Foundations of Physics最新文献

Discussions of quantum mechanics often loosely claim that time evolution logically must be unitary, in order for the probabilistic interpretation of the amplitudes of the state vector to make sense at all times. We discuss from first principles whether this claim is true: if we assume only that the time-evolution operator is linear, then does the stronger requirement that it be unitary follow from the other axioms of quantum mechanics? The answer is subtle. We discuss two mathematically distinct but physically equivalent formulations of the axioms of quantum mechanics, and consider generalizing each to postulate only that time evolution is linear. Within one formulation, the unitarity of time evolution follows logically from the other axioms – but within the other formulation, it does not. Allowing the time-evolution operator to be (a priori) arbitrarily linear does not change the physical observables in one formulation of quantum mechanics, but changes the other formulation to a distinct (internally consistent) physical theory that allows new phenomenology like (e.g.) faster-than-light communication. Therefore, the unitarity of time evolution is arguably better thought of as a logically independent and experimentally falsifiable axiom of quantum mechanics, not as a tautological consequence of the other axioms.

It is possible to solve the Einstein constraint equations as an evolutionary rather than an elliptic system. Here we consider the Gauss constraint in electrodynamics as a toy model for this. We use a combination of the evolutionary method with the gluing construction to produce initial data for an electromagnetic pulse surrounded by vacuum. It turns out that solving the evolutionary form of the constraint is straightforward, and explicitly yields the desired type of initial data. In contrast, proving the existence of a solution to the same problem within the elliptic setting requires sophisticated arguments based on functional analysis

We consider the observables describing spatiotemporal properties in the context of two of the most popular approaches to quantum gravity (QG), namely String Theory and Loop QG. In both approaches these observables are described by non-commuting operators. In analogy with recent arguments put forward in the context of non-relativistic quantum mechanics [see Calosi and Mariani (Philos. Compass 16(4):e12731, 2021) for a review], we suggest that the physical quantities corresponding to those observables may be interpreted as ontologically indeterminate—i.e., indeterminate in a way that is non-epistemic and semantic-independent. This working hypothesis has not received enough attention in the current debate on QG, and yet it may prove explanatory useful in several respects. First, it provides a clear background for understanding how some features of QG are ontologically continuous to features of quantum mechanics. Second, it sets the stage for asking new interesting questions about QG, for instance concerning the status of the so-called Eigenstate-Eigenvalue link. Third, it indirectly shows how the debate on ontological indeterminacy may extend well beyond the non-relativistic case, contrary to what seems to be assumed. Fourth, and perhaps more importantly, it provides a promising alternative to the received view on QG [Wüthrich et al. (Philosophy Beyond Spacetime: Implications from Quantum Gravity, Oxford University Press, Oxford, 2021)] according to which spacetime is not fundamental. On the view we shall suggest, spacetime may be indeterminate and yet fundamental.

Bohmian mechanics supplements the quantum wavefunction with deterministic particle trajectories, offering an alternate, dynamical language for quantum theory. However, the Bohmian wavefunction evolves independently of these trajectories, and is thus unaffected by the observable properties of the system. While this property is widely assumed necessary to ensure agreement with quantum mechanics, much work has recently been dedicated to understanding classical pilot-wave systems, which feature a two-way coupling between particle and wave. These systems—including the “walking droplet” system of Couder and Fort (Couder and Fort (2006) Phys. Rev. Lett. 97:154101) and its various abstractions (Dagan and Bush (2020) CR Mecanique 348:555–571; Durey and Bush (2020) Front. Phys. 8:300; (2021) Chaos 31:033136; Darrow and Bush (2024) Symmetry 16:149)—allow us to investigate the limits of classical systems and offer a touchstone between quantum and classical dynamics. In this work, we present a general result that bridges Bohmian mechanics with this classical pilot-wave theory. Namely, Darrow and Bush ((2024) Symmetry 16:149) recently introduced a Lagrangian pilot-wave framework to study quantum-like behaviours in classical systems; with a particular choice of particle-wave coupling, they recover key dynamics hypothesised in de Broglie’s early double-solution theory (de Broglie (1970) Foundations Phys. 1:5–15). We here show that, with a different choice of coupling, their de Broglie-like system reduces exactly to single-particle Bohmian mechanics in the non-relativistic limit. Our result clarifies that, while multi-particle entanglement is impossible to replicate in general with local, classical theories, no such restriction exists for single-particle quantum mechanics. Moreover, connecting with the previous work of Darrow and Bush, our work demonstrates that de Broglie’s and Bohm’s theories can be connected naturally within a single Lagrangian framework. Finally, we present an application of the present work in developing a single-particle analogue for position measurement in a de Broglie-like setting.

Legendre transform between thermodynamic quantities such as the Helmholtz free energy and entropy plays a key role in the formulation of the canonical ensemble. In the standard treatment, the transform exchanges the independent variable from the system’s internal energy to its conjugate variable—the inverse temperature of the heat reservoir. In this article, we formulate a microscopic version of the transform between the free energy and Shannon entropy of the system, where the conjugate variables are the microstate probabilities and the energies (scaled by the inverse temperature). The present approach gives a non-conventional perspective on the connection between information-theoretic measure of entropy and thermodynamic entropy. We focus on the exact differential property of Shannon entropy, utilizing it to derive central relations within the canonical ensemble. Thermodynamics of a system in contact with the heat reservoir is discussed in this framework. Other approaches, in particular, Jaynes’ maximum entropy principle is compared with the present approach.

This study explores the historical concept of ether within the framework of modern theoretical physics by deriving Maxwell’s equations that incorporate magnetic monopoles from the Navier-Cauchy equation with stress couples. We demonstrate that the elastomechanical interpretation of electromagnetism not only revitalizes the ether concept but also provides a coherent theoretical foundation for understanding electromagnetic phenomena. This interpretation reveals a significant link between mechanical properties and electromagnetic behaviors, for example, the charge of fundamental particles, such as electrons, is inherently connected to rotational dynamics within the elastomechanical medium. Additionally, we introduce the magnetic monopole as a critical component of our framework, showing how it is associated with mass flux and volume changes in the medium, thus contributing to the dynamics of particle generation. Our findings highlight the profound interplay between elastodynamics, classical electromagnetism, and contemporary concepts in physics, paving the way for new epistemological perspectives. This research underscores the potential for integrating diverse physical theories to foster innovative developments in theoretical physics, challenging traditional views and inviting further exploration of the fundamental forces that govern the universe.

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.