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In relativity theory, proper acceleration〔Edwin F. Taylor & John Archibald Wheeler (1966 1st ed. only) ''Spacetime Physics'' (W.H. Freeman, San Francisco) ISBN 0-7167-0336-X, Chapter 1 Exercise 51 page 97-98: "Clock paradox III" ((pdf )).〕 is the physical acceleration (i.e., measurable acceleration as by an accelerometer) experienced by an object. It is thus acceleration relative to a free-fall, or inertial, observer who is momentarily at rest relative to the object being measured. Gravitation therefore does not cause proper acceleration, since gravity acts upon the inertial observer that any proper acceleration must depart from (accelerate from). A corollary is that all inertial observers always have a proper acceleration of zero. Proper acceleration contrasts with coordinate acceleration, which is dependent on choice of coordinate systems and thus upon choice of observers. In the standard inertial coordinates of special relativity, for unidirectional motion, proper acceleration is the rate of change of proper velocity with respect to coordinate time. In an inertial frame in which the object is momentarily at rest, the proper acceleration 3-vector, combined with a zero time-component, yields the object's four-acceleration, which makes proper-acceleration's magnitude Lorentz-invariant. Thus the concept is useful: (i) with accelerated coordinate systems, (ii) at relativistic speeds, and (iii) in curved spacetime. In an accelerating rocket after launch, or even in a rocket standing at the gantry, the proper acceleration is the acceleration felt by the occupants, and which is described as g-force (which is ''not'' a force but rather an acceleration; see that article for more discussion of proper acceleration) delivered by the vehicle only.〔Relativity By Wolfgang Rindler pg 71〕 The "acceleration of gravity" ("force of gravity") never contributes to proper acceleration in any circumstances, and thus the proper acceleration felt by observers standing on the ground is due to the mechanical force ''from the ground'', not due to the "force" or "acceleration" of gravity. If the ground is removed and the observer allowed to free-fall, the observer will experience coordinate acceleration, but no proper acceleration, and thus no g-force. Generally, objects in such a fall or generally any such ballistic path (also called inertial motion), including objects in orbit, experience no proper acceleration (neglecting small tidal accelerations for inertial paths in gravitational fields). This state is also known as "zero gravity," ("zero-g") or "free-fall," and it always produces a sensation of weightlessness. Proper acceleration reduces to coordinate acceleration in an inertial coordinate system in flat spacetime (i.e. in the absence of gravity), provided the magnitude of the object's proper-velocity〔Francis W. Sears & Robert W. Brehme (1968) ''Introduction to the theory of relativity'' (Addison-Wesley, NY) (LCCN 680019344 ), section 7-3〕 (momentum per unit mass) is much less than the speed of light ''c''. Only in such situations is coordinate acceleration ''entirely'' felt as a "g-force" (i.e., a proper acceleration, also defined as one that produces measurable weight). In situations in which gravitation is absent but the chosen coordinate system is not inertial, but is accelerated with the observer (such as the accelerated reference frame of an accelerating rocket, or a frame fixed upon objects in a centrifuge), then g-forces and corresponding proper accelerations felt by observers in these coordinate systems are caused by the mechanical forces which resist their weight in such systems. This weight, in turn, is produced by fictitious forces or "inertial forces" which appear in all such accelerated coordinate systems, in a manner somewhat like the weight produced by the "force of gravity" in systems where objects are fixed in space with regard to the gravitating body (as on the surface of the Earth). The total (mechanical) force which is calculated to induce the proper acceleration on a mass at rest in a coordinate system that has a proper acceleration, via Newton's law F = ''m'' a, is called the proper force. As seen above, the proper force is equal to the opposing reaction force that is measured as an object's "operational weight" (i.e., its weight as measured by a device like a spring scale, in vacuum, in the object's coordinate system). Thus, the proper force on an object is always equal and opposite to its measured weight. ==Examples== For instance, when holding onto a carousel that turns at constant angular velocity you experience a radially inward (centripetal) proper-acceleration due to the interaction between the handhold and your hand. This cancels the radially outward ''geometric acceleration'' associated with your spinning coordinate frame. This outward acceleration (from the spinning frame's perspective) will become the coordinate acceleration when you let go, causing you to fly off along a zero proper-acceleration (geodesic) path. Unaccelerated observers, of course, in their frame simply see your equal proper and coordinate accelerations vanish when you let go. : Similarly, standing on a non-rotating planet (and on earth for practical purposes) we experience an upward proper-acceleration due to the normal-force exerted by the earth on the bottom of our shoes. This cancels the downward ''geometric acceleration'' due to our choice of coordinate system (a so-called shell-frame〔Edwin F. Taylor and John Archibald Wheeler (2000) ''Exploring black holes'' (Addison Wesley Longman, NY) ISBN 0-201-38423-X〕). That downward acceleration becomes coordinate if we inadvertently step off a cliff into a zero proper-acceleration (geodesic or rain-frame) trajectory. : Note that ''geometric accelerations'' (due to the connection term in the coordinate system's covariant derivative below) act on ''every ounce of our being'', while proper-accelerations are usually caused by an external force. Introductory physics courses often treat gravity's downward (geometric) acceleration as one that's due to a mass-proportional force. This, along with diligent avoidance of unaccelerated frames, allows them to treat proper and coordinate acceleration as the same thing. Even then if an object maintains a ''constant proper-acceleration'' from rest over an extended period in flat spacetime, observers in the rest frame will see the object's coordinate acceleration decrease as its coordinate velocity approaches lightspeed. The rate at which the object's proper-velocity goes up, nevertheless, remains constant. : Thus the distinction between proper-acceleration and coordinate acceleration〔cf. C. W. Misner, K. S. Thorne and J. A. Wheeler (1973) ''Gravitation'' (W. H. Freeman, NY) ISBN 978-0-7167-0344-0, section 1.6〕 allows one to track the experience of accelerated travelers from various non-Newtonian perspectives. These perspectives include those of accelerated coordinate systems (like a carousel), of high speeds (where proper time differs from coordinate time), and of curved spacetime (like that associated with gravity on earth). 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「proper acceleration」の詳細全文を読む スポンサード リンク
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