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

A heuristic but pedagogical derivation is given of an explicit formula which accurately reproduces the period of a simple pendulum even for large amplitudes. The formula is compared with others in the literature.

The second-order gravitational self-force on a small body is an important problem for gravitational-wave astronomy of extreme mass-ratio inspirals. We give a first-principles derivation of a prescription for computing the first and second…

Krasinsky and Brumberg (2004 Celest. Mech. Dyn. Astron., 90, 267) reported a secular increase of the astronomical unit (AU) of 15 meters per century. Recently, Miura et al. (2009, PASJ, 61) proposed that a possible angular momentum transfer…

We discuss the twin paradox or the clock paradox under the small velocity approximation of special relativity. In this paper the traveller twin of the standard twin parable sets out with a non-relativistic speed for the trip leaving behind…

In this article, we investigate the debated Instantaneous Frequency (IF) topic. Here, we show that IF is non-unique inherently. We explain how this non-uniqueness can be quantified and explained from a mathematical perspective. The…

The world appears to be well described by gauge theories; why? I suggest that gauge is more than mathematical redundancy. Gauge-dependent quantities can not be predicted, but there is a sense in which they can be measured. They describe…

It is demonstrated that the collapse of the wave function is equivalent to the continuity of measurement outcomes. The latter states that a second measurement has to result in the same outcome as the first measurement of the same observable…

This paper shows the study of interesting mechanical properties of Wilberforce pendulum. Analyzing qualitatively of the pendulum, it is able to know how the phenomenon occurs. By setting of the quantitative model, equation of the motion is…

What is the distance between 11 (a prime number) and 12 (a highly composite number)? If your answer is 1, then ask yourself "is this reasonable?" In this work, we will introduce a distance between natural numbers based on their arithmetic…

An accelerating elevator changes the apparent weight of any object inside it from the original weight, as measured inside the elevator, because the acceleration causes an inertial force on it. For any object in a running elevator, the…

We discuss the equation of motion of the driven pendulum and generalize it to arbitrary driving angle. The pendulum will oscillate about a stable angle other than straight down if the drive amplitude and frequency are large enough for a…

It is rarely emphasized in modern physics textbooks that our definitions of space and time have to reflect their complete interdependence. Our intuitive methods of always picturing one-dimensional space as a sum of unit-length rods and of…

This thesis addresses two major problems in the philosophy of physics. The first is how to identify the minimal physical content of a theory; that is, what features of a theory are truly needed to make predictions, and what can be removed…

A modulated oscillation in two or three dimensions can be represented as the trajectory traced out in space by a particle orbiting an ellipse, the properties of which vary as a function of time. Generalizing ideas from signal analysis, the…

A calculus based on pointer-mark coincidences is proposed to define, in a mathematically rigorous way, measurements of space and time intervals. The connection between such measurements in different inertial frames according to the Galilean…

We consider the period of a simple pendulum in the gravitational field of the spherical Earth. Effectively, gravity is enhanced compared with the often used flat Earth approximation, such that the period of the pendulum is shortened. We…

We point out that, if one accepts the view that the standard second on an atomic clock is dilated at low gravitational potential (ordinary gravitational time dilation), then the standard meter must also be dilated at low gravitational…

In combination with post-selection, weak measurements can lead to surprising results known as anomalous weak values. These lie outside the bounds of the spectrum of the relevant observable, as in the canonical example of measuring the spin…

Textbooks introduce the Debye temperature to simplify the integration of the heat capacity. This approach gives the impression that the Debye temperature is a parameter which makes the integration more convenient. The Debye frequency cut…

The existence of an internal frequency associated to any elementary particle conjectured by de Broglie is compared with a classical description of the electron, where this internal structure corresponds to the motion of the centre of charge…