Foundations of Physics最新文献

There are two metaphysical pictures of spacetime: The evolutionary picture and the all-at-once picture. According to the evolutionary picture, spacetime is nothing but the evolution of space over time. In contrast, the all-at-once picture considers spacetime as ‘a global, four-dimensional boundary value problem’ that can be solved only in an all-at-once manner, i.e. as a whole which is fundamentally four-dimensional and non-decomposable into spatial and temporal parts. The two most-known formulations of general theory of relativity, i.e. the Hamiltonian (or the canonical) and the Lagrangian (or the standard) formulations, enjoy the evolutionary and all-at-once pictures of spacetime respectively. Here, we have argued that (1) the all-at-once picture is more aligned with the philosophy of relativity theory, i.e. uniting space and time into spacetime, (2) the evolutionary picture is not as general as the all-at-once, since only in special cases, such as globally hyperbolic spacetimes, is it possible to deal with spacetime as the evolution of a spatial slice over time, and (3) the all-at-once picture paves the way to better understanding four-dimensional physical entities, like event horizons, which cannot be explained within an evolutionary picture without raising a paradox. Therefore, the evolutionary picture is neither the fundamentally-true nor the naturally-chosen picture of spacetime. Rather, we choose the evolutionary picture for practical and computational reasons. While the all-at-once picture seems a more appropriate description of the quantum and cosmological reality, the evolutionary picture can be applied occasionally and locally, or quasi-locally, and is not the proper metaphysical picture of spacetime at the fundamental level of reality.

Sean Carroll has recently argued that theories predicting that observations are dominated by Boltzmann Brains should be rejected because they are cognitively unstable: “they cannot simultaneously be true and justifiably believed.” While such Boltzmann Brain theories are indeed cognitively unstable, one does not need to appeal to this argumentation to reject them. Instead, they may be ruled out by conventional Bayesian reasoning, which is sufficient to keep Boltzmann Brains at bay.

How to compute the probability distribution of a detection time, i.e., of the time which a detector registers as the arrival time of a quantum particle, is a long-debated problem. In this regard, Bohmian mechanics provides in a straightforward way the distribution of the time at which the particle actually does arrive at a given surface in 3-space in the absence of detectors. However, as we discuss here, since the presence of detectors can change the evolution of the wave function and thus the particle trajectories, it cannot be taken for granted that the arrival time of the Bohmian trajectories in the absence of detectors agrees with the one in the presence of detectors, and even less with the detection time. In particular, we explain why certain distributions that Das and Dürr (Sci. Rep. 9: 2242, 2019) presented as the distribution of the detection time in a case with spin, based on assuming that all three times mentioned coincide, are actually not what Bohmian mechanics predicts.

We discuss the two-dimensional harmonic oscillator in the presence of a uniform radial electric field around a cylindrical cavity. By including the Aharonov-Bohm flux and by assuming the existence and the absence of an infinity wall located at the radius of the cylindrical cavity, we show that bound states can be achieved around the cylindrical cavity in this two-dimensional charged harmonic oscillator in a uniform radial electric field.

The normalization in the path integral approach to quantum field theory, in contrast with statistical field theory, can contain physical information. The main claim of this paper is that the inner product on the space of field configurations, one of the fundamental pieces of data required to be added to quantize a classical field theory, determines the normalization of the path integral. In fact, dimensional analysis shows that the introduction of this structure necessarily introduces a scale that is left unfixed by the classical theory. We study the dependence of the theory on this scale. This allows us to explore mechanisms that can be used to fix the normalization based on cutting and gluing different integrals. “Self-normalizing” path integrals, those independent of the scale, play an important role in this process. Furthermore, we show that the scale dependence encodes other important physical data: we use it to give a conceptually clear derivation of the chiral anomaly. Several explicit examples, including the scalar and compact bosons in different geometries, supplement our discussion.

This paper examines the tension between wave function realism and interpretations of gauge symmetries within quantum mechanics. We explore how traditional views of gauge symmetries as descriptive redundancies challenge the principles of wave function realism, which regards the wave function as a real entity. By noting that, through the case study of a quantum particle in an electromagnetic field, gauge transformations impact the wave function’s phase, we present a dilemma for wave function realism. We discuss potential resolutions, including redefining ontological commitments to accommodate gauge-invariance.

