object will be heavier, therefore, it will be a diferent object. When we put the objects together gently they make something whose mass is 2mo; when we put them together forcefully, they make something whose mass is greater. When the mass is different, we can tell that it is different. So, necessarily, the conservation of energy must go along with the conservation of momentum in the This has interesting consequences. For example, suppose that we have an object whose mass M is measured, and suppose something happens so that it flies into two equal pieces moving with speed w, so that they each have a mass mu. Now suppose that these pieces encounter enough material to slow them up until they stop; then they will have mass mo. How much energy will they have given to the material when they have stopped? Each will give an amount (me -mo)c, by the theorem that we proved before. This much energy is left in the material in some form, as heat, potential energy, or whatever. Now 2mw M, so the liberated energy is e=(M- 2mo)c. This equation was used to estimate how much energy would be liberated under fission in the for example.(Although the fragments are not exactly equal, they are nearly equal) The mass of the uranium atom was known-it had been measured ahead of time- and the atoms into which it split, iodine, xenon, and so on, all were of known mass By masses, we do not mean the masses while the atoms are moving, we mean the masses when the atoms are at rest. In other words, both M and mo are known by subtracting the two numbers one can calculate how much energy will be released if M can be made to split in"half "For this reason poor old Einstein was called the"father"of the atomic bomb in all the newspapers. Of course all that meant was that he could tell us ahead of time how much energy would be released if we told him what process would occur. The energy that should be berated when an atom of uranium undergoes fission was estimated about six months before the first direct test, and as soon as the energy was in fact liberated someone measured it directly(and if Einstein's formula had not worked, they would have measured it anyway), and the moment they measured it they no longer needed the formula. Of course, we should not belittle Einstein, but rather should criticize the newspapers and many popular descriptions of what causes what in the history of physics and technology. The problem of how to get the thing to occur in an effective and rapid manner is a completely different matter The result is just as significant in chemistry. For instance, if we were to weigh he carbon dioxide molecule and compare its mass with that of the carbon and the oxygen, we could find out how much energy would be liberated when carbon and oxygen form carbon dioxide. The only trouble here is that the differences in masses are so small that it is technically very diffcult to do Now let us turn to the question of whether we should add moc to the kinetic energy and say from now on that the total energy of an object is mc. First,if we can still see the component pieces of rest mass mo inside M, then we could say that some of the mass M of the compound object is the mechanical rest mass of the parts, part of it is kinetic energy of the parts, and part of it is potential energy of the parts. But we have discovered, in nature, particles of various kinds which undergo reactions just like the one we have treated above, in which with all the study in the world, we cannot see the parts inside. For instance, when a K-meson disintegrates into two pions it does so according to the law(16. 11), but the idea that a K is made out of 2 T's is a useless idea, because it also disintegrates into 3 T's! Therefore we have a new idea: we do not have to know what things are made of inside; we cannot and need not identify, inside a particle, which of the energy rest energy of the parts into which it is going to disintegrate. It is not convenient and often not possible to separate the total mc energy of an object into rest energy of the inside pieces, kinetic energy of the pieces, and potential energy of the pieces instead, we simply speak of the total energy of the particle. We"shift the origin of energy by adding a constant moeto everything, and say that the total energy of a particle is the mass in motion times c, and when the object is standing still, the energy is the mass at rest times c