Commons

increases and decreases in some quantity such as the gravitationalconstant G, or the speed of light, or the mass of the electron.We can therefore conclude that the following two hypotheses areclosely related.The principle of inertiaThe results of experiments don’t depend on the straight-line,constant-speed motion of the apparatus.Translation symmetryThe laws of physics are the same at every point in space. Specifically,experiments don’t give different results just because you set up yourapparatus in a different place.A state of absolute rest example 1Suppose that translation symmetry is violated. The laws of physicsare different in one region of space than in another. Cruising inour spaceship, we monitor the fluctuations in the laws of physicsby watching the needle on a meter that measures some fundamentalquantity such as the gravitational constant. We make ashort blast with the ship’s engines and turn them off again. Nowwe see that the needle is wavering more slowly, so evidently it’staking us more time to move from one region to the next. Wekeep on blasting with the ship’s engines until the fluctuations stopentirely. Now we know that we’re in a state of absolute rest. Theviolation of translation symmetry logically resulted in a violation ofthe principle of inertia.self-check ASuppose you do an experiment to see how long it takes for a rock todrop one meter. This experiment comes out different if you do it on themoon. Does this violate translation symmetry? ⊲ Answer, p. 1812.3 MomentumConservation of momentumLet’s return to the impossible story of Jen Yu and Iron ArmLu on page 39. For simplicity, we’ll model them as two identical,featureless pool balls, a. This may seem like a drastic simplification,but even a collision between two human bodies is really just a seriesof many collisions between atoms. The film shows a series of instantsin time, viewed from overhead. The light-colored ball comes in,hits the darker ball, and rebounds. It seems strange that the darkball has such a big effect on the light ball without experiencingany consequences itself, but how can we show that this is reallyimpossible?42 Chapter 2 Conservation of Momentum