reperiendi

Entropic gravity

Posted in Astronomy, General physics, Math by Mike Stay on 2010 July 19

Erik Verlinde has been in the news recently for revisiting Ted Jacobson’s suggestion that gravity is an entropic force rather than a fundamental one. The core of the argument is as follows:

Say we have two boxes, one inside the other:

+---------------+
|               |
| +----------+  |
| |          |  |
| |          |  |
| |          |  |
| +----------+  |
+---------------+

Say the inner box has room for ten bits on its surface and the outer one room for twenty. Each box can use as many “1”s as there are particles inside it:

+---------------+
|      X        |
| +----------+  |
| |          |  |
| |  X       |  |
| |          |  |
| +----------+  |
+---------------+

In this case, the inner box has only one particle inside, so there are 10 choose 1 = 10 ways to choose a labeling of the inner box; the outer box has two particles inside, so there are 20 choose 2 = 190 ways. Thus there are 1900 ways to label the system in all.

If both particles are in the inner box, though, the number of ways increases:

+---------------+
|               |
| +----------+  |
| |          |  |
| |  X  X    |  |
| |          |  |
| +----------+  |
+---------------+

The inner box now has 10 choose 2 ways = 45, while the outer box still has 190. So using the standard assumption that all labelings are equally likely, it’s 4.5 times as likely to find both particles in the inner box, and we get an entropic force drawing them together.

The best explanation of Verlinde’s paper I’ve seen is Sabine Hossenfelder’s Comments on and Comments on Comments on Verlinde’s paper “On the Origin of Gravity and the Laws of Newton”.

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