Einstein 1920: Galileian Co-ordinates

Reference: Einstein’s 1920 Book

This paper presents Part 1, Chapter 4 from the book RELATIVITY: THE SPECIAL AND GENERAL THEORY by A. EINSTEIN. The contents are from the original publication of this book by Henry Holt and Company, New York (1920).

The paragraphs of the original material (in black) are accompanied by brief comments (in color) based on the present understanding.  Feedback on these comments is appreciated.

The heading below is linked to the original materials.

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The Galileian System of Co-ordinates

AS is well known, the fundamental law of the mechanics of Galilei-Newton, which is known as the law of inertia, can be stated thus: A body removed sufficiently far from other bodies continues in a state of rest or of uniform motion in a straight line.

What is omitted here is that bodies of different inertia shall have different uniform motions (speeds). According to the laws of mechanics, in a system of rotating bodies, the more massive body is closer to the common center of mass and rotates more slowly. Therefore, the speed of Sun is much slower than the speed of Earth. In short, the greater is the mass (inertia) of a body, the slower is its free speed in space.

This law not only says something about the motion of the bodies, but it also indicates the reference-bodies or systems of co-ordinates, permissible in mechanics, which can be used in mechanical description. The visible fixed stars are bodies for which the law of inertia certainly holds to a high degree of approximation. Now if we use a system of co-ordinates which is rigidly attached to the earth, then, relative to this system, every fixed star describes a circle of immense radius in the course of an astronomical day, a result which is opposed to the statement of the law of inertia. So that if we adhere to this law we must refer these motions only to systems of co-ordinates relative to which the fixed stars do not move in a circle.

A system of fixed starts have no motion, while earth has motion, because their inertia is infinite compared to the inertia of earth. Therefore, fixed stars shall act as reference bodies (systems of co-ordinates) and not earth.

A system of co-ordinates of which the state of motion is such that the law of inertia holds relative to it is called a “Galileian system of co-ordinates.” The laws of the mechanics of Galilei-Newton can be regarded as valid only for a Galileian system of co-ordinates.

A body that has inertia, and which is in a state of uniform motion, forms a Galileian system of co-ordinates. Its uniform motion (speed), however, shall depend on its inertia.

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