Theoretical physics

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Visual representation of a Schwarzschild wormhole. Wormholes have never been observed, but they are predicted to exist through mathematical models and scientific theory.

Theoretical physics is a branch of physics that employs mathematical models and abstractions of physical objects and systems to rationalize, explain and predict natural phenomena. This is in contrast to experimental physics, which uses experimental tools to probe these phenomena.

The advancement of

mathematical rigour while giving little weight to experiments and observations.[a] For example, while developing special relativity, Albert Einstein was concerned with the Lorentz transformation which left Maxwell's equations invariant, but was apparently uninterested in the Michelson–Morley experiment on Earth's drift through a luminiferous aether.[1] Conversely, Einstein was awarded the Nobel Prize for explaining the photoelectric effect, previously an experimental result lacking a theoretical formulation.[2]

Overview

A physical theory is a model of physical events. It is judged by the extent to which its predictions agree with empirical observations. The quality of a physical theory is also judged on its ability to make new predictions which can be verified by new observations. A physical theory differs from a

mathematical theory, in the sense that the word "theory" has a different meaning in mathematical terms.[b]

The equations for an Einstein manifold, used in general relativity to describe the curvature of spacetime

A physical theory involves one or more relationships between various measurable quantities.

motions of unseen particles and the quantum mechanical idea that (action and) energy
are not continuously variable.

Theoretical physics consists of several different approaches. In this regard,

unify, formalise, reinterpret or generalise extant theories, or create completely new ones altogether.[e] Sometimes the vision provided by pure mathematical systems can provide clues to how a physical system might be modeled;[f] e.g., the notion, due to Riemann and others, that space itself might be curved. Theoretical problems that need computational investigation are often the concern of computational physics
.

Theoretical advances may consist in setting aside old, incorrect

Bohr complementarity principle
.

Relationship between mathematics and physics

Physical theories become accepted if they are able to make correct predictions and no (or few) incorrect ones. The theory should have, at least as a secondary objective, a certain economy and elegance (compare to mathematical beauty), a notion sometimes called "Occam's razor" after the 13th-century English philosopher William of Occam (or Ockham), in which the simpler of two theories that describe the same matter just as adequately is preferred (but conceptual simplicity may mean mathematical complexity).[10] They are also more likely to be accepted if they connect a wide range of phenomena. Testing the consequences of a theory is part of the scientific method.

Physical theories can be grouped into three categories: mainstream theories, proposed theories and fringe theories.

History

Theoretical physics began at least 2,300 years ago, under the

liberal arts of the Trivium like grammar, logic, and rhetoric and of the Quadrivium like arithmetic, geometry, music and astronomy. During the Middle Ages and Renaissance, the concept of experimental science, the counterpoint to theory, began with scholars such as Ibn al-Haytham and Francis Bacon. As the Scientific Revolution gathered pace, the concepts of matter, energy, space, time and causality slowly began to acquire the form we know today, and other sciences spun off from the rubric of natural philosophy. Thus began the modern era of theory with the Copernican paradigm shift in astronomy, soon followed by Johannes Kepler's expressions for planetary orbits, which summarized the meticulous observations of Tycho Brahe
; the works of these men (alongside Galileo's) can perhaps be considered to constitute the Scientific Revolution.

The great push toward the modern concept of explanation started with

experimentalist. The analytic geometry and mechanics of Descartes were incorporated into the calculus and mechanics of Isaac Newton, another theoretician/experimentalist of the highest order, writing Principia Mathematica.[11] In it contained a grand synthesis of the work of Copernicus, Galileo and Kepler; as well as Newton's theories of mechanics and gravitation, which held sway as worldviews until the early 20th century. Simultaneously, progress was also made in optics (in particular colour theory and the ancient science of geometrical optics), courtesy of Newton, Descartes and the Dutchmen Snell and Huygens. In the 18th and 19th centuries Joseph-Louis Lagrange, Leonhard Euler and William Rowan Hamilton would extend the theory of classical mechanics considerably.[12] They picked up the interactive intertwining of mathematics and physics
begun two millennia earlier by Pythagoras.

Among the great conceptual achievements of the 19th and 20th centuries were the consolidation of the idea of

electromagnetic theory
, unifying the previously separate phenomena of electricity, magnetism and light.

The pillars of

.

All of these achievements depended on the theoretical physics as a moving force both to suggest experiments and to consolidate results — often by ingenious application of existing mathematics, or, as in the case of Descartes and Newton (with

Leibniz), by inventing new mathematics. Fourier's studies of heat conduction led to a new branch of mathematics: infinite, orthogonal series.[13]

Modern theoretical physics attempts to unify theories and explain phenomena in further attempts to understand the Universe, from the cosmological to the elementary particle scale. Where experimentation cannot be done, theoretical physics still tries to advance through the use of mathematical models.

Mainstream theories

Mainstream theories (sometimes referred to as central theories) are the body of knowledge of both factual and scientific views and possess a usual scientific quality of the tests of repeatability, consistency with existing well-established science and experimentation. There do exist mainstream theories that are generally accepted theories based solely upon their effects explaining a wide variety of data, although the detection, explanation, and possible composition are subjects of debate.

