Particle Physics
For the longest time as history records, science has held that all matter is composed of fundamental building blocks. Even though they could not see it, the ancient Greeks for example presumed that a stone could be ground up into finer and finer grains until it reached single indivisible points of matter which they called átomos, meaning “uncuttable”. Their suspicions proved correct, as some two-and-a-half-thousand years later scientists in the early 20th century discovered that indivisible unit and named it the atom.
This naming turned out to be premature as it was later found these atoms could be further broken into smaller particles, namely the proton, neutron and electron. But that was not the end of the tale. Over the following decades particle accelerator experiments revealed there to be large number of, what were labeled, sub-atomic particles. This gave birth to a new branch of science called particle physics.
Developmental Problems
As time passed and more and more particles were discovered, it became clear that something was amiss with these ‘fundamental’ units of nature. Their numbers ran into tens then to over a hundred. Could nature be this complicated? A study of their properties and interactions led to the idea that many of these were made up of still smaller units. This led to the discovery of quarks, which are said to compose protons, neutrons and other particles.
While it is true that a large number of particles might pose a philosophical problem, a more fundamental problem must be the way in which they are said to interact. In the world of particle physics, matter is constantly flashing in and out of existence as new particles are created and destroyed. And while this process may seem strange, it is stranger still that many of these interactions appear to occur without regard to mass conservation. Take muons for example.
Muons
Muons are charged particles that are primarily generated as a result of cosmic bombardment in the upper atmosphere. They are mostly negatively charged and can be thought of as heavy but unstable electrons. Muons have a short half-life of 2.2 microseconds, after which they decay into an electron and a couple of neutrinos. The decay process goes like this:
This reaction obeys the charge conservation rule in that both muon and electron have an equal negative charge while the neutrinos are neutral. But a muon is 206 times heavier than an electron and the neutrinos weigh nothing (or next to nothing). Where did all that mass go? According to modern physics, mass must either be conserved or converted to an equivalent amount of energy, determined via the E=mc2 relation. This energy must be released in the form of electromagnetic radiation, i.e. as photons. But there is no suggestion in the standard texts that photons are released during this process.
Actually, the above diagram is incomplete because there should also be a W– boson particle involved. This W particle weighs in at 157 thousand times heavier than an electron and quickly flashes in-and-out of existence while creating the electron and one of the neutrinos. Here again is another apparent violation of mass conservation, and a huge one at that! But since it quickly disappears we could give it the benefit of doubt and say that it causes no overall conservation problem.
One possibility for mass conservation may have to do neutrino momentum. I will discuss this further on.
Pions
The next question has to do with where muons come from. Muons come from pion decay, which in turn are generated from high-energy proton collisions in the upper atmosphere. The pion to muon conversion process looks like this:
Again there is a temporary intermediate W particle involved which I’ve not shown. The pion has a mass of 273 electrons which is only slightly above the muon (at 206) and there are no photons in sight. Hence again we have a mass conservation problem, albeit only minor. Ignoring the various neutrinos then, the complete process goes something like this:
Notice something amiss? That’s right: the positive proton yields a negative pion! This is surely impossible according to charge conservation rules. Now to be fair, the interaction is not stated in full like this. Various literatures on the subject discuss the pion/muon and muon/electron decays separately and each decay process shown preserves charge correctly. But when it comes to the full process the literature becomes somewhat vague, particularly in regard to the pion’s charge. For example on Wikipedia’s muon page we find the following [1]:
When a cosmic ray proton impacts atomic nuclei of air atoms in the upper atmosphere, pions are created. These decay within a relatively short distance (meters) into muons (the pion's preferred decay product), and neutrinos.
The above excerpt does not say what charge these pions have except they are somehow created from protons. Since protons are positive this indicates the created pions must also be positive, in which case they could not decay into negative muons. The webpage from SLAC helps clear this up when it says [2]:
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