Foundations of Physics最新文献

We study implications of Leibnizian ideas such as the identity of indiscernibles, and variety (due to Barbour and Smolin) in the context of Wolfram Model, which has been put forward in 2020. We have provided (at the moment) speculative interpretations for Leibnizian and non-Leibnizian hypergraphs. We introduced an action based on variety, to select paths where it is maximized. The specific universe which is of concern here is the one with name ‘wm1268’ from the Registry of Notable Universe Models, which is used as a test case in the present study.

We have revised the problem of the motion of a heavy symmetric top. When formulating equations of the Lagrange top with the diagonal inertia tensor, the potential energy has more complicated form as compared with that assumed in the literature on dynamics of a rotating body. This implies the corresponding improvements in equations of motion. Using the Liouville’s theorem, we solve the improved equations in quadratures and present the explicit expressions for the resulting elliptic integrals.

We investigate a model of becoming—classical sequential growth (CSG)—that has been proposed within the framework of causal sets (causets), with the latter defined as order types of certain partial orderings. To investigate how causets grow, we introduce special sequences of causets, which we call “csg-paths”. We prove a number of results concerning relations between csg-paths and causets. These results paint a highly non-trivial picture of csg-paths. There are uncountably many csg-paths, all of them sharing the same beginning, after which they branch. Every infinite csg-path achieves in the limit an infinite causet, and vice versa, every infinite causet is achieved in the limit by an infinite csg-path. However, coalescing csg-paths, i.e., ones that achieve the same causet even after forking off at some point, are ubiquitous.

We provide the construction of a de Broglie–Bohm model of the N-body system within the framework of Pure Shape Dynamics. The equation of state of the curve in shape space is worked out, with the instantaneous shape being guided by a wave function. In order to get a better understanding of the dynamical system, we also give some numerical analysis of the 3-body case. Remarkably enough, our simulations typically show the attractor-driven behaviour of complexity, well known in the classical case, thereby providing further evidence for the claim that the arrow of complexity is the ultimate cause of the experienced arrow of time.

A classification of different interpretations of the quantum formalism is examined and the concept of perspectival interpretation is presented. A perspectival interpretation implies that the truth is relative to the observer. The degree to which Convivial Solipsism and QBism in its different versions are perspectival is examined.

The persistent challenge of formulating ontic structuralism in a rigorous manner, which prioritizes structures over the entities they contain, calls for a transformation of traditional logical frameworks. I argue that Univalent Foundations (UF), which feature the axiom that all isomorphic structures are identical, offer such a foundation and are more attractive than other proposed structuralist frameworks. Furthermore, I delve into the significance in the case of the hole argument and, very briefly, the nature of symmetries.

We propose a model of physics that blends Rovelli’s relational quantum mechanics (RQM) interpretation with the language of finite information quantities (FIQs), defined by Gisin and Del Santo in the spirit of intuitionistic mathematics. We discuss deficiencies of using real numbers to model physical systems in general, and particularly under the RQM interpretation. With this motivation for an alternative mathematical language, we propose the use of FIQs to model the world under the RQM interpretation, wherein we view the propensities that make up a FIQ as quantifications of potential interaction. Under this model, the stable facts, relative facts, and shifting perspectives that make up the relational interpretation correspond to shifting digits and propensities of the FIQs. The model’s predictions agree with those of both classical and quantum physics, and it is indeterministic. We also propose explanations, with examples, for how the propensities of a FIQ are distributed, and how its digits become actualized. This is equivalent to the notion of the measurement problem, and the question of what causes wave function collapse. In short, by stepping through the “new door” opened by the language of FIQs, we attempt to describe the world under the relational interpretation.

We discuss the solution proposed by Fermi to the so called “4/3 problem” in the classical theory of the electron, a problem which puzzled the physics community for many decades before and after his contribution. Unfortunately his early resolution of the problem in 1922–1923 published in three versions in Italian and German journals (after three preliminary articles on the topic) went largely unnoticed. Even more recent texts devoted to classical electron theory still do not present his argument or acknowledge the actual content of those articles. The calculations initiated by Fermi at the time are completed here by formulating and discussing the conservation of the total 4-momentum of the accelerated electron as seen from the instantaneous rest frame in which it is momentarily at rest.

It has been claimed that Massimi’s recent perspectival approach to science sits in tension with a realist stance. I shall argue that this tension can be defused in the quantum context by recasting Massimi’s perspectivalism within a phenomenological framework. I shall begin by indicating how the different but complementary forms of the former are manifested in the distinction between certain so-called ‘-epistemic’ and ‘-ontic’ understandings of quantum mechanics, namely QBism and Relational Quantum Mechanics, respectively. A brief consideration of Dieks’ perspectivism will then lead to a consideration of the much-maligned and typically dismissed role of the observer in the measurement process. This opens the door to London and Bauer’s presentation of a form of ‘phenomenological quantum perspectivalism’ that brings together Massimi’s two forms and explicitly eschews the ‘naïve’ realism that creates the above tension. I shall conclude with some reflections on how intersubjectivity can still be established within this framework, focusing in particular on how Massimi’s idea of ‘interlacing’ scientific perspectives can be accommodated, using the example of a ‘new cosmopolitanism’ that gave rise to Bose-Einstein statistics.

In a recent paper, Cabbolet argues that the PBR theorem is nonreal since in the ensemble interpretation of quantum mechanics the entangled measurement used in the derivation of the PBR theorem is nonexisting. However, Cabbolet (1) does not provide any argument for the nonexistence of entangled measurements beyond the incompatibility of the existence of entangled measurements and the existence of (psi)-epistemic models which we already know from the PBR theorem; and (2) he does not show why it is more reasonable to abandon entangled measurements instead of (psi)-epistemic models. Hence, the PBR theorem remains intact.