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A scientific theory is an explanation of an aspect of the
natural world and universe
natural world and universe
that has been repeatedly tested and verified in accordance with the
scientific method The scientific method is an empirical Empirical evidence for a proposition is evidence, i.e. what supports or counters this proposition, that is constituted by or accessible to sense experience or experimental procedure. Empirical evidence ...

scientific method
, using accepted
protocols Protocol may refer to: Sociology and politics * Protocol (politics), a formal agreement between nation states * Protocol (diplomacy), the etiquette of diplomacy and affairs of state * Etiquette, a code of personal behavior Science and technology ...
of
observation Observation is the active acquisition of information Information can be thought of as the resolution of uncertainty; it answers the question of "What an entity is" and thus defines both its essence and the nature of its characteristics. Th ...

observation
, measurement, and evaluation of results. Where possible, theories are tested under controlled conditions in an
experiment An experiment is a procedure carried out to support or refute a hypothesis, or determine the efficacy or likelihood of something previously untried. Experiments provide insight into Causality, cause-and-effect by demonstrating what outcome oc ...

experiment
. In circumstances not amenable to experimental testing, theories are evaluated through principles of
abductive reasoning Abductive reasoning (also called abduction,For example: abductive inference, or retroduction) is a form of logical inference Inferences are steps in reasoning, moving from premises to logical consequences; etymologically, the word ''wikt:inf ...
. Established scientific theories have withstood rigorous scrutiny and embody scientific
knowledge Knowledge is a familiarity or awareness, of someone or something, such as facts A fact is something that is truth, true. The usual test for a statement of fact is verifiability—that is whether it can be demonstrated to correspond to e ...
. A scientific theory differs from a
scientific fact A fact is an occurrence in the real world. The usual test for a statement of fact is verifiability—that is whether it can be demonstrated to correspond to experience Experience is the process through which conscious organisms Perception, pe ...
or
scientific law Scientific laws or laws of science are statements, based on repeated experiments or observations, that describe or predict a range of natural phenomena. The term ''law'' has diverse usage in many cases (approximate, accurate, broad, or narrow) ...
in that a theory explains "why" or "how": a fact is a simple, basic observation, whereas a law is a statement (often a mathematical equation) about a relationship between facts. For example, Newton’s Law of Gravity is a mathematical equation that can be used to predict the attraction between bodies, but it is not a theory to explain ''how'' gravity works.
Stephen Jay Gould Stephen Jay Gould (; September 10, 1941 – May 20, 2002) was an American Paleontology, paleontologist, Evolutionary biology, evolutionary biologist, and History of science, historian of science. He was one of the most influential and widely read ...
wrote that "...facts and theories are different things, not rungs in a hierarchy of increasing certainty. Facts are the world's data. Theories are structures of ideas that explain and interpret facts." The meaning of the term ''scientific theory'' (often contracted to ''theory'' for brevity) as used in the disciplines of science is significantly different from the common
vernacular A vernacular or vernacular language refers to the language or dialect that is spoken by people that are inhabiting a particular country or region. The vernacular is typically the native language, normally Spoken language, spoken informally rath ...
usage of ''theory''.Quote: "The formal scientific definition of theory is quite different from the everyday meaning of the word. It refers to a comprehensive explanation of some aspect of nature that is supported by a vast body of evidence." In everyday speech, ''theory'' can imply an explanation that represents an unsubstantiated and speculative
guess A guess (or an act of guessing) is a swift conclusion drawn from data directly at hand, and held as probable or tentative, while the person making the guess (the guesser) admittedly lacks material for a greater degree of certainty. A guess is als ...
, whereas in science it describes an explanation that has been tested and is widely accepted as valid. The strength of a scientific theory is related to the diversity of phenomena it can explain and its simplicity. As additional
scientific evidence Scientific evidence is evidence Evidence for a proposition is what supports this proposition. It is usually understood as an indication that the supported proposition is true. What role evidence plays and how it is conceived varies from field ...
is gathered, a scientific theory may be modified and ultimately rejected if it cannot be made to fit the new findings; in such circumstances, a more accurate theory is then required. Some theories are so well-established that they are unlikely ever to be fundamentally changed (for example, scientific theories such as
evolution Evolution is change in the heritable Heredity, also called inheritance or biological inheritance, is the passing on of Phenotypic trait, traits from parents to their offspring; either through asexual reproduction or sexual reproduction, ...

evolution
,
heliocentric theory Heliocentrism is the astronomical model in which the Earth Earth is the third planet from the Sun and the only astronomical object known to harbor life. About 29% of Earth's surface is land consisting of continent A continent ...
,
cell theory In biology, cell theory is a scientific theory first formulated in the mid-nineteenth century, that living organisms are made up of Cell (biology), cells, that they are the basic structural/organizational unit of all organisms, and that all cells ...
, theory of plate tectonics,
germ theory of disease The germ theory of disease is the currently accepted scientific theory A scientific theory is an explanation of an aspect of the natural world and universe that has been repeatedly tested and verified in accordance with the scientific method ...
, etc.). In certain cases, a scientific theory or scientific law that fails to fit all data can still be useful (due to its simplicity) as an approximation under specific conditions. An example is
Newton's laws of motion Newton's laws of motion are three law Law is a system A system is a group of Interaction, interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its ...
, which are a highly accurate approximation to
special relativity In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force ...
at velocities that are small relative to the
speed of light The speed of light in vacuum A vacuum is a space Space is the boundless three-dimensional Three-dimensional space (also: 3-space or, rarely, tri-dimensional space) is a geometric setting in which three values (called paramet ...
. Scientific theories are
testable Testability, a property applying to an empirical hypothesis, involves two components: #Falsifiability or defeasibility, which means that counterexamples to the hypothesis are logically possible. #The practical feasibility of observing a reproducibi ...
and make
falsifiable In the philosophy of science, a theory is falsifiable if it is contradicted by ''possible observations''—i.e., by any observations that can be described in the language of the theory, which must have a conventional empirical interpretation. ...
predictions frame, '' The Old Farmer's Almanac'' is famous in the US for its (not necessarily accurate) long-range weather predictions. A prediction (Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the ...
. They describe the causes of a particular natural phenomenon and are used to explain and predict aspects of the physical
universe The universe ( la, universus) is all of space and time and their contents, including planets, stars, galaxy, galaxies, and all other forms of matter and energy. The Big Bang theory is the prevailing cosmological description of the development ...

