Footnote 1 in Section 24.1 is mistaken

[MichaelAllenWarner]

Footnote 1 of Section 24.1 asserts that under a Lorentz boost, the component of force that's perpendicular to the boost-direction is left unchanged. That's not true, as the force three-vector $\vec f$ is not the spatial component of a four-vector (rather, the quantity $\gamma \vec f$ is the spatial component of the four-force).

Under a boost along the $x$-axis, the $y$-component of force actually transforms like:

$$ f_y^\prime = \frac{fy}{\gamma{boost} \left( 1 \pm \beta_{boost} \beta_x \right)} $$

where

• $\beta_x = v_x/c$ is the unprimed $x$-component of the velocity of the thing that's being subjected to the force,
• $\beta_{boost}$ is the relative speed of the frames (sign determined by whether the unprimed frame moves in the positive or negative $x^\prime$-direction),
• and $\gamma_{boost}$ is the relative Lorentz factor of the frames.

Only in the Newtonian limit ($\gamma{boost} \approx 1$, and $\beta{boost} \beta_x \approx 0$) does $f_y^\prime \approx f_y$.

[ryanmartinneutrino]

Oh, thanks for pointing that one out! Yes indeed, we will fix that next time we commit some updates.