In physics, a sign convention is a choice of the signs (plus or minus) of a set of quantities, in a case where the choice of sign is arbitrary. "Arbitrary" here means that the same physical system can be correctly described using different choices for the signs, as long as one set of definitions is used consistently. The choices made may differ between different authors. Disagreement about sign conventions is a frequent source of confusion, frustration, misunderstandings, and even outright errors. Physics (from the Greek, (phúsis), nature and (phusiké), knowledge of nature) is the science concerned with the discovery and understanding of the fundamental laws which govern matter, energy, space, and time. ... A negative number is a number that is less than zero, such as −3. ...

Sometimes, sign convention is used more broadly to include factors of i and 2π, rather than just choices of sign. In mathematics, the imaginary unit (sometimes also represented by the Latin or the Greek iota) allows the real number system to be extended to the complex number system . ... When a circles diameter is 1, its circumference is Ï€. The mathematical constant Ï€ is an irrational real number, approximately equal to 3. ...

Relativity

In relativity, the metric signature could either be +--- or -+++. The latter form is often called the Landau-Lifshitz (spacelike) sign convention. A similar dual convention is used in higher-dimensional relativistic theories. General relativity (GR) is the geometrical theory of gravitation published by Albert Einstein in 1915/16. ... The signature of a metric tensor (or more generally a nondegenerate symmetric bilinear form, thought of as quadratic form) is the number of positive and negative eigenvalues of the metric. ... Lev Davidovich Landau (Ле́в Дави́дович Ланда́у) (January 22, 1908 – April 1, 1968) was a prominent Soviet physicist and winner of the Nobel Prize for Physics whose broad field of work included the theory of superconductivity and superfluidity, quantum electrodynamics, nuclear physics and particle physics. ... Evgeny Mikhailovich Lifshitz (Евгений Михайлович Лифшиц) (February 21, 1915 – October 29, 1985) was a Russian physicist. ...

The Ricci tensor is defined as the contraction of the Riemann tensor. Some authors use the contraction , whereas others use the alternative . Due to the symmetries of the Riemann tensor, these two definitions differ by a minus sign. In differential geometry, the Ricci curvature tensor is (0,2)-valent tensor, obtained as a trace of the full curvature tensor. ... In differential geometry, the Riemann curvature tensor is the most standard way to express curvature of Riemannian manifolds, or more generally, any manifold with an affine connection, torsionless or with torsion. ... In differential geometry, the Riemann curvature tensor is the most standard way to express curvature of Riemannian manifolds, or more generally, any manifold with an affine connection, torsionless or with torsion. ...

In fact the second definition of the Ricci tensor is . The sign of the Ricci tensor does not change, because the two sign conventions concern the sign of the Riemann tensor. The second definition just compensates the sign and it works together with the second definition of the Riemann tensor (see e.g. Barrett O'Neill's Semi-riemannian geometry).

Regarding the choice of -+++ versus +---, a survey of some classic textbooks reveals that Misner, Thorne, & Wheeler chose -+++ while Weinberg chose +---. Subsequent authors writing in particle physics have generally followed Weinberg, while authors of papers in classical gravitation have generally followed MTW (as do most WP articles related to relativistic physics). // Books Popular Geroch, Robert (1981). ... For a non-technical introduction to the topic, please see Introduction to Special relativity. ...

Einstein's "ex cathedra" pronouncement

While in some sense this is a mere notational convention, the choice of the signature has always engendered considerable passion and even some degree of "controversy" (not entirely serious).

In an interview given on the campus of University of California, Berkeley, Wallace Givens (an applied mathematician who was active in the early development of computer science) recalled an incident from his experiences as a graduate student at Princeton University, circa 1955: The University of California, Berkeley (also known as UC Berkeley, Berkeley, Cal, and by other names, see below) is the oldest and flagship campus of the ten-campus University of California system. ... To meet Wikipedias quality standards, this article may require cleanup. ... Princeton University is a coeducational private university located in Princeton, New Jersey in the United States of America. ... 1955 (MCMLV) was a common year starting on Saturday of the Gregorian calendar. ...

