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Feynman’s Lectures on Physics 11-4: Vectors – The Mathematics of Symmetry

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In the preceding sections of The Feynman Lectures on Physics , Richard Feynman has been developing an argument about the relationship between physical laws and the coordinate systems we use to describe the world. In Chapter 11-1, he introduces the idea that the laws of physics should not depend on where we choose to place the origin of our coordinate system. In 11-2, he considers translations: moving the coordinate axes from one position to another. In 11-3, he examines rotations, demonstrating that the laws of mechanics should remain unchanged when we turn our coordinate system. In section 11-4, Vectors , Feynman arrives at an important mathematical consequence of these ideas. Rather than continuing to work through the increasingly cumbersome algebra of coordinate transformations, he introduces a mathematical language that allows us to express physical relationships in a way that is independent of our choice of axes. This is the purpose of vector analysis. However, Feynman’s discuss...
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Symmetry, coordinate systems and the universality of Newton’s laws

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One of the most powerful ideas in physics is that the fundamental laws of nature do not depend on the perspective from which we observe them. An experiment conducted in one orientation should, under the appropriate conditions, produce the same results when the apparatus is rotated. The laws of physics should not favour one direction in space over another. In Lecture 11-3, Rotations , Richard Feynman explores this proposition through a characteristically accessible combination of thought experiments, geometrical reasoning and mathematical demonstration. Following his discussion of translations in the preceding lecture, he now considers whether Newton’s laws remain valid when we change the orientation of our coordinate axes. What makes this lecture particularly interesting is not simply the mathematical result, but the methodology Feynman employs to arrive at it. He begins with an apparently obvious assumption, challenges it with an everyday example, identifies the hidden physical influ...
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