Relativity Lite

To c or Not to c  | 13 To see how this works, imagine a spaceship powered by small nuclear bombs that are dropped through a small hole in a radiation shield attached to the passenger cabin. When a bomb explodes, half of the exploded material and associated photons push against the radiation shield, shoving the rocket faster in its direction of travel. As the rocket’s veloc- ity increases, the time dilation increases on Earth, which the passengers have left behind. As the rocket crew steadily drops and explodes bombs (at a steady proper-time interval), there are longer and longer time intervals between when Earth folk see the photons from the explosions arrive. In fact, as the people on Earth see the rocket’s speed approach the speed of light, they have to wait through an infinite time interval for the explosion that would have just pushed the rocket past the limit. Thus, the rocket never reaches the speed of light relative to the Earth. One might rephrase the classic Western koan as “What happens when an irresistible force meets an interminable stasis?” Some readers will note that many science popularizers and introductory physics teachers used to invoke the idea that [t]he faster a particle is pushed, the more its mass increases, thereby resulting in less and less response to the accelerating force. . . . [A]s v approaches c , m approaches infinity! [To push a particle] to the speed of light . . . would require an infinite force, which is clearly impossible. * Let me caution you that research physicists rely heavily upon the fact † that the mass of a particle is the same in all frames of references; it is an invariant quantity . ‡ See, for instance, the caption of figure 4 in the paper publishing the discovery of the Higgs boson, § reproduced below, that begins with the explicit acknowledgment of the “[i]nvariant mass distribution,” while the simpler and equivalent “mass” is also used through- out, such as in the section G, following that figure: “The measured Higgs boson mass [is] 125.98 ± 0.50 GeV. . . .” The (invariant) mass of an object is sometimes referred to in older texts as the “rest mass.” * Paul G. Hewitt, Conceptual Physics , 6th ed. (Scott, Foresman & Co., Boston, 1989), p. 662. † For a complete history of this, see Lev. B. Okun, Phys. Today 42 , 31–36 (June 1989). ‡ See, for instance, the standard textbook by John D. Jackson, Classical Electrodynamics (John Wiley & Sons, New York, 1975), p. 531, eq. (11.54). § G. Aad et al. (ATLAS Collaboration), Phys. Rev. D 90 , 052004 (2014).