相关论文: Why does the meter beat the second?

In pregeometry a metric arises as a composite object at large distances. We investigate if its signature, which distinguishes between time and space, could be a result of the dynamics rather than being built in already in the formulation of…

This is a translation from Latin of 'De novo oscillationum genere', which was motivated by Krafft's accidental observation of a suspended clock setting itself in constant motion as a pendulum. This publication, in turn, motivated Euler to…

We propose a new system for the fundamental units, which includes and goes beyond the present redefinition of the SI, by choosing also $c=\hbar=1$. By fixing $c=c_\circ $m/s = 1, $\hbar=\hbar_\circ $ Js = 1 and…

In an apparently unexplored region of relativistic spacetime, a simple thought experiment demonstrates that conjoined Lorentz transformations predict a proper clock at rest will run backwards and that prediction violates the logical…

Basic for the definition of 'time' are clocks operating under stationary conditions. The periods of two clocks can be compared with each other via two return experiments. The central clock mediates between the rotating and the inertial…

In any setting in which observable properties have a quantitative flavour, it is natural to compare computational objects by way of \emph{metrics} rather than equivalences or partial orders. This holds, in particular, for probabilistic…

The gap between classical mechanics and quantum mechanics has an important interpretive implication: the Universe must have an irreducible fundamental level, which determines the properties of matter at higher levels of organization. We…

When are two collider events similar? Despite the simplicity and generality of this question, there is no established notion of the distance between two events. To address this question, we develop a metric for the space of collider events…

The purpose of these notes is to clarify the duality between a natural class of jump processes on compact ultrametric spaces - studied in current work of Bendikov, Girgor'yan and Pittet - and nearest neighbour walks on trees. Processes of…

The motion of a pendulum is described as Simple Harmonic Motion (SHM) in case the initial displacement given is small. If we relax this condition then we observe the deviation from the SHM. The equation of motion is non-linear and thus…

The Ulam's metric is the minimal number of moves consisting in removal of one element from a permutation and its subsequent reinsertion in different place, to go between two given permutations. Thet elements that are not moved create…

We describe and explain the desire, common among mathematicians, both for unity and independence in its major themes. In the dialogue that follows, we express our spontaneous and considered judgment and reservations by contrasting the…

Young's double-slit experiment requires two waves produced simultaneously at two different points in space. In quantum mechanics the waves correspond to a single quantum object, even as complex as a big molecule. An interference is present…

Idioms are unlike most phrases in two important ways. First, the words in an idiom have non-canonical meanings. Second, the non-canonical meanings of words in an idiom are contingent on the presence of other words in the idiom. Linguistic…

It is proposed that an event that constitutes a quantum measurement corresponds to the spontaneous breaking of a symmetry in the measuring device over time.

We show why and when entanglement is needed for quantum-enhanced precision measurements, and which type of entanglement is useful. We give a simple, intuitive construction that shows how entanglement transforms parallel estimation…

In this article we study the nature of time in Mechanics. The fundamental principle, according to which a mechanical system evolves governed by a second order differential equation, implies the existence of an absolute time-duration in the…

After some more than four centuries from the formulation and publication (in Astronomia Nova) of the Kepler's Equation, which relates the eccentric (and, intermediately, the true) anomaly of the planetary trajectories to the uniformly…

Power-meter measurements are used to study a model that accounts for the use of power by a cyclist. The focus is on relations between rates of change of model quantities, such as power and speed, both in the context of partial derivatives,…

Let P_1 and P_2 be two sets of points in the plane, so that P_1 is contained in a line L_1, P_2 is contained in a line L_2, and L_1 and L_2 are neither parallel nor orthogonal. Then the number of distinct distances determined by the pairs…