MOND as a transformation between non-inertial reference frames via Sciama's interpretation of Mach's Principle

Abstract: Milgrom's Modified Newtonian Dynamics (MOND) correction to Newtonian gravity or inertia is shown to be equivalent to a more fundamental transformation between a non-inertial local reference frame and the fixed background of the observable universe, complying with Mach's principle. Both Newton's gravitational constant and Milgrom's MOND acceleration parameter or scale constant are substituted for two varying, measurable, physical, and cosmological parameters under the justification of Sciama's interpretation of Mach's principle: causally connected mass and size of the universe. This Machian interpretation, scale-invariant and free from fundamental constants and free parameters with the exception of the speed of light as the speed of causality and gravity, is based on relative field intensities of the small and large scale of the universe. It respects the Machian effect from Sciama's model, by which, in absence of a background, rotational speed is undefined up to the speed of light. The Machian MOND approximation is a necessary feature of a phenomenological nonlinear theory of modified inertia or nonlinear theory of modified gravity which incorporates Mach's principle in agreement with galaxy rotation curves.

• The paper demonstrates that MOND can be reformulated by replacing traditional gravitational constants with measurable cosmological parameters.
• It employs Sciama’s interpretation of Mach’s Principle to transform non-inertial frames, unifying local galactic dynamics with universal scale metrics.
• This reinterpretation potentially eliminates the need for dark matter in explaining galactic rotation curves while addressing inconsistencies in cluster dynamics.

An Examination of MOND through the Lens of Mach's Principle

The paper under review presents an intriguing exploration of Modified Newtonian Dynamics (MOND) by postulating a significant reinterpretation grounded in Mach's Principle, specifically through the insights offered by Sciama’s interpretation. The author suggests that MOND corrections, traditionally understood within the landscape of galactic rotation anomalies, can be equivalently viewed as transformations between non-inertial reference frames, directly engaging with the Machian perspective of inertia in relation to the entire universe.

Reformulating MOND in a Machian Framework

At the core of this work lies the assertion that MOND, as originally proposed by Milgrom, can be reframed without reliance on conventional gravitational constants or the MOND acceleration constant $a_0$. The author substitutes these constants with cosmological parameters and the speed of light, thus aligning with the Schrödinger and Sciama interpretation of Mach's Principle. Specifically, the traditional gravitational constant $G$ and Milgrom’s $a_0$ are revisited and expressed via the speed of light and the mass and radius of the observable universe $M_u$ and $R_u$. This transformation underscores a Machian interpretation, suggesting changes in gravitational force contingent on relative field intensities and anchored in the universe's total mass and size.

Implications of the Machian Perspective

The implications of this novel perspective are multifaceted. From a theoretical standpoint, it liberates MOND from dependence on ad hoc fundamental constants, instead rooting it in parameters that are intrinsically measurable and universe-centric. This Montesquieu approach implies a unification of local galactic dynamics with broader cosmological properties, potentially extending Mach’s Principle beyond its philosophical origins into a tangible phenomenological application.

Practically, as the paper posits, this Machian reinterpretation could eliminate the need for dark matter hypotheses in explaining galactic rotation curves, provided the universe's observable mass adequately accounts for gravitational effects. Additionally, this theoretical framework may address inconsistencies related to MOND in galactic clusters by accommodating a dynamical and potentially large-scale varying $a_0$.

Theoretical Speculation and Future Directions

By situating MOND within a Machian framework, this work nudges the scientific community toward revisiting core assumptions about the interplay between inertia, gravity, and the universe at large. The Machian MOND may pave the way for alternate interpretations of gravitational and inertial interactions, aligning with the quest for a universal theory reconciliatory to both quantum mechanics and general relativity.

The author highlights potential avenues for further inquiry, including the exploration of relativistic models that preserve this reformulated MOND's alignment with Mach's principle, particularly through adjusting Sciama's interpretation to enhance predictive accuracy. Moreover, testing these ideas through cosmological observations could illuminate the temporal and spatial evolution of the universal constants involved.

Concluding Remarks

This paper proposes an innovative yet technically rigorous reinterpretation of MOND through a Machian lens. In doing so, it not only challenges traditional reliance on dark matter-driven explanations for galactic anomalies but also hints at a paradigm where universal laws stem directly from the universe’s large-scale structure. Such discourse invites continued investigation into the fundamental nature of inertia and gravity, potentially pointing towards an era of post-Newtonian physics deeply integrated with cosmological insights.