Inertial coordinate system - inertial frame of reference; inertial system

Japanese: 慣性座標系 - かんせいざひょうけい（英語表記）inertial frame of reference; inertial system

Also known as an inertial system or coasting system. A coordinate system in which Newton's equation of motion ma = f ( m is mass, a is acceleration, and f is force) holds true. It is called an inertial system because in this system, speed does not change when no force is acting, so an object can be considered to have inertia. A coordinate system that moves translationally at a uniform speed relative to another inertial system is also an inertial system, and they are connected to each other by Galilean transformations. These inertial systems cannot be distinguished from each other mechanically. In Newtonian mechanics, this is said to be due to Galilean relativity. Inertial and non-inertial systems can be distinguished by mechanical observations, and it is known that a coordinate system fixed to the star system is approximately an inertial system. In an attempt to find a specific absolute inertial system by optically or electromagnetically distinguishing inertial systems, the stationary system of the ether, which was assumed to be the medium of light and electromagnetic fields, was assumed to be the absolute inertial system. However, this assumption was overturned by the Michelson-Morley experiment, and Einstein's special theory of relativity, which denies the very existence of the ether, was created. In this theory, a coordinate system in which Maxwell's equations, the fundamental laws of electromagnetism, hold is called an inertial system. As in Newtonian mechanics, a coordinate system that moves in translation at a uniform speed relative to a certain inertial system is also an inertial system, but they are connected to each other by Lorentz transformations and cannot be distinguished from each other optically or electromagnetically. This is said to be the case in electromagnetism, where Einstein's principle of relativity holds. Newtonian mechanics and electromagnetism have different principles of relativity, and the transformations that connect inertial systems are different, so even if they are called the same inertial system, the two inertial systems are different. However, when it became clear that Newtonian mechanics was incorrect for objects moving at high speeds, it was revised to relativistic mechanics, and mechanics and electromagnetism came to share a common inertial system. An inertial system is a special system among all coordinate systems, but the laws of physics do not want such a special coordinate system to exist. Therefore, Einstein developed the general theory of relativity, which treats all coordinate systems completely equally, and eliminated special coordinate systems such as inertial systems.

Source: Encyclopaedia Britannica Concise Encyclopedia About Encyclopaedia Britannica Concise Encyclopedia Information

Japanese:

慣性系，惰性系ともいう。ニュートンの運動方程式 ma＝f ( m は質量，a は加速度，f は力) が成り立つ座標系。慣性系と呼ばれるのは，この系では力が働かないときに速度は変化しないので，物体が慣性をもつとみなせるからである。ある慣性系に対し等速度で並進運動する座標系もまた慣性系であって，互いにガリレイ変換で結ばれる。これらの慣性系同士は力学的に互いに区別できない。これをニュートン力学ではガリレイの相対性原理が成り立つという。慣性系と非慣性系とは力学的な観測によって区別でき，恒星系に固定した座標系は近似的に慣性系であることが知られている。慣性系同士を光学的または電磁気的に互いに区別して特定の絶対的な慣性系を見出そうとの考えから，光や電磁場の媒質として仮定されたエーテルの静止系を絶対慣性系と想定したが，その想定はマイケルソン＝モーリーの実験によってくつがえされ，エーテルの存在そのものを否定するアインシュタインの特殊相対性理論が生み出された。この理論では，電磁気学の基礎法則であるマクスウェルの方程式が成り立つ座標系を慣性系と呼ぶ。ニュートン力学と同様に，ある慣性系に対し等速度で並進運動する座標系もまた慣性系であるが，それらは互いにローレンツ変換で結ばれ，互いに光学的または電磁気的に区別されない。これを電磁気学ではアインシュタインの相対性原理が成り立つという。ニュートン力学と電磁気学とで別の相対性原理が成り立ち，慣性系同士を結ぶ変換が違うのであるから，同じ慣性系と呼ばれても両者の慣性系は違ったものであった。しかし，ニュートン力学が高速度で運動する物体については正しくないことが明らかとなって相対論的力学へと修正されたので，力学と電磁気学とは共通の慣性系をもつようになった。慣性系はすべての座標系のなかでは特殊な系であるが，物理法則ではこのような特殊な座標系があるのは望ましくない。そこでアインシュタインは，すべての座標系を完全に同等に扱った一般相対性理論を展開して，慣性系のような特殊な座標系を排除した。

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