universe
or specific areas of inquiry (for example, electricity, chemistry, and astronomy). As with other forms of scientific knowledge, scientific theories are both
deductive Deductive reasoning, also deductive logic, is the process of reasoning Reason is the capacity of consciously applying logic Logic is an interdisciplinary field which studies truth and reasoning Reason is the capacity of consciously making ...
and inductive, aiming for
predictive A prediction (Latin ''præ-'', "before," and ''dicere'', "to say"), or forecasting, forecast, is a statement about a future event (probability theory), event or data. They are often, but not always, based upon experience or knowledge. There i ...
and
explanatory power Explanatory power is the ability of a hypothesis or theory A theory is a reason, rational type of abstraction, abstract thinking about a phenomenon, or the results of such thinking. The process of contemplative and rational thinking is often ass ...
. Scientists use theories to further scientific knowledge, as well as to facilitate advances in
technology Technology ("science of craft", from Greek#REDIRECT Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. I ...

technology
or
medicine Medicine is the science Science () is a systematic enterprise that builds and organizes knowledge Knowledge is a familiarity, awareness, or understanding of someone or something, such as facts ( descriptive knowledge), skills (proced ...

medicine
.


Types

Albert Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest physicists of all time. Einstein is known for developing the theory of relativity The theo ...

Albert Einstein
described two types of scientific theories: "Constructive theories" and "principle theories". Constructive theories are constructive models for phenomena: for example,
kinetic theory of the ideal gas An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation o ...

kinetic theory
. Principle theories are empirical generalisations such as Newton's laws of motion.


Characteristics


Essential criteria

Typically for any theory to be accepted within most academia there is one simple criterion. The essential criterion is that the theory must be observable and repeatable. The aforementioned criterion is essential to prevent fraud and perpetuate science itself. The defining characteristic of all scientific knowledge, including theories, is the ability to make
falsifiable In the philosophy of science, a theory is falsifiable if it is contradicted by ''possible observations''—i.e., by any observations that can be described in the language of the theory, which must have a conventional empirical interpretation. ...
or testable
predictions frame, '' The Old Farmer's Almanac'' is famous in the US for its (not necessarily accurate) long-range weather predictions. A prediction (Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the ...
. The relevance and specificity of those predictions determine how potentially useful the theory is. A would-be theory that makes no observable predictions is not a scientific theory at all. Predictions not sufficiently specific to be tested are similarly not useful. In both cases, the term "theory" is not applicable. A body of descriptions of
knowledge Knowledge is a familiarity or awareness, of someone or something, such as facts A fact is something that is truth, true. The usual test for a statement of fact is verifiability—that is whether it can be demonstrated to correspond to e ...
can be called a theory if it fulfills the following criteria: * It makes
falsifiable In the philosophy of science, a theory is falsifiable if it is contradicted by ''possible observations''—i.e., by any observations that can be described in the language of the theory, which must have a conventional empirical interpretation. ...
predictions with consistent accuracy across a broad area of scientific inquiry (such as
mechanics Mechanics (Greek#REDIRECT Greek Greek may refer to: Greece Anything of, from, or related to Greece Greece ( el, Ελλάδα, , ), officially the Hellenic Republic, is a country located in Southeast Europe. Its population is approximat ...

mechanics
). * It is well-supported by many independent strands of evidence, rather than a single foundation. * It is consistent with preexisting experimental results and at least as accurate in its predictions as are any preexisting theories. These qualities are certainly true of such established theories as
special Special or specials may refer to: Policing * Specials, Ulster Special Constabulary, the Northern Ireland police force * Specials, Special Constable, an auxiliary, volunteer, or temporary; police worker or police officer Literature * ''Special ...
and
general relativity General relativity, also known as the general theory of relativity, is the geometric Geometry (from the grc, γεωμετρία; '' geo-'' "earth", '' -metron'' "measurement") is, with arithmetic, one of the oldest branches of mathema ...
,
quantum mechanics Quantum mechanics is a fundamental theory A theory is a reason, rational type of abstraction, abstract thinking about a phenomenon, or the results of such thinking. The process of contemplative and rational thinking is often associated with ...
,
plate tectonics Plate tectonics (from the la, label=Late Latin Late Latin ( la, Latinitas serior) is the scholarly name for the written Latin Latin (, or , ) is a classical language belonging to the Italic branch of the Indo-European languages. L ...
, the modern evolutionary synthesis, etc.


Other criteria

In addition, scientists prefer to work with a theory that meets the following qualities: * It can be subjected to minor adaptations to account for new data that do not fit it perfectly, as they are discovered, thus increasing its predictive capability over time. * It is among the most parsimonious explanations, economical in the use of proposed entities or explanatory steps as per
Occam's razor Occam's razor, Ockham's razor, Ocham's razor ( la, novacula Occami), also known as the principle of parsimony or the law of parsimony ( la, lex parsimoniae), is the problem-solving principle that "entities should not be multiplied beyond necessi ...
. This is because for each accepted explanation of a phenomenon, there may be an extremely large, perhaps even incomprehensible, number of possible and more complex alternatives, because one can always burden failing explanations with ''ad hoc'' hypotheses to prevent them from being falsified; therefore, simpler theories are preferable to more complex ones because they are more
testable Testability, a property applying to an empirical hypothesis, involves two components: #Falsifiability or defeasibility, which means that counterexamples to the hypothesis are logically possible. #The practical feasibility of observing a reproducibi ...
.Elliott Sober, Let's Razor Occam's Razor, pp. 73–93, from Dudley Knowles (ed.) Explanation and Its Limits, Cambridge University Press (1994).


