Four known already in the large-scale classical world
1. Energy (including mass)
2. Momentum
3. Angular momentum, including spin
4. Charge
Three that hold sway in the submicroscopic world
5. Quark number (and, by implication, baryon number)
6. Color (a property of quarks, analogous to charge)
7. TCP (time reversal-charge conjugation-parity [space inversion], an invariance principle)
It is fair to say (if you are a committed “reductionist”) that the first four quantities are conserved in the large-scale world because they are conserved in the small-scale world. The last three are identifiable only in the small-scale world, but they, too, have implications in the large-scale world—the stability of matter for instance!1
There are two different kinds of quantities here, which can be called (a) properties of motion and (b) intrinsic properties, but the two are not clearly separated. The intrinsic particle properties that enter into these conservation laws are mass, spin, charge, color, and quark number. The properties of motion are kinetic energy, momentum, and angular momentum, the last frequently being called orbital angular momentum to avoid possible confusion with intrinsic spin. Spin, although an intrinsic property, is also a form of angular momentum. In the laws of energy conservation and angular-momentum conservation, the intrinsic properties and properties of motion become mixed.
Two remarks on the list above. 1. “Absolute” is a word that scientists must use with the utmost caution, and with due humility. It means “without known exceptions at this time.” No scientist will be surprised if at some future time processes are discovered that violate one or more of these laws. 2. The last three in the list is presented only for the sake of completeness. To this author there is no compelling case for going beyond the first four entries in the list in an introductory physics course.
The interactions and transformations of the fundamental particles serve admirably to illustrate the conservation laws, even those of the large-scale world. When a neutron decays into a proton, an electron, and an antineutrino, for instance (an example of what is called beta decay), energy, momentum, angular momentum, and charge are all conserved.2 The evidence so far is that conservation laws valid in the submicroscopic domain also hold true in the macroscopic world. Whether they can be extrapolated on into the cosmological domain is uncertain, since gravity, whose effects in the particle world appear to be entirely negligible, becomes of dominant importance in the astronomical realm.
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A quantity that is conserved when some forces act but not conserved for all processes is said to be partially conserved. Here are some partially conserved quantities:
1. Isospin (conserved in strong interactions, not in electromagnetic or weak)
2. Quark flavor (conserved in strong and electromagnetic interactions, not in weak)
3. Lepton flavor (conserved except in neutrino oscillations)
Whoa. Isospin? Flavor?? Let me explain the terminology, then the laws.
Following the discovery of the neutron in 1932, Werner Heisenberg3, noticing that the new neutron and the “old” proton seemed strikingly similar—same spin, nearly the same mass, and both constituents of atomic nuclei—suggested that they could be regarded as two “states” of the same particle, and that this particle, the “nucleon,” could be “flipped” from one state to the other—that is, from n to p or p to n—in much the same way that an electron’s spin can be “flipped” from up to down or down to up. The name isospin came into use because nucleon “flipping” and spin “flipping” are treated with the same mathematics, not because they are physically similar.
Initially isospin conservation meant that the neutron and proton experienced identical strong force. Since the weak force—in beta decay, for instance—can change a proton to a neutron or a neutron to a proton, isospin is a property not conserved in the weak interaction. And since the proton experiences an electric force and the neutron does not4, it is also a property not conserved in electromagnetic interactions. So it is conserved only for the strong force.
The neutron was the first of many more strongly interacting particles to be discovered. Among these are pions—positive, negative, and neutral. We refer to a pion “triplet,” whereas neutron and proton form a nucleon “doublet.” Just as a nucleon can “flip” between its neutron and proton states, a pion can flip among its three charge states. In short, the pion is a single entity with three manifestations. It is said to have isospin 1 (since a “real” spin of 1 unit has three possible orientations). An implication of isospin conservation is that all three pions exhibit identical strong interactions. Among other particles that exhibit isospin conservation are the lambda, an uncharged “singlet,” and the sigma, with three charge states, a “triplet” like the pion.
What about “flavor?” Each of the six quarks, with names that only a physicist can love (up, down, strange, charm, bottom, top), is said to have its own flavor. Quarks have positive flavor; antiquarks have negative flavor. (Yes, we give a sign to flavor.) In strong and electromagnetic processes, flavor is preserved. In weak interactions it is not. A process that conserves quark flavor, for example, is the collision of one proton with another in an accelerator to produce a proton, a neutron, and a positive pion. The initial two protons contain four up quarks and two down quarks. The final proton, neutron, and pion contain four up quarks, three down quarks, and one down antiquark, balancing the quark-flavor books. The initial charge of two units is also preserved—from two positive protons to a positive proton and a positive pion. This is a strong-interaction process.
A process that does not conserve quark flavor is the decay of neutron into a proton, electron, and antineutrino. Then two up quarks and one down quark change into one up quark and two down quarks. This is a weak-interaction process.
Each of the three known electrically charged leptons5—electron, muon, and tau—is said to have its own flavor, paralleling the “flavorfulness” of quarks. Lepton flavor is conserved in strong and electromagnetic interactions, and in most weak interactions as well. But in a phenomenon known as neutrino oscillation, it is not. Shooting from the Sun as a result of the thermonuclear reactions at the Sun’s core, for example, are electron neutrinos. But upon reaching Earth, this spray of neutrinos has become a mixture of all three types. Early experiments to search for solar neutrinos, in the 1960s and 1970s, gave puzzling results. There were seemingly too few neutrinos. Contemplating this shortage, one astrophysicist reportedly remarked, “If we don’t find more neutrinos, we will have proved that the Sun is not shining.” Neutrino oscillation saved the day. Those early experiments were sensitive only to electron neutrinos, not to the muon and tau neutrinos that were also coursing through the apparatus.6
1 If the proton is ever found to be unstable, quark number conservation would make its exit from the list.
2 Around 1930, before the neutrino had been postulated (its actual discovery came much later), Niels Bohr was willing to entertain the idea that energy might not be conserved in individual atomic events. Despite Bohr’s stature, it was very hard for physicists to imagine letting go of energy conservation. Fortunately, to date they have not had to do so.
3 In 1925, Heisenberg introduced the first mathematical theory of quantum mechanics, and two years later offered the uncertainty principle, for which he is now best known.
4 Since the neutron behaves as a tiny magnet, it does experience some electromagnetic force, but is not pulled or pushed by a simple electric field.
5 We have reason to believe that there are no more. Why exactly three? No one knows.
6 Additional discussions of conservation laws, both absolute and partial, can be found in my book 101 Quantum Questions (Harvard University Press, 2011), Questions 58 and 60.