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===== The Geometry of Special Relativity =====

==== Errata =====

(Last update: 2/28/19)

  * Page 10, last paragraph, line 2: ``observer a rest'' should be ``observer at rest''.

  * Page 16, Equation (3.12): The matrix should be transposed (the minus sign should be in the upper right).

  * Page 26, first two full paragraphs:  The unit conversions with $c$ are backward.  The best fix is to swap ``...measure distance in seconds'' with ``... measure time in meters'', and probably also swap the two subsequent sentences (each starting with ``Thus,'') in their entirety.

  * Pages 30--35: The examples in (ss)5.5 assume that both vectors lie on the same branch of the hyperbola.  For instance, all timelike vectors are assumed to be future-pointing.  In most cases, this restriction can be removed by replacing $\cosh\alpha$ by $\pm\cosh\alpha$.

  * Page 34, Figure 5.6: The labels are reversed; (a) shows timelike vectors, and (b) shows spacelike vectors.

  * Page 35, Figure 5.7: The caption is misleading; both figures show projections between a timelike and a spacelike vector.

  * Page 38, first full paragraph, line 9: $\beta$ is an angle, not a distance, so ``$\beta$ is precisely'' should be ``$\rho\beta$ is precisely''.

  * Page 43, Equation (6.9): Both $t$ and $t'$ should be preceded by $\Delta$; the equation should read $\Delta t'=\frac{\Delta t}{\cosh\beta}$.

  * Page 53, Equation (7.18): The penultimate expression should be $\frac{\tan\theta}{1-\frac{v}{u\cos\theta}}$; the full equation should read:
\[
\tan\theta'
 = \frac{u_y'}{u_x'}
 = \frac{u_y}{u_x-v}
 = \frac{\tan\theta}{1-\frac{v}{u\cos\theta}}
 = \frac{u\sin\theta}{u\cos\theta-v}
\]

  * Page 54, Figure 7.8(b): The side labeled ``$\Delta x$'' should be labeled ``$\Delta x'$''.

  * Page 68, Figure 9.1: The hyperbolic angle $\beta$ should be $\alpha$.

  * Page 72, Figure 9.2: The hyperbolic angle $\beta$ should be $\alpha$.

  * Page 72, penultimate paragraph, line 1: ``makes sense'' should be ``make sense''.

  * Page 75, lines 3--4: "elastic" should be "inelastic" (or the first part of the sentence should be omitted entirely).

  * Page 83, just before (11.2): "current density" should be "current".

  * Page 85, Equation (11.12): $\lambda$ should be $\lambda_0$ (2x).

  * Page 86, Equation (11.20): There should be no minus sign on the RHS.

  * Page 91, Equation (11.54): $u$ should be $\mathbf{u}$.

  * Page 91, line 9: The extra "is" should be deleted.

  * Page 93, Equation (11.71): $F^{uv}$ should be $F^{\mu\nu}$.

  * Page 94, Equation (11.80): $\partial t$ should be $c\,\partial t$.  The full equation should read:
\[\Partial{F^{\mu\nu}}{x^\nu} = \frac{1}{c}\Partial{F^{\mu0}}{t} + \Partial{F^{\mu1}}{x} + \Partial{F^{\mu2}}{y} + \Partial{F^{\mu3}}{z}\]

  * Page 95, Equation (11.92): The last instance of $G_{\mu\nu}$ should be $G^{\mu\nu}$.  The full equation should read:
\[
\frac12 F_{\mu\nu} F^{\mu\nu}
  = -\frac{1}{c^2}\,{|\EE|}^2 + |\BB|^2
  = - \frac12 G_{\mu\nu} G^{\mu\nu}
\]

  * Page 96, Equation (11.96): Delete $m$ on the LHS (or replace $p^\mu$ by $u^\mu$).

  * Page 109, Equation (14.3): The minus sign is in the wrong place; the correct equation is:
\[d_H(U,V) = \rho\,\cosh^{-1}\left(-\frac{\uu\cdot\vv}{\rho^2}\right)\]

  * Page 109, next sentence: The sentence should end with a period.

  * Page 109, Equation (14.6): There should be absolute values in the last expression; the full equation should read:
\begin{align*}
d_H(U,V)
 &= \rho\,\cosh^{-1}(-\sinh\alpha\sinh\beta+\cosh\alpha\cosh\beta) \\
 &= \rho\,\cosh^{-1}(\cosh(\beta-\alpha)) \\
 &= \rho\,|\beta-\alpha|
\end{align*}

  * Page 112, Equation (14.15): There should be an overall minus sign; the correct equation is:
\[
X + iY = -2\frac{i(x+iy)+\rho}{(x+iy)+\rho\,i}
\]

  * Page 112, next sentence: "unit disk" should be "disk of radius $\rho$", and $y\ge0$ should be $Y\ge0$.

  * Page 112, Equation (14.16): The first denominator is incorrect; the correct equation is:
\[
ds^2
 = \frac{4\,\rho^4\left(dx^2+dy^2\right)}{(\rho^2-x^2-y^2)^2}
 = \rho^2\>\frac{dX^2+dY^2}{Y^2}
\]

  * Page 115, last paragraph: The closed interval $[0,\pi/2]$ should be the half-open interval $(0,\pi/2]$.

  * Pages 120--125: The points $A$ and $B$ have been interchanged here compared to (ss)4.3.  One fix is to interchange $A$ and $B$ throughout (ss)4.3, including in Figure 4.2, also in Figure 5.2, and finally in (ss)6.2.

  * Page 123, line -4: ``$\rho\,\sinh\beta$'' should be ``$\rho\,\sinh\alpha$''.

  * Page 123, Equation (15.24): $A$ should be $B$ in the derivative; the full equation should read $B^\perp = (\rho\,\cosh\beta,\rho\,\sinh\beta)=\frac{dB}{d\beta}$.