Related papers: RESOLUTION OF A ``RETRODICTION PARADOX''
To clarify some aspects of the application of Special Relativity, spacetime is sliced into null geodesic hypersurfaces as an alternative to the hypersurfaces of simultaneity normally adopted. Events at particle locations on the hypersurface…
In this note our aim is to show a paradox in the spectral representation of stationary random processes.
Recently, several authors have criticized the time-symmetrized quantum theory originated by the work of Aharonov et al. (1964). The core of this criticism was a proof, appearing in various forms, which showed that the counterfactual…
The method of maximum entropy has been very successful but there are cases where it has either failed or led to paradoxes that have cast doubt on its general legitimacy. My more optimistic assessment is that such failures and paradoxes…
In this expository article, we describe the recent approach, motivated by ergodic theory, towards detecting arithmetic patterns in the primes, and in particular establishing that the primes contain arbitrarily long arithmetic progressions.…
We present a few charge distributions for which the application of Gauss' law in its integral form, as typically outlined in standard textbooks, results in a contradiction. We identify the root cause of such contradictions and put forward a…
Rebilas argues that time-reversal can occur even in an indeterministic system. This hypothesis is untestable, hence lying beyond physics.
The Halting Problem is a version of the Liar's Paradox.
The problem of induction has persisted since Hume exposed the logical gap between repeated observation and universal inference. Traditional attempts to resolve it have oscillated between two extremes: the probabilistic optimism of Laplace…
We provide here a thermodynamic analog of the Braess road-network paradox with irreversible engines working between reservoirs that are placed at vertices of the network. Paradoxes of different kinds reappear, emphasizing the specialty of…
In this paper I suggest a possible explanation for the asymmetry of time. In the case that I study, the dynamical laws and the boundary conditions are symmetric, but the behavior of time is not. The underlying mechanism is statistical and…
In this paper we give a proof of an epiperimetric inequality in the setting of the lower dimensional obstacle problem. The inequality was introduced by Weiss (Invent. Math., 138 (1999), no. 1, 23-50) for the classical obstacle problem and…
Any theory that states that the basic laws of physics are time-symmetric must be strictly deterministic. Only determinism enables time reversal of entropy increase. A contradiction therefore arises between two statements of Hawking. A…
The paper presents a counterexample to the Hodge conjecture.
Roman Schnabel's article argues that the Einstein-Podolsky-Rosen (EPR) paradox can be resolved by identifying a flaw in what the author calls the "EPR implication" and by using radioactive alpha decay as an example showing that…
The first paper: We describe principles of new cybernetics and use these principles for resolution of basic physical paradoxes. It demonstrates universality of the principles of new cybernetics. The second paper: recent letter by Maccone…
Confidence intervals are assessed according to two criteria, namely expected length and coverage probability. In an attempt to apply the decision-theoretic method to finding a good confidence interval, a loss function that is a linear…
We approach the sorites paradox (SP) through an observer-based and time-dependent approach to truth of vague assertions. Formally the approach gives rise to a semantics, called fluxing-object semantics (FOS), because it involves models that…
In Mathematics is common to make a mistake and therefore a false conclusion arises. In each case it is important to recognize the mistake in order to avoid a similar one in the future. Geometric figures provide decisive help in order to…
The classical methods used by recursion theory and formal logic to block paradoxes do not work in quantum information theory. Since quantum information can exist as a coherent superposition of the classical ``yes'' and ``no'' states,…