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Mass as information: A definition and its consequences

Aniruddha Joshi

Published Apr 14, 2026• 0 citations
Publisher

Abstract

Abstract Mass has never been defined. It has been measured, related to other quantities, and given a mechanism through the Higgs field. But what mass physically is has not been stated. This paper proposes a definition: mass is the information encoding that matter acquires from the field — the degree to which a state is distinguishable from the vacuum, measured in Shannon bits. From this single definition, without additional assumptions, three consequences follow. First, the Schrödinger equation becomes nonlinear: mass depends on the wavefunction itself, superposition is approximate for massive particles, and wavefunction collapse has a self-reinforcing mechanism without requiring an external observer. Second, the source of spacetime curvature in Einstein’s field equations is not mass but information content — distinguishability of matter from the vacuum. Third, the quantum-classical transition is not a boundary to be explained but a process driven by mass accumulation: as encoding increases, classicality follows automatically. The Higgs vacuum expectation value v = 246 GeV is identified as the conversion factor between bits of distinguishability and kilograms of mass. The photon and neutrino are natural consistency checks: the photon has zero encoding and zero mass; the neutrino has near-zero encoding and near-zero mass

DOI
10.5281/zenodo.19561029

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Abstract Mass has never been defined. It has been measured, related to other quantities, and given a mechanism through the Higgs field. But what mass physically is has not been stated. This paper proposes a definition: mass is the information encoding that matter acquires from the field — the degree to which a state is distinguishable from the vacuum, measured in Shannon bits. From this single definition, without additional assumptions, three consequences follow. First, the Schrödinger equation becomes nonlinear: mass depends on the wavefunction itself, superposition is approximate for massive particles, and wavefunction collapse has a self-reinforcing mechanism without requiring an external observer. Second, the source of spacetime curvature in Einstein’s field equations is not mass but information content — distinguishability of matter from the vacuum. Third, the quantum-classical transition is not a boundary to be explained but a process driven by mass accumulation: as encoding increases, classicality follows automatically. The Higgs vacuum expectation value v = 246 GeV is identified as the conversion factor between bits of distinguishability and kilograms of mass. The photon and neutrino are natural consistency checks: the photon has zero encoding and zero mass; the neutrino has near-zero encoding and near-zero mass
We assume that particles are point-like objects even when not observed. We report on the consequences of our assumption within the realm of quantum theory. An important consequence is the necessity of vacuum fields to account for particle dynamics. The zero-point energy is evidence of the reality of vacuum fields. The dynamics of vacuum fields depends on wave equations, boundary conditions and external sources. The wavefunction is an expression of vacuum fields. Particle events are described by probabilistic distribution functions obtained from vacuum fields. We solve the measurement problem by noticing that in our model the wavefunction does not collapse.
The century-long conflict between quantum mechanics and general relativity is essentially a dispute over the definition of the fundamental measurement benchmark of the universe. Quantum mechanics treats time as an absolute external background, while general relativity regards mass as the measurement benchmark of curved spacetime. The two theories cannot be self-consistently unified under extreme conditions. Based on the core axiomatic system of Time Field Theory (TFT), this paper proposes a first-principles self-consistent interpretation of quantum mechanics: the wave function is neither the physical reality of a particle nor an encoding of our knowledge, but the probability amplitude for the time field to condense mass at a spatial point and thereby establish a measurement benchmark; the Schrödinger equation is the evolution law of the measurability probability amplitude of the time field in the uniform γ=1 background; wave function collapse corresponds to a physical phase transition of the time field from a uniform state to a locally condensed state, and the observer is essentially a massive entity with intrinsic time flow. This interpretation requires no assumptions of external observers, many worlds, or hidden variables, naturally unifies the quantum and classical worlds, and is fully compatible with all known experimental results in the weak-field low-speed limit, providing a completely new metrological foundation for the problem of quantum gravity.
The way, in which quantum information can unify quantum mechanics (and therefore the Standard model) and general relativity, is investigated. Quantum information is defined as the generalization of the concept of information as to the choice among infinite sets of alternatives. Relevantly, the axiom of choice is necessary in general. The unit of quantum information, a qubit is interpreted as a relevant elementary choice among an infinite set of alternatives generalizing that of a bit. The invariance to the axiom of choice shared by quantum mechanics is introduced: It constitutes quantum information as the relation of any state unorderable in principle (e.g. any coherent quantum state before measurement) and the same state already well-ordered (e.g. the well-ordered statistical ensemble of the measurement of the quantum system at issue). This allows of equating the classical and quantum time correspondingly as the well-ordering of any physical quantity or quantities and their coherent superposition. That equating is interpretable as the isomorphism of Minkowski space and Hilbert space. Quantum information is the structure interpretable in both ways and thus underlying their unification. Its deformation is representable correspondingly as gravitation in the deformed pseudo-Riemannian space of general relativity and the entanglement of two or more quantum systems. The Standard model studies a single quantum system and thus privileges a single reference frame