Anyway, (Veblen) had been trying to persuade me that in the metric for general relativity the signature of the quadratic form was quite clearly three minuses and a plus rather than three pluses and a minus, just a change in sign because it's the foundation of the concept of causality and no other signature will do for that. It really should be called a causality metric rather than a gravitational metric, but after all it was done by a physicist instead of a logician or a mathematician. Anyhow, Veblen had been trying to persuade me that it made a difference which you used, three minuses and a plus, or its negative, three pluses and a minus. Well, he was much too good a mathematician in every respect to tell me authoritatively. That was not the nature of the relationship. Veblen wasn't that kind of a person. He didn't do that to graduate students, and he didn't do it to me. But he was not without guile. Oswald Veblen (24 June 1880 - 10 August 1960) was an American mathematician. ...

The occasion was that I was in my office waiting for the usual morning call to go into Veblen's office and talk. No one came. Veblen didn't knock, and I guess it was getting along towards lunch, so I thought I had better see what was going on. I stepped out my door and knocked on Veblen's door, and Veblen said come in and I went in. I saw what the difficulty was. He had been having a conversation with Einstein. Well, I'd met Einstein—his office was two or three doors down the hall—but I never knocked on Einstein's office because I had too much respect for his privacy and his time.

Anyway, on this occasion Veblen took the opportunity to fire a big gun on this little question of the signature. Well, both of us knew perfectly well what was going on. I don't know what the subject of the conversation with Einstein had been about. They both agreed that they were concluding it, and Einstein was about to leave. So Veblen said, "Professor Einstein, perhaps you'll decide ex cathedra a little question for us in regard to the signature of the metric." Well, Einstein laughed, quite a hearty laugh; he rumbled in laughter I think would be an appropriate way to describe it. He was flattered a little; he enjoyed it. He understood the question (and its phrasing!) and remarked quietly with some answer. This was more or less the end of the conversation and Einstein left, and I had a quiet, brief conversation with Veblen.

Now the story doesn't quite end there. Someone is supposed to ask which signature Einstein chose. Well, as a matter of fact, I don't remember, but the nature of the work at that time was of the following character. Einstein didn't give his reasons, so why did it matter which he said. That was the way things were done at Princeton in those days. Actually of course the question is easily answered by looking in Einstein's little book called Relativity, and I think it's three minuses and a plus. I think that's what he said, but I can't even be absolutely sure of that. But as I point out, I don't really think it matters very much. At least I wasn't convinced, even as a graduate student that it mattered very much.

Thermodynamics

The sign of work in the [[first law of thermodynaics]]. joijoi

Other conventions

• The choice of in the Dirac equation.
• The sign of the field strength tensor in gauge theories and classical electrodynamics.
• Time dependence of a positive-frequency wave:
  • (mainly used by physicists)
  • (mainly used by engineers)
• The signs of distances and radii of curvature of optical surfaces in optics

It is often considered good form to state explicitly which sign convention is to be used at the beginning of each book or article. In physics, the Dirac equation is a relativistic quantum mechanical wave equation formulated by British physicist Paul Dirac in 1928 and provides a description of elementary spin-½ particles, such as electrons, consistent with both the principles of quantum mechanics and the theory of special relativity. ... To meet Wikipedias quality standards, this article or section may require cleanup. ... In physics, gauge theories are a class of physical theories based on the idea that symmetry transformations can be performed locally as well as globally. ... In electromagnetics, Maxwells equations are a set of four equations, compiled by James Clerk Maxwell, that describe the behavior of both the electric and magnetic fields, as well as their interactions with matter. ... The term radius of curvature has specific meaning and sign convention in optical design. ... Table of Opticks, 1728 Cyclopaedia Optics ( appearance or look in ancient Greek) is a branch of physics that describes the behavior and properties of light and the interaction of light with matter. ...