A fudge factor is an ad hoc quantity or element introduced into a calculation, formula or model in order to make it fit observations or expectations. Also known as a correction coefficient, which is defined by
Examples include Einstein's cosmological constant, dark energy, the initial proposals of dark matter and inflation. [1]
Some quantities in scientific theory are set arbitrarily according to measured results rather than by calculation (for example, the Planck constant). However, in the case of these fundamental constants, their arbitrariness is usually explicit. To suggest that other calculations may include a "fudge factor" may suggest that the calculation has been somehow tampered with to make results give a misleadingly good match to experimental data.
In theoretical physics, when Albert Einstein originally tried to produce a general theory of relativity, he found that the theory seemed to predict the gravitational collapse of the universe: it seemed that the universe should either be expanding or collapsing, and to produce a model in which the universe was static and stable (which seemed to Einstein at the time to be the "proper" result), he introduced an expansionist variable (called the cosmological constant), whose sole purpose was to cancel out the cumulative effects of gravitation. He later called this, "the biggest blunder of my life". [2]
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A common feature of "fudge factors" in science is their arbitrariness, and their retrospective nature.
However, in project management it is common to build a certain error margin into the predicted "resource cost" of a project to make predictions more realistic: there are many unforeseen factors that may delay a project or make it more costly, but very few factors that could result in it being delivered before time or under the calculated budget ... so to some degree, "unexpected" overruns are to be expected, even if their precise nature can't be predicted. Experienced planners may know that a certain type of project will tend to overrun by a certain percentage of its calculated resource requirements, and may multiply the "ideal" calculations by a safety margin to produce a more realistic estimate, and this margin may sometimes be referred to as a fudge factor. However, when planning ahead for expected unpredictabilities, these "error margins" are usually assigned other, more specific names: for instance in warehouse stock control, where a certain amount of stock is expected to disappear naturally through damage, pilfering or other unexplained problems, the discrepancy is referred to as shrinkage.
In engineering, a "fudge factor" may be introduced to allow a margin of error in unknown quantities.
In physics, the fundamental interactions or fundamental forces are the interactions that do not appear to be reducible to more basic interactions. There are four fundamental interactions known to exist:
General relativity, also known as the general theory of relativity and Einstein's theory of gravity, is the geometric theory of gravitation published by Albert Einstein in 1915 and is the current description of gravitation in modern physics. General relativity generalizes special relativity and refines Newton's law of universal gravitation, providing a unified description of gravity as a geometric property of space and time or four-dimensional spacetime. In particular, the curvature of spacetime is directly related to the energy and momentum of whatever matter and radiation are present. The relation is specified by the Einstein field equations, a system of second order partial differential equations.
The theory of relativity usually encompasses two interrelated physics theories by Albert Einstein: special relativity and general relativity, proposed and published in 1905 and 1915, respectively. Special relativity applies to all physical phenomena in the absence of gravity. General relativity explains the law of gravitation and its relation to the forces of nature. It applies to the cosmological and astrophysical realm, including astronomy.
A theory of everything (TOE), final theory, ultimate theory, unified field theory or master theory is a hypothetical, singular, all-encompassing, coherent theoretical framework of physics that fully explains and links together all aspects of the universe. Finding a theory of everything is one of the major unsolved problems in physics.
In physics, gravity (from Latin gravitas 'weight') is a fundamental interaction which causes mutual attraction between all things that have mass. Gravity is, by far, the weakest of the four fundamental interactions, approximately 1038 times weaker than the strong interaction, 1036 times weaker than the electromagnetic force and 1029 times weaker than the weak interaction. As a result, it has no significant influence at the level of subatomic particles. However, gravity is the most significant interaction between objects at the macroscopic scale, and it determines the motion of planets, stars, galaxies, and even light.
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.
A gravitational singularity, spacetime singularity or simply singularity is a condition in which gravity is predicted to be so intense that spacetime itself would break down catastrophically. As such, a singularity is by definition no longer part of the regular spacetime and cannot be determined by "where" or "when". Gravitational singularities exist at a junction between general relativity and quantum mechanics; therefore, the properties of the singularity cannot be described without an established theory of quantum gravity. Trying to find a complete and precise definition of singularities in the theory of general relativity, the current best theory of gravity, remains a difficult problem. A singularity in general relativity can be defined by the scalar invariant curvature becoming infinite or, better, by a geodesic being incomplete.
