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Algebraical Entropy and Arrow of Time
1Department of Physics, Javakhishvili Tbilisi State University, 3 Chavchavadze Avenue, 0179 Tbilisi, Georgia.
Entropy (Basel, Switzerland)
|November 11, 2022
Summary
This study proposes a microphysical arrow of time based on non-associative algebra. Using octonions in measurements generates relative entropy, analogous to thermodynamic entropy, to define time
Area of Science:
- Theoretical Physics
- Quantum Mechanics
- Mathematical Physics
Background:
- The arrow of time is typically observed only in macrophysics.
- A fundamental understanding of time's directionality at the microphysical level remains elusive.
Purpose of the Study:
- To introduce a microphysical arrow of time.
- To explore the implications of non-associative algebra in fundamental physics.
Main Methods:
- Utilizing octonions as the fundamental algebra for physical measurements.
- Analyzing the ordering dependence and ambiguity in non-associative measurement outcomes.
- Quantifying relative entropy between active and passive transformations.
Main Results:
- Non-associative measurements, specifically using octonions, introduce an unavoidable 18.6 bit relative entropy.
- This entropy arises from the probability density functions of active (G2) and passive (SO(7)) transformations.
- The generated algebraic entropy provides a potential mechanism for determining the arrow of time.
Conclusions:
- Non-associativity at a fundamental level can lead to a microphysical arrow of time.
- Algebraic entropy, derived from octonion algebra, offers an analogy to thermodynamic entropy for defining time's direction.
- This framework opens new avenues for understanding time's fundamental nature.
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