A Minimal Theoretical Framework for Assessing Field-Propulsion Theories: Momentum Closure, Limiting Conditions, and Background Momentum Reservoirs

A wide variety of field-propulsion concepts have been proposed that invoke electromagnetic fields, the quantum vacuum, inertia, spacetime, the distant universe, and other physical entities. However, when a propulsion device acquires net momentum, the momentum-conservation requirements—specifically, which physical degree of freedom receives the equal and opposite momentum, and whether that reaction momentum remains outside the device after a complete operating cycle—have generally been discussed in proposal-specific terms and have not always been formulated as a unified minimal assessment framework. The purpose of this Working Paper is therefore to construct a minimal theoretical framework that researchers in this field can use to compare different propulsion concepts on a common physical basis. First, it is shown that a closed, periodically driven steady-state electromagnetic system cannot generate sustained average thrust solely from asymmetric internal electromagnetic forces, and an external degree of freedom capable of carrying reaction momentum is introduced as a momentum reservoir R. The reservoir is required to possess independently definable energy and momentum, a dispersion relation, a local exchange law, and the ability to retain or transport reaction momentum outside the device after each cycle. A scalar field coupled to the electromagnetic invariant FμνFμν is then introduced as the minimal field model FP-1, and the conditions under which two phase-controlled sources can generate a directional field-momentum flux are derived. For an ordinary free relativistic positive-energy field, the thrust-to-power ratio cannot exceed the photon-rocket limit $1/c$, and three-dimensional directionality is additionally strongly suppressed for compact sources in the long-wavelength regime. On this basis, FP-1 is extended to a hypothetical background field χ supporting slow-dispersion excitations. This leads to the general performance relation |F|/Pelectrical=β3Dη_χ(k_χ/ω) and to the condition β3Dη_χ>vₚₕ/c for exceeding the photon-rocket limit. Although a $P(X)$-type background supplemented by higher spatial derivatives can mathematically support slow dispersion within an effective-field-theory description, the physical existence of the χ background, its coupling strength to electromagnetic fields, the conversion efficiency, and consistency with existing experimental and observational constraints remain unverified. FP-1 is therefore not presented as an experimentally established propulsion theory, but as an exploratory theoretical framework for screening field-propulsion proposals in terms of momentum closure, energy balance, coupling, dispersion relations, phase matching, directionality, conversion efficiency, and falsifiability.