In this discussion, we will develop an ad hoc model that makes informational sense. The only point is to illustrate how Digital Philosophy can guide one’s thinking with regard to informational aspects of processes such as particle interactions. In ordinary physics, we accept as good theories those that correspond to mathematical models based on conservation laws or rules for calculating with amplitudes, and these are verified by experimental data. We can quickly throw out proposed mathematical models by showing that they violate one of the standard conservation laws. There is nothing wrong with that process but Digital Philosophy demands more. In addition, there must be an informational model that also makes sense. Digital Philosophy assumes that there are information laws, including Conservation of Information that must also be observed. A useful additional test involves looking at a process in reverse, to see that it still obeys all the laws. Strangely enough, we sometimes find it useful (as a heuristic) to look at the reverse of the reversed process!
In order to understand this process we will take a look at the idealized interaction of 2 colliding billiard balls. For these examples we assume nothing other than translational motion in a plane and that the 2 balls are identical. If we make a movie of the collision of 2 perfectly elastic billiard balls, we see that kinetic energy and momentum are both conserved. If we look at the movie going backwards, everything still looks like good physics. From an informational point of view, one must be able to compute the trajectories of the 2 balls after the collision from information about the trajectories before the collision. No information is lost and the process is perfectly reversible.
Now let’s redo the experiment, except instead of elastic billiard balls, we are going to use a kind of cohesive putty so that the putty balls will stick to each other and not stick to anything else. Now, 2 putty balls on a collision course merge into one bigger ball when they collide. A careful set of experiments would reveal that momentum is conserved exactly. The kinetic energy of the 2 putty balls is not conserved. Instead, we assume that the lost kinetic energy has been converted into heat; the merged putty ball must be somewhat warmer than the 2 balls were before the collision. If we look at the movie going backwards, there appears to be a mystery as to how the one merged putty ball can separate into 2 identical balls, which are following the exact original trajectories in reverse.
Where in the one merged putty ball do we find the information defining the 2 trajectories? The answer is that it is encoded into the motions and vibrations of the molecules of the merged putty balls. The information was not destroyed because the putty had the possibility of lower modes of energy (heat) that could represent the information.
With fundamental particles the situation is much more interesting since there may not be the possibility of lower modes that can encode information as heat. To illustrate what we mean, we will consider the decay of a muon. A muon is much like an electron except that it is about 200 times as massive and it decays with a mean life of about 2 microseconds. It almost always decays into 3 particles, an electron, a muon neutrino and an electron antineutrino. A muon has a magnetic dipole field and when it decays, the electron is emitted in a direction that is correlated with the direction of the dipole field. Now we will look at the unlikely but physically correct reverse process. Along come an electron, a muon neutrino and an electron antineutrino. All three collide in the proper way and the result is a single muon whose magnetic dipole field is correlated with the direction of the electron. What we have is the trajectories of 3 particles that happen to come together and the result is the trajectory of one particle plus the direction of a magnetic dipole field! That process as stated conserves energy. It conserves momentum. It conserves lepton number. It conserves angular momentum. It conserves charge. However, how does it conserve information? Within DP there is the possibility that the vacuum state of some DM models can represent information the way that heat is able to do for macroscopic events like the collision of 2 putty balls. Cellular automata are wonderful systems for seeming to generate complexity out of simple beginnings. Computer models might enable us to take a look at how various DM models might deal with this informational situation. QM does so by characterizing the entire process as being the consequences of the reversible evolution of the wave function. However, that approach is not very satisfying. This particular DM model is designed to explore the concept of a particle model, in the Feynman sense, of all aspects of physics.
A long time ago there was a problem in physics associated with beta decay. When a neutron decays, it was observed that the decay products included a proton and an electron. This might have made sense in terms of conservation of energy, momentum and charge however it could not make sense in terms of spin. This is because each fermion has a spin of ½. There is no way that the combined spin of the proton and the electron could add up to ½.
±½ ± ½ ¹ ±½
The solution was to invent another fermion, the neutrino with spin ½. As it turned out, the neutrino had a lot of other reasons for existence.
While it may all seem obvious today, solving the problem by inventing a new kind of particle was pretty brave.
