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One-way Speed Of Light
When using the term ' the speed of light' it is sometimes necessary to make the distinction between its one-way speed and its two-way speed. The "one-way" speed of light, from a source to a detector, cannot be measured independently of a convention as to how to synchronize the clocks at the source and the detector. What can however be experimentally measured is the round-trip speed (or "two-way" speed of light) from the source to a mirror (or other method of reflection) and back again to detector. Albert Einstein chose a synchronization convention (see Einstein synchronization) that made the one-way speed equal to the two-way speed. The constancy of the one-way speed in any given inertial frame is the basis of his special theory of relativity, although all experimentally verifiable predictions of this theory do not depend on that convention. Experiments that attempt to directly probe the one-way speed of light independent of synchronization have been proposed, but none have suc ...
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Speed Of Light
The speed of light in vacuum, commonly denoted , is a universal physical constant that is important in many areas of physics. The speed of light is exactly equal to ). According to the special theory of relativity, is the upper limit for the speed at which conventional matter or energy (and thus any signal carrying information) can travel through space. All forms of electromagnetic radiation, including visible light, travel at the speed of light. For many practical purposes, light and other electromagnetic waves will appear to propagate instantaneously, but for long distances and very sensitive measurements, their finite speed has noticeable effects. Starlight viewed on Earth left the stars many years ago, allowing humans to study the history of the universe by viewing distant objects. When communicating with distant space probes, it can take minutes to hours for signals to travel from Earth to the spacecraft and vice versa. In computing, the speed of light fixes ...
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Kennedy–Thorndike Experiment
The Kennedy–Thorndike experiment, first conducted in 1932 by Roy J. Kennedy and Edward M. Thorndike, is a modified form of the Michelson–Morley experimental procedure, testing special relativity. The modification is to make one arm of the classical Michelson–Morley (MM) apparatus shorter than the other one. While the Michelson–Morley experiment showed that the speed of light is independent of the ''orientation'' of the apparatus, the Kennedy–Thorndike experiment showed that it is also independent of the ''velocity'' of the apparatus in different inertial frames. It also served as a test to indirectly verify time dilation – while the negative result of the Michelson–Morley experiment can be explained by length contraction alone, the negative result of the Kennedy–Thorndike experiment requires time dilation in addition to length contraction to explain why no phase shifts will be detected while the Earth moves around the Sun. The first ''direct'' confirmation of time dil ...
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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 sen ...
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Generalizations Of Lorentz Transformations With Anisotropic One-way Speeds
A generalization is a form of abstraction whereby common properties of specific instances are formulated as general concepts or claims. Generalizations posit the existence of a domain or set of elements, as well as one or more common characteristics shared by those elements (thus creating a conceptual model). As such, they are the essential basis of all valid deductive inferences (particularly in logic, mathematics and science), where the process of verification is necessary to determine whether a generalization holds true for any given situation. Generalization can also be used to refer to the process of identifying the parts of a whole, as belonging to the whole. The parts, which might be unrelated when left on their own, may be brought together as a group, hence belonging to the whole by establishing a common relation between them. However, the parts cannot be generalized into a whole—until a common relation is established among ''all'' parts. This does not mean that the ...
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Ad Hoc Hypothesis
In science and philosophy, an ''ad hoc'' hypothesis is a hypothesis added to a theory in order to save it from being falsified. Often, ''ad hoc'' hypothesizing is employed to compensate for anomalies not anticipated by the theory in its unmodified form. In the scientific community Scientists are often skeptical of theories that rely on frequent, unsupported adjustments to sustain them. This is because, if a theorist so chooses, there is no limit to the number of ''ad hoc'' hypotheses that they could add. Thus the theory becomes more and more complex, but is never falsified. This is often at a cost to the theory's predictive power, however. ''Ad hoc'' hypotheses are often characteristic of pseudoscientific subjects. An ''ad hoc'' hypothesis is not necessarily incorrect; in some cases, a minor change to a theory was all that was necessary. For example, Albert Einstein's addition of the cosmological constant to general relativity in order to allow a static universe was ''ad hoc' ...
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Slow Clock-transport
In everyday use and in kinematics, the speed (commonly referred to as ''v'') of an object is the magnitude of the change of its position over time or the magnitude of the change of its position per unit of time; it is thus a scalar quantity. The average speed of an object in an interval of time is the distance travelled by the object divided by the duration of the interval; the instantaneous speed is the limit of the average speed as the duration of the time interval approaches zero. Speed is not the same as velocity. Speed has the dimensions of distance divided by time. The SI unit of speed is the metre per second (m/s), but the most common unit of speed in everyday usage is the kilometre per hour (km/h) or, in the US and the UK, miles per hour (mph). For air and marine travel, the knot is commonly used. The fastest possible speed at which energy or information can travel, according to special relativity, is the speed of light in a vacuum ''c'' = metres per second (a ...