turning out to be inertial for the generalized symmetry U(1)XSU(2)XSU(3) “gauging” the Standard model. As the Standard model refers to a single quantum system, it is necessarily linear and thus the corresponding privileged reference frame is necessary inertial. The Higgs mechanism U(1) → U(1)XSU(2) confirmed enough already experimentally describes exactly the choice of the initial position of a privileged reference frame as the corresponding breaking of the symmetry. The Standard model defines ‘mass at rest’ linearly and absolutely, but general relativity non-linearly and relatively. The “Big Bang” hypothesis is additional interpreting that position as that of the “Big Bang”. It serves also in order to reconcile the linear Standard model in the singularity of the “Big Bang” with the observed nonlinearity of the further expansion of the universe described very well by general relativity. Quantum information links the Standard model and general relativity in another way by mediation of entanglement. The linearity and absoluteness of the former and the nonlinearity and relativeness of the latter can be considered as the relation of a whole and the same whole divided into parts entangled in general
Quantum information is discussed as the universal substance of the world. It is interpreted as that generalization of classical information, which includes both finite and transfinite ordinal numbers. On the other hand, any wave function and thus any state of any quantum system is just one value of quantum information. Information and its generalization as quantum information are considered as quantities of elementary choices. Their units are correspondingly a bit and a qubit. The course of time is what generates choices by itself, thus quantum information and any item in the world in final analysis. The course of time generates necessarily choices so: The future is absolutely unorderable in principle while the past is always well-ordered and thus unchangeable. The present as the mediation between them needs the well-ordered theorem equivalent to the axiom of choice. The latter guarantees the choice even among the elements of an infinite set, which is the case of quantum information. The concrete and abstract objects share information as their common base, which is quantum as to the formers and classical as to the latter. The general quantities of matter in physics, mass and energy can be considered as particular cases of quantum information. The link between choice and abstraction in set theory allows of “Hume’s principle” to be interpreted in terms of quantum mechanics as equivalence of “many” and “much” underlying quantum information. Quantum information as the universal substance of the world calls for the unity of physics and mathematics rather than that of the concrete and abstract objects and thus for a form of quantum neo-Pythagoreanism in final analysis.
Abstract We develop and apply the Yugen wavefunction framework, a phase-geometric reformulation of quantum theory in which the vacuum is treated as an active medium with intrinsic stiffness set by the Planck scale. In this approach, physical fields and particles emerge from internal phase geometry rather than from fundamental point-like interactions. By identifying the amplitude of the Yugen wavefunction with the Planck energy, the Planck scale becomes a physical parameter governing vacuum rigidity and nonlinear phase response. We present explicit numerical predictions across atomic, particle, and mesoscopic regimes. In the atomic sector, the framework predicts small but systematic nonlinear deviations in isotope-shift spectroscopy, arising from coherent vacuum phase effects and consistent with recent high-precision datasets. In the neutrino sector, neutrino masses emerge naturally from localized topological phase interference, yielding the observed mass scale without introducing additional heavy fields. We further address the quantum–classical transition by deriving a nonlinear phase-induced decoherence mechanism for macroscopic objects. The resulting mass- and size-dependent decoherence times place mesoscopic systems near the picogram scale at the threshold of sustained quantum superpositions, a regime accessible to current optomechanical experiments. These results suggest that precision spectroscopy, neutrino phenomenology, and mesoscopic quantum tests probe a common underlying phase structure of the vacuum. The Yugen wavefunction thus provides a unified and experimentally falsifiable framework linking quantum fields, particle properties, and the emergence of classicality.
Quantum mechanics was reformulated as an information theory involving a generalized kind of information, namely quantum information, in the end of the last century. Quantum mechanics is the most fundamental physical theory referring to all claiming to be physical. Any physical entity turns out to be quantum information in the final analysis. A quantum bit is the unit of quantum information, and it is a generalization of the unit of classical information, a bit, as well as the quantum information itself is a generalization of classical information. Classical information refers to finite series or sets while quantum information, to infinite ones. Quantum information as well as classical information is a dimensionless quantity. Quantum information can be considered as a “bridge” between the mathematical and physical. The standard and common scientific epistemology grants the gap between the mathematical models and physical reality. The conception of truth as adequacy is what is able to transfer “over” that gap. One should explain how quantum information being a continuous transition between the physical and mathematical may refer to truth as adequacy and thus to the usual scientific epistemology and methodology. If it is the overall substance of anything claiming to be physical, one can question how different and dimensional physical quantities appear. Quantum information can be discussed as the counterpart of action. Quantum information is what is conserved, action is what is changed in virtue of the fundamental theorems of Emmy Noether (1918). The gap between mathematical models and physical reality, needing truth as adequacy to be overcome, is substituted by the openness of choice. That openness in turn can be interpreted as the openness of the present as a different concept of truth recollecting Heidegger’s one as “unconcealment” (ἀλήθεια). Quantum information as what is conserved can be thought as the conservation of that openness