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Mach's Principle
In theoretical physics, particularly in discussions of gravitation theories, Mach's principle
Mach's principle
(or Mach's conjecture[1]) is the name given by Einstein to an imprecise hypothesis often credited to the physicist and philosopher Ernst Mach. The idea is that local inertial frames are determined by the large-scale distribution of matter, as exemplified by this anecdote:[citation needed]You are standing in a field looking at the stars. Your arms are resting freely at your side, and you see that the distant stars are not moving. Now start spinning. The stars are whirling around you and your arms are pulled away from your body. Why should your arms be pulled away when the stars are whirling? Why should they be dangling freely when the stars don't move? Mach's principle
Mach's principle
says that this is not a coincidence—that there is a physical law that relates the motion of the distant stars to the local inertial frame
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Theoretical Physics
Theoretical physics
Theoretical physics
is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experimental tools to probe these phenomena. The advancement of science generally depends on the interplay between experimental studies and theory
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Holism
Holism
Holism
(from Greek ὅλος holos "all, whole, entire") is the idea that systems (physical, biological, chemical, social, economic, mental, linguistic) and their properties should be viewed as wholes, not just as a collection of parts.[1][2] The term holism was coined by J. C. Smuts in Holism
Holism
and Evolution.[3][4] It was Smuts' opinion that holism is a concept that represents all of the wholes in the universe, and these wholes are the real factors in the universe. Further, that Holism
Holism
also denoted a theory of the universe in the same vein as Materialism and Spiritualism.[3]:120–121 The derived adjective holistic has been applied to a wide range of fields where they incorporate the concept of holism
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Luminiferous Aether
In the late 19th century, luminiferous aether, aether, or ether, meaning light-bearing aether, was the postulated medium for the propagation of light.[1] It was invoked to explain the ability of the apparently wave-based light to propagate through empty space, something that waves should not be able to do. The assumption of a spatial plenum of luminiferous aether, rather than a spatial vacuum, provided the theoretical medium that was required by wave theories of light. The concept was the topic of considerable debate throughout its history, as it required the existence of an invisible and infinite material with no interaction with physical objects. As the nature of light was explored, especially in the 19th century, the physical qualities required of the aether became increasingly contradictory
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Hubble Time
Hubble's law
Hubble's law
is the name for the observation in physical cosmology that:Objects observed in deep space - extragalactic space, 10 megaparsecs (Mpc) or more - are found to have a red shift, interpreted as a relative velocity away from Earth; This Doppler-shift-measured velocity of various galaxies receding from the Earth
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Gravitational Constant
The gravitational constant, also known as the universal gravitational constant, or as Newton's constant, denoted by the letter G, is an empirical physical constant involved in the calculation of gravitational effects in Sir Isaac Newton's law of universal gravitation and in Albert Einstein's general theory of relativity
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Cauchy Surface
Intuitively, a Cauchy surface is a plane in space-time which is like an instant of time; its significance is that giving the initial conditions on this plane determines the future (and the past) uniquely. More precisely, a Cauchy surface is any subset of space-time which is intersected by every inextensible, non-spacelike (i.e
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Globally Hyperbolic Manifold
In mathematical physics, global hyperbolicity is a certain condition on the causal structure of a spacetime manifold (that is, a Lorentzian manifold). This is relevant to Einstein's theory of general relativity, and potentially to other metric gravitational theories.Contents1 Definitions 2 Remarks 3 See also 4 ReferencesDefinitions[edit] There are several equivalent definitions of global hyperbolicity. Let M be a smooth connected Lorentzian manifold without boundary. We make the following preliminary definitions:M is causal if it has no closed causal curves. M is non-total imprisoning if no inextendible causal curve is contained in a compact set. This property implies causality. M is strongly causal if for every point p and any neighborhood U of p there is a causally convex neighborhood V of p contained in U, where causal convexity means that any causal curve with endpoints in V is entirely contained in V
