Related papers: Bertrand's paradox: a physical solution
Recently, the educational initiative TED-Ed has published a popular brain teaser coined the 'frog riddle', which illustrates non-intuitive implications of conditional probabilities. In its intended form, the frog riddle is a reformulation…
This paper revisits the classical problem of determining the bias of a weighted coin, where the bias is known to be either $p = 1/2 + \varepsilon$ or $p = 1/2 - \varepsilon$, while minimizing the expected number of coin tosses and the error…
By using both, the weak-value formulation as well as the standard probabilistic approach, we analyze the Hardy's experiment introducing a complex and dimensionless parameter ($\epsilon$) which eliminates the assumption of complete…
We propose a solution to the quantum measurement paradox by first identifying its classical counterpart.
We present a resolution of the celebrated "Surprise Exam Paradox". We argue that if the surprise exam story is analyzed using the exact same meaning of the notion of "surprise" as is dictated by the story itself, then no paradox arises.
In statistical mechanics, the generally called Stirling approximation is actually an approximation of Stirling's formula. In this article, it is shown that the term that is dropped is in fact the one that takes fluctuations into account.…
The paradox of the divergence of the resonant scattering cross section of a cylinder with the permittivity equals minus unity and vanishing radius (R) irradiated by a monochromatic electromagnetic wave is discussed. Within the framework of…
Past studies of the billiard-ball paradox, a problem involving an object that travels back in time along a closed timelike curve (CTC), typically concern themselves with entirely classical histories, whereby any trajectorial effects…
In 1733, Georges-Louis Leclerc, Comte de Buffon in France, set the ground of geometric probability theory by defining an enlightening problem: What is the probability that a needle thrown randomly on a ground made of equispaced parallel…
Relativistic length contraction is revisited and a simple but new thought experiment is proposed in which an apparent asymmetric situation is developed between two different inertial frames regarding detection of light that comes from a…
The inverse problem of determining the cross-sectional area of a human vocal tract during the utterance of a vowel is considered. The frequency-dependent boundary condition at the lips is expressed in terms of the acoustic impedance of a…
Quantum theory is formulated as the only consistent way to manipulate probability amplitudes. The crucial ingredient is a consistency constraint: if there are two different ways to compute an amplitude the two answers must agree. This…
The prediction of the final state probabilities of a general cuboid randomly thrown onto a surface is a problem that naturally arises in the minds of men and women familiar with regular cubic dice and the basic concepts of probability.…
The statistical precision of a chord method for estimating fractal dimension from a correlation integral is derived. The optimal chord length is determined, and a comparison is made to other estimators. These calculations use the…
Consider a free Schr\"odinger particle inside an interval with walls characterized by the Dirichlet boundary condition. Choose a parabola as the normalized state of the particle that satisfies this boundary condition. To calculate the…
We study the solutions for a one-dimensional electrostatic potential in the Dirac equation when the incoming wave packet exhibits the Klein paradox (pair production). With a barrier potential we demonstrate the existence of multiple…
I present a variant of the Buffon Needle method for determination of the value of the mathematical constant, pi. The original method is based on the random casting of a needle of length l onto a planked floor of plank width L. The described…
Suppose that in a multiple choice examination the leading digit of the correct options follows Benford's Law, while the the leading digit of the distractors are uniform. Consider a strategy for guessing at answers that selects the option…
We offer a reader-friendly introduction to the attracting edge problem (also known as the "triangle conjecture") and its most general current solution of Limic and Tarr\`es (2007). Little original research is reported; rather this article…
We present two complementary proofs that, if the lengths of $n$ sticks are sampled at random, then the probability that no $p+1$ sticks can form a $(p+1)$-sided polygon can be expressed as the product of the reciprocals of a series of terms…