Question
Einstein’s theory of general relativity is quite a doozy, mathematically. For 10 points each, answer some questions about the math behind the physics.
[10m] The Einstein field equations are solved to obtain this object, but the non-linearity of the equations means that the sum of two solutions is generally not a solution. This tensor is used to compute dot products of vectors on a manifold.
ANSWER: metric tensor
[10h] In general relativity, derivatives are generally replaced with covariant derivatives, which do not commute. The degree of non-commutativity is measured by this four-index tensor field, whose contraction gives the Ricci tensor.
ANSWER: Riemann curvature tensor [or Riemann tensor; prompt on curvature tensor]
[10e] When the Riemann tensor vanishes, spacetime is flat, and general relativity is no longer necessary. Instead, this simpler theory, which Einstein developed by postulating the constancy of the speed of light, can be used.
ANSWER: special relativity [or SR]
<RA, Physics>
Summary
| 2023 ARCADIA at UC Berkeley | Premiere | Y | 2 | 25.00 | 100% | 50% | 100% |
| 2023 ARCADIA at Carleton University | Premiere | Y | 2 | 10.00 | 100% | 0% | 0% |
| 2023 ARCADIA at Claremont Colleges | Premiere | Y | 1 | 10.00 | 100% | 0% | 0% |
| 2023 ARCADIA at Indiana | Premiere | Y | 5 | 12.00 | 80% | 40% | 0% |
| 2023 ARCADIA at RIT | Premiere | Y | 2 | 15.00 | 100% | 50% | 0% |
| 2023 ARCADIA at WUSTL | Premiere | Y | 3 | 6.67 | 67% | 0% | 0% |
Data
| Berkeley A | Berkeley B | 0 | 10 | 10 | 20 |
| Stanford A | Berkeley C | 10 | 10 | 10 | 30 |