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Concept
Sign convention
Summary
In physics, a sign convention is a choice of the physical significance of signs (plus or minus) for 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 authors. Disagreement about sign conventions is a frequent source of confusion, frustration, misunderstandings, and even outright errors in scientific work. In general, a sign convention is a special case of a choice of coordinate system for the case of one dimension.
Sometimes, the term "sign convention" is used more broadly to include factors of i and 2π, rather than just choices of sign.
In relativity, the metric signature can be either (+,−,−,−) or (−,+,+,+). (Note that throughout this article we are displaying the signs of the eigenvalues of the metric in the order that presents the timelike component first, followed by the spacelike components). A similar convention is used in higher-dimensional relativistic theories; that is, (+,−,−,−,...) or (−,+,+,+,...). A choice of signature is associated with a variety of names:
(+,−,−,−):
Timelike convention
Particle physics convention
West coast convention
Mostly minuses
Landau–Lifshitz sign convention.
(−,+,+,+):
Spacelike convention
Relativity convention
East coast convention
Mostly pluses
Pauli convention
Cataloged below are the choices of various authors of some graduate textbooks:
(+,−,−,−):
Landau & Lifshitz
Gravitation: an introduction to current research (L. Witten)
Ray D'Inverno, Introducing Einstein's relativity.
(−,+,+,+):
Misner, Thorne and Wheeler
Spacetime and Geometry: An Introduction to General Relativity (Sean M. Carroll)
General Relativity (Wald) (Note that Wald changes signature to the timelike convention for Chapter 13 only.)
The signature (+,−,−,−) corresponds to the metric tensor:
and gives m^2 = p^μp_μ as the relationship between mass and four momentum
whereas the signature (−,+,+,+) corresponds to:
and gives m^2 = −p^μp_μ.
Official source
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