There have been a number of recent attempts to identify the best metaphysical framework for capturing Rovelli’s Relational Quantum Mechanics (RQM). All such accounts commit to some form of fundamentalia, whether they be traditional objects, physical relations, events or ‘flashes’, or the cosmos as a fundamental whole. However, Rovelli’s own recommendation is that ‘a natural philosophical home for RQM is an anti-foundationalist perspective' (Rovelli in Philos Trans R Soc 376:10, 2018). This gives us some prima facie reason to explore options beyond these foundationalist frameworks, and take seriously a picture that lacks fundamentalia. I construct an argument from elimination in favour of an anti-foundationalist interpretation of RQM. The argument notes that priority monism and priority pluralism are exhaustive foundationalist options, and then shows that there are reasons to reject their union with RQM. I finish by recommending metaphysical coherentism as a promising anti-foundationalist alternative, which captures the key characteristics of RQM through accepting symmetrical dependence, whilst avoiding challenges by jettisoning any commitment to fundamental entities.

Successful applications of a conceptually novel setup of Quantum Field Theory, that accounts for all subtheories of the Standard Model (QED, Electroweak Interaction and Higgs, Yang–Mills and QCD) and beyond (Helicity 2), call for a perspective view in a broader conceptual context. The setting is “autonomous” in the sense of being intrinsically quantum. Its principles are: Hilbert space, Poincaré symmetry and causality. Its free quantum fields are obtained from Wigner’s unitary representations of the Poincaré group, with only physical and observable degrees of freedom. A “quantization” of an “underlying” classical theory is not needed. It allows renormalizable perturbation theory with interactions whose detailed structure, and in some cases even the particle content, is predicted by internal consistency. The results confirm and extend observable predictions for the interactions of the Standard Model without assuming a “principle” of gauge invariance.

Quantum physics is a linear theory, so it is somewhat puzzling that it can underlie very complex systems such as digital computers and life. This paper investigates how this is possible. Physically, such complex systems are necessarily modular hierarchical structures, with a number of key features. Firstly, they cannot be described by a single wave function: only local wave functions can exist, rather than a single wave function for a living cell, a cat, or a brain. Secondly, the quantum to classical transition is characterised by contextual wave-function collapse shaped by macroscopic elements that can be described classically. Thirdly, downward causation occurs in the physical hierarchy in two key ways: by the downward influence of time dependent constraints, and by creation, modification, or deletion of lower level elements. Fourthly, there are also logical modular hierarchical structures supported by the physical ones, such as algorithms and computer programs, They are able to support arbitrary logical operations, which can influence physical outcomes as in computer aided design and 3-d printing. Finally, complex systems are necessarily open systems, with heat baths playing a key role in their dynamics and providing local arrows of time that agree with the cosmological direction of time that is established by the evolution of the universe.

Using the position as an independent variable, and time as the dependent variable, we derive the function ({mathcal{P}}^{(pm )}=pm sqrt{2m({mathcal{H}}-{mathcal{V}}(q))}), which generates the space evolution under the potential ({mathcal{V}}(q)) and Hamiltonian ({mathcal{H}}). No parametrization is used. Canonically conjugated variables are the time and minus the Hamiltonian ((-{mathcal{H}})). While the classical dynamics do not change, the corresponding Quantum operator ({{{hat{mathcal P}}}}^{(pm )}) naturally leads to a 1/2-fractional time evolution, consistent with a recent proposed space–time symmetric formalism of the Quantum Mechanics. Using Dirac’s procedure, separation of variables is possible, and while the two-coupled position-independent Dirac equations depend on the 1/2-fractional derivative, the two-coupled time-independent Dirac equations lead to positive and negative shifts in the potential, proportional to the force. Both equations couple the (±) solutions of ({{{hat{mathcal P}}}}^{(pm )}) and the kinetic energy ({mathcal{K}}_{0}) (separation constant) is the coupling strength. Thus, we obtain a pair of coupled states for systems with finite forces, not necessarily stationary states. The potential shifts for the harmonic oscillator (HO) are (pm {hbar {omega}} /2), and the corresponding pair of states are coupled for ({mathcal{K}}_{0}ne 0). No time evolution is present for ({mathcal{K}}_{0}=0), and the ground state with energy ({hbar {omega}} /2) is stable. For ({mathcal{K}}_{0}>0), the ground state becomes coupled to the state with energy (-{hbar {omega}} /2), and this coupling allows to describe higher excited states in the HO. Energy quantization of the HO leads to the quantization of ({mathcal{K}}_{0}=k{hbar {omega}}) ((k=1,2,ldots)). For the one-dimensional Hydrogen atom, the potential shifts become imaginary and position-dependent. Decoupled case ({mathcal{K}}_{0}=0) leads to plane-waves-like solutions at the threshold. Above the threshold (({mathcal{K}}_{0}>0)), we obtain a plane-wave-like solution, and for the bounded states (({mathcal{K}}_{0}<0)), the wave-function becomes similar to the exact solutions but squeezed closer to the nucleus.