Interactions

I do not know why, I always have enjoyed making an analogy between physical laws and the governing patterns in a collection of people. The element of will and intelligence makes the dynamics of society much more complicated, though. Nevertheless, I do believe, that we can learn some general trends from this analogy. After all I have not lost anything doing this analogy.
Somehow I want to understand, what are the hidden unwritten rules in social communications. Society reminds me of a large collection of people undergoing interacting Brownian motions. Sometimes clashing, if the population density is high, sometimes dancing together.

From now on, sometimes I will write posts about my observations in society and connecting them to physical laws.

Today, I want to discuss the analogy of two-particle interactions and the relation between two people. The particles of my model system are human beings. The particles have both attractive or repulsive interactions together or neutral, i.e. no interaction energy, this is often the case when particles (people) are far away. This is a good approximation, since at any moment there are features of our friends which we like (attraction) or do not (repulsion).

Therefore our relation with people is the defined in terms of the sum of all these attractions and repulsions. The general behavior that we expect is an interaction potential that is repulsive at very close distances and zero if we are far enough.It has a minimum in between.




If you pass the minimum of interactions, you feel the repulsion.
Therefore the optimum distance for every two people will be the distance at which the total interaction energy is minimized. Of course this distance will depend on the type of interaction between people (the functional dependence of V(r)).