[Paper Review] Permanently rotating devices: extracting rotation from quantum vacuum fluctuations?

M. N. Chernodub|arXiv (Cornell University)|Mar 29, 2012

Quantum Electrodynamics and Casimir Effect3 citations

TL;DR

This paper proposes a theoretical mechanism for macroscopic, permanent rotation in quantum vacuum fluctuations using specially designed devices with asymmetric boundary conditions. By engineering vacuum energy via Dirichlet-type boundary conditions on a rotating ring or tube, the system's vacuum energy is minimized at a nonzero angular frequency, leading to spontaneous rotation without external energy input, with the optimal frequency determined by geometry and vacuum fluctuations.

ABSTRACT

We propose a set of devices of simple geometrical design which may exhibit a permanent rotation due to quantum (vacuum) fluctuations. These objects - which have no moving parts - impose certain boundary conditions on quantum fluctuations thus affecting their vacuum energy similarly to the standard Casimir effect. The boundary conditions are chosen in such a way that the vacuum energy for a static device is larger compared to the energy of the vacuum fluctuations in a state when the device rotates about a certain axis. The optimal frequency of rotation is determined by geometry and moment of inertia of the device. We illustrate our ideas in a vacuum of a massless scalar field theory using simplest Dirichlet-type boundary conditions. We also propose an experimental setup to verify the existence of the rotational vacuum effect.

Motivation & Objective

• To explore whether quantum vacuum fluctuations can induce permanent rotation in macroscopic devices without moving parts.
• To investigate if vacuum energy can be engineered to have a minimum at a nonzero angular frequency, enabling spontaneous rotation.
• To propose a field-theoretic mechanism analogous to the Casimir effect but for rotational degrees of freedom.
• To suggest experimental setups using nanotubes or graphene-based structures to test the rotational vacuum effect.
• To analyze the stability and dissipative properties of such rotating systems in quantum vacuum.

Proposed method

• Model a (1+1)-dimensional massless scalar field on a ring with a cut, imposing Dirichlet boundary conditions at the ends to break rotational symmetry.
• Calculate the vacuum energy of the system in both static and rotating frames using mode-sum regularization and subtract divergent free-space contributions.
• Derive the effective rotational energy as a function of angular frequency, showing a nontrivial minimum at nonzero Ω due to quantum fluctuations.
• Use the Lüscher energy for an open string and Casimir energy for a rectangular geometry as reference vacuum energies in the static limit.
• Analyze the curvature of the vacuum energy near Ω=0 to extract the effective moment of inertia, finding it negative in the limit of infinite length.
• Generalize the model to three dimensions using a cylindrical device with a central bar and asymmetric boundary conditions on each side to break reflection symmetry.

Experimental results

Research questions

• RQ1 Can quantum vacuum fluctuations induce a permanent, spontaneous rotation in a macroscopic object with no moving parts?
• RQ2 Does the vacuum energy of a system with boundary conditions exhibit a minimum at a nonzero angular frequency, leading to stable rotation?
• RQ3 What is the optimal frequency of rotation determined by geometry and vacuum fluctuations in such a system?
• RQ4 How does the effective moment of inertia of the vacuum fluctuation contribution behave, and can it be negative?
• RQ5 Can asymmetric boundary conditions in a 3D device break reflection symmetry and lead to a preferred direction of rotation?

Key findings

• The vacuum energy of a rotating ring with Dirichlet boundary conditions has a nontrivial minimum at a nonzero angular frequency, indicating spontaneous rotation.
• The optimal frequency for rotation in the infinite-length limit is Ω_opt = 1/√2R, independent of the field's mass and universal in form.
• The effective moment of inertia of the vacuum fluctuations at Ω=0 is negative, with a value of -3ζ(3)ħ/(32π³c) per unit length, indicating a destabilizing quantum contribution.
• For a finite-length tube, the minimum is trivial (Ω_min=0) if L < L_c, but becomes nontrivial for L > L_c, with L_c depending on R.
• In asymmetric boundary conditions, the system breaks reflection symmetry, favoring one rotational direction and enabling a potentially observable effect.
• The proposed mechanism does not violate energy conservation, as the rotating state is the ground state and cannot extract energy.