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Experiments In Which Light Follows A Unidirectional Path
An experiment is a procedure carried out to support or refute a hypothesis, or determine the efficacy or likelihood of something previously untried. Experiments provide insight into cause-and-effect by demonstrating what outcome occurs when a particular factor is manipulated. Experiments vary greatly in goal and scale but always rely on repeatable procedure and logical analysis of the results. There also exist natural experimental studies. A child may carry out basic experiments to understand how things fall to the ground, while teams of scientists may take years of systematic investigation to advance their understanding of a phenomenon. Experiments and other types of hands-on activities are very important to student learning in the science classroom. Experiments can raise test scores and help a student become more engaged and interested in the material they are learning, especially when used over time. Experiments can vary from personal and informal natural comparisons (e. ...
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Test Theories Of Special Relativity
Test theories of special relativity give a mathematical framework for analyzing results of experiments to verify special relativity. An experiment to test the theory of relativity cannot assume the theory is true, and therefore needs some other framework of assumptions that are wider than those of relativity. For example, a test theory may have a different postulate about light concerning one-way speed of light vs. two-way speed of light, it may have a preferred frame of reference, and may violate Lorentz invariance in many different ways. Test theories predicting different experimental results from Einstein's special relativity, are ''Robertson's test theory (1949)'', and the ''Mansouri–Sexl theory (1977)'' which is equivalent to Robertson's theory. Another, more extensive model is the Standard-Model Extension, which also includes the standard model and general relativity. Robertson–Mansouri–Sexl framework Basic principles Howard Percy Robertson (1949) extended the L ...
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Isotropy
Isotropy is uniformity in all orientations; it is derived . Precise definitions depend on the subject area. Exceptions, or inequalities, are frequently indicated by the prefix ' or ', hence ''anisotropy''. ''Anisotropy'' is also used to describe situations where properties vary systematically, dependent on direction. Isotropic radiation has the same intensity regardless of the direction of measurement, and an isotropic field exerts the same action regardless of how the test particle is oriented. Mathematics Within mathematics, ''isotropy'' has a few different meanings: ; Isotropic manifolds: A manifold is isotropic if the geometry on the manifold is the same regardless of direction. A similar concept is homogeneity. ; Isotropic quadratic form: A quadratic form ''q'' is said to be isotropic if there is a non-zero vector ''v'' such that ; such a ''v'' is an isotropic vector or null vector. In complex geometry, a line through the origin in the direction of an isotropic vecto ...
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Clifford Will
Clifford Martin Will (born 1946) is a Canadian-born theoretical physicist noted for his contributions to general relativity. Life and work Will was born in Hamilton, Ontario. In 1968, he earned a B.Sc. from McMaster University. At Caltech, he studied under Kip Thorne, earning his Ph.D. in 1971. He has taught at the University of Chicago and Stanford University, and in 1981 joined the faculty of Washington University in St. Louis. In 2012, he moved to a faculty position at the University of Florida. Will's theoretical work has centered on Post-Newtonian expansions of approximate solutions to the Einstein field equation, a notoriously difficult area which forms the theoretical underpinnings essential for such achievements as the indirect verification by Russell Hulse and Joseph Taylor of the existence of gravitational radiation from observations of a binary pulsar. Will's book reviewing experimental tests of general relativity is widely regarded as the essential resource for ...
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Lorentz Transformation
In physics, the Lorentz transformations are a six-parameter family of Linear transformation, linear coordinate transformation, transformations from a Frame of Reference, coordinate frame in spacetime to another frame that moves at a constant velocity relative to the former. The respective inverse transformation is then parameterized by the negative of this velocity. The transformations are named after the Dutch physicist Hendrik Lorentz. The most common form of the transformation, parametrized by the real constant v, representing a velocity confined to the -direction, is expressed as \begin t' &= \gamma \left( t - \frac \right) \\ x' &= \gamma \left( x - v t \right)\\ y' &= y \\ z' &= z \end where and are the coordinates of an event in two frames with the origins coinciding at 0, where the primed frame is seen from the unprimed frame as moving with speed along the -axis, where is the speed of light, and \gamma = \left ( \sqrt\right )^ is the Lorentz factor. When speed is m ...
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Simple Stellar Aberration Diagram
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