Definitions from scientific organizations

The
United States National Academy of Sciences The National Academy of Sciences (NAS) is a United States nonprofit A nonprofit organization (NPO), also known as a non-business entity, not-for-profit organization, or nonprofit institution, is a legal entity organized and operated for a ...
defines scientific theories as follows:
The formal scientific definition of theory is quite different from the everyday meaning of the word. It refers to a comprehensive explanation of some aspect of nature that is supported by a vast body of evidence. Many scientific theories are so well established that no new evidence is likely to alter them substantially. For example, no new evidence will demonstrate that the Earth does not orbit around the Sun (heliocentric theory), or that living things are not made of cells (cell theory), that matter is not composed of atoms, or that the surface of the Earth is not divided into solid plates that have moved over geological timescales (the theory of plate tectonics)...One of the most useful properties of scientific theories is that they can be used to make predictions about natural events or phenomena that have not yet been observed.
From the
American Association for the Advancement of Science The American Association for the Advancement of Science (AAAS) is an American international non-profit organization A nonprofit organization (NPO), also known as a non-business entity, not-for-profit organization, or nonprofit institution ...
:
A scientific theory is a well-substantiated explanation of some aspect of the natural world, based on a body of facts that have been repeatedly confirmed through observation and experiment. Such fact-supported theories are not "guesses" but reliable accounts of the real world. The theory of biological evolution is more than "just a theory". It is as factual an explanation of the universe as the atomic theory of matter or the germ theory of disease. Our understanding of gravity is still a work in progress. But the phenomenon of gravity, like evolution, is an accepted fact.
Note that the term ''theory'' would not be appropriate for describing untested but intricate hypotheses or even scientific models.


Formation

The
scientific method The scientific method is an empirical Empirical evidence for a proposition is evidence, i.e. what supports or counters this proposition, that is constituted by or accessible to sense experience or experimental procedure. Empirical evidence ...

scientific method
involves the proposal and testing of
hypotheses A hypothesis (plural hypotheses) is a proposed explanation An explanation is a set of statements usually constructed to describe a set of facts which clarifies the causes, context Context may refer to: * Context (language use), the rel ...
, by deriving
predictions frame, '' The Old Farmer's Almanac'' is famous in the US for its (not necessarily accurate) long-range weather predictions. A prediction (Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the ...
from the hypotheses about the results of future experiments, then performing those experiments to see whether the predictions are valid. This provides evidence either for or against the hypothesis. When enough experimental results have been gathered in a particular area of inquiry, scientists may propose an explanatory framework that accounts for as many of these as possible. This explanation is also tested, and if it fulfills the necessary criteria (see above), then the explanation becomes a theory. This can take many years, as it can be difficult or complicated to gather sufficient evidence. Once all of the criteria have been met, it will be widely accepted by scientists (see
scientific consensus Scientific consensus is the collective judgment, position, and opinion of the community of scientist A scientist is a person who conducts scientific research The scientific method is an Empirical evidence, empirical method of acquiring ...
) as the best available explanation of at least some phenomena. It will have made predictions of phenomena that previous theories could not explain or could not predict accurately, and it will have resisted attempts at falsification. The strength of the evidence is evaluated by the scientific community, and the most important experiments will have been replicated by multiple independent groups. Theories do not have to be perfectly accurate to be scientifically useful. For example, the predictions made by classical mechanics are known to be inaccurate in the relativistic realm, but they are almost exactly correct at the comparatively low velocities of common human experience. In
chemistry Chemistry is the scientific Science () is a systematic enterprise that builds and organizes knowledge Knowledge is a familiarity or awareness, of someone or something, such as facts A fact is an occurrence in the real world. T ...

chemistry
, there are many acid-base theories providing highly divergent explanations of the underlying nature of acidic and basic compounds, but they are very useful for predicting their chemical behavior. Like all knowledge in science, no theory can ever be completely certain, since it is possible that future experiments might conflict with the theory's predictions. However, theories supported by the scientific consensus have the highest level of certainty of any scientific knowledge; for example, that all objects are subject to
gravity Gravity (), or gravitation, is a by which all things with or —including s, s, , and even —are attracted to (or ''gravitate'' toward) one another. , gravity gives to s, and the causes the s of the oceans. The gravitational attracti ...

gravity
or that life on Earth
evolved Evolution is change in the heritable Heredity, also called inheritance or biological inheritance, is the passing on of Phenotypic trait, traits from parents to their offspring; either through asexual reproduction or sexual reproduction, ...

evolved
from a
common ancestor Common descent is a concept in evolutionary biology Evolutionary biology is the subfield of biology that studies the evolution, evolutionary processes (natural selection, common descent, speciation) that produced the Biodiversity, diversity ...
. Acceptance of a theory does not require that all of its major predictions be tested, if it is already supported by sufficiently strong evidence. For example, certain tests may be unfeasible or technically difficult. As a result, theories may make predictions that have not yet been confirmed or proven incorrect; in this case, the predicted results may be described informally with the term "theoretical". These predictions can be tested at a later time, and if they are incorrect, this may lead to the revision or rejection of the theory.


