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The problem of defining and locating free will (FW) in physics is studied. On basis of logical paradoxes, we argue that FW has a meta-theoretic character, like the concept of truth in Tarski's undefinability theorem. Free will exists…
Using physical arguments, I derive the physically correct equations of motion for a classical charged particle from the Lorentz-Abraham-Dirac equations (LAD) which are well known to be physically incorrect. Since a charged particle can…
One of the major difficulties of modern science underlies at the unification of general relativity and quantum mechanics. Different approaches towards such theory have been proposed. Noncommutative theories serve as the root of almost all…
We consider a thought experiment where the preparation of a macroscopically massive or charged particle in a quantum superposition and the associated dynamics of a distant test particle apparently allow for superluminal communication. We…
In light of G\"{o}del's undecidability results (incomplete theorems) for math, quantum indeterminism indicates that physics and the Universe may be indeterministic, incomplete, and open in nature, and therefore demand no single unification…
The paper considers the claim that quantum theories with a deterministic dynamics of objects in ordinary space-time, such as Bohmian mechanics, contradict the assumption that the measurement settings can be freely chosen in the EPR…
Recent work has examined how undecidable problems can arise in quantum information science. We augment this by introducing three new undecidable problems stated in terms of tensor networks. These relate to ideas of Penrose about the…
The paradox of a free falling radiating charged particle in a gravitational field, is a well-known fascinating conceptual challenge that involves classical electrodynamics and general relativity. We discuss this paradox considering the…
The resource-theoretic approach to quantum thermodynamics assumes complete knowledge of the thermal equilibrium against which thermodynamic resources are defined. In practice, however, this state is determined by the system Hamiltonian and…
After more than a century of history, the radiation-reaction problem in classical electrodynamics still surprises and puzzles new generations of researchers. Here we revise and explain some of the paradoxical issues that one faces when…
The uncertainty principle limits quantum states such that when one observable takes predictable values there must be some other mutually unbiased observables which take uniformly random values. We show that this restrictive condition plays…
Analyzing decision problems under uncertainty commonly relies on idealizing assumptions about the describability of the world, with the most prominent examples being the closed world and the small world assumption. Most assumptions are…
Freely falling point-like objects converge towards the center of the Earth. Hence the gravitational field of the Earth is inhomogeneous, and possesses a tidal component. The free fall of an extended quantum object such as a hydrogen atom…
Recent work by Faizal et al. (2025) claims that G\"odelian undecidability of non-algorithmic truths in our universe imply the impossibility of a formal, algorithmic simulation of the universe. This paper clarifies the distinction between…
Uncertainty is an important and fundamental concept in physics education. Students are often first exposed to uncertainty in introductory labs, expand their knowledge across lab courses, and then are introduced to quantum mechanical…
After discussing two senses in which the notion of undecidability is used, we present a survey of undecidable decision problems arising in various branches of mathematics.
It is often claimed that the fundamental laws of physics are deterministic and time-symmetric and that therefore our experience of the passage of time is an illusion. This paper will critically discuss these claims and show that they are…
We consider the decidability of state-to-state reachability in linear time-invariant control systems over discrete time. We analyse this problem with respect to the allowable control sets, which in general are assumed to be defined by…
A striking general bound on the energy gap in topological matter was recently discovered in Ref. [Onishi and Fu, Phys. Rev. X {\bf 14}, 011052 (2024)]. A non-trivial indirect derivation builds on the properties of optical conductivity at an…
A recent series of experiments have demonstrated that a classical fluid mechanical system, constituted by an oil droplet bouncing on a vibrating fluid surface, can be induced to display a number of behaviours previously considered to be…