Commons

Everyone else thinks energy is conserved, but your secret techniqueallows you to keep on increasing and increasing the amount of energyin the universe (and the amount of money in your bank account).The scheme can be made to work if anything about physicschanges over time, not just gravity. For instance, suppose that themass of an electron had one value today, and a slightly differentvalue tomorrow. Electrons are one of the basic particles from whichatoms are built, so on a day when the mass of electrons is low, everyphysical object has a slightly lower mass. In problem 14 on page37, you’ll work out a way that this could be used to manufactureenergy out of nowhere.Sorry, but it won’t work. Experiments show that G doesn’tchange measurably over time, nor does there seem to be any timevariation in any of the other rules by which the universe works. 6 Ifarchaeologists find a copy of this book thousands of years from now,they’ll be able to reproduce all the experiments you’re doing in thiscourse.I’ve probably convinced you that if time symmetry was violated,then conservation of energy wouldn’t hold. But does it work theother way around? If time symmetry is valid, must there be a lawof conservation of energy? Logically, that’s a different question. Wemay be able to prove that if A is false, then B must be false, butthat doesn’t mean that if A is true, B must be true as well. Forinstance, if you’re not a criminal, then you’re presumably not injail, but just because someone is a criminal, that doesn’t mean heis in jail — some criminals never get caught.Noether’s theorem does work the other way around as well: ifphysics has a certain symmetry, then there must be a certain correspondingconservation law. This is a stronger statement. Thefull-strength version of Noether’s theorem can’t be proved withouta model of light and matter more detailed than the one currently atour disposal.1.7 Equivalence of Mass and EnergyMass-energyYou’ve encountered two conservation laws so far: conservationof mass and conservation of energy. If conservation of energy is aconsequence of symmetry, is there a deeper reason for conservation6 In 2002, there have been some reports that the properties of atoms as observedin distant galaxies are slightly different than those of atoms here and now.If so, then time symmetry is weakly violated, and so is conservation of energy.However, this is a revolutionary claim, and it needs to be examined carefully.The change being claimed is large enough that, if it’s real, it should be detectablefrom one year to the next in ultra-high-precision laboratory experiments here onearth.30 Chapter 1 Conservation of Mass and Energy