Question
These objects can be roughly, though circularly, defined as anything that transforms like these objects. For 10 points each:
[10m] Name these mathematical objects exemplified in physics by “metric” and “stress–energy” ones.
ANSWER: tensors [accept metric tensor; accept stress–energy tensor; prompt on matrix or matrices]
[10h] A distinguishing feature of tensors is that they are multiplied by the Jacobian under this type of operation. Galileo names instances of this type of operation that do not preserve delta-s-squared.
ANSWER: coordinate transformations [accept descriptions of changing coordinate systems or changing reference frame or change of basis; prompt on transformations or Galilean transformations by asking “of what?”; prompt on descriptions of change of variables by asking “which variables?”]
[10e] The metric tensor is related to the stress–energy tensor by equations fundamental to this theory. Einstein developed this theory to explain gravitation, extending an earlier theory that uses Lorentz transformations.
ANSWER: general relativity [or GR or general theory of relativity; prompt on relativity]
<Forrest Weintraub, Science - Physics> ~23333~ <Editor: David Bass>
Data
Summary
| Tournament | Edition | Exact Match? | Heard | PPB | Easy % | Medium % | Hard % |
|---|---|---|---|---|---|---|---|
| 2024 PACE NSC | 06/08/2024 | Y | 36 | 18.06 | 89% | 89% | 3% |