From arXiv · · 1 min
Beyond the Spherical Cow: A Multipolar Expansion
Physicists take the famous spherical cow joke to its logical extreme by calculating higher-order multipole moments and gravitational wave emissions.
In brief
Physicists take the famous spherical cow joke to its logical extreme by calculating higher-order multipole moments and gravitational wave emissions. Complex physics models often begin with drastic simplifications, but higher-order mathematical expansions allow researchers to systematically reintroduce realistic…
Physics' favorite joke gets rigorous
The famous spherical cow approximation is ubiquitous in physics, but it rarely receives formal justification. A theoretical paper extends this classic simplification into a full mathematical expansion.
“The spherical cow approximation is widely used in the literature, but is rarely justified.”
Building a multipolar cow
By expanding beyond simple spherical symmetry, physicists can define a cow's precise geometry across higher-order terms. The traditional spherical cow becomes merely the leading-order term.
“I propose several schemes for extending the spherical cow approximation to a full multipole expansion, in which the spherical cow is simply the first term.”
Computing bovine potentials
This mathematical framework enables the exact calculation of bovine fields and interactions that only occur once perfect spherical symmetry is broken.
“This allows for the computation of bovine potentials and interactions beyond spherical symmetry...”
Emitting gravitational waves
Higher-order multipoles are required to study physical effects suppressed by symmetry, such as the spindown of a rapidly rotating cow emitting gravitational waves.
“...such as the spindown of a rotating cow due to the emission of gravitational waves.”
Testing the benchmark model
The framework was tested by computing multipole coefficients for a benchmark cow to prove its applicability. Naturally, no real animals were harmed during the theoretical analysis.
“April Fools' paper that got a little out of hand. No cows were harmed.”
The bottom line
Complex physics models often begin with drastic simplifications, but higher-order mathematical expansions allow researchers to systematically reintroduce realistic asymmetries.