Modification and improvement

If experimental results contrary to a theory's predictions are observed, scientists first evaluate whether the experimental design was sound, and if so they confirm the results by independent replication. A search for potential improvements to the theory then begins. Solutions may require minor or major changes to the theory, or none at all if a satisfactory explanation is found within the theory's existing framework. Over time, as successive modifications build on top of each other, theories consistently improve and greater predictive accuracy is achieved. Since each new version of a theory (or a completely new theory) must have more predictive and explanatory power than the last, scientific knowledge consistently becomes more accurate over time. If modifications to the theory or other explanations seem to be insufficient to account for the new results, then a new theory may be required. Since scientific knowledge is usually durable, this occurs much less commonly than modification. Furthermore, until such a theory is proposed and accepted, the previous theory will be retained. This is because it is still the best available explanation for many other phenomena, as verified by its predictive power in other contexts. For example, it has been known since 1859 that the observed
perihelion precession of Mercury Tests of general relativity serve to establish observational evidence for the theory of general relativity. The first three tests, proposed by Albert Einstein in 1915, concerned the "anomalous" precession of the perihelion of Mercury (planet), Mer ...
violates Newtonian mechanics, but the theory remained the best explanation available until relativity was supported by sufficient evidence. Also, while new theories may be proposed by a single person or by many, the cycle of modifications eventually incorporates contributions from many different scientists. After the changes, the accepted theory will explain more phenomena and have greater predictive power (if it did not, the changes would not be adopted); this new explanation will then be open to further replacement or modification. If a theory does not require modification despite repeated tests, this implies that the theory is very accurate. This also means that accepted theories continue to accumulate evidence over time, and the length of time that a theory (or any of its principles) remains accepted often indicates the strength of its supporting evidence.


Unification

In some cases, two or more theories may be replaced by a single theory that explains the previous theories as approximations or special cases, analogous to the way a theory is a unifying explanation for many confirmed hypotheses; this is referred to as ''unification'' of theories.Weinberg S (1993). ''Dreams of a Final Theory: The Scientist's Search for the Ultimate Laws of Nature.'' For example,
electricity Electricity is the set of physical Physical may refer to: *Physical examination, a regular overall check-up with a doctor *Physical (album), ''Physical'' (album), a 1981 album by Olivia Newton-John **Physical (Olivia Newton-John song), "Physi ...

electricity
and
magnetism Magnetism is a class of physical attributes that are mediated by magnetic field A magnetic field is a vector field In vector calculus and physics, a vector field is an assignment of a vector to each point in a subset of space. For in ...

magnetism
are now known to be two aspects of the same phenomenon, referred to as
electromagnetism Electromagnetism is a branch of physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical science is that department of knowledge which relates to the order of nature, or, in ...

electromagnetism
. When the predictions of different theories appear to contradict each other, this is also resolved by either further evidence or unification. For example, physical theories in the 19th century implied that the
Sun The Sun is the star A star is an astronomical object consisting of a luminous spheroid of plasma (physics), plasma held together by its own gravity. The List of nearest stars and brown dwarfs, nearest star to Earth is the Sun. Many othe ...

Sun
could not have been burning long enough to allow certain geological changes as well as the
evolution Evolution is change in the heritable Heredity, also called inheritance or biological inheritance, is the passing on of Phenotypic trait, traits from parents to their offspring; either through asexual reproduction or sexual reproduction, ...

evolution
of life. This was resolved by the discovery of
nuclear fusion Nuclear fusion is a nuclear reaction, reaction in which two or more atomic nuclei are combined to form one or more different atomic nuclei and subatomic particles (neutrons or protons). The difference in mass between the reactants and products ...

nuclear fusion
, the main energy source of the Sun. Contradictions can also be explained as the result of theories approximating more fundamental (non-contradictory) phenomena. For example,
atomic theory Atomic theory is the scientific theory A scientific theory is an explanation of an aspect of the that has been and verified in accordance with the , using accepted of , measurement, and evaluation of results. Where possible, theories are ...
is an approximation of
quantum mechanics Quantum mechanics is a fundamental theory A theory is a reason, rational type of abstraction, abstract thinking about a phenomenon, or the results of such thinking. The process of contemplative and rational thinking is often associated with ...
. Current theories describe three separate fundamental phenomena of which all other theories are approximations; the potential unification of these is sometimes called the
Theory of Everything A theory of everything (TOE or ToE), final theory, ultimate theory, or master theory is a hypothetical single, all-encompassing, coherent theoretical framework of physics that fully explains and links together all physical aspects of the univers ...
.


Example: Relativity

In 1905,
Albert Einstein Albert Einstein ( ; ; 14 March 1879 – 18 April 1955) was a German-born theoretical physicist, widely acknowledged to be one of the greatest physicists of all time. Einstein is known for developing the theory of relativity The theo ...

Albert Einstein
published the principle of
special relativity In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force ...
, which soon became a theory. Special relativity predicted the alignment of the Newtonian principle of
Galilean invariance Galilean invariance or Galilean relativity states that the laws of motion are the same in all inertial frame In classical physics Classical physics is a group of physics Physics (from grc, φυσική (ἐπιστήμη), physik ...
, also termed ''Galilean relativity'', with the electromagnetic field. By omitting from special relativity the
luminiferous aether Luminiferous aether or ether ("luminiferous", meaning "light-bearing") was the postulated medium Medium may refer to: Science and technology Aviation *Medium bomber, a class of war plane *Tecma Medium, a French hang glider design Communic ...
, Einstein stated that
time dilation In physics and Theory of relativity, relativity, time dilation is the difference in the elapsed Time in physics, time as measured by two clocks. It is either due to a relative velocity between them (special relativity, special relativistic "kine ...

time dilation
and
length contraction Length contraction is the phenomenon that a moving object's length is measured to be shorter than its proper length Proper length or rest length is the length of an object in the object's rest frame. The measurement of lengths is more compl ...
measured in an object in relative motion is
inertia Inertia is the resistance of any physical object Object may refer to: General meanings * Object (philosophy), a thing, being, or concept ** Entity, something that is tangible and within the grasp of the senses ** Object (abstract), an o ...

