range. In fact, from the perspective of this framework, the existing equations with t parameter in textbooks are actually the local time by default.
One example: the clock slowness effect in Relativity manifests as different transformation times in different local spaces.
Every local space transformation constitutes a part of the universal evolution. Global time progression (△Tglobal) does not necessitate synchronous local transformations, the state matrix of a given local space may remain invariant despite cosmic-scale changes ( △tlocal≈ 0) when this local space undergoes no state transition.
5.2 The proper time in Relativity is related to local transformations count of physics process entities. (Section 9.1,Section9.5.6 present the physical mechanism underlying proper time dilation in GR.)
5.3 Understanding on Lorentz-covariant rules in Special Relativity theory: The time perception of physical processes across distinct reference frames fundamentally corresponds to the observation of transformation counts. The observation time discrepancy between frames derives from the accumulated difference in their frame SEQ transformation counts. An observer measures another frame's time evolution through the differential transformation count ΔN, while he can't perceive their own transformation count N₀. The observed ΔN is fundamentally governed by the dynamic light-path difference between the observer's frame and the moving reference frame of the measured object. Under the principle of non-additivity of light speed (c-invariance), this formulation naturally derives Lorentz-covariant rules through counting operations.
Key Distinction from GR Effects
While the mathematical derivation process aligns with standard special relativity textbooks—replacing continuous spacetime metrics with discrete counting operations—the physical interpretation differs substantially in conceptualization:
- SR Effects as Perceptual Phenomena
- Time dilation and length contraction emerge purely as observer-dependent measurement consequences in SR
- Originate from information transmission constraints via discrete light-signal counting
Contrast with GR Mechanisms
- Gravitational time dilation involves actual deformation of the SEQ network's transformation frequency
- Equivalence principle effects require space compression as well (see §9.5)
5.4 Physical Meaning of Planck Time
In this framework, the Planck time (tₚ) corresponds to the fundamental harmonic period of the SEQ network in its equilibrium state—the duration for a complete energy transfer (or harmonic oscillation period) between adjacent SEQ. This period defines the theoretical minimum transformation cycle (i.e., maximum transformation frequency) of the universe as a whole.
While gravitational fields or equivalent interactions can locally modulate the harmonic frequency by deforming the SEQ network (e.g., compression/stretching, as in gravitational time dilation), the global maximum theoretical transformation frequency remains anchored by in the equilibrium state. However, due to the omnipresence of gravitational effects, the empirically observable maximum transformation frequency of space may marginally less than this theoretical limit.
