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Discrete mechanics and special relativistic random walks
1Department of Chemistry, B-017, University of California at San Diego, La Jolla, CA 92093.
Summary
This study explores random walks at light speed, revealing how statistical equivalence between observers leads to Lorentz transformations and explains motion
Area of Science:
- Physics
- Relativity
- Statistical Mechanics
Background:
- Random walks are fundamental models for diffusion and particle movement.
- Special relativity describes physics in inertial frames of reference.
- Submicroscopic behavior and probability distributions are key concepts.
Purpose of the Study:
- To investigate random walks under special relativity.
- To reconcile statistical equivalence with relativistic motion.
- To explain the origin of Lorentz transformations from random walk principles.
Main Methods:
- Considering random walks with minimal step lengths.
- Analyzing probability distributions from two inertial observers' perspectives.
- Applying the requirement of statistical equivalence.
Main Results:
- Statistical equivalence necessitates Lorentz transformations for random walks.
- Motion at the speed of light is linked to particle transitions between uncertainty cells.
- Apparent smooth motion arises from biased submicroscopic randomness.
Conclusions:
- Random walks at the speed of light provide a novel derivation of Lorentz transformations.
- The model explains the diffusive spreading of probability distributions.
- This framework unifies concepts of random motion and relativistic physics.
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