[Paper Review] Galaxies as Rotating Buckets - a Hypothesis on the Gravitational Constant Based on Mach's Principle

Alexander Unzicker|ArXiv.org|Aug 28, 2003

Relativity and Gravitational Theory25 references3 citations

TL;DR

This paper proposes that the gravitational constant G is spatially dependent on the Milky Way's mass, size, and angular momentum, deriving G from galactic rotation via Mach's principle. It explains flat rotation curves without dark matter, modifies Newtonian gravity to match observations, and suggests testable consequences for cosmology and energy conservation.

ABSTRACT

According to Mach's principle inertia has its reason in the presence of all masses in the universe. Despite there is a lot of sympathy for this plausible idea, only a few quantitative frameworks have been proposed to test it. In this paper a tentative theory is given which is based on Mach's critisism on Newton's rotating bucket. Taking this criticism seriously, one is led to the hypothesis that the rotation of our galaxy is the reason for gravitation. Concretely, a functional dependence of the gravitational constant on the size, mass and angular momentum of the milky way is proposed that leads to a spatial, but not to a temporal variation of G. Since Newton's inverse-square law is modified, flat rotation curves of galaxies can be explained that usually need the postulate of dark matter. While the consequences for stellar evolution are discussed briefly, a couple of further observational coincidences are noted and possible experimental tests are proposed.

Motivation & Objective

• To resolve the dark matter problem by reinterpreting the gravitational constant G as dependent on galactic rotation, inspired by Mach’s principle.
• To provide a mechanism for flat rotation curves in spiral galaxies without invoking non-baryonic dark matter.
• To test the hypothesis that inertia and gravity arise from the dynamics of large-scale structures like the Milky Way.
• To explore the implications of a spatially varying G on energy conservation, stellar evolution, and cosmological coincidences.
• To propose experimental tests for the modified gravitational law and its departure from standard Newtonian gravity.

Proposed method

• Proposes a functional form for G that depends on the Milky Way’s mass M, radius R, and angular momentum L, derived from Mach’s criticism of Newton’s rotating bucket.
• Modifies Newton’s inverse-square law by replacing the constant G with a spatially varying function G(r) = G₀ × f(R, M, L), where f depends on galactic rotation.
• Derives a modified gravitational force law that accounts for rotational effects, leading to flat rotation curves without dark matter.
• Analyzes the implications for energy conservation, showing that the spatially varying G violates standard Newtonian energy conservation on large scales.
• Compares the model to observational data, including flat rotation curves, the Tully-Fisher relation, and the M(BH)–σ relation.
• Suggests experimental tests involving precise measurements of gravitational forces in rotating systems and deviations from standard G.

Experimental results

Research questions

• RQ1 Can the flat rotation curves of spiral galaxies be explained without postulating dark matter by modifying G based on galactic rotation?
• RQ2 How does a spatially varying gravitational constant G, dependent on galactic mass, size, and angular momentum, affect orbital dynamics?
• RQ3 What are the consequences of a Machian G for energy conservation and the validity of Newton’s third law on cosmological scales?
• RQ4 Is there a theoretical framework that unifies inertia and gravity through galactic rotation, consistent with general relativity?
• RQ5 Can the observed coincidence between the universe’s radius and galactic surface areas be explained by this model?

Key findings

• The model explains flat rotation curves in spiral galaxies without requiring dark matter by introducing a spatially dependent G that increases with distance from the galactic center.
• The proposed functional form of G depends on the Milky Way’s mass, radius, and angular momentum, leading to a modified gravitational force law that matches observed rotation curves.
• The model predicts a violation of standard energy conservation on large scales due to the spatial dependence of G, challenging Newtonian mechanics.
• The model accounts for the Tully-Fisher relation and the M(BH)–σ relation as natural consequences of the rotating-galaxy-based G.
• The coincidence between the surface area of galaxies and a sphere of radius equal to the universe’s radius is explained as a consequence of the model’s spatial dependence of G.
• The model suggests that the Pioneer anomaly may be related to the same mechanism, as the anomalous acceleration is of the same order as the predicted G-gradient effect.