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K-calculus
Bondi ''k''-calculus is a method of teaching special relativity popularised by Sir Hermann Bondi, that has been used in university-level physics classes (e.g. at The University of Oxford), and in some relativity textbooks. The usefulness of the ''k''-calculus is its simplicity. Many introductions to relativity begin with the concept of velocity and a derivation of the Lorentz transformation. Other concepts such as time dilation, length contraction, the relativity of simultaneity, the resolution of the twins paradox and the relativistic Doppler effect are then derived from the Lorentz transformation, all as functions of velocity. Bondi, in his book ''Relativity and Common Sense'', first published in 1964 and based on articles published in ''The Illustrated London News'' in 1962, reverses the order of presentation. He begins with what he calls "a fundamental ratio" denoted by the letter k (which turns out to be the radial Doppler factor).d'Inverno (1992), p.40 From this he explain ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
K-calculus Diagram For K-factor Definition
Bondi ''k''-calculus is a method of teaching special relativity popularised by Sir Hermann Bondi, that has been used in university-level physics classes (e.g. at The University of Oxford), and in some relativity textbooks. The usefulness of the ''k''-calculus is its simplicity. Many introductions to relativity begin with the concept of velocity and a derivation of the Lorentz transformation. Other concepts such as time dilation, length contraction, the relativity of simultaneity, the resolution of the twins paradox and the relativistic Doppler effect are then derived from the Lorentz transformation, all as functions of velocity. Bondi, in his book ''Relativity and Common Sense'', first published in 1964 and based on articles published in ''The Illustrated London News'' in 1962, reverses the order of presentation. He begins with what he calls "a fundamental ratio" denoted by the letter k (which turns out to be the radial Doppler factor).d'Inverno (1992), p.40 From this he explai ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hermann Bondi
Sir Hermann Bondi (1 November 1919 – 10 September 2005) was an Austrian- British mathematician and cosmologist. He is best known for developing the steady state model of the universe with Fred Hoyle and Thomas Gold as an alternative to the Big Bang theory. He contributed to the theory of general relativity,Obituaries: Professor Sir Hermann Bondi(12 September 2005) in ''The Independent''. Professor Sir Hermann Bondi(2005-09-13) in ''The Telegraph''. Sir Hermann Bondi(2005-09-14) in ''The Guardian''. Sir Hermann Bondi: 1919–2005(2005-09-14) in '' Physics World'', IOP. Black hole scientist Bondi dies(2005-09-17), BBC News. and was the first to analyze the inertial and gravitational interaction of negative mass and the first to explicate correctly the nature of gravitational waves. In his 1990 autobiography, Bondi regarded the 1962 work on gravitational waves as his "best scientific work". Early life Bondi was born in Vienna, the son of a Jewish medical doctor. He was ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Special Relativity
In physics, the special theory of relativity, or special relativity for short, is a scientific theory regarding the relationship between space and time. In Albert Einstein's original treatment, the theory is based on two postulates: # The laws of physics are invariant (that is, identical) in all inertial frames of reference (that is, frames of reference with no acceleration). # The speed of light in vacuum is the same for all observers, regardless of the motion of the light source or the observer. Origins and significance Special relativity was originally proposed by Albert Einstein in a paper published on 26 September 1905 titled "On the Electrodynamics of Moving Bodies".Albert Einstein (1905)''Zur Elektrodynamik bewegter Körper'', ''Annalen der Physik'' 17: 891; English translatioOn the Electrodynamics of Moving Bodiesby George Barker Jeffery and Wilfrid Perrett (1923); Another English translation On the Electrodynamics of Moving Bodies by Megh Nad Saha (1920). The ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rapidity
In relativity, rapidity is commonly used as a measure for relativistic velocity. Mathematically, rapidity can be defined as the hyperbolic angle that differentiates two frames of reference in relative motion, each frame being associated with distance and time coordinates. For one-dimensional motion, rapidities are additive whereas velocities must be combined by Einstein's velocity-addition formula. For low speeds, rapidity and velocity are proportional but, for higher velocities, rapidity takes a larger value, with the rapidity of light being infinite. Using the inverse hyperbolic function , the rapidity corresponding to velocity is where ''c'' is the velocity of light. For low speeds, is approximately . Since in relativity any velocity is constrained to the interval the ratio satisfies . The inverse hyperbolic tangent has the unit interval for its domain and the whole real line for its image; that is, the interval maps onto . History In 1908 Hermann Minkowski ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Twin Paradox
In physics, the twin paradox is a thought experiment in special relativity involving identical twins, one of whom makes a journey into space in a high-speed rocket and returns home to find that the twin who remained on Earth has aged more. This result appears puzzling because each twin sees the other twin as moving, and so, as a consequence of an incorrect and naive application of time dilation and the principle of relativity, each should paradoxically find the other to have aged less. However, this scenario can be resolved within the standard framework of special relativity: the travelling twin's trajectory involves two different inertial frames, one for the outbound journey and one for the inbound journey. Another way of looking at it is to realize the travelling twin is undergoing acceleration, which makes him a non-inertial observer. In both views there is no symmetry between the spacetime paths of the twins. Therefore, the twin paradox is not actually a paradox in the sens ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
The Illustrated London News
''The Illustrated London News'' appeared first on Saturday 14 May 1842, as the world's first illustrated weekly news magazine. Founded by Herbert Ingram, it appeared weekly until 1971, then less frequently thereafter, and ceased publication in 2003. The company continues today as Illustrated London News Ltd, a publishing, content, and digital agency in London, which holds the publication and business archives of the magazine. History 1842–1860: Herbert Ingram ''The Illustrated London News'' founder Herbert Ingram was born in Boston, Lincolnshire, in 1811, and opened a printing, newsagent, and bookselling business in Nottingham around 1834 in partnership with his brother-in-law, Nathaniel Cooke.Isabel Bailey"Ingram, Herbert (1811–1860)" ''Oxford Dictionary of National Biography'', Oxford University Press, 2004 accessed 17 September 2014] As a newsagent, Ingram was struck by the reliable increase in newspaper sales when they featured pictures and shocking stories. Ingram ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Relativistic Doppler Effect
The relativistic Doppler effect is the change in frequency (and wavelength) of light, caused by the relative motion of the source and the observer (as in the classical Doppler effect), when taking into account effects described by the special theory of relativity. The relativistic Doppler effect is different from the non-relativistic Doppler effect as the equations include the time dilation effect of special relativity and do not involve the medium of propagation as a reference point. They describe the total difference in observed frequencies and possess the required Lorentz symmetry. Astronomers know of three sources of redshift/blueshift: Doppler shifts; gravitational redshifts (due to light exiting a gravitational field); and cosmological expansion (where space itself stretches). This article concerns itself only with Doppler shifts. Summary of major results In the following table, it is assumed that for \beta = v/c > 0 the receiver and the source are moving away from eac ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
