What does this research mean for the field?

The applicability of physical laws transitions smoothly and continuously across ultra-micro, micro, macro, and cosmic scales, and can be modeled using a Sigmoid transition function to ensure physical self-consistency without discontinuities. Novelty: ClaimNovelty.METHODOLOGICAL. Consensus alignment: ConsensusAlignment.NEUTRAL.

What question did this study set out to answer?

This research aims to define transition centers that illustrate how physical laws apply differently across various scales.

May 16, 2026Open Access

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Scale Isolation: Applicable Scales of Physical Laws with Continuous Gradient Transition

Key Points

This research aims to define transition centers that illustrate how physical laws apply differently across various scales.
Defines characteristic scale L and three transition centers (L₁, L₂, L₃)
Uses the sigmoid smooth transition function for continuous gradient transitions
Ensures differentiability and physical self-consistency across scales.
Identifies three key transition centers: L₁, L₂, L₃ for different scale interactions
Demonstrates a continuous, boundary-free cosmic scale
Illustrates the gradual variability in applicability weight of physical laws.

Abstract

Scale Isolation: Applicable Scales of Physical Laws with Continuous Gradient Transition The cosmic scale is continuous, gradual, and boundary-free. Define characteristic scale L and three transition centers: • L₁: ultra-micro ↔ micro transition center • L₂: micro ↔ macro transition center • L₃: macro ↔ cosmic transition center The applicability weight of physical laws varies smoothly and continuously with scale, using the Sigmoid smooth transition function to ensure no discontinuity, differentiability, and physical self-consistency.

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Scale Isolation: Applicable Scales of Physical Laws with Continuous Gradient Transition

Key Points

Abstract

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