The spherical cow is a humorous metaphor for highly simplified scientific models of complex phenomena. [1] [2] [3] [4] Originating in theoretical physics, the metaphor refers to physicists' tendency to develop toy models that reduce a problem to the simplest form imaginable, making calculations more feasible, even if the simplification hinders the model's application to reality.
The metaphor and variants have subsequently been used in other disciplines.
The phrase comes from a joke that spoofs the simplifying assumptions sometimes used in theoretical physics. [5]
Milk production at a dairy farm was low, so the farmer wrote to the local university, asking for help from academia. A multidisciplinary team of professors was assembled, headed by a theoretical physicist, and two weeks of intensive on-site investigation took place. The scholars then returned to the university, notebooks crammed with data, where the task of writing the report was left to the team leader. Shortly thereafter the physicist returned to the farm, saying to the farmer, "I have the solution, but it works only in the case of spherical cows in a vacuum."
It is told in many variants, [6] including a joke about a physicist who said he could predict the winner of any race provided it involved spherical horses moving through a vacuum. [7] [8] A 1973 letter to the editor in the journal Science describes the "famous story" about a physicist whose solution to a poultry farm's egg-production problems began with "Postulate a spherical chicken". [9]
The concept is familiar enough that the phrase is sometimes used as shorthand for the entire issue of proper modeling. For example, Consider a Spherical Cow is a 1988 book about problem solving using simplified models. [10] A 2015 paper on the systemic errors introduced by simplifying assumptions about spherical symmetries in galactic dark-matter haloes was titled "Milking the spherical cow – on aspherical dynamics in spherical coordinates". [11]
References to the joke appear even outside the field of scientific modeling. "Spherical Cow" was chosen as the code name for the Fedora 18 Linux distribution. [12] In the sitcom The Big Bang Theory , a joke is told by Dr. Leonard Hofstadter with the punchline mentioning "spherical chickens in a vacuum", in "The Cooper-Hofstadter Polarization" episode. [13] In the space gravity simulator educational video game Universe Sandbox , a spherical cow was added as a user-placeable object in March 2023. [14]
In physical cosmology, cosmic inflation, cosmological inflation, or just inflation, is a theory of exponential expansion of space in the early universe. The inflationary epoch is believed to have lasted from 10−36 seconds to between 10−33 and 10−32 seconds after the Big Bang. Following the inflationary period, the universe continued to expand, but at a slower rate. The re-acceleration of this slowing expansion due to dark energy began after the universe was already over 7.7 billion years old.
In theories of quantum gravity, the graviton is the hypothetical quantum of gravity, an elementary particle that mediates the force of gravitational interaction. There is no complete quantum field theory of gravitons due to an outstanding mathematical problem with renormalization in general relativity. In string theory, believed by some to be a consistent theory of quantum gravity, the graviton is a massless state of a fundamental string.
In physics, string theory is a theoretical framework in which the point-like particles of particle physics are replaced by one-dimensional objects called strings. String theory describes how these strings propagate through space and interact with each other. On distance scales larger than the string scale, a string looks just like an ordinary particle, with its mass, charge, and other properties determined by the vibrational state of the string. In string theory, one of the many vibrational states of the string corresponds to the graviton, a quantum mechanical particle that carries the gravitational force. Thus, string theory is a theory of quantum gravity.
In cosmology, the cosmological constant, alternatively called Einstein's cosmological constant, is the constant coefficient of a term that Albert Einstein temporarily added to his field equations of general relativity. He later removed it; however, much later it was revived and reinterpreted as the energy density of space, or vacuum energy, that arises in quantum mechanics. It is closely associated with the concept of dark energy.
Observations show that the expansion of the universe is accelerating, such that the velocity at which a distant galaxy recedes from the observer is continuously increasing with time. The accelerated expansion of the universe was discovered in 1998 by two independent projects, the Supernova Cosmology Project and the High-Z Supernova Search Team, which used distant type Ia supernovae to measure the acceleration. The idea was that as type Ia supernovae have almost the same intrinsic brightness, and since objects that are farther away appear dimmer, the observed brightness of these supernovae can be used to measure the distance to them. The distance can then be compared to the supernovae's cosmological redshift, which measures how much the universe has expanded since the supernova occurred; the Hubble law established that the farther away that an object is, the faster it is receding. The unexpected result was that objects in the universe are moving away from one another at an accelerating rate. Cosmologists at the time expected that recession velocity would always be decelerating, due to the gravitational attraction of the matter in the universe. Three members of these two groups have subsequently been awarded Nobel Prizes for their discovery. Confirmatory evidence has been found in baryon acoustic oscillations, and in analyses of the clustering of galaxies.
