Coulomb's Probability

The word "and" is normally associated with addition. If Jack has three apples and Jill has four apples, Jack and Jill have seven apples all together. If Jack pulls a pale up a hill with a certain force, and Jill pulls the same pale with another force, we add their combined force together to calculate their combined effect on the pale.

However, in some cases the word "and" is associated with multiplication. If Jack rolls a dice, he has a one in six chance of rolling a four. Jill too has a one in six chance of rolling a four. The chance of Jack and Jill both rolling a four is one in thirty-six. That is on in six multiplied by one in six.

This applies to collisions as well. If the chance of Jack being in a certain spot is one in a thousand, and the chance of Jill being in the same spot is also one in a thousand, then the chance of Jack and Jill both being in that spot at the same time is one in a million. That is one in a thousand multiplied by one in a thousand.

Should Jack and Jill for some reason increase their likelihood of occupying said spot by ten times, so that they each suddenly have a one in hundred chance of being there, the chance of a collision goes up by hundred times, from one in  a million to one in ten thousand.

If we now suppose that the reason Jack and Jill increased their likelihood of occupying a certain spot was because they cloned themselves into ten identical individuals, we start to see the outline of the multiplication part of Coulomb's Law.

Coulomb's Law

If Jack is a neutrino carrying charge information from q1 and Jill is a neutrino carrying charge information from q2, then their chance of collision is the chance of Jack and Jill being at the same place at the same time.

The number of Jacks and Jills are determined by the charge of q1 and q2, so if the charge on both points increase ten fold, the chance of a collision increases a hundred fold.

Furthermore, the density of Jacks and Jills around q1 and q2 falls off at the square of their distance. If we triple the distance r between the two points q1 and q2, the likelihood of a collision drops by nine times.

From this we can see that Coulomb's Law is nothing more than a probability formula expressing the likelihood of collisions between Jacks and Jills, with the overall supply of Jacks and Jills being expressed in the constant k.