Holmberg's Light Bulb N-body Simulation

Ever thought to use one of these to simulate gravity? Erik Holmberg did back in 1941. Seeking to understand how galaxies interact Erik Holmberg developed a new method for studying these complex systems which were too difficult to study analytically.

It turns out that the flux of light emitting from a point source falls off with radius the same way as the force of gravity, 1/r^2. Since gravity is so weak one could not make a scale model of an interacting system in the lab that worked via gravity. However, if one substituted light one could do a crude simulation of how the system worked. For example, let us consider the Earth and the Sun. If we wanted to simulate how these two bodies interact with each other via gravity using light instead we could do the following:

1. Scale the relative brightnesses of the light bulb to be the ratio of the masses between the Earth and the Sun. For reference lets set the Earth mass to be equivalent to a 60 Watt light bulb, which means the Sun would be a 20 MWatt light bulb.
2. Now that we have our light bulbs we can set up a light detector at each of them to detect how much light they receive from the other bulb. The amount of light received equals the amount of force felt. Since the Sun is so much brighter than the Earth, the Earth will detect more light from the Sun and thus more force. Meanwhile the Sun will feel very little force from the Earth.
3. Now that we know the forces we can calculate the accelerations and move our lights a short distance to new positions based on those calculated forces.
4. After we move them we can recalculate the forces and repeat the process.

If one gave the Earth and appropriate starting velocity one could simulate the Earth going around the Sun by this method. This type of technique is called a N-body simulation.

Now Holmberg didn't just simulate the interaction of two bodies, but of 37 bodies interacting with each other. The 74 bodies were arranged to simulate 2 galaxies colliding with each other (37 light bulbs for each galaxy). Each light bulb stood in for a collection of stars, and the mass of those stars was indicated by the brightness of the light bulb. Each galaxy then is approximated by a collection of light bulbs, which serve as proxies for the collection of stars that make up galaxies.

Much pains taking work was needed for this calculation, but the results were stunning. Holmberg notice tidal tails in his simulations, as well as the ejection of stars from the interacting pair (take a look at the paper for details). This gave him insight into the complexities of these types of interactions that served as a pioneering step forward in simulation.

Now a days N-body simulations are the norm of astrophysics and are done on supercomputers not via light bulbs. However Holmberg's simulation occurred 20 years before any attempt was made to simulate these types of interactions via a computer. Truly a remarkable accomplishment.