Physical laws such as the conservation of linear and angular momentum are important. For example, angular momentum was the key to solving the hydrogen atom in Chapter 4.3. In general, conservation laws are often the central element in explaining how simple systems work. And conservation laws are usually the most reliable and valuable source of information about complex and poorly understood systems such as atomic nuclei. Finally, the relationship between conservation laws and symmetries gives more confidence in conservation laws. For example, nuclei, as mentioned, are still poorly understood. It may therefore seem quite reasonable to suspect that nuclear forces may not receive angular momentum. And indeed, the force between proton and neutron in a deuteron nucleus does not receive orbital angular momentum. But it is another thing to assume that forces do not receive the net angular momentum of the nucleus, including the spins of the proton and neutron. This would mean that empty space has an inherent preferred direction.
It`s much harder to swallow. Such a preferred direction has never been observed, and there is no known mechanism or cause that would lead to it. Physicists are therefore quite confident that nuclei will receive angular momentum, like anything else. The deuteron retains its net angular momentum when the proton and neutron spins are included in the total. All particles have antiparticles. Protons have antiprotons, neutrons have antineutrons, and so on. Replacing each particle in a system with its antiparticle produces almost the same physics. You can create an antihydrogen atom from an antiproton and positron that appears to behave like a normal hydrogen atom. As a second example of additional symmetry in empty space, physics generally works the same way when viewed in the mirror.
The result is a very useful conservation set called parity. Parity is slightly different from momentum. While a component of linear or angular momentum can have any value, parity can only be 1, called “even” or 1, called “odd”. As the contributions of the parts of a system add up to the total components of dynamics, their contributions to parity multiply, {A.19}. Therefore, the parities of the parts of a system can be combined into a corresponding system parity, which is always 1 or 1. It turns out that conservation laws are related to the fundamental symmetries of physics. Symmetry means you can do something that makes no difference. For example, if you place a particle system in an empty space, away from anything that might affect it, it doesn`t matter where exactly you place it. There are no preferred locations in empty space; All locations are equal. This symmetry leads to the law of conservation of linear momentum. A system of particles in otherwise empty space retains its total amount of linear momentum. If you place a particle system in empty space, the angle at which you place it makes no difference.
There are no preferred directions in empty space. This leads to the preservation of angular momentum. See Appendix {A.19} for details. Another reason why the relationship between conservation laws and symmetries is important is the information they produce about physical properties. For example, imagine a kernel that has a net angular momentum of zero. Because of the relationship between angular momentum and angular symmetry, such a nucleus looks alike in all directions. It is spherically symmetrical.