The Big Crunch is a hypothetical scenario for the ultimate fate of the universe, in which the expansion of the universe eventually reverses and the universe recollapses, ultimately causing the cosmic scale factor to reach zero, an event potentially followed by a reformation of the universe starting with another Big Bang. The vast majority of evidence indicates that this hypothesis is not correct. Instead, astronomical observations show that the expansion of the universe is accelerating rather than being slowed by gravity, suggesting that a Big Freeze is more likely. However, some physicists have proposed that a "Big Crunch-style" event could result from a dark energy fluctuation.
Vacuum energy is an underlying background energy that exists in space throughout the entire universe. The vacuum energy is a special case of zero-point energy that relates to the quantum vacuum.
The Big Bounce hypothesis is a cosmological model for the origin of the known universe. It was originally suggested as a phase of the cyclic model or oscillatory universe interpretation of the Big Bang, where the first cosmological event was the result of the collapse of a previous universe. It receded from serious consideration in the early 1980s after inflation theory emerged as a solution to the horizon problem, which had arisen from advances in observations revealing the large-scale structure of the universe.
Alan Harvey Guth is an American theoretical physicist and cosmologist who is the Victor Weisskopf Professor of Physics at the Massachusetts Institute of Technology. Along with Alexei Starobinsky and Andrei Linde, he won the 2014 Kavli Prize "for pioneering the theory of cosmic inflation." Guth's research focuses on elementary particle theory and how particle theory is applicable to the early universe.
Andrei Dmitriyevich Linde is a Russian-American theoretical physicist and the Harald Trap Friis Professor of Physics at Stanford University.
In general relativity, Birkhoff's theorem states that any spherically symmetric solution of the vacuum field equations must be static and asymptotically flat. This means that the exterior solution must be given by the Schwarzschild metric. The converse of the theorem is true and is called Israel's theorem. The converse is not true in Newtonian gravity.
An asymptotically flat spacetime is a Lorentzian manifold in which, roughly speaking, the curvature vanishes at large distances from some region, so that at large distances, the geometry becomes indistinguishable from that of Minkowski spacetime.
Edward P. Tryon was an American scientist and a professor emeritus of physics at Hunter College of the City University of New York (CUNY). He was the first physicist to propose that our universe originated as a quantum fluctuation of the vacuum.
The Boltzmann brain thought experiment suggests that it might be more likely for a single brain to spontaneously form in space, complete with a memory of having existed in our universe, rather than for the entire universe to come about in the manner cosmologists think it actually did. Physicists use the Boltzmann brain thought experiment as a reductio ad absurdum argument for evaluating competing scientific theories.
In physical cosmology and astronomy, dark energy is an unknown form of energy that affects the universe on the largest scales. Its primary effect is to drive the accelerating expansion of the universe. Assuming that the lambda-CDM model of cosmology is correct, dark energy is the dominant component of the universe, contributing 68% of the total energy in the present-day observable universe while dark matter and ordinary (baryonic) matter contribute 26% and 5%, respectively, and other components such as neutrinos and photons are nearly negligible. Dark energy's density is very low: 7×10−30 g/cm3, much less than the density of ordinary matter or dark matter within galaxies. However, it dominates the universe's mass–energy content because it is uniform across space.
In cosmology, the cosmological constant problem or vacuum catastrophe is the substantial disagreement between the observed values of vacuum energy density and the much larger theoretical value of zero-point energy suggested by quantum field theory.
Lev Borisovich Okun was a Soviet theoretical physicist. He is known for his contributions to particle physics and quantum chromodynamics. He coined the term hadron.
The index of physics articles is split into multiple pages due to its size.
The index of physics articles is split into multiple pages due to its size.
Alexei Alexandrovich Starobinsky was a Soviet and Russian theoretical physicist and cosmologist. He was a pioneer of the theory of cosmic inflation, for which he received the 2014 Kavli Prize in Astrophysics together with Alan Guth and Andrei Linde.