The relativistic dot product | Wild Linear Algebra B 33 | NJ Wildberger

We introduce the planar relativistic dot product which underlies Einstein's Special theory of Relativity (SR). This is a small variant on the usual Euclidean dot product (a plus sign is replaced with a minus sign) and there are both important similarities and important differences between the two.

In this video we show that many of the standard geometrical ideas that we discussed in the Euclidean setting hold also in this relativistic case. This includes the notion of quadrance, Pythagoras' theorem, linear functionals, equations of lines, projections and circles (which appear to us as particular rectangular hyperbolas).

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[MortenBunesGustavsen]

Not often I eagerly awaits the next math lecture, like it´s the next episode of game of thrones, but this time I do :-)  Very interesting ideas !

[pickeyberry]

Video Content

00:00 Introduction
04:34 Here we introduce a mathematical framework for SR, using linear algebra and a new kind of dot product
07:55 Quadrance
15:52 Pythagora's theorem
19:54 Linear functionals, lines and normals

[brendanward]

For Ex 33.3 I tried applying Euclid's Book I Proposition I: How to construct an equilateral triangle. I began by drawing C1, the unit circle in red geometry. I then took a point on C1, (1, 0), and constructed another unit circle "about" this point. The branches of the resulting rectangular hyperbola are just translations of C1 by 1 unit in the x-direction. So C1 and its translation don't intersect. So I can't complete the triangle by joining the two centres of my circles (0, 0) and (1, 0) with a point of intersection.

Is this a valid solution?