Both classical and quantum mechanics assume that physical laws are invariant under changes in the way that the world is labeled. This Principle of Decompositional Equivalence is formalized, and shown to forbid finite experimental demonstrations that given pointer states |p1> and |p2> refer to the same physical system S. It is then shown that any extra-theoretical assumption that given pointer states |p1> and |p2> with indistinguishable coefficients in a Schmidt basis for the universe refer to the same physical system S is stronger than the assumption of classicality. Standard interpretations of quantum mechanics make such as assumption in analyzing measurement; hence they are logically inconsistent.
Both classical and quantum mechanics assume that physical laws are invariant under changes in the way that the world is labeled. This Principle of Decompositional Equivalence is formalized, and shown to forbid finite experimental demonstrations that given pointer states |p1> and |p2> refer to the same physical system S. It is then shown that any extra-theoretical assumption that given pointer states |p1> and |p2> with indistinguishable coefficients in a Schmidt basis for the universe refer to the same physical system S is stronger than the assumption of classicality. Standard interpretations of quantum mechanics make such as assumption in analyzing measurement; hence they are logically inconsistent.
Quantum mechanics is empirically unrivalled, yet the origin of its distinctive non-classical features remains a foundational question. This paper proves, within the unchanged standard quantum formalism, that these features—collectively termed “quantumness”—arise if and only if certain configurations of the system are indistinguishable in principle. Quantumness is defined as any deviation from classical probability distributions, i.e., probabilities that require coherent amplitude addition rather than incoherent probability addition. Three theorems are established using only the standard Hilbert-space formalism and unitary evolution: 1. Indistinguishability of configurations is necessary and sufficient for quantumness.2. Indistinguishability of identical particles is neither necessary nor sufficient.3. An equivalent restatement in precise operational terms: quantumness occurs exactly when a variable lacks physical definition (distinguishability in principle by macroscopic outcomes). These results are presented and interpreted within the Logical Interpretation of quantum mechanics, a minimalist framework that adds no new postulates and applies classical logic strictly to physically defined facts. The interpretation provides the conceptual tools—particularly the precise notion of “indistinguishability in principle”—that make the theorems sharp and unified. This work unifies the origin of quantumness and serves as the conceptual prequel to the full Logical Interpretation developed in the author’s companion paper.
Assuming the validity of the equivalence principle in the quantum regime, we argue that one of the assumptions of the usual definition of quantum mechanics, namely separation between the “classical” detector and the “quantum” system, must be relaxed. We argue, therefore, that if both the equivalence principle and quantum mechanics continue to survive experimental tests, then this favors “informational” interpretations of quantum mechanics (where formalism is built around relations between observables, defined as information that can be accessed by an observer of the system. In particular “collapse” is understood as a change of relative information as the detector interacts with the system) over “ontic ones” (assuming the physical reality of states and wave functions, which are assumed to be more than informational objects. In particular collapse is understood as a physical process). In particular, we show that relational-type interpretations can readily accommodate the equivalence principle via a minor modification of the assumptions used to justify the formalism. We qualitatively speculate what a full generally covariant quantum dynamics could look like, and comment on experimental investigations.
According to classical physics particles are basic building blocks of the world. Classical particles are distinguishable objects, individuated by physical characteristics. By contrast, in quantum mechanics the standard view is that particles of the same kind ("identical particles") are in all circumstances indistinguishable from each other. This indistinguishability doctrine is motivated by the (anti)symmetrization postulates together with the assumption (``factorism'') that each single particle is represented in exactly one factor space in the tensor product Hilbert space of a many-particles system. Although the factorist assumption is standard in the literature, it is conceptually problematic. Particle indistinguishability is incompatible with the everyday meaning of ``particle'', and also with how this term is used both in classical physics and in the experimental practice of physics. The standard view requires quantum particles of the same kind to remain indistinguishable even in the classical limit, so that a transition to the classical picture of the world seems impossible. Earlier we have proposed an alternative conception of quantum particles that does not rely on factorism and that avoids these and other problems. We further explain and develop this proposal here. In our view, particles in quantum theory are not fundamental but \emph{emergent}. However, in those situations where the particle concept is applicable, quantum particles---identical or not---are distinguishable in the same way as classical particles.
