Quantised inertia from relativity and the uncertainty principle (1610.06787v1)

Abstract: It is shown here that if we assume that what is conserved in nature is not simply mass-energy, but rather mass-energy plus the energy uncertainty of the uncertainty principle, and if we also assume that position uncertainty is reduced by the formation of relativistic horizons, then the resulting increase of energy uncertainty is close to that needed for a new model for inertial mass (MiHsC, quantised inertia) which has been shown to predict galaxy rotation without dark matter and cosmic acceleration without dark energy. The same principle can also be used to model the inverse square law of gravity, and predicts the mass of the electron.

• The paper establishes a model where inertia emerges from Unruh radiation interacting with relativistic horizons.
• It employs a modified inertia equation to reproduce standard terrestrial inertia while predicting deviations in low-acceleration regimes.
• The framework offers an alternative explanation for dark matter and dark energy effects, evidenced by accurate mass predictions for elementary particles.

Quantised Inertia from Relativity and the Uncertainty Principle

The paper by M.E. McCulloch advances a theoretical framework that attempts to reconcile some aspects of quantum mechanics and general relativity through the concept of quantised inertia, also referred to as Modified Inertia by a Hubble-scale Casimir effect (MiHsC). The research outlines a methodology by which both gravity and inertia can be derived by incorporating relativistic horizons within the Heisenberg uncertainty principle, leading to the proposition that the resulting uncertainty in energy can become real.

Fundamental Concepts and Methodology

The paper builds upon previous attempts to merge general relativity with quantum mechanics, particularly focusing on the behavior of inertial mass in light of the Unruh effect. The proposed model, MiHsC, suggests that inertia is not a fundamental property of objects but rather an emergent one due to the interaction between Unruh radiation and relativistic Rindler horizons. This interaction is asserted to yield an anisotropic radiation pressure that manifests as inertial mass.

The model is encapsulated in Equation 1, which modifies standard inertial mass ($m$) to a new form ($m_i$), incorporating large-scale cosmological constraints: $m_i = m \left(1 - \frac{2c}{|a|\Theta}\right)$ where $c$ is the speed of light, $|a|$ is the magnitude of the object's acceleration, and $\Theta$ is the universe's observable diameter. The importance of this equation lies in its ability to reproduce standard inertia at typical terrestrial accelerations while predicting altered inertia in low-acceleration regimes, such as those found at the peripheries of galaxies.

Numerical Results and Implications

Through a comprehensive application of this framework, the paper addresses several cosmological phenomena commonly explained through dark matter and dark energy. For example, the reduction of inertial mass at low accelerations offers an alternative explanation for the rotation curves of galaxies without invoking dark matter. Similarly, the cosmic acceleration could be accounted for without dark energy under this model.

A salient point in this research is the prediction of elementary particle masses using the same principles. By applying the Heisenberg uncertainty principle to confined particles like electrons, the masses are computed using initial confinement at a cosmic scale and subsequent confinement at a subatomic scale. Notably, the calculated electron mass closely corresponds to its experimentally observed value, showcasing the model's utility.

Theoretical and Practical Implications

The findings could potentially offer new insights into the gravitation-inertia dichotomy, proposing a theoretical unification under the quantum and relativistic framework posed by MiHsC. The ability of this model to address longstanding astronomical anomalies suggests that further investigation and refinement could contribute significantly to the current understanding of cosmological mechanics.

Moreover, McCulloch's derivation of gravity through uncertainty principles extends upon earlier works, proposing that gravitational and inertial phenomena might be fundamentally intertwined with quantum mechanics at macroscopic scales. This perspective could challenge conventional interpretations, paving the way for novel approaches to solving some of the prevailing issues in physics.

Speculation on Future Developments

Future developments in this area could revolve around empirical validation of the model's predictions under extreme astrophysical conditions. Observations in low-acceleration environments, for both natural and artificial objects, could provide a testing ground for MiHsC's tenets. Additionally, this approach may inspire alternative interpretations or the development of quantum gravity models, incorporating parametric modifications to further align MiHsC with existing experimental data.

In conclusion, M.E. McCulloch's formulation offers a compelling hypothesis that reinterprets the phenomenology of inertia and gravity through the lens of quantum uncertainty and relativistic horizons. The paper's associations between cosmic phenomena and quantum mechanics underscore the ever-present potential for synergy between these foundational domains of physics.