Sanctus, J and Varda, Shubhang (2025) Entropy Constrained Knowledge Principle. [Preprint]
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Abstract
We often marvel at the beautiful randomness in quantum mechanics, but what if
it is simply entropy fulfilling its role as dictated by causality? This paper explores the
idea that Heisenberg’s uncertainty principle may not represent an intrinsic limitation,
but rather a thermodynamic outcome, a cost we pay for achieving precision. We examine
Gaussian wavefunctions, investigate entropic uncertainty, and demonstrate that
increased knowledge of one variable (such as position) leads to a corresponding increase
in entropy in its complementary variable (such as momentum). Nature does not conceal
the truth; rather, the process of acquiring knowledge alters the equilibrium. By
associating entropy with quantum uncertainty, we are not simply reinterpreting mathematics;
We are redefining the implications of quantum indeterminacy. Perhaps the
universe is not inherently uncertain; it is simply economical with certainty. We propose
that the Heisenberg Uncertainty Principle can be interpreted through the concept
of entropy, framing it as an emergent characteristic of the system’s overall information
content rather than merely a constraint imposed by quantum mechanics. Investigating
this relationship may yield profound insights into the essence of quantum systems
and their relationship with the macroscopic realm governed by thermodynamics. This
paper offers both a philosophical and mathematical framework that unifies the ideas
of entropy and uncertainty, providing a novel viewpoint on one of the most essential
principles of quantum mechanics. By analyzing the influence of entropy on quantum
uncertainty, this study contests traditional interpretations and encourages a renewed
dialogue regarding the foundational principles of physics. It posits that uncertainty
transcends mere measurement concerns and may be embedded in the very structure of
the universe, prompting a reevaluation of how quantum mechanics integrates into the
wider context of physical laws.
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