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In physics, a frame of reference (or reference frame) consists of an abstract coordinate system and the set of physical reference points that uniquely fix (locate and orient) the coordinate system and standardize measurements. In n dimensions, n+1 reference points are sufficient to fully define a reference frame. Using rectangular (Cartesian) coordinates, a reference frame may be defined with a reference point at the origin and a reference point at one unit distance along each of the n coordinate axes. In Einsteinian relativity, reference frames are used to specify the relationship between a moving observer and the phenomenon or phenomena under observation. In this context, the phrase often becomes "observational frame of reference" (or "observational reference frame"), which implies that the observer is at rest in the frame, although not necessarily located at its origin. A relativistic reference frame includes (or implies) the coordinate time, which does not correspond across different frames moving relatively to each other. The situation thus differs from Galilean relativity, where all possible coordinate times are essentially equivalent. == Different aspects of "frame of reference" == The need to distinguish between the various meanings of "frame of reference" has led to a variety of terms. For example, sometimes the type of coordinate system is attached as a modifier, as in ''Cartesian frame of reference''. Sometimes the state of motion is emphasized, as in ''rotating frame of reference''. Sometimes the way it transforms to frames considered as related is emphasized as in ''Galilean frame of reference''. Sometimes frames are distinguished by the scale of their observations, as in ''macroscopic'' and ''microscopic frames of reference''.〔The distinction between macroscopic and microscopic frames shows up, for example, in electromagnetism where constitutive relations of various time and length scales are used to determine the current and charge densities entering Maxwell's equations. See, for example, . These distinctions also appear in thermodynamics. See .〕 In this article, the term ''observational frame of reference'' is used when emphasis is upon the ''state of motion'' rather than upon the coordinate choice or the character of the observations or observational apparatus. In this sense, an observational frame of reference allows study of the effect of motion upon an entire family of coordinate systems that could be attached to this frame. On the other hand, a ''coordinate system'' may be employed for many purposes where the state of motion is not the primary concern. For example, a coordinate system may be adopted to take advantage of the symmetry of a system. In a still broader perspective, the formulation of many problems in physics employs ''generalized coordinates'', ''normal modes'' or ''eigenvectors'', which are only indirectly related to space and time. It seems useful to divorce the various aspects of a reference frame for the discussion below. We therefore take observational frames of reference, coordinate systems, and observational equipment as independent concepts, separated as below: *An observational frame (such as an inertial frame or non-inertial frame of reference) is a physical concept related to state of motion. *A coordinate system is a mathematical concept, amounting to a choice of language used to describe observations.〔 In very general terms, a coordinate system is a set of arcs ''x''i = ''x''i (''t'') in a complex Lie group; see . Less abstractly, a coordinate system in a space of n-dimensions is defined in terms of a basis set of vectors ; see As such, the coordinate system is a mathematical construct, a language, that may be related to motion, but has no necessary connection to motion. 〕 Consequently, an observer in an observational frame of reference can choose to employ any coordinate system (Cartesian, polar, curvilinear, generalized, …) to describe observations made from that frame of reference. A change in the choice of this coordinate system does not change an observer's state of motion, and so does not entail a change in the observer's ''observational'' frame of reference. This viewpoint can be found elsewhere as well.〔 〕 Which is not to dispute that some coordinate systems may be a better choice for some observations than are others. *Choice of what to measure and with what observational apparatus is a matter separate from the observer's state of motion and choice of coordinate system. Here is a quotation applicable to moving observational frames and various associated Euclidean three-space coordinate systems (''R′'', ''etc.'' ): and this on the utility of separating the notions of and (''R′'', ''etc.'' ): and this, also on the distinction between and (''R′'', ''etc.'' ): and from J. D. Norton:〔John D. Norton (1993). (''General covariance and the foundations of general relativity: eight decades of dispute'' ), ''Rep. Prog. Phys.'', 56, pp. 835-7.〕 The discussion is taken beyond simple space-time coordinate systems by Brading and Castellani. Extension to coordinate systems using generalized coordinates underlies the Hamiltonian and Lagrangian formulations of quantum field theory, classical relativistic mechanics, and quantum gravity. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Frame of reference」の詳細全文を読む スポンサード リンク
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