A mathematician trying to construct a structure using OOP is comparable to a game designer who designs the environment and gameplay of a game. That mathematician sets up all necessary tools and designs the environment where that particular construct is contained. The same method will be used in developing wave probability. It means at first, scenarios should be written about how different elements will be in the structure and then trying to construct them using OOP. So this is the scenario phase of constructing the wave probability. Evidently, this construction and scenario is not unique.
To estimate the probability distribution of something (call it P), the experiment should be repeated several times. Denote N as the number of times that experiment is repeated. if N is small then the variance around the mean is large, when N is large the variance shrinks. Each experiment can be considered to be one observation. Several observations are then required to produce an exact image of that thing. Precision here refers to low probability. In fact probability and observation are opposite concepts. when something is observed there is no probability. When a coin is tossed, the probability it lands head is 1/2 but when the outcome is observed, it has certainly landed head or tail, no probability. In fact, when observation has not occurred the outcome is a superposition of head or tail but when the outcome is observed, the wave collapses into either head or tail. This is similar to quantum mechanics.
About the previous example about the distribution of P, each experiment is one observation. but each observation alone provides a vague image of P, which is why the variance of P is so large when N is small. To re-construct this using OOP this scenario can be used (again this scenario is not unique):
P is a n-d wave rotating around itself. Each time its image is captured (i.e. after each experiment – equivalently each time the wave is observed) a blurred image of the wave will be produced. That is similar to a wave packet. In this scenario a wave packet is not a combination of several waves rather it is a wave with an added fuzziness. When more and more images are taken, the combination of these blurred images produces a somehow accurate image of the 3d wave. More images (i.e. large N), produce less probability (i.e. less inaccuracy). In this scenario, waves come with intrinsic rotations and motions. that links wave probability to SR. Note that SR and probability both depend on the concept of observation.
UPDATE 1:
Spin in the wave probability is similar to the same phenomenon in quantum mechanics. Due to the connection between SR and the wave probability, it’s beneficial to express a constant velocity in the form of spin. An object moving with constant velocity retains its velocity forever. It’s better to express that as an intrinsic rotation (or spin). Then it’s easier to connect SR to the wave probability.