The Geometry of Special Relativity


(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 §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 §4.3. One fix is to interchange $A$ and $B$ throughout §4.3, including in Figure 4.2, also in Figure 5.2, and finally in §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 $B^\perp = (\rho\,\cosh\beta,\rho\,\sinh\beta)=\frac{dB}{d\beta}$.

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