Foundations of Physics最新文献

In this short paper, we propose a special class of quantum systems with implicit quantum uncertainties without any probability structure followed by the dynamical behavior of the systems. When a system is deterministic or random, it does not capture the essence of freedom of choice (FOC), which is the ability to make decisions followed by one’s preferences, free from both deterministic and random outcomes. The proposed special class of quantum systems contains non-deterministic yet non-random outcomes, and so they open the possibility of having FOC within the systems. We also examine examples of such a special class of quantum systems that do not violate the postulates of quantum mechanics.

We revisit the concept of de Sitter (dS) ‘tachyonic’ scalar fields, characterized by discrete negative squared mass values, and assess their physical significance through a rigorous Wigner-inspired group-theoretical analysis. This perspective demonstrates that such fields, often misinterpreted as inherently unstable due to their mass parameter, are best understood within the framework of unitary irreducible representations (UIRs) of the dS group. The discrete mass spectrum arises naturally in this representation framework, offering profound insights into the interplay between dS relativity and quantum field theory. Contrary to their misleading nomenclature, we argue that the ‘mass’ parameter associated with these fields lacks intrinsic physical relevance, challenging traditional assumptions that link it to physical instability. Instead, any perceived instability originates from mismanagement of the system’s inherent gauge invariance rather than the fields themselves. A proper treatment of this gauge symmetry, particularly through the Gupta–Bleuler formalism, restores the expected characteristics of these fields as free quantum entities in a highly symmetric spacetime. This study seeks to dispel misconceptions surrounding dS ‘tachyonic’ fields, underscoring the importance of precise terminology and robust theoretical tools in addressing their unique properties.

The fact that the “probability density” expression provided by the Klein–Gordon equation can take on negative values is usually seen as an obstacle to formulating a particle interpretation of quantum mechanics. Nevertheless, reconciling this expression with a particle ontology is quite possible once a careful distinction is drawn between the outcomes of measurements and the positions of particles between measurements. Following this path, however, points to the involvement of retrocausality, as proposed by various authors in other contexts.

We introduce a new structure, the critical multi-cubic lattice. Notably the critical multi-cubic lattice is the first true generalization of the cubic lattice to higher dimensional spaces. We then introduce the notion of a homomorphism in the category of critical multi-cubic lattices, compute its automorphism group, and construct a Hilbert space over which we represent the group. With this unitary representation, we re-derive the generalized Pauli matrices common in quantum computation while also defining an algebraic framework for an infinite system of qudits. We also briefly explore the critical multi-cubic lattice as a novel implication algebra serving as a logical framework for qudit gates.

This short note addresses the criticisms recently proposed by Shan Gao against our article “On the Reality of the Quantum State Once Again: A No-Go Theorem for (psi)-Ontic Models” (Found. Phys. 54:14). The essay aims to respond to such objections and to show once again that the theorem proved in our paper is correct, and therefore true—contrary to Gao’s claims. Philosophical consequences of this fact are briefly discussed.

The minimal ingredients to describe a quantum system are a Hamiltonian, an initial state, and a preferred tensor product structure that encodes a decomposition into subsystems. We explore a top-down approach in which the subsystems emerge from the spectrum of the whole system. This approach has been referred to as quantum mereology. First we show that decomposing a system into subsystems is equivalent to decomposing a spectrum into other spectra. Then we argue that the number of subsystems (the volume of the system) can be inferred from the spectrum itself. In local models, this information is encoded in finite size corrections to the Gaussian density of states.

In conceptual debates involving the quantum gravity community, the literature discusses the so-called “emergence of space–time”. However, which interpretation of quantum mechanics (QM) could be coherent with such claim? We show that a modification of the Copenhagen Interpretation of QM is compatible with the claim that space–time is emergent for the macroscopic world of measurements. In other words, pure quantum states do not admit space–time properties until we measure them. We call this approach “Achronotopic” (ACT) Interpretation of QM, which yields a simple and natural interpretation of the most puzzling aspects of QM, such as particle-wave duality, wave function collapse, entanglement, and quantum superposition. Our interpretation yields the same results in all measurements as the Copenhagen Interpretation, but provides clues toward the sub-Planckian physics. In particular, it suggests the non-existence of quantum gravity in the conventional sense understood as the quantization of a classical theory.

We consider the question of whether thermodynamic macrostates are objective consequences of dynamics, or subjective reflections of our ignorance of a physical system. We argue that they are both; more specifically, that the set of macrostates forms the unique maximal partition of phase space which (1) is consistent with our observations (a subjective fact about our ability to observe the system) and (2) obeys a Markov process (an objective fact about the system’s dynamics). We review the ideas of computational mechanics, an information-theoretic method for finding optimal causal models of stochastic processes, and argue that macrostates coincide with the “causal states” of computational mechanics. Defining a set of macrostates thus consists of an inductive process where we start with a given set of observables, and then refine our partition of phase space until we reach a set of states which predict their own future, i.e. which are Markovian. Macrostates arrived at in this way are provably optimal statistical predictors of the future values of our observables.

In a recent paper as an alternative to models based on the notion of ideal mathematical point, characterized by a property of separatedness, we considered a viewpoint based on the notion of continuous change, making use of elements of a non-classical logic, in particular the fuzzy sets theory, with events represented as spatiotemporally blurred blobs. Here we point out and discuss a number of aspects of this imperfect symbolic description that might potentially be misleading. Besides that, we analyze its relation to various concepts used commonly to model physical systems, denoted by terms like: point, set, continuous, discrete, infinite, or local, clarifying further how our viewpoint is different and asking whether, in light of our main postulate, any of these notions, or their opposites, if exist, are in their usual meanings suitable to accurately describe the natural phenomena.