Wikipedia - Scientific Theory
In scientific usage, a theory does not mean an unsubstantiated guess or hunch, as it often does in other contexts. A theory is a logically self-consistent model or framework for describing the behavior of a related set of natural or social phenomena. It originates from and/or is supported by experimental evidence (see scientific method). In this sense, a theory is a systematic and formalized expression of all previous observations that is predictive, logical and testable. In principle, scientific theories are always tentative, and subject to corrections or inclusion in a yet wider theory. Commonly, a large number of more specific hypotheses may be logically bound together by just one or two theories. As a general rule for use of the term, theories tend to deal with much broader sets of universals than do hypotheses, which ordinarily deal with much more specific sets of phenomena or specific applications of a theory.
The term theoretical is sometimes used to describe a result that is predicted by theory but has not yet been adequately tested by observation or experiment. It is not uncommon for a theory to produce predictions that are later confirmed by experiment. If enough experiments and observations are made by many researchers, such a theory may become sufficiently well-tested to be considered so reliable that its premises may after that stage be termed scientific laws in the sense of being a generalizations based on empirical observations (not to be confused with laws which prescribe how the world should be). Depending on the context, an extremely well-tested theory may allow the terms "theory" and "law" to be used interchangeably without any objection by experts familiar with the current state of the research. In the example given below, electromagnetic theory as a whole is today sufficiently investigated that it is often referred to simply as "electromagnetism". Newton's theory of gravity is today normally referred to as the "law of gravity" as it provides a generalization useful for many practical purposes, but beyond certain limits the more accurate general relativity theory must be used. Because it is has given consistently correct predictions despite intense testing, the theory of relativity today is often simply referred to as "relativity." As another example, until recently black holes were considered theoretical. Failed predictions also occur, however, and sometimes work to falsify a theory. Conversely, at any time, confirmed experimental results may exist that are not yet explained by theory.
In physics, the term theory is generally used for a mathematical framework — derived from a small set of basic principles (usually symmetries - like equality of locations in space or in time, or identity of electrons, etc) — which is capable of producing experimental predictions for a given category of physical systems. A good example is electromagnetic theory, which encompasses the results that can be derived from gauge symmetry (sometimes called gauge invariance) in a form of a few equations called Maxwell's equations. Another name for this theory is classical electromagnetism. Note that the specific theoretical aspects of classical electromagnetic theory, which have been consistently and successfully replicated for well over a century, are termed "laws of electromagnetism", reflecting the fact that they are today taken as granted. 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 as yet.
The term theory is occasionally stretched to refer to theoretical speculation that is currently unverifiable. Examples are string theory and various theories of everything. In common speech, theory has a far wider and less defined meaning than its use in the sciences.
Wikipedia - Physical/Scientific Law
A physical law, scientific law, or a law of nature is a scientific generalization based on empirical observations of physical behavior. They are typically conclusions based on repeated scientific experiments over many years, and which have become accepted universally within the scientific community...
Several general properties of physical laws have been identified (see Davies (1992) and Feynman (1965) as noted, although each of the characterizations is not necessarily original to them). Physical laws are:
True (a.k.a. valid). By definition, there have never been repeatable contradicting observations.
Universal. They appear to apply everywhere in the universe. (Davies)
Simple. They are typically expressed in terms of a single mathematical equation. (Davies)
Absolute. Nothing in the universe appears to affect them. (Davies)
Stable. Unchanged since first discovered (although they may have been shown to be approximations of more accurate laws—see "Laws as approximations" below),
Eternal. they appear unchanged since the beginning of the universe (according to observations). It is thus presumed that they will remain unchanged in the future. (Davies)
Omnipotent. Everything in the universe apparently must comply with them (according to observations). (Davies)
Generally conservative of quantity. (Feynman)
Often expressions of existing homogeneities (symmetries) of space and time. (Feynman)
Typically theoretically reversible in time (if non-quantum), although time itself is irreversible. (Feynman)
Often, those who understand the mathematics and concepts well enough to understand the essence of the physical laws also feel that they possess an inherent intellectual beauty. Many scientists state that they use intuition as a guide in developing hypotheses, since laws are reflection of symmetries and there is a connection between beauty and symmetry. However, this has not always been the case; Newton himself justified his belief in the asymmetry of the universe because his laws appeared to imply it.
Physical laws are distinguished from scientific theories by their simplicity. Scientific theories are generally more complex than laws; they have many component parts, and are more likely to be changed as the body of available experimental data and analysis develops. This is because a physical law is a summary observation of strictly empirical matters, whereas a theory is a model that accounts for the observation, explains it, relates it to other observations, and makes testable predictions based upon it. Simply stated, while a law notes that something happens, a theory explains why and how something happens.
Wikipedia - Scientific Hypothesis
A scientific hypothesis is a hypothesis (a testable conjecture) that has not been tested by the prediction validation process for a scientific theory.
Theories can become accepted if they are able to make correct predictions and avoid incorrect ones. Theories which are simpler, and more mathematically elegant, tend to be accepted over theories which are complex. Theories are more likely to be accepted if they connect a wide range of phenonomena. The process of accepting theories is part of the scientific method.
Add any other clarifications (on specific laws or theories for example) that you feel should be available for easy reference.