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Compact Space
In mathematics, and more specifically in general topology, compactness is a property that generalizes the notion of a subset of Euclidean space being closed (that is, containing all its limit points) and bounded (that is, having all its points lie within some fixed distance of each other). Examples include a closed interval, a rectangle, or a finite set of points. This notion is defined for more general topological spaces than Euclidean space
Euclidean space
in various ways. One such generalization is that a topological space is sequentially compact if every infinite sequence of points sampled from the space has an infinite subsequence that converges to some point of the space. The Bolzano–Weierstrass theorem
Bolzano–Weierstrass theorem
states that a subset of Euclidean space is compact in this sequential sense if and only if it is closed and bounded
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Asymptotically Flat Spacetime
An asymptotically flat spacetime is a Lorentzian manifold in which, roughly speaking, the curvature vanishes at large distances from some region, so that at large distances, the geometry becomes indistinguishable from that of Minkowski spacetime. While this notion makes sense for any Lorentzian manifold, it is most often applied to a spacetime standing as a solution to the field equations of some metric theory of gravitation, particularly general relativity. In this case, we can say that an asymptotically flat spacetime is one in which the gravitational field, as well as any matter or other fields which may be present, become negligible in magnitude at large distances from some region
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Elliptic Partial Differential Equation
Second order linear partial differential equations (PDEs) are classified as either elliptic, hyperbolic, or parabolic
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Coriolis Force
In physics, the Coriolis force
Coriolis force
is an inertial force[1] that acts on objects that are in motion relative to a rotating reference frame. In a reference frame with clockwise rotation, the force acts to the left of the motion of the object. In one with anticlockwise (or counterclockwise) rotation, the force acts to the right. Deflection of an object due to the Coriolis force
Coriolis force
is called the Coriolis effect. Though recognized previously by others, the mathematical expression for the Coriolis force
Coriolis force
appeared in an 1835 paper by French scientist Gaspard-Gustave de Coriolis, in connection with the theory of water wheels
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Precession
Precession
Precession
is a change in the orientation of the rotational axis of a rotating body. In an appropriate reference frame it can be defined as a change in the first Euler angle, whereas the third Euler angle defines the rotation itself. In other words, if the axis of rotation of a body is itself rotating about a second axis, that body is said to be precessing about the second axis. A motion in which the second Euler angle changes is called nutation. In physics, there are two types of precession: torque-free and torque-induced. In astronomy, precession refers to any of several slow changes in an astronomical body's rotational or orbital parameters
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Discussions
Debate is contention in argument; strife, dissension, quarrelling, controversy; especially a formal discussion of subjects before a public assembly or legislature, in Parliament or in any deliberative assembly.[1] Logical consistency, factual accuracy and some degree of emotional appeal to the audience are elements in debating, where one side often prevails over the other party by presenting a superior "context" or framework of the issue. In a formal debating contest, there are rules for participants to discuss and decide on differences, within a framework defining how they will interact. Debating is carried out in debating chambers and assemblies of various types to discuss matters and to make resolutions about action to be taken, often by voting.[citation needed] Deliberative bodies such as parliaments, legislative assemblies, and meetings of all sorts engage in debates. In particular, in parliamentary democracies a legislature debates and decides on new laws
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Thought Experiment
A thought experiment (German: Gedankenexperiment,[1] Gedanken-Experiment[2] or Gedankenerfahrung[3]) considers some hypothesis, theory,[4] or principle for the purpose of thinking through its consequences
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Philosophiae Naturalis Principia Mathematica
Philosophiæ Naturalis Principia Mathematica
Principia Mathematica
(English pronunciation /fɪləˈsɒfi.aɪ nætʃəˈrɑːlɪs prɪnˈkɪpiə mæθəˈmætɪkə/, Latin
Latin
for Mathematical Principles of Natural Philosophy),[1] often referred to as simply the Principia, is a work in three books by
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