Published August 29, 2026
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The Irreversibility of Time Originates from Information Compression ― The Arrow of Time as an Observer's Necessary Illusion
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Description
The arrow of time constitutes a fundamental problem in physics. Based on the mathematical
structure of “irreducibility under information compression”, this paper presents an
independent argument: the arrow of time is not an intrinsic property of fundamental physics,
but a temporal manifestation of irreversibility inevitably generated when a finite observer
performs information compression on a physical system.
Fundamental physical evolution ― whether classical Hamiltonian dynamics or quantum unitary
evolution ― is reversible under a complete description. The finiteness of an observation window
is mathematically equivalent to a non-injective mapping, namely information compression.
Information compression gives rise to irreducibility of information, i.e., irreversibility; this
irreversibility manifests itself as the arrow of time in the observer’s perception. Consequently,
the arrow of time is a necessary consequence of the observer’s structure, a “necessary
illusion” relative to the reversible fundamental reality.
This paper examines the arrow of time in statistical mechanics (macroscopic coarse-graining)
and in quantum mechanics (measurement projection). It shows that although the two cases
differ in physical mechanisms, they share identical informational structure, both stemming from
non-injective mappings. The macroscopic and microscopic arrows of time are homologous at
the level of informational structure.