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Crown Dependencies are self-governing territories under the sovereignty of the British Crown, comprising the Channel Islands and the Isle of Man. Although they are not part of the United Kingdom or the European Union, they rely on the UK for defense and international representation, while maintaining autonomy over internal affairs and local legislation.
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Special Relativity, formulated by Albert Einstein in 1905, revolutionized the understanding of space and time by introducing the idea that the laws of physics are the same for all non-accelerating observers and that the speed of light in a vacuum is constant regardless of the motion of the light source or observer. This theory fundamentally altered the concepts of simultaneity, length, and time, leading to groundbreaking implications such as time dilation and length contraction.
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General relativity, formulated by Albert Einstein, is a theory of gravitation that describes gravity as the warping of spacetime by mass and energy, rather than as a force acting at a distance. It fundamentally changed our understanding of the universe, predicting phenomena such as the bending of light around massive objects and the existence of black holes.
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The Lorentz transformation is a set of linear equations in Einstein's theory of special relativity that describes how the measurements of time and space by two observers are related to each other when the observers are moving at constant velocity relative to each other. It ensures that the speed of light is constant in all inertial frames of reference, leading to phenomena such as time dilation and length contraction.
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Time dilation is a phenomenon predicted by Einstein's theory of relativity, where time passes at different rates depending on the relative speed of an observer or the presence of a gravitational field. It reveals that time is not an absolute constant but is influenced by velocity and gravity, fundamentally altering our understanding of space-time.
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Length contraction is a phenomenon predicted by the theory of special relativity, where an object in motion relative to an observer is measured to be shorter along the direction of motion than when it is at rest. This effect becomes significant only at velocities close to the speed of light and is a direct consequence of the invariance of the speed of light for all observers.
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Mass-energy equivalence is a fundamental principle of physics encapsulated by Einstein's equation E=mc², which states that mass and energy are interchangeable and can be converted into each other. This principle explains phenomena such as nuclear reactions, where small amounts of mass are converted into large amounts of energy, and is a cornerstone of both relativity and quantum mechanics.
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Four-vectors are mathematical objects used in the theory of relativity to describe physical quantities in a way that is invariant under Lorentz transformations. They combine time and three-dimensional space into a single four-dimensional spacetime framework, facilitating the analysis of relativistic phenomena.
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The invariant interval is a fundamental concept in the theory of relativity, representing the spacetime separation between two events that remains constant regardless of the observer's frame of reference. This interval can be categorized as time-like, space-like, or light-like, determining the causal relationship between the events.
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Relativistic momentum is an extension of classical momentum that accounts for the effects of special relativity, becoming significant as an object's velocity approaches the speed of light. It is calculated using the formula p = γmv, where γ is the Lorentz factor, m is the rest mass, and v is the velocity of the object.
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Relativistic energy refers to the energy of an object moving at a significant fraction of the speed of light, where classical mechanics fails to accurately describe its dynamics. It combines kinetic and rest energy, incorporating Einstein's famous equation E=mc², which shows how mass can be converted into energy.
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Proper time is the time interval measured by a clock that is at rest relative to the observer, providing an invariant measure of time in the framework of relativity. It is a fundamental concept in understanding how time is perceived differently by observers in relative motion or in varying gravitational fields.
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Minkowski space is a four-dimensional spacetime framework that combines three-dimensional Euclidean space and time into a single manifold, crucial for the formulation of special relativity. It provides the geometric interpretation of the invariant interval, which remains constant for all observers regardless of their relative motion, encapsulating the essence of relativistic effects such as time dilation and length contraction.
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The Lorentz group is a fundamental symmetry group in physics that describes how the laws of physics are invariant under transformations between inertial frames in special relativity. It includes rotations and boosts, which are transformations that relate different observers moving at constant velocities relative to each other.
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