Question
A 1995 paper by Ted Jacobsen uses this inequality and the laws of thermodynamics to derive the Einstein field equations. For 10 points each:
[10h] Name this inequality. This inequality can be derived through proof by contradiction by demonstrating that the second law of thermodynamics would be broken if a box that violated this inequality were lowered into a black hole.
ANSWER: Bekenstein bound [or Bekenstein limit]
[10e] The Bekenstein bound limits the amount of this quantity contained in a finite object; otherwise, dropping the object in a black hole will cause this quantity to decrease for the universe, violating the second law of thermodynamics.
ANSWER: entropy [or information]
[10m] Bekenstein predicted that black holes themselves have entropy directly proportional to this quantity for their event horizons. The scaling of entropy with this quantity inspired the holographic principle.
ANSWER: surface area [prompt on size of event horizon]
<Physics>
Summary
| 2024 ACF Regionals @ JMU | 01/27/2024 | Y | 3 | 3.33 | 33% | 0% | 0% |
| 2024 ACF Regionals @ Imperial | 01/27/2024 | Y | 1 | 20.00 | 100% | 100% | 0% |
| 2024 ACF Regionals @ Vanderbilt | 01/27/2024 | Y | 5 | 10.00 | 80% | 20% | 0% |
| 2024 ACF Regionals @ MIT | 01/27/2024 | Y | 1 | 20.00 | 100% | 100% | 0% |
Data
| Yale A | Brandeis A | 0 | 10 | 10 | 20 |