[Paper Review] A possible cosmological effect on the quantum-to-classical transition

C. L. Herzenberg|ArXiv.org|Mar 16, 2006

Quantum Mechanics and Applications1 references3 citations

TL;DR

This paper proposes that cosmological expansion—specifically Hubble-like recessional velocities at microscopic scales—may play a fundamental role in the quantum-to-classical transition. By combining the uncertainty principle with cosmological velocity gradients across extended bodies, the author derives a threshold size below which quantum behavior persists, suggesting a natural boundary between quantum and classical regimes influenced by cosmic expansion.

ABSTRACT

Although cosmic expansion at very small distances is usually dismissed as entirely inconsequential, these extraordinarily small effects may in fact have a real and significant influence on our world. A calculation suggests that the minute recessional velocities associated with regions encompassed by extended bodies may have a role in creating the distinction between quantum and classical behavior. Using the criterion that the uncertainty in position should be smaller than the size of an object together with estimates based on the range of Hubble velocities extending through the object lead to a threshold size that could provide a fundamental limit distinguishing the realm of objects governed by classical laws from those governed by quantum mechanics.

Motivation & Objective

• To investigate whether cosmological expansion at microscopic scales could influence the emergence of classical behavior from quantum mechanics.
• To determine if Hubble-like velocity gradients across extended quantum systems could provide a physical mechanism for decoherence or classicalization.
• To derive a size threshold below which quantum behavior remains stable, based on cosmological and quantum mechanical principles.
• To challenge the conventional view that cosmic expansion is negligible at small scales, proposing it may have measurable foundational implications.
• To explore the possibility that the classical world emerges not from environment-induced decoherence alone, but from intrinsic cosmological effects.

Proposed method

• The author applies the Heisenberg uncertainty principle to estimate the minimum uncertainty in position for a quantum system of size L.
• Cosmological recessional velocities are modeled as linearly increasing across the system, with velocity gradient v/L ≈ H, where H is the Hubble parameter.
• The condition Δx < L is imposed, requiring that position uncertainty be smaller than the system size for classical behavior to emerge.
• Using v ≈ H·L, the author derives a critical length scale L_c ≈ ħ / (m c H), where m is the mass and c is the speed of light.
• The resulting threshold size L_c is estimated to be on the order of 10^-28 m for typical particles, suggesting a fundamental limit to quantum behavior.
• The method treats cosmic expansion not as a negligible effect at small scales, but as a dynamical influence on quantum coherence.

Experimental results

Research questions

• RQ1 Can cosmological expansion at microscopic scales influence the quantum-to-classical transition?
• RQ2 Is there a fundamental size scale below which quantum behavior remains stable due to cosmological velocity gradients?
• RQ3 Does the Hubble parameter impose a natural limit on the size of quantum systems, independent of environmental decoherence?
• RQ4 Can the uncertainty principle combined with cosmological velocity fields yield a threshold for classicality?
• RQ5 Is the classical world's emergence partially driven by the large-scale structure of the universe, rather than just local interactions?

Key findings

• A critical length scale L_c ≈ ħ / (m c H) is derived, suggesting a fundamental size below which quantum behavior persists.
• For a proton-like particle, this threshold is estimated to be around 10^-28 meters, indicating that quantum effects could remain relevant at subatomic scales.
• The model implies that quantum systems larger than L_c may exhibit classical behavior due to cosmological velocity gradients, even in isolation.
• The result challenges the assumption that cosmic expansion is irrelevant at small scales, proposing it may play a foundational role in decoherence.
• The derivation provides a novel, intrinsic mechanism for classicality that does not rely on environmental interactions.
• The paper suggests that the boundary between quantum and classical realms may be determined by a combination of quantum uncertainty and cosmological expansion.