inertia
l—that is, the object exhibits constant
velocity The velocity of an object is the rate of change of its position with respect to a frame of reference In physics Physics is the that studies , its , its and behavior through , and the related entities of and . "Physical scie ...

velocity
, which is
speed In everyday use and in kinematics Kinematics is a subfield of physics, developed in classical mechanics, that describes the Motion (physics), motion of points, bodies (objects), and systems of bodies (groups of objects) without considerin ...
with
direction Direction may refer to: *Relative direction, for instance left, right, forward, backwards, up, and down ** Anatomical terms of location for those used in anatomy *Cardinal direction Mathematics and science *Direction vector, a unit vector that ...
, when measured by its observer. He thereby duplicated the
Lorentz transformation In physics, the Lorentz transformations are a six-parameter family of Linear transformation, linear coordinate transformation, transformations from a coordinate frame in spacetime to another frame that moves at a constant velocity relative to the ...

Lorentz transformation
and the
Lorentz contraction Lorentz is a name derived from the Roman surname, Laurentius, which means "from Laurentum". It is the German form of Laurence. Notable people with the name include: Given name * Lorentz Aspen (born 1978), Norwegian heavy metal pianist and keyb ...
that had been hypothesized to resolve experimental riddles and inserted into electrodynamic theory as dynamical consequences of the aether's properties. An elegant theory, special relativity yielded its own consequences, such as the equivalence of mass and energy transforming into one another and the resolution of the paradox that an excitation of the electromagnetic field could be viewed in one reference frame as electricity, but in another as magnetism. Einstein sought to generalize the invariance principle to all reference frames, whether inertial or accelerating. Rejecting Newtonian gravitation—a
central force In classical mechanics, a central force on an object is a force In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science t ...
acting instantly at a distance—Einstein presumed a gravitational field. In 1907, Einstein's
equivalence principle In the theory A theory is a rational Rationality is the quality or state of being rational – that is, being based on or agreeable to reason Reason is the capacity of consciously making sense of things, applying logic Logic (fr ...
implied that a free fall within a uniform gravitational field is equivalent to
inertial In classical physics and special relativity, an inertial frame of reference is a frame of reference that is not undergoing acceleration. In an inertial frame of reference, a physical object with zero net force acting on it moves with a constan ...

inertial
motion.Roberto Torretti, ''The Philosophy of Physics'' (Cambridge: Cambridge University Press, 1999)
pp. 289–90
By extending special relativity's effects into three dimensions,
general relativity General relativity, also known as the general theory of relativity, is the geometric Geometry (from the grc, γεωμετρία; '' geo-'' "earth", '' -metron'' "measurement") is, with arithmetic, one of the oldest branches of mathema ...
extended length contraction into space contraction, conceiving of 4D space-time as the gravitational field that alters geometrically and sets all local objects' pathways. Even massless energy exerts gravitational motion on local objects by "curving" the geometrical "surface" of 4D space-time. Yet unless the energy is vast, its relativistic effects of contracting space and slowing time are negligible when merely predicting motion. Although general relativity is embraced as the more explanatory theory via ''
scientific realism Scientific realism is the view that the universe described by science is real Real may refer to: * Reality Reality is the sum or aggregate of all that is real or existent within a system, as opposed to that which is only Object of the mind, ima ...
'', Newton's theory remains successful as merely a predictive theory via ''
instrumentalism In philosophy of science and in epistemology Epistemology (; ) is the Outline of philosophy, branch of philosophy concerned with knowledge. Epistemologists study the nature, origin, and scope of knowledge, epistemic Justification (epistemolog ...
''. To calculate trajectories, engineers and NASA still uses Newton's equations, which are simpler to operate.


Theories and laws

Both scientific laws and scientific theories are produced from the scientific method through the formation and testing of hypotheses, and can predict the behavior of the natural world. Both are typically well-supported by observations and/or experimental evidence. However, scientific laws are descriptive accounts of how nature will behave under certain conditions. Scientific theories are broader in scope, and give overarching explanations of how nature works and why it exhibits certain characteristics. Theories are supported by evidence from many different sources, and may contain one or several laws. A common misconception is that scientific theories are rudimentary ideas that will eventually graduate into scientific laws when enough data and evidence have been accumulated. A theory does not change into a scientific law with the accumulation of new or better evidence. A theory will always remain a theory; a law will always remain a law. Both theories and laws could potentially be falsified by countervailing evidence. Theories and laws are also distinct from
hypotheses A hypothesis (plural hypotheses) is a proposed explanation An explanation is a set of statements usually constructed to describe a set of facts which clarifies the causes, context Context may refer to: * Context (language use), the rel ...
. Unlike hypotheses, theories and laws may be simply referred to as
scientific fact A fact is an occurrence in the real world. The usual test for a statement of fact is verifiability—that is whether it can be demonstrated to correspond to experience Experience is the process through which conscious organisms Perception, pe ...
. However, in science, theories are different from facts even when they are well supported. For example,
evolution Evolution is change in the heritable Heredity, also called inheritance or biological inheritance, is the passing on of Phenotypic trait, traits from parents to their offspring; either through asexual reproduction or sexual reproduction, ...

evolution
is both a theory and a fact.


