In a case of truly mad physics, a paper by Dr. Erik Verlinde proposes that gravity is not a fundamental force, but is instead an "entropic force", which is to say that gravity is merely a side effect the increase in entropy in the universe. A series of posts at the Hammock Physicist, break it down, and in the process the author proposes a toy model that shows how simple entropic action can generate what appears at the macroscopic scale to be an attractive force.
The mikado universe is a 2-dimensional square which is intersected by many line segments, or "rays" (let's say 200). Each ray can be "on" or "off", and thus represents a degree of freedom of the system. In other words the entire state of the system can be described by 200 bits. The system starts out with two or more "particles" (circles) of a given radius that are not intersected by any "on" rays. These regions of space intersected only with "off" rays are called "holes". The system evolves in time based on the following simple rules:
1. Pick a random ray
2. If the ray is on, turn it off.
3. If the ray is off, turn if on ONLY IF turning it on doesn't shrink a hole to the point where the particle can no longer exist without being intersected with an on ray. So if the ray is just shaving a bit off the edge it is ok.
4. Repeat ad infinitum.
What happens if you run this experiment? Over time the particle regions (holes) will merge. Try it yourself by clicking the "start" button below!
Why is it that the particles move towards each other vs just jiggling around forever? Because there are many more ways for this system to exist with particles overlapping vs separate. In the entire configuration space of all possible states of the system, more of them have the particles near, or overlapping. Consider if a given particle has 30 rays intersecting it. A single particle will thus force those 30 rays to be off, leaving only 2^170 possible unique configurations of the system. But two particles far apart force 30+30=60 rays to be off, leaving only 2^140 possible configurations. So the number of configurations available with particles overlapping is 2^170/2^140 = 2^30 = 1 billion times more than the number of configurations available with particles far apart. The rules by which the system evolves are more or less a random exploration of this configuration space, and thus it is overwhelmingly likely that the system will end up in a state with particles overlapping. This is no different from the way a teaspoon of milk when poured into a cup of coffee is overwhelmingly likely to spread out and blend evenly within the coffee, all due to more or less random thermal jiggling of the molecules involved. This is a very intuitive result of entropy. What makes the mikado universe interesting is that it represents a system where entropic action causes particles to attract together, vs spread evenly apart.
Source code at http://github.com/gtoubassi/mikado-universe
(Note: running in a few trials, it seems Chrome is about 25-30% faster than Safari, which is about twice as fast as Firefox 6)
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