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mechanics, relativistic

The generalization of classical mechanics that takes into account the effects of special relativity. The basic laws are almost unchanged: First of all, bodies on which no external forces act stay at rest or move with constant speed along straight paths – in the language of special relativity: such bodies move on straight lines in spacetime. Secondly: The total force acting on a body is equal to the change of its momentum over time (but notice: this momentum is defined using the body’s relativistic mass, which depends on the bodies speed relative to the observer). Thirdly, mass and momentum are conserved quantities – their total sum is the same whenever particles interact (this is equivalent to a slightly modified version of the “action equals reaction” principle of classical mechanics).

There exists an elegant reformulation of these laws of mechanics using four-dimensional concepts adapted to the geometry of spacetime, such as the “four-momentum”.

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speed

An object's average speed is the distance it moves during a given period of time, divided by the length of the time interval. If you make the time interval infinitely small, the result is the object's speed at one particular moment in time. The notion of speed can be applied to waves in different ways; for instance, for a simple wave, the phase speed is the speed at which any given wave crest or wave propagates through space. See also the more general entry velocity.

spacetime

Already in special relativity, observers in motion relative to each other will not, in general, agree as to whether two events happen simultaneously, or as to how great is the distance between two objects. They do, however, agree as to what events there are, although not to when and where they happen. This observer-independent totality of all events is called spacetime. How spacetime is split into space and time can differ from observer to observer. Every-day space has three dimensions. Adding time adds another dimension - spacetime has four dimensions, all in all. We are used to the idea of a point in space - an object that has only one location and is completely defined once its space coordinates are given. In spacetime, a spacetime point is an object defined completely once its space coordinates and its time coordinate are given - which makes a spacetime point nothing but an elementary event. The idea of spacetime is, in addition to its role in special relativity, a building block of general relativity. Analogous to how a plane is flat, but the surface of a sphere is curved, in general relativity, curved or distorted versions of the simple, flat spacetime of special relativity play a role. Spacetime curvature, in general relativity, is intimately connected with gravity. For an introduction to the basics of both theories of relativity, check out the chapters Special relativity and General relativity in Elementary Einstein. Sometimes, it can be helpful to view spacetime in analogy to ordinary space - such analogies are explored in the spotlight topics Time dilation on the road (for time dilation) and Twins on the road (for the twin effect).

observer

In the context of relativity, "observer" can mean two different things. Often, observer is synonymous with reference frame or (spacetime-)coordinate system: An observer in this sense is someone who assigns coordinates to everything that happens around him. In particular, all events are assigned space coordinate values and a time coordinate value. In the context of special relativity, it is often the case that when one talks about an observer, what is really meant is an inertial observer, corresponding to a special type of reference frame. On other occasions, the term is used in a more narrow sense - in those cases, an observer is someone sitting at a certain point in space and using the light signals reaching that location to construct an image of his surroundings. In the context of optical effects in relativity, for instance gravitational lensing, observer is usually meant in this way.

momentum

Physical quantity that is equal to a body's mass times its velocity (in special relativity: its relativistic mass times its velocity). What makes momentum a useful quantity is that it is conserved - if several bodies interact, the sum of their momenta before and after the interaction is the same. Momentum is neither created nor destroyed, merely passed on from one body to another. In general relativity, momentum is one of a number of quantities (like mass and energy) that acts as a source of gravity.

mechanics

Branch of physics dealing with the motions of objects and how they react to forces acting on them. Depending on the framework used, there is classical mechanics, relativistic mechanics and quantum mechanics.

mass

In classical physics, mass plays a triple role. First of all, it is a measure for how easy it is to influence the motion of a body. Imagine that you're drifting in emtpy space. Drifting by are an elephant and a mouse, and you give each of them a push of equal strength. The fact that the mouse abruptly changes its path, while the elephant's course is as good as unaltered, is a sure sign that the mass (or, in the language of physics, the inertia or inertial mass) of the elephant is much greater than that of the mouse. Secondly, mass is a measure of how many atoms there are in a body, and of what type they are. All atoms of one and the same type have the same mass, and adding up all those tiny component masses, the total mass of the body results. Thirdly, in Newton's theory of gravity, mass determines how strongly a body attracts other bodies via the gravitational force, and how strongly these bodies attract it (in this sense, mass is the charge associated with the gravitational force). In special relativity, one can also define a mass that is a measure for a bodies resistance to changing its motion. However, the value of this relativistic mass depends on the relative motion of the body and the observer. The relativistic mass is the "m" in Einstein's famous E=mc² (cf. equivalence of mass and energy). The relativistic mass has a minimum for an observer that is at rest relative to the body in question. This value is the so-called rest mass of the body, and when particle physicists talk of mass, this is usually what they mean. Just as in classical physics, the rest mass is a kind of measure for how much matter the body is made up of - with one caveat: For composite bodies, the energies associated with the forces holding the body together contribute to the total mass, as well (another consequence of the equivalence of mass and energy). In general relativity, mass still plays a role as a source of gravity; however, it has been joined by physical quantities such as energy, momentum and pressure.

geometry

That part of mathematics concerning itself with surfaces or more general spaces as well as objects defined on such spaces, such as points or lines as well as the objects constructable from points and lines, such as triangles.

conserved quantities (conservation laws)

Some of the most important quantities in physics are conserved : What they measure can neither be created nor destroyed, and their total sum is constant over time. Such statements of constancy over time are called conservation laws. The most important conserved quantity is energy. Energy can neither be created from nothing nor simply vanish. If the energy contained in a system increases, it must be because energy has been transported into the system (and there is now less energy outside the system); if the energy decreases, it must be because energy has been transferred from the system (and there is now more energy outside). Another important class of conserved quantities are charges, for instance electric charge. A further conserved quantity in mechanics is angular momentum; a quantity associated with a body's rotation.

classical

In physics, the word is used with two meanings. First of all, it denotes physical models or theories that take into account neither the effects of Einstein's theories of relativity nor those of quantum physics, for example classical mechanics. However, it is also used to denote models or theories that are not formulated in the framework of quantum physics; in that sense, general relativity is an example for a classical theory.

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mechanics, relativistic

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