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Bell's Spaceship Paradox
Bell's spaceship paradox is a thought experiment in special relativity. It was designed by E. Dewan and M. Beran in 1959 and became more widely known when J. S. Bell included a modified version.J. S. Bell: ''How to teach special relativity'', Progress in Scientific culture 1(2) (1976), pp. 1–13. Reprinted in J. S. Bell: ''Speakable and unspeakable in quantum mechanics'' (Cambridge University Press, 1987), chapter 9, pp. 67–80. A delicate thread hangs between two spaceships. They start accelerating simultaneously and equally as measured in the inertial frame S, thus having the same velocity at all times as viewed from S. Therefore, they are all subject to the same Lorentz contraction, so the entire assembly seems to be equally contracted in the S frame with respect to the length at the start. At first sight, it might appear that the thread will not break during acceleration. This argument, however, is incorrect as shown by Dewan and Beran and Bell. The distance between the spac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Intermolecular Force
An intermolecular force (IMF) (or secondary force) is the force that mediates interaction between molecules, including the electromagnetic forces of attraction or repulsion which act between atoms and other types of neighbouring particles, e.g. atoms or ions. Intermolecular forces are weak relative to intramolecular forces – the forces which hold a molecule together. For example, the covalent bond, involving sharing electron pairs between atoms, is much stronger than the forces present between neighboring molecules. Both sets of forces are essential parts of force fields frequently used in molecular mechanics. The investigation of intermolecular forces starts from macroscopic observations which indicate the existence and action of forces at a molecular level. These observations include non-ideal-gas thermodynamic behavior reflected by virial coefficients, vapor pressure, viscosity, superficial tension, and absorption data. The first reference to the nature of microscopic forc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hyperbolic Motion (relativity)
Hyperbolic motion is the motion of an object with constant proper acceleration in special relativity. It is called hyperbolic motion because the equation describing the path of the object through spacetime is a hyperbola, as can be seen when graphed on a Minkowski diagram whose coordinates represent a suitable inertial (non-accelerated) frame. This motion has several interesting features, among them that it is possible to outrun a photon if given a sufficient head start, as may be concluded from the diagram. History Hermann Minkowski (1908) showed the relation between a point on a worldline and the magnitude of four-acceleration and a "curvature hyperbola" (german: Krümmungshyperbel). In the context of Born rigidity, Max Born (1909) subsequently coined the term "hyperbolic motion" (german: Hyperbelbewegung) for the case of constant magnitude of four-acceleration, then provided a detailed description for charged particles in hyperbolic motion, and introduced the corresponding ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proper Acceleration
In relativity theory, proper acceleration is the physical acceleration (i.e., measurable acceleration as by an accelerometer) experienced by an object. It is thus acceleration relative to a free-fall, or inertial, observer who is momentarily at rest relative to the object being measured. Gravitation therefore does not cause proper acceleration, because the same gravity acts equally on the inertial observer. As a consequence, all inertial observers always have a proper acceleration of zero. Proper acceleration contrasts with coordinate acceleration, which is dependent on choice of coordinate systems and thus upon choice of observers (see three-acceleration in special relativity). In the standard inertial coordinates of special relativity, for unidirectional motion, proper acceleration is the rate of change of proper velocity with respect to coordinate time. In an inertial frame in which the object is momentarily at rest, the proper acceleration 3-vector, combined with a zero t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rindler Coordinates
In relativistic physics, the coordinates of a ''hyperbolically accelerated reference frame'' constitute an important and useful coordinate chart representing part of flat Minkowski spacetime. In special relativity, a uniformly accelerating particle undergoes hyperbolic motion, for which a uniformly accelerating frame of reference in which it is at rest can be chosen as its proper reference frame. The phenomena in this hyperbolically accelerated frame can be compared to effects arising in a homogeneous gravitational field. For general overview of accelerations in flat spacetime, see Acceleration (special relativity) and Proper reference frame (flat spacetime). In this article, the speed of light is defined by , the inertial coordinates are , and the hyperbolic coordinates are . These hyperbolic coordinates can be separated into two main variants depending on the accelerated observer's position: If the observer is located at time at position (with as the constant proper acceler ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Dewan And Beran
''Dewan'' (also known as ''diwan'', sometimes spelled ''devan'' or ''divan'') designated a powerful government official, minister, or ruler. A ''dewan'' was the head of a state institution of the same name (see Divan). Diwans belonged to the elite families in the history of Mughal and post-Mughal India and held high posts within the government. Etymology The word is Persian in origin and was loaned into Arabic. The original meaning was "bundle (of written sheets)", hence "book", especially "book of accounts," and hence "office of accounts," "custom house," "council chamber". The meaning of the word, ''divan'' "long, cushioned seat" is due to such seats having been found along the walls in Middle Eastern council chambers. It is a common surname among Sikhs in Punjab. Council The word first appears under the Caliphate of Omar I (A.D. 634–644). As the Caliphate state became more complicated, the term was extended over all the government bureaus. The ''divan of the Sublime P ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Loedel Diagram
