When Is a Theorem True?
What a Proof Establishes
Think of geometry as a building. Its foundations are a few basic ideas, point, straight line, plane, and a few simple statements about them, the axioms, which we accept because they feel obvious.
Library · Public domain
Relativity: The Specialand General Theory
Über die spezielle und die allgemeine Relativitätstheorie (Gemeinverständlich)
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Einstein’s own account of relativity, written in 1916 for readers without higher mathematics: what space, time and motion mean once the speed of light is the same for everyone.
This is a sample: 4 of 29 sections. · Made in 170 min
From the lectures
When Is a Theorem True?
From Geometry to Physical Test
Why then does the theorem feel so true at the table? Because the ideas of geometry grew out of real objects in the first place.
Where Is the Cloud?
Reaching the Cloud
Now the question of where. Every statement of where something is, Einstein says, names the point of some rigid body that the thing coincides with. That rigid body is the reference body, and everyday speech works this way as much as science does.
Where Is the Cloud?
Three Distances Fix a Point
Physics does so with the coordinate system: picture two walls and the floor meeting in the corner of a room, three flat rigid surfaces at right angles, joined into one rigid body. Any point in the room is fixed by three distances, how far it is from one wall, from the other wall, and above the floor.
One Stone, Two Paths
Places Paired With Clock Readings
We must also say when the stone is at each point of the path, and those times, Einstein insists, must be things that can be measured, not numbers assumed out of the air.
Which Reference Bodies Are Allowed?
Earth-Fixed Versus Galilean
Motion may then be referred only to reference bodies with respect to which the fixed stars do not circle. Such a reference body, one in which the law of inertia holds, he calls a Galilean coordinate system, and the mechanics of Galileo and Newton claims to be valid only for those.
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Examples for: a curious adult with school physics; add one modern instance per idea, such as GPS satellite clocks
The source
The lectures retell the German text of Project Gutenberg #77850, the 1917 Vieweg edition. The author died in 1955; the work is in the public domain. The retelling, the drawings and the voice are made by AI and checked against the book by a second model; nothing was edited by hand. How AI is used.
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