Examples

Proposed theories

The proposed theories of physics are usually relatively new theories which deal with the study of physics which include scientific approaches, means for determining the validity of models and new types of reasoning used to arrive at the theory. However, some proposed theories include theories that have been around for decades and have eluded methods of discovery and testing. Proposed theories can include fringe theories in the process of becoming established (and, sometimes, gaining wider acceptance). Proposed theories usually have not been tested. In addition to the theories like those listed below, there are also different interpretations of quantum mechanics, which may or may not be considered different theories since it is debatable whether they yield different predictions for physical experiments, even in principle. For example, AdS/CFT correspondence, Chern–Simons theory, graviton, magnetic monopole, string theory, theory of everything.


Fringe theories

Fringe theories include any new area of scientific endeavor in the process of becoming established and some proposed theories. It can include speculative sciences. This includes physics fields and physical theories presented in accordance with known evidence, and a body of associated predictions have been made according to that theory.

Some fringe theories go on to become a widely accepted part of physics. Other fringe theories end up being disproven. Some fringe theories are a form of protoscience and others are a form of pseudoscience. The falsification of the original theory sometimes leads to reformulation of the theory.

Examples

Thought experiments vs real experiments

"Thought" experiments are situations created in one's mind, asking a question akin to "suppose you are in this situation, assuming such is true, what would follow?". They are usually created to investigate phenomena that are not readily experienced in every-day situations. Famous examples of such thought experiments are

tested to various degrees of rigor, leading to the acceptance of the current formulation of quantum mechanics and probabilism as a working hypothesis
.

See also

Notes

  1. ^ There is some debate as to whether or not theoretical physics uses mathematics to build intuition and illustrativeness to extract physical insight (especially when normal experience fails), rather than as a tool in formalizing theories. This links to the question of it using mathematics in a less formally rigorous, and more intuitive or heuristic way than, say, mathematical physics.
  2. ^ Sometimes the word "theory" can be used ambiguously in this sense, not to describe scientific theories, but research (sub)fields and programmes. Examples: relativity theory, quantum field theory, string theory.
  3. Johann Balmer and Johannes Rydberg in spectroscopy, and the semi-empirical mass formula
    of nuclear physics are good candidates for examples of this approach.
  4. Ptolemaic and Copernican models of the Solar system, the Bohr model of hydrogen atoms and nuclear shell model
    are good candidates for examples of this approach.
  5. ^ Arguably these are the most celebrated theories in physics: Newton's theory of gravitation, Einstein's theory of relativity and Maxwell's theory of electromagnetism share some of these attributes.
  6. ^ This approach is often favoured by (pure) mathematicians and mathematical physicists.

References

  1. .
  2. ^ "The Nobel Prize in Physics 1921". The Nobel Foundation. Retrieved 2008-10-09.
  3. ^ Theorems and Theories Archived 2014-08-19 at the Wayback Machine, Sam Nelson.
  4. ^ Mark C. Chu-Carroll, March 13, 2007:Theorems, Lemmas, and Corollaries.[permanent dead link] Good Math, Bad Math blog.
  5. ^ Bokulich, Alisa, "Bohr's Correspondence Principle", The Stanford Encyclopedia of Philosophy (Spring 2014 Edition), Edward N. Zalta (ed.)
  6. ^ Enc. Britannica (1994), pg 844.
  7. ^ Enc. Britannica (1994), pg 834.
  8. ^ Simplicity in the Philosophy of Science (retrieved 19 Aug 2014), Internet Encyclopedia of Philosophy.
  9. ^ See 'Correspondence of Isaac Newton, vol.2, 1676–1687' ed. H W Turnbull, Cambridge University Press 1960; at page 297, document #235, letter from Hooke to Newton dated 24 November 1679.
  10. ^ Penrose, R (2004). The Road to Reality. Jonathan Cape. p. 471.
  11. ^ Penrose, R (2004). "9: Fourier decompositions and hyperfunctions". The Road to Reality. Jonathan Cape.

Further reading

  • Physical Sciences. Vol. 25 (15th ed.). 1994. {{cite book}}: |work= ignored (help)
  • Duhem, Pierre. La théorie physique - Son objet, sa structure, (in French). 2nd edition - 1914. English translation: The physical theory - its purpose, its structure. Republished by .
  • Feynman, et al. The Feynman Lectures on Physics (3 vol.). First edition: Addison–Wesley, (1964, 1966).
Bestselling three-volume textbook covering the span of physics. Reference for both (under)graduate student and professional researcher alike.
Famous series of books dealing with theoretical concepts in physics covering 10 volumes, translated into many languages and reprinted over many editions. Often known simply as "Landau and Lifschits" or "Landau-Lifschits" in the literature.
A set of lectures given in 1909 at Columbia University.
A series of lessons from a master educator of theoretical physicists.

External links