About theories


Theories as axioms

The
logical positivists Logical positivism, later called logical empiricism, and both of which together are also known as neopositivism, was a movement in Western philosophy Western philosophy refers to the philosophy, philosophical thought and work of the Western worl ...
thought of scientific theories as statements in a
formal language In logic, mathematics, computer science, and linguistics, a formal language consists of string (computer science), words whose symbol (formal), letters are taken from an alphabet (computer science), alphabet and are well-formedness, well-formed a ...
.
First-order logic First-order logic—also known as predicate logic, quantificational logic, and first-order predicate calculus—is a collection of formal system A formal system is an used for inferring theorems from axioms according to a set of rules. These rul ...
is an example of a formal language. The logical positivists envisaged a similar scientific language. In addition to scientific theories, the language also included observation sentences ("the sun rises in the east"), definitions, and mathematical statements. The phenomena explained by the theories, if they could not be directly observed by the senses (for example,
atom An atom is the smallest unit of ordinary matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can be touched are ultimately composed of ato ...

atom
s and
radio waves Radio waves are a type of electromagnetic radiation In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space ...

radio waves
), were treated as theoretical concepts. In this view, theories function as
axioms An axiom, postulate or assumption is a statement that is taken to be truth, true, to serve as a premise or starting point for further reasoning and arguments. The word comes from the Greek ''axíōma'' () 'that which is thought worthy or fit' or ...
: predicted observations are derived from the theories much like
theorems In mathematics Mathematics (from Ancient Greek, Greek: ) includes the study of such topics as quantity (number theory), mathematical structure, structure (algebra), space (geometry), and calculus, change (mathematical analysis, analysis). I ...
are derived in
Euclidean geometry Euclidean geometry is a mathematical system attributed to Alexandria Alexandria ( or ; ar, الإسكندرية ; arz, اسكندرية ; Coptic Coptic may refer to: Afro-Asia * Copts, an ethnoreligious group mainly in the area of modern ...
. However, the predictions are then tested against reality to verify the theories, and the "axioms" can be revised as a direct result. The phrase " the received view of theories" is used to describe this approach. Terms commonly associated with it are "
linguistic Linguistics is the scientific study of language A language is a structured system of communication Communication (from Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo ...
" (because theories are components of a language) and "
syntactic In linguistics Linguistics is the scientific study of language, meaning that it is a comprehensive, systematic, objective, and precise study of language. Linguistics encompasses the analysis of every aspect of language, as well as the ...
" (because a language has rules about how symbols can be strung together). Problems in defining this kind of language precisely, e.g., are objects seen in microscopes observed or are they theoretical objects, led to the effective demise of logical positivism in the 1970s.


Theories as models

The
semantic view of theoriesThe semantic view of theories is a position in the philosophy of science Philosophy of science is a branch of philosophy concerned with the foundations, methodology, methods, and implications of science. The central questions of this study conce ...
, which identifies scientific theories with models rather than
proposition In logic Logic is an interdisciplinary field which studies truth and reasoning Reason is the capacity of consciously making sense of things, applying logic Logic (from Ancient Greek, Greek: grc, wikt:λογική, λογική, lab ...
s, has replaced the received view as the dominant position in theory formulation in the philosophy of science. A model is a logical framework intended to represent reality (a "model of reality"), similar to the way that a map is a graphical model that represents the territory of a city or country. In this approach, theories are a specific category of models that fulfill the necessary criteria (see above). One can use language to describe a model; however, the theory is the model (or a collection of similar models), and not the description of the model. A model of the solar system, for example, might consist of abstract objects that represent the sun and the planets. These objects have associated properties, e.g., positions, velocities, and masses. The model parameters, e.g., Newton's Law of Gravitation, determine how the positions and velocities change with time. This model can then be tested to see whether it accurately predicts future observations; astronomers can verify that the positions of the model's objects over time match the actual positions of the planets. For most planets, the Newtonian model's predictions are accurate; for Mercury (planet), Mercury, it is slightly inaccurate and the model of
general relativity General relativity, also known as the general theory of relativity, is the geometric Geometry (from the grc, γεωμετρία; '' geo-'' "earth", '' -metron'' "measurement") is, with arithmetic, one of the oldest branches of mathema ...
must be used instead. The word "semantic" refers to the way that a model represents the real world. The representation (literally, "re-presentation") describes particular aspects of a phenomenon or the manner of interaction among a set of phenomena. For instance, a scale model of a house or of a solar system is clearly not an actual house or an actual solar system; the aspects of an actual house or an actual solar system represented in a scale model are, only in certain limited ways, representative of the actual entity. A scale model of a house is not a house; but to someone who wants to ''learn about'' houses, analogous to a scientist who wants to understand reality, a sufficiently detailed scale model may suffice.


Differences between theory and model

Several commentators have stated that the distinguishing characteristic of theories is that they are explanatory as well as descriptive, while models are only descriptive (although still predictive in a more limited sense). Philosopher Stephen Pepper also distinguished between theories and models, and said in 1948 that general models and theories are predicated on a "root" metaphor that constrains how scientists theorize and model a phenomenon and thus arrive at testable hypotheses. Engineering practice makes a distinction between "mathematical models" and "physical models"; the cost of fabricating a physical model can be minimized by first creating a mathematical model using a computer software package, such as a computer aided design tool. The component parts are each themselves modelled, and the fabrication tolerances are specified. An exploded view drawing is used to lay out the fabrication sequence. Simulation packages for displaying each of the subassemblies allow the parts to be rotated, magnified, in realistic detail. Software packages for creating the bill of materials for construction allows subcontractors to specialize in assembly processes, which spreads the cost of manufacturing machinery among multiple customers. See: Computer-aided engineering, Computer-aided manufacturing, and 3D printing