A spacetime diagram is a graphical illustration of the properties of space and time in the special theory of relativity. Spacetime diagrams allow a qualitative understanding of the corresponding phenomena like time dilation and length contraction without mathematical equations. The history of an object's location throughout all time traces out a line, referred to as the object's world line, in a spacetime diagram. Points in spacetime diagrams represent a fixed position in space and time and are referred to as events. The most well-known class of spacetime diagrams are known as Minkowski diagrams, developed by Hermann Minkowski in 1908. Minkowski diagrams are two-dimensional graphs that depict events as happening in a universe consisting of one space dimension and one time dimension. Unlike a regular distance-time graph, the distance is displayed on the horizontal axis and time on the vertical axis. Additionally, the time and space units of measurement are chosen in such a way t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Angular Acceleration
In physics, angular acceleration refers to the time rate of change of angular velocity. As there are two types of angular velocity, namely spin angular velocity and orbital angular velocity, there are naturally also two types of angular acceleration, called spin angular acceleration and orbital angular acceleration respectively. Spin angular acceleration refers to the angular acceleration of a rigid body about its centre of rotation, and orbital angular acceleration refers to the angular acceleration of a point particle about a fixed origin. Angular acceleration is measured in units of angle per unit time squared (which in SI units is radians per second squared), and is usually represented by the symbol alpha (α). In two dimensions, angular acceleration is a pseudoscalar whose sign is taken to be positive if the angular speed increases counterclockwise or decreases clockwise, and is taken to be negative if the angular speed increases clockwise or decreases counterclockwise. I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Ladder Paradox
The ladder paradox (or barn-pole paradox) is a thought experiment in special relativity. It involves a ladder, parallel to the ground, travelling horizontally at relativistic speed (near the speed of light) and therefore undergoing a Lorentz length contraction. The ladder is imagined passing through the open front and rear doors of a garage or barn which is shorter than its rest length, so if the ladder was not moving it would not be able to fit inside. To a stationary observer, due to the contraction, the moving ladder is able to fit entirely inside the building as it passes through. On the other hand, from the point of view of an observer moving with the ladder, the ladder will not be contracted, and it is the building which will be Lorentz contracted to an even smaller length. Therefore, the ladder will not be able to fit inside the building as it passes through. This poses an apparent discrepancy between the realities of both observers. This apparent paradox results from the m ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Analysis
Analysis ( : analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (384–322 B.C.), though ''analysis'' as a formal concept is a relatively recent development. The word comes from the Ancient Greek ἀνάλυσις (''analysis'', "a breaking-up" or "an untying;" from ''ana-'' "up, throughout" and ''lysis'' "a loosening"). From it also comes the word's plural, ''analyses''. As a formal concept, the method has variously been ascribed to Alhazen, René Descartes (''Discourse on the Method''), and Galileo Galilei. It has also been ascribed to Isaac Newton, in the form of a practical method of physical discovery (which he did not name). The converse of analysis is synthesis: putting the pieces back together again in new or different whole. Applications Science The field of chemistry uses analysis in thr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Minkowski Diagram
A spacetime diagram is a graphical illustration of the properties of space and time in the special theory of relativity. Spacetime diagrams allow a qualitative understanding of the corresponding phenomena like time dilation and length contraction without mathematical equations. The history of an object's location throughout all time traces out a line, referred to as the object's world line, in a spacetime diagram. Points in spacetime diagrams represent a fixed position in space and time and are referred to as events. The most well-known class of spacetime diagrams are known as Minkowski diagrams, developed by Hermann Minkowski in 1908. Minkowski diagrams are two-dimensional graphs that depict events as happening in a universe consisting of one space dimension and one time dimension. Unlike a regular distance-time graph, the distance is displayed on the horizontal axis and time on the vertical axis. Additionally, the time and space units of measurement are chosen in such a way th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
History Of Lorentz Transformations
The history of Lorentz transformations comprises the development of linear transformations forming the Lorentz group or Poincaré group preserving the Lorentz interval -x_^+\cdots+x_^ and the Minkowski inner product -x_y_+\cdots+x_y_. In mathematics, transformations equivalent to what was later known as Lorentz transformations in various dimensions were discussed in the 19th century in relation to the theory of quadratic forms, hyperbolic geometry, Möbius geometry, and sphere geometry, which is connected to the fact that the group of motions in hyperbolic space, the Möbius group or projective special linear group, and the Laguerre group are isomorphic to the Lorentz group. In physics, Lorentz transformations became known at the beginning of the 20th century, when it was discovered that they exhibit the symmetry of Maxwell's equations. Subsequently, they became fundamental to all of physics, because they formed the basis of special relativity in which they exhibit the symmetry ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
