Testing quantised inertia on the emdrive (1604.03449v1)

Abstract: It has been shown that truncated cone-shaped cavities with microwaves resonating within them move slightly towards their narrow ends (the emdrive). Standard physics has no explanation for this and an error has not yet been found. It is shown here that this effect can be predicted by assuming that the inertial mass of the photons in the cavity is caused by Unruh radiation, whose wavelengths must fit exactly within the cavity, using a theory already applied successfully to astrophysical anomalies such as galaxy rotation where the Unruh waves have to fit within the Hubble scale. In the emdrive this means that more Unruh waves are allowed at the wide end, leading to a greater inertial mass for the photons there, and to conserve momentum the cavity must move towards its narrow end, as observed. The model predicts thrusts of: 3.8, 149, 7.3, 0.23, 0.57, 0.11, 0.64 and 0.02 mN compared with the observed thrusts of: 16, 147, 9, 0.09, 0.05, 0.06, 0.03, and 0.02 mN and predicts that if the axial length is equal to the diameter of the small end of the cavity, the thrust should be reversed.

• The paper introduces a quantised inertia framework explaining EmDrive thrust via Unruh radiation constraints within a cavity.
• It uses mathematical models to predict inertial mass variations that match observed thrust values from various experiments.
• Results imply that MiHsC could redefine our understanding of inertia and enable propellantless propulsion in space exploration.

Testing Quantised Inertia on the EmDrive

The paper "Testing Quantised Inertia on the EmDrive" by M.E. McCulloch presents a theoretical framework that seeks to explain the thrust observed in the EmDrive experiments using the concept of quantised inertia, or Modified Inertia due to a Hubble-scale Casimir effect (MiHsC). This theory posits that the inertial mass of photons confined within a truncated cone-shaped cavity resonating with microwaves is affected by Unruh radiation, which must comply with boundary conditions similar to the Casimir effect.

The EmDrive, a cavity resonator, allegedly generates thrust when microwaves resonate within it, specifically in the direction of the narrow end of the cavity. Traditional physics cannot account for this phenomenon due to the apparent violation of the conservation of momentum. McCulloch's model proposes that the discrepancy is due to the behavior of Unruh waves, which become limited by the geometry of the cavity. This limitation, he argues, leads to varying inertial masses at different ends of the cavity, producing observable thrust.

Technical Summary

The theoretical underpinning of the paper involves several key developments:

1. Unruh Radiation and MiHsC: The model asserts that photons possess inertia due to Unruh radiation, which is an effect observed when an object accelerates. The spectral distribution of this radiation is influenced by the cavity's dimensions. As the cavity's width varies, so does the number of fitting wavelengths, causing an effective change in inertia.
2. Mathematical Model and Predictions: The paper provides a quantitative analysis through equations that predict the inertial mass differences leading to measured thrusts. McCulloch proposes that the inertial mass shift due to spatial constraints on Unruh radiation within the cavity can be captured by the formula $$F = -\frac{6PQL}{c} \left(\frac{1}{L + 4w_{s}} - \frac{1}{L + 4w_{b}} \right)$$, where $P$ is the power input, $Q$ is the quality factor, and $w_s$ and $w_b$ are the small and big ends of the cavity.
3. Comparison with Experimental Results: The model's predictions are compared to experimental data from various EmDrive tests. The paper presents a table showcasing the thrusts predicted by the MiHsC model against the observed results from multiple experiments, including those conducted by Shawyer, Fetta, Brady at NASA, and others. In many cases, the model predicts similar orders of magnitude thrusts, bolstering the argument for MiHsC.

Implications

The potential implications of this research are far-reaching. The validation of the MiHsC model using laboratory-based EmDrive experiments could provide a novel explanation for inertia, impact our understanding of conservation principles in physics, and challenge conventional models which require dark matter and dark energy to explain astrophysical phenomena. Furthermore, the practical implications could include new methods of propulsion without on-board propellant, profoundly affecting space exploration technologies.

Future Directions

Future work necessitates further experimental validations to refine the model and explore its boundary conditions. The need to test the predicted reversal of thrust direction, adjust design parameters to amplify thrust, and verify results across diversified experimental setups poses a coherent path forward. Continued research into the interplay of cavity geometry, microwave input parameters, and resonance conditions will be crucial to understand the full potential and limitations of the MiHsC model as applied to the EmDrive.

In conclusion, McCulloch's paper contributes to the theoretical exploration of propellantless propulsion and offers a rational model that aligns with observed phenomena. While criticism and skepticism exist due to the fundamental implications of MiHsC, the work encourages an empirical approach to challenging established physical laws, warranting further scrutiny and investigation.