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The special theory of relativity is known for its paradoxes: the twin paradox and the ladder-in-barn paradox, for example. Neither are true paradoxes; they merely expose flaws in our understanding, and point the way toward deeper understanding of nature. The ladder paradox exposes the breakdown of simultaneity, while the twin paradox highlights the distinctions of accelerated frames of reference. So it is with the paradox of a charged particle at rest in a gravitational field; it is a paradox between the theories of electrodynamics and general relativity. ==Recap of Key Points of Gravitation and Electrodynamics== It is a standard result from the Maxwell equations of classical electrodynamics that an accelerated charge radiates. That is, it produces an electric field that falls off as in addition to its rest-frame Coulomb field. This radiation electric field has an accompanying magnetic field, and the whole oscillating electromagnetic radiation field propagates independently of the accelerated charge, carrying away momentum and energy. The energy in the radiation is provided by the work that accelerates the charge. We understand a photon to be the quantum of the electromagnetic radiation field, but the radiation field is a classical concept. The theory of general relativity is built on the principle of the equivalence of gravitation and inertia. This means that it is impossible to distinguish through any local measurement whether one is in a gravitational field or being accelerated. An elevator out in deep space, far from any planet, could mimic a gravitational field to its occupants if it could be accelerated continuously "upward". Whether the acceleration is from motion or from gravity makes no difference in the laws of physics. This can also be understood in terms of the equivalence of so-called gravitational mass and inertial mass. The mass in Newton's law of gravity (gravitational mass) is the same as the mass in Newton's second law of motion (inertial mass). They cancel out when equated, with the result discovered by Galileo that all bodies fall at the same rate in a gravitational field, independent of their mass. A famous demonstration of this principle was performed on the Moon during the Apollo 15 mission, when ( a hammer and a feather were dropped ) at the same time and, of course, struck the surface at the same time. Closely tied in with this equivalence is the fact that gravity vanishes in free fall. For objects falling in an elevator whose cable is cut, all gravitational forces vanish, and things begin to look like the free-floating absence of forces one sees in videos from the International Space Station. One can find the weightlessness of outer space right here on earth: just jump out of an airplane. It is a lynchpin of general relativity that everything must fall together in free fall. Just as with acceleration versus gravity, no experiment should be able to distinguish the effects of free fall in a gravitational field, and being out in deep space far from any forces. 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「Paradox of a charge in a gravitational field」の詳細全文を読む スポンサード リンク
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