Inertia from an asymmetric Casimir effect

Abstract: The property of inertia has never been fully explained. A model for inertia (MiHsC or quantised inertia) has been suggested that assumes that 1) inertia is due to Unruh radiation and 2) this radiation is subject to a Hubble-scale Casimir effect. This model has no adjustable parameters and predicts the cosmic acceleration, and galaxy rotation without dark matter, suggesting that Unruh radiation indeed causes inertia, but the exact mechanism by which it does this has not been specified. The mechanism suggested here is that when an object accelerates, for example to the right, a dynamical (Rindler) event horizon forms to its left, reducing the Unruh radiation on that side by a Rindler-scale Casimir effect whereas the radiation on the other side is only slightly reduced by a Hubble-scale Casimir effect. This produces an imbalance in the radiation pressure on the object, and a net force that always opposes acceleration, like inertia. A formula for inertia is derived, and an experimental test is suggested.

• The paper proposes Quantised Inertia (MiHsC), explaining inertia as arising from Unruh radiation's interaction with an asymmetric Casimir effect, aiming to explain astrophysical phenomena without dark matter.
• A formula is derived predicting inertia scaling with Unruh radiation energy density, avoiding prior model limitations and aligning potential inertia values with the Planck mass scale.
• The model offers a potential explanation for galactic rotation curves and suggests future experimental testing using metamaterials to explore inertia manipulation.

Overview of "Inertia from an Asymmetric Casimir Effect" by M.E. McCulloch

The paper by M.E. McCulloch proposes a novel model of inertia called "Quantised Inertia" or MiHsC, which stands for "Modification of inertia resulting from a Hubble-scale Casimir effect". It suggests that inertia arises from the interaction between Unruh radiation and an asymmetric form of the Casimir effect. This model aligns inertia with fundamental cosmological parameters without introducing adjustable parameters and purports to explain astrophysical phenomena that traditionally require the existence of dark matter.

Main Contributions

The primary hypothesis is that when an object accelerates, a Rindler horizon forms in the direction opposite to acceleration. This results in a differential pressure on the object due to the varying density of Unruh radiation. Due to this unbalanced Casimir effect, a resistive force arises opposing the acceleration, providing a novel explanation for inertia.

• Unruh Radiation and Casimir Effect:

The paper employs Unruh radiation, a predicted phenomenon where an accelerating observer detects blackbody radiation absent for an inertial observer. Additionally, McCulloch hypothesizes the interaction of this radiation with large-scale (Hubble) and small-scale (Rindler) Casimir effects, creating an asymmetry that could underlie inertial resistance.

• Formula Derivation:

Using an integral approach over possible radiation directions, a specific formula for the inertial force is derived. Significantly, the model predicts inertia that scales with the energy density of this Unruh radiation, sidestepping the need for supplementary high-frequency cutoffs unlike previous theories.

• Quantitative Alignment with Astrophysics:

The MiHsC model correlates potential inertia values (derived from Unruh radiation's interaction with Rindler horizons) with the observed Planck mass scale. The implications extend to cosmic-scale phenomena, offering potentially explanatory frameworks for galactic rotation curves traditionally attributed to dark matter.

Theoretical Implications

MiHsC challenges the foundational equivalence principle by suggesting a modification in the understanding of inertial mass, positing it as a function of both gravitational mass and radiation pressure. This diverges from classical Newtonian mechanics, yet aligns with quantum field predictions under extreme conditions (consistent with Fulling, Davies, and Unruh effects).

While MiHsC points towards an integrated cosmological framework, further theoretical work is required to reconcile the model with standard cosmology and quantum gravity. Specifically, the implications for equivalence violation require rigorous testing in controlled conditions.

Practical Implications and Future Directions

The potential to experimentally test MiHsC-like effects through engineered metamaterials offers an intriguing application. Advances in manipulating electromagnetic fields using metamaterials might allow engineers to artificially create situations mimicking cosmic-scale event horizons. If successful, this could lead to novel methods of inertia manipulation, impacting propulsion technology and related fields.

Furthermore, addressing auxiliary phenomena, such as anomalies in spacecraft trajectories (e.g., the Pioneer anomaly), and reconciling these with MiHsC could spur additional validation or refinement of the model.

Conclusions

McCulloch’s work proposes a fresh ontological view of inertia with foundations rooted in quantum field theory and cosmology. By linking Unruh radiation with Casimir effects through a robust mathematical framework, MiHsC offers an innovative approach to long-standing puzzles in physics. It is precisely these speculative yet testable predictions that make MiHsC worthy of further empirical scrutiny and theoretical analysis within the physics community.