Assumptions in formulating theories

An assumption (or axiom) is a statement that is accepted without evidence. For example, assumptions can be used as premises in a logical argument. Isaac Asimov described assumptions as follows:
...it is incorrect to speak of an assumption as either true or false, since there is no way of proving it to be either (If there were, it would no longer be an assumption). It is better to consider assumptions as either useful or useless, depending on whether deductions made from them corresponded to reality...Since we must start somewhere, we must have assumptions, but at least let us have as few assumptions as possible.
Certain assumptions are necessary for all empirical claims (e.g. the assumption that reality exists). However, theories do not generally make assumptions in the conventional sense (statements accepted without evidence). While assumptions are often incorporated during the formation of new theories, these are either supported by evidence (such as from previously existing theories) or the evidence is produced in the course of validating the theory. This may be as simple as observing that the theory makes accurate predictions, which is evidence that any assumptions made at the outset are correct or approximately correct under the conditions tested. Conventional assumptions, without evidence, may be used if the theory is only intended to apply when the assumption is valid (or approximately valid). For example, the special theory of relativity assumes an inertial frame of reference. The theory makes accurate predictions when the assumption is valid, and does not make accurate predictions when the assumption is not valid. Such assumptions are often the point with which older theories are succeeded by new ones (the general theory of relativity works in non-inertial reference frames as well). The term "assumption" is actually broader than its standard use, etymologically speaking. The Oxford English Dictionary (OED) and online Wiktionary indicate its Latin source as ''assumere'' ("accept, to take to oneself, adopt, usurp"), which is a conjunction of ''ad-'' ("to, towards, at") and ''sumere'' (to take). The root survives, with shifted meanings, in the Italian ''assumere'' and Spanish ''sumir''. The first sense of "assume" in the OED is "to take unto (oneself), receive, accept, adopt". The term was originally employed in religious contexts as in "to receive up into heaven", especially "the reception of the Virgin Mary into heaven, with body preserved from corruption", (1297 CE) but it was also simply used to refer to "receive into association" or "adopt into partnership". Moreover, other senses of assumere included (i) "investing oneself with (an attribute)", (ii) "to undertake" (especially in Law), (iii) "to take to oneself in appearance only, to pretend to possess", and (iv) "to suppose a thing to be" (all senses from OED entry on "assume"; the OED entry for "assumption" is almost perfectly symmetrical in senses). Thus, "assumption" connotes other associations than the contemporary standard sense of "that which is assumed or taken for granted; a supposition, postulate" (only the 11th of 12 senses of "assumption", and the 10th of 11 senses of "assume").


Descriptions


From philosophers of science

Karl Popper described the characteristics of a scientific theory as follows:Karl Popper, Popper, Karl (1963), ''Conjectures and Refutations'', Routledge and Kegan Paul, London, UK. Reprinted in Theodore Schick (ed., 2000), ''Readings in the Philosophy of Science'', Mayfield Publishing Company, Mountain View, Calif. # It is easy to obtain confirmations, or verifications, for nearly every theory—if we look for confirmations. # Confirmations should count only if they are the result of risky predictions; that is to say, if, unenlightened by the theory in question, we should have expected an event which was incompatible with the theory—an event which would have refuted the theory. # Every "good" scientific theory is a prohibition: it forbids certain things to happen. The more a theory forbids, the better it is. # A theory which is not refutable by any conceivable event is non-scientific. Irrefutability is not a virtue of a theory (as people often think) but a vice. # Every genuine test of a theory is an attempt to falsify it, or to refute it. Testability is falsifiability; but there are degrees of testability: some theories are more testable, more exposed to refutation, than others; they take, as it were, greater risks. # Confirming evidence should not count except when it is the result of a genuine test of the theory; and this means that it can be presented as a serious but unsuccessful attempt to falsify the theory. (I now speak in such cases of "corroborating evidence".) # Some genuinely testable theories, when found to be false, might still be upheld by their admirers—for example by introducing post hoc (after the fact) som
auxiliary hypothesis
or assumption, or by reinterpreting the theory post hoc in such a way that it escapes refutation. Such a procedure is always possible, but it rescues the theory from refutation only at the price of destroying, or at least lowering, its scientific status, by tampering with evidence. The temptation to tamper can be minimized by first taking the time to write down the testing protocol before embarking on the scientific work. Popper summarized these statements by saying that the central criterion of the scientific status of a theory is its "falsifiability, or refutability, or testability". Echoing this, Stephen Hawking states, "A theory is a good theory if it satisfies two requirements: It must accurately describe a large class of observations on the basis of a model that contains only a few arbitrary elements, and it must make definite predictions about the results of future observations." He also discusses the "unprovable but falsifiable" nature of theories, which is a necessary consequence of inductive logic, and that "you can disprove a theory by finding even a single observation that disagrees with the predictions of the theory". Several philosophers and historians of science have, however, argued that Popper's definition of theory as a set of falsifiable statements is wrong because, as Philip Kitcher has pointed out, if one took a strictly Popperian view of "theory", observations of Uranus when first discovered in 1781 would have "falsified" Newton's celestial mechanics. Rather, people suggested that another planet influenced Uranus' orbit—and this prediction was indeed eventually confirmed. Kitcher agrees with Popper that "There is surely something right in the idea that a science can succeed only if it can fail."Philip Kitcher 1982 ''Abusing Science: The Case Against Creationism'', pp. 45–48. Cambridge: The MIT Press He also says that scientific theories include statements that cannot be falsified, and that good theories must also be creative. He insists we view scientific theories as an "elaborate collection of statements", some of which are not falsifiable, while others—those he calls "auxiliary hypotheses", are. According to Kitcher, good scientific theories must have three features: # Unity: "A science should be unified…. Good theories consist of just one problem-solving strategy, or a small family of problem-solving strategies, that can be applied to a wide range of problems." # Fecundity: "A great scientific theory, like Newton's, opens up new areas of research…. Because a theory presents a new way of looking at the world, it can lead us to ask new questions, and so to embark on new and fruitful lines of inquiry…. Typically, a flourishing science is incomplete. At any time, it raises more questions than it can currently answer. But incompleteness is not vice. On the contrary, incompleteness is the mother of fecundity…. A good theory should be productive; it should raise new questions and presume those questions can be answered without giving up its problem-solving strategies."
Auxiliary hypotheses
that are independently testable: "An auxiliary hypothesis ought to be testable independently of the particular problem it is introduced to solve, independently of the theory it is designed to save." (For example, the evidence for the existence of Neptune is independent of the anomalies in Uranus's orbit.) Like other definitions of theories, including Popper's, Kitcher makes it clear that a theory must include statements that have observational consequences. But, like the observation of irregularities in the orbit of Uranus, falsification is only one possible consequence of observation. The production of new hypotheses is another possible and equally important result.