A recent concept in theoretical physics, motivated in string duality and M-theory, is the notion that not all quantum theories arise from quantising a classical system. Also, a given quantum model may possess more than just one classical limit. In view of these developments, we analyse some general properties that quantum mechanics must satisfy, if it is not to be formulated as a quantisation of a given classical mechanics. Instead, our approach to quantum mechanics is modelled on a statement that is close in spirit to the equivalence principle of general relativity, thus bearing a strong resemblance with the equivalence principle of quantum mechanics formulated by Faraggi-Matone.
A type of mechanics will be presented that possesses some distinctive properties. On the one hand, its physical description & rules of operation are readily comprehensible & intuitively clear. On the other, it fully satisfies all observable predictions of non-relativistic quantum mechanics. Within it, particles exist at points in space, follow continuous, piecewise differentiable paths, and their linear momentum is equal to their mass times their velocity along their path. Yet the probabilities for position and momentum, conditioned on the state of the particle's environment, follow the rules of quantum theory. Indeed, all observable consequences of quantum theory are satisfied; particles can be entangled, have intrinsic spin, this spin is not local to the particle, particle identity can effect probabilities, and so forth. All the rules of quantum mechanics are obeyed, and all arise in a straightforward fashion. After this is established, connections will be drawn out between this type of mechanics and other types of quantum worlds; those that obey Bohmian mechanics, stochastic mechanics, the many worlds interpretation, and physical collapse. In the final section, a relativistic version of the mechanics will be presented.
This component develops the formal consequences of Invariant Core Theory and analyzes time, dynamics, Hilbert-space, and spacetime representations as regime-dependent realizations of the invariant core. Version "v7 Clean"removes publisher branding; content unchanged. Orientation for Readers – P2: Formal Structure and Consequences of the Invariant Core Theory This paper develops the structural consequences of the Invariant Core Theory (ICT) established in P1. It does not extend the formal core and does not introduce new axioms. Instead, it analyzes how familiar physical description frameworks arise—or fail to arise—as admissible representations of that core. What this paper does It examines time, dynamics, Hilbert-space formalisms, and spacetime geometry as representations, not as fundamental structures. It formulates explicit admissibility criteria (e.g. kernel-faithfulness and regime transparency). It explains why certain features of modern physics - entanglement, absence of global time, probabilistic structure, spacetime curvature - are structurally necessary, not dynamical assumptions. It derives structural no-go results that constrain admissible theory construction. This paper answers the question: Given the invariant core, which forms of physical description are possible - and under which conditions do they break down? What this paper deliberately does not do It does not propose new physical laws or interactions. It does not unify quantum theory and general relativity dynamically. It does not derive numerical predictions or fit experimental data. It does not claim ontological priority for any representational framework. Any reading of this paper as a competing physical theory, interpretation, or model would therefore be a category error. How to read this paper All results are structural and representational, not dynamical. “Predictions” are constraints on admissibility, not empirical forecasts. No-go statements exclude classes of explanations, not observed phenomena. Apparent conflicts between quantum and geometric descriptions are treated as representational conflicts, not physical contradictions. The paper should be read as a map of representational regimes and limits, not as a proposal for new dynamics. Intended audience This work is addressed to readers with background in: theoretical or mathematical physics, foundations of quantum theory or relativity, philosophy of physics with interest in structure and representation. Familiarity with standard formalisms is assumed, but the paper does not presuppose agreement with any particular interpretation or unification program. Relation to P1 and scope of validity P2 presupposes the formal core developed in P1. No concept introduced here has independent meaning outside that core. Conversely, P1 is structurally complete without P2, while P2 is conceptually dependent on P1. Together, the two papers form a closed framework: P1 establishes what must be structurally true. P2 analyzes how physical descriptions can be admissible given those truths.