Question
Einstein’s theory of general relativity is quite a doozy, mathematically. Answer the following questions about the math behind the physics, for 10 points each.
[10m] The Einstein field equations are solved to obtain this object, but the nonlinearity of the equations means that the sum of two solutions is generally not a solution. This tensor assigns an inner product to each point of a manifold, allowing one to define distances.
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, one can use this simpler theory, which Einstein developed by postulating the constancy of the speed of light.
ANSWER: special relativity [or SR]
<RA, Physics>
Summary
| 2023 ARCADIA at Duke | Emory, Duke, Yale | Y | 3 | 6.67 | 67% | 0% | 0% |
| 2023 ARCADIA at Emory | Emory, Duke, Yale | Y | 4 | 7.50 | 75% | 0% | 0% |
| 2023 ARCADIA at Imperial | Imperial | Y | 5 | 18.00 | 80% | 60% | 40% |
| 2023 ARCADIA at Maryland | Maryland, Online | Y | 3 | 6.67 | 33% | 33% | 0% |
| 2023 ARCADIA at Ohio State | Ohio State, Texas | Y | 2 | 15.00 | 100% | 50% | 0% |
| 2023 ARCADIA Online | Maryland, Online | Y | 3 | 10.00 | 100% | 0% | 0% |
| 2023 ARCADIA at Texas | Ohio State, Texas | Y | 3 | 13.33 | 100% | 33% | 0% |
Data
| Birmingham | Imperial A | 0 | 0 | 10 | 10 |
| Edinburgh | Bristol | 0 | 0 | 10 | 10 |
| Cambridge B | Warwick | 10 | 10 | 10 | 30 |
| Durham | Cambridge A | 10 | 10 | 10 | 30 |
| Oxford | Imperial B | 10 | 0 | 0 | 10 |