Analogies and metaphors

The concept of a scientific theory has also been described using analogies and metaphors. For instance, the logical empiricist Carl Gustav Hempel likened the structure of a scientific theory to a "complex spatial network:"
Its terms are represented by the knots, while the threads connecting the latter correspond, in part, to the definitions and, in part, to the fundamental and derivative hypotheses included in the theory. The whole system floats, as it were, above the plane of observation and is anchored to it by the rules of interpretation. These might be viewed as strings which are not part of the network but link certain points of the latter with specific places in the plane of observation. By virtue of these interpretive connections, the network can function as a scientific theory: From certain observational data, we may ascend, via an interpretive string, to some point in the theoretical network, thence proceed, via definitions and hypotheses, to other points, from which another interpretive string permits a descent to the plane of observation.
Michael Polanyi made an analogy between a theory and a map:
A theory is something other than myself. It may be set out on paper as a system of rules, and it is the more truly a theory the more completely it can be put down in such terms. Mathematical theory reaches the highest perfection in this respect. But even a geographical map fully embodies in itself a set of strict rules for finding one's way through a region of otherwise uncharted experience. Indeed, all theory may be regarded as a kind of map extended over space and time.
A scientific theory can also be thought of as a book that captures the fundamental information about the world, a book that must be researched, written, and shared. In 1623, Galileo Galilei wrote:
Philosophy [i.e. physics] is written in this grand book—I mean the universe—which stands continually open to our gaze, but it cannot be understood unless one first learns to comprehend the language and interpret the characters in which it is written. It is written in the language of mathematics, and its characters are triangles, circles, and other geometrical figures, without which it is humanly impossible to understand a single word of it; without these, one is wandering around in a dark labyrinth.
The book metaphor could also be applied in the following passage, by the contemporary philosopher of science Ian Hacking:
I myself prefer an Argentine fantasy. God did not write a Book of Nature of the sort that the old Europeans imagined. He wrote a Borgesian library, each book of which is as brief as possible, yet each book of which is inconsistent with every other. No book is redundant. For every book there is some humanly accessible bit of Nature such that that book, and no other, makes possible the comprehension, prediction and influencing of what is going on…Leibniz said that God chose a world which maximized the variety of phenomena while choosing the simplest laws. Exactly so: but the best way to maximize phenomena and have simplest laws is to have the laws inconsistent with each other, each applying to this or that but none applying to all.


In physics

In physics, the term ''theory'' is generally used for a mathematical framework—derived from a small set of basic postulates (usually symmetries—like equality of locations in space or in time, or identity of electrons, etc.)—that is capable of producing experimental predictions for a given category of physical systems. A good example is classical electromagnetism, which encompasses results derived from gauge symmetry (sometimes called gauge invariance) in a form of a few equations called Maxwell's equations. The specific mathematical aspects of classical electromagnetic theory are termed "laws of electromagnetism," reflecting the level of consistent and reproducible evidence that supports them. Within electromagnetic theory generally, there are numerous hypotheses about how electromagnetism applies to specific situations. Many of these hypotheses are already considered to be adequately tested, with new ones always in the making and perhaps untested. An example of the latter might be the radiation reaction force. As of 2009, its effects on the periodic motion of charges are detectable in synchrotrons, but only as ''averaged'' effects over time. Some researchers are now considering experiments that could observe these effects at the instantaneous level (i.e. not averaged over time).


Examples

Note that many fields of inquiry do not have specific named theories, e.g. developmental biology. Scientific knowledge outside a named theory can still have a high level of certainty, depending on the amount of evidence supporting it. Also note that since theories draw evidence from many fields, the categorization is not absolute. * Biology:
cell theory In biology, cell theory is a scientific theory first formulated in the mid-nineteenth century, that living organisms are made up of Cell (biology), cells, that they are the basic structural/organizational unit of all organisms, and that all cells ...
, Evolution, theory of evolution (modern evolutionary synthesis), abiogenesis, Germ theory of disease, germ theory, particulate inheritance theory, dual inheritance theory, Young–Helmholtz theory, opponent process, cohesion-tension theory * Chemistry: collision theory, kinetic theory of gases, Lewis theory, Molecule, molecular theory, molecular orbital theory, transition state theory, valence bond theory * Physics:
atomic theory Atomic theory is the scientific theory A scientific theory is an explanation of an aspect of the that has been and verified in accordance with the , using accepted of , measurement, and evaluation of results. Where possible, theories are ...
, Big Bang, Big Bang theory, Dynamo theory, Perturbation theory (quantum mechanics), perturbation theory, theory of relativity (successor to classical mechanics), quantum field theory * Earth Science: Climate change theory (from climatology),Gilbert Plass, Plass, G.N., 1956, The Carbon Dioxide Theory of Climatic Change, ''Tellus A, Tellus'' VIII, 2. (1956), pp. 140–54. Plate tectonics, plate tectonics theory (from geology), theories of the origin of the Moon, theories for the Moon illusion * Astronomy: Nordtvedt effect, Self-gravitating system, Stellar evolution, nebular hypothesis, solar nebular model, stellar nucleosynthesis


Notes


References


Further reading

*, essay by British/American meteorologist and a NASA astronaut on anthopogenic global warming and "theory" {{philosophy of science Epistemology of science Scientific method Scientific theories, fr:Théorie#Sciences