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Physical forces between humans and how humans attract and repel each other based on their social interactions in an online world

Physical interactions between particles are the result of the exchange of gauge bosons. Human interactions are mediated by the exchange of messages, goods, money, promises, hostilities, etc. While in the physical world interactions and their associated forces have immediate dynamical consequences (Newton's law) the situation is not clear for human interactions. Here we study the acceleration between humans who interact through the exchange of messages, goods and hostilities in a massive multiplayer online game. For this game we have complete information about all interactions (exchange events) between about 1/2 million players, and about their trajectories (positions) in a metric space of the game universe at any point in time. We derive the interaction potentials for communication, trade and attacks and show that they are harmonic in nature. Individuals who exchange messages and trade goods generally attract each other and start to separate immediately after exchange events stop. The interaction potential for attacks mirrors the usual "hit-and-run" tactics of aggressive players. By measuring interaction intensities as a function of distance, velocity and acceleration, we show that "forces" between players are directly related to the number of exchange events. The power-law of the likelihood for interactions vs. distance is in accordance with previous real world empirical work. We show that the obtained potentials can be understood with a simple model assuming an exchange-driven force in combination with a distance dependent exchange rate.