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.
In theoretical physics, the anti-de Sitter/conformal field theory correspondence is a conjectured relationship between two kinds of physical theories. On one side are anti-de Sitter spaces (AdS) that are used in theories of quantum gravity, formulated in terms of string theory or M-theory. On the other side of the correspondence are conformal field theories (CFT) that are quantum field theories, including theories similar to the Yang–Mills theories that describe elementary particles.
General relativity is a theory of gravitation developed by Albert Einstein between 1907 and 1915. The theory of general relativity says that the observed gravitational effect between masses results from their warping of spacetime.
General relativity is a theory of gravitation that was developed by Albert Einstein between 1907 and 1915, with contributions by many others after 1915. According to general relativity, the observed gravitational attraction between masses results from the warping of space and time by those masses.
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.
Physics is a scientific discipline that seeks to construct and experimentally test theories of the physical universe. These theories vary in their scope and can be organized into several distinct branches, which are outlined in this article.
The zero-energy universe hypothesis proposes that the total amount of energy in the universe is exactly zero: its amount of positive energy in the form of matter is exactly canceled out by its negative energy in the form of gravity. Some physicists, such as Lawrence Krauss, Stephen Hawking or Alexander Vilenkin, call or called this state "a universe from nothingness", although the zero-energy universe model requires both a matter field with positive energy and a gravitational field with negative energy to exist. The hypothesis is broadly discussed in popular sources. Other cancellation examples include the expected symmetric prevalence of right- and left-handed angular momenta of objects, the observed flatness of the universe, the equal prevalence of positive and negative charges, opposing particle spin in quantum mechanics, as well as the crests and troughs of electromagnetic waves, among other possible examples in nature.
Albert Einstein conducted several unsuccessful investigations. These pertain to quantum mechanics, superconductivity, and his details on his own theory of relativity.
In particle physics and physical cosmology, Planck units are a system of units of measurement defined exclusively in terms of four universal physical constants: c, G, ħ, and kB. Expressing one of these physical constants in terms of Planck units yields a numerical value of 1. They are a system of natural units, defined using fundamental properties of nature rather than properties of a chosen prototype object. Originally proposed in 1899 by German physicist Max Planck, they are relevant in research on unified theories such as quantum gravity.
The asymptotic safety approach to quantum gravity provides a nonperturbative notion of renormalization in order to find a consistent and predictive quantum field theory of the gravitational interaction and spacetime geometry. It is based upon a nontrivial fixed point of the corresponding renormalization group (RG) flow such that the running coupling constants approach this fixed point in the ultraviolet (UV) limit. This suffices to avoid divergences in physical observables. Moreover, it has predictive power: Generically an arbitrary starting configuration of coupling constants given at some RG scale does not run into the fixed point for increasing scale, but a subset of configurations might have the desired UV properties. For this reason it is possible that — assuming a particular set of couplings has been measured in an experiment — the requirement of asymptotic safety fixes all remaining couplings in such a way that the UV fixed point is approached.
The term physical constant expresses the notion of a physical quantity subject to experimental measurement which is independent of the time or location of the experiment. The constancy (immutability) of any "physical constant" is thus subject to experimental verification.
Lucas Lombriser is a Swiss National Science Foundation Professor at the Department of Theoretical Physics, University of Geneva. His research is in Theoretical Cosmology, Dark Energy, and Alternative Theories of Gravity. In 2020 and 2021 Lombriser proposed that the Hubble tension and other discrepancies between cosmological measurements imply significant evidence that we are living in a Hubble Bubble of 250 million light years in diameter which is 20% less dense than the cosmic average and lowers the locally measured cosmic microwave background temperature over its cosmic average. Previously, in 2019, he has proposed a solution to the cosmological constant problem from arguing that Newton's constant varies globally. In 2015 and 2016, Lombriser predicted the measurement of the gravitational wave speed with a neutron star merger and that this would rule out alternative theories of gravity as the cause of the late-time accelerated expansion of our Universe, a prediction that proved true with GW170817. Lombriser is a member of the Romansh-speaking minority in Switzerland.
