Foundations of Physics最新文献

Recently, a counter-argument has been presented regarding the invalidity of the Pusey-Barrett-Rudolph (PBR) theorem (Cabbolet, Found. Phys. 53, 64 2023). This claim has sparked a debate, with some authors defending the PBR theorem (Hofer-Szabó, Found. Phys. 54, 36 2024), but the proponent of the claim has insisted on his argument (Cabbolet, Found. Phys. 54, 69 2024; Cabbolet, Found. Phys. 54, 48 2024). Moreover, the author claimed to have proved that the PBR theorem is incorrect by a generic counterexample (Cabbolet, Found. Phys. 54, 48 2024). In this paper, we contribute to the discussion with some new arguments. We demonstrate that the PBR theorem contains no errors and remains intact.

Perspectivist positions have been proposed in physics, notably in order to address the interpretive difficulties of quantum mechanics. Recently, some versions of perspectivism have also been proposed in general philosophy of science to account for the plurality of scientific practice. Both kinds of views share the rejection of what they metaphorically call the “view from nowhere”. However, beyond this superficial similarity, they are very different: while quantum perspectivism entertains a concrete notion of perspective associated with individual agents or systems or concrete contexts, perspectival realism adopts a more abstract notion associated with explanatory aims or conceptual schemes. The aim of this paper is to clarify what is at stake with perspectivism in general. The general notion of a perspective, as well as the various attitudes one can entertained towards them, are characterised using the concepts of harmless contradiction and cross-perspectival accessibility. A taxonomy of positions ranging from absolutism to relativism is proposed on this basis. Then the framework is applied to quantum perspectivism and perspectival realism to show its fruitfulness. Finally, I argue that abstract versions of perspectivism are bound to be metaphysically weaker than concrete versions.

The multiplicative Lagrangian and Hamiltonian introduce an additional parameter that, despite its variation, results in identical equations of motion as those derived from the standard Lagrangian. This intriguing property becomes even more striking in the case of a free particle. By manipulating the parameter and integrating out, the statistical average of the multiplicative Lagrangian and Hamiltonian naturally arises. Astonishingly, from this statistical viewpoint, the relativistic Lagrangian and Hamiltonian emerge with remarkable elegance. On the action level, this formalism unveils a deeper connection: the spacetime of Einstein’s theory reveals itself from a statistical perspective through the action associated with the multiplicative Lagrangian. This suggests that the multiplicative Lagrangian/Hamiltonian framework offers a profound and beautiful foundation, one that reveals the underlying unity between classical and relativistic descriptions in a way that transcends traditional formulations. In essence, the multiplicative approach introduces a richer and more intricate structure to our understanding of physics, bridging the gap between different theoretical realms through a statistical perspective.

Causal Set Theory (CST) is a promising approach to fundamental physics that seems to treat causation as a basic posit. But in exactly what sense is CST causal? We argue that if the growth dynamics is interpreted as a physical process, then CST employs relations of actual causation between causal set elements, whereby elements bring one another into existence. This is important, as it provides a better sense of how CST works, highlights important differences from general relativity—where relations between spacetime points are typically seen as cases of mere causal connectibility rather than actual causation of the relevant type—and points toward a specific understanding of the emergence of spacetime within CST.

This work presents an alternative approach to obtain the quantum field equations in curved spacetime, considering that sufficiently small particles follow stochastic trajectories around geodesic. Our proposal is based on a stochastic differential equation in which the noise term experienced by the quantum particles is a consequence of the stochastic background in spacetime. This fact allows the particles to describe erratic movements and locally the universe exhibits characteristics akin to a lake with gentle ripples rather than a flat unyielding surface. Building upon this foundational understanding, we investigate the influence of this background on quantum-scale particles without considering the metric to be stochastic, rather we let test particles move randomly around the geodesic of macroscopic particles. Their behavior aligns with solutions to the Klein-Gordon (KG) equation specific to this curved spacetime. As the KG equation, in its non-relativistic limit within a flat spacetime, reduces to the Schrödinger equation, consequently, we propose a compelling connection: the Schrödinger equation may emerge directly from a spacetime lacking local smoothness.

The principal goal of this paper and its originality consist in passing all formulas for quantum probability to the projective space associated to the complex Hilbert space of a given quantum system, thereby providing a geometric foundation of quantum probability, which should be considered as a step towards an eventual axiomization. Quantum events have consecutive and conditional probabilities, which have been used in the author’s work to clarify ‘collapse of the state’ and to generalize the concept of entanglement by incorporating it into quantum probability theory. In this way much of standard textbook quantum theory can be understood in the setting of the geometry of a projective space and its subspaces. The ultimate, future goal is to formulate all of quantum theory as the probability theory of projective subspaces, or equivalently, of quantum events. For the sake of simplicity the ideas are developed here in the context of a type I factor, but comments will be given about how to adopt this approach to more general von Neumann algebras.

Weak values characterize a quantum system in the period of time between preparation and measurement and may lie outside the eigenvalue spectrum of the measured operator. The probability of such “superweak" values for random quantum states has been calculated and applied to Klein–Gordon and Dirac waves, where the maximal probability for superluminal propagation was shown to be 1/2. In a recent paper, a different definition for the velocity of a relativistic quantum particle was proposed in terms of a ratio of two weak values. In this paper, we find the probability distribution of such ratios. With the new definition, the superluminal probability of photons is found to be bounded between (1-1/sqrt{2}) and (1/sqrt{2}), while for general eigenvalue distributions the superluminal probability can take any value between 0 and 1.

Global time is a gauge or relational choice of time variable in canonical gravity. Local time is the time used in a flat patch of spacetime. We compare the dynamics of a scalar field with respect to choices of global time and Minkowski patch time in an expanding cosmology. Our main results are that evolutions starting from the same initial conditions are similar on the time scales of terrestrial experiments, and that global time leads to a mechanism for evolving coupling constants.

We construct an explicit model of inhomogeneous gravitational collapse leading to a naked singularity in which gravitational absorption is both efficient and observable. We propose that the infeasibility of (efficient) graviton detection is simply a consequence of Nature’s conspiracy to hide regions of strong curvature behind event horizons.

This work explores the connection between logical independence and the algebraic structure of quantum mechanics. Building on results by Brukner et al., it introduces the notion of onto-epistemic ignorance: situations in which the truth of a proposition is not deducible due to an objective breakdown in the phenomenal chain that transmits information from a system A to a system B, rather than to any subjective lack of knowledge. It is shown that, under such conditions, the probabilities accessible to a real observer are necessarily conditioned by decidability and obey a non-commutative algebra, formally equivalent to the fundamental postulates of quantum mechanics.