Apparent Weight (Wapp) in the Context of Extended Classical Mechanics:
Soumendra Nath Thakur | ORCiD:0000-0003-1871-7803 | postmasterenator@gmail.com | November 26, 2024
Apparent weight (Wapp) is the perceived lightness or heaviness of an object, shaped by the interplay between its matter mass and effective mass within the surrounding environment. In regions with strong gravitational potential energy but minimal or no external gravitational force, the object’s effective mass can reduce its apparent weight or even make it seem weightless. This happens because the gravitational environment alters how the object’s mass interacts with external forces, potentially making the object appear lighter due to the negative value of apparent mass or as though it’s being pushed upward due to the effect of negative effective mass. Thus, apparent weight reflects not only the force of gravity but the combined effects of the object’s matter mass, its effective mass influenced by apparent mass, the surrounding gravitational field, and any other external forces acting on it.
The apparent weight can also be influenced by the object’s motion. When moving upward, the object can feel heavier due to the opposing force needed to overcome gravity. In contrast, when in free fall, the object experiences weightlessness, as the forces acting on it, including gravity, are effectively in balance, and there is no contact force to give the sensation of weight.
Classical Mechanical Interpretation of Apparent Weight
However, the interpretation of apparent weight within the framework of extended classical mechanics (ECM) introduces a redefined and expanded perspective. Here, apparent weight is not merely the perceived weight of an object, as described in classical mechanics, but a dynamic property shaped by the interaction between matter mass and effective mass, influenced by negative apparent mass (NAM).
This interpretation diverges from the classical view, which attributes apparent weight solely to the imbalance between gravitational force and contact force. For instance, in classical mechanics, an object submerged in water has an apparent weight equal to its actual gravitational force minus the buoyant force exerted by the fluid. In contrast, extended classical mechanics considers how the gravitational environment and external forces dynamically modify the object's effective mass, offering a more comprehensive understanding of weight under varied conditions, including strong gravitational potentials or near-weightless states.
The apparent weight (Wapp) can be expressed dynamically as:
Wapp = Meff⋅geff,ext
Where geff,ext is the weak external gravitational acceleration, when Meff has a negative component due to the negative apparent mass (Mapp):
Meff = MM + (-Mapp)
Where Meff includes both matter mass and apparent mass contributions.
Gravitational Mass, Effective Mass, and Apparent Weight in the Presence of Negative Apparent Mass (NAM)
Apparent weight (Wapp), under Extended Classical Mechanics (ECM). This page articulates how field-induced negative apparent mass modulates gravitational response and perceived weight across physical regimes.
Overview
Extended Classical Mechanics (ECM) departs from the classical one-to-one association of inertial mass and gravitational response. Instead, ECM introduces effective mass as the operative quantity that determines gravitational behaviour. Effective mass is a dynamic balance between the intrinsic matter content and the counteracting, field-induced apparent mass often referred to as Negative Apparent Mass (NAM).
Core Concept: Gravitational Mass as Effective Mass
In ECM the gravitational mass of a body corresponds directly to its effective mass. Gravitational behaviour therefore depends on the net outcome of two interacting components: the positive matter component and the negative apparent mass developed through energy redistribution and field coupling. Apparent weight is then the observable manifestation of this local field–mass equilibrium rather than a fixed attribute of matter.
Three Fundamental Regimes of Apparent Weight
The interplay between intrinsic matter content and NAM produces three distinct gravitational regimes that determine the sign and magnitude of apparent weight. Each regime is presented below with a concise physical interpretation.
Positive Apparent Weight
When the intrinsic matter component dominates over the field-induced NAM, the effective mass remains positive and the body exhibits normal downward gravitational attraction. This is the familiar regime of everyday experience where objects feel heavy relative to activity or location.
Zero Apparent Weight
When intrinsic and apparent mass components reach exact balance, the effective mass vanishes. The body experiences no net gravitational response - a state corresponding to weightlessness, orbital free-fall, or neutral levitation where attraction and field effects precisely cancel.
Negative Apparent Weight
If the magnitude of the negative apparent mass exceeds that of the matter content, the effective mass becomes negative and the gravitational response reverses. The system behaves as if repelled by the gravitational source, producing buoyant-like or antigravitational motion.
Physical Interpretation & Broader Implications
Apparent weight in ECM is fundamentally a measure of energy redistribution within the local field structure. The effective mass - equivalent to gravitational mass in this formulation - is the determining parameter for whether an object is attracted, neutral, or repelled by its surrounding gravitational field. This unified perspective accommodates microphysical behaviour (for example, the antigravitational tendencies of photons), macroscopic variations (subtle changes in weight with gravitational potential) and cosmological phenomena (large-scale repulsion driving cosmic acceleration).
Consequently, what we measure as weight is a transient energetic state: a balance between existence (the matter mass) and its entropic counterpart (the negative apparent mass field).