Μετρική Υπογραφή
Metric signature, Causal structure

Μετρική Minkowski


Δαλαβερτιανή (Dalabertian)

Στην Σχετικότητα του Μακρόκοσμου
η υπογραφή της Μετρικής
είναι + + + -
οπότε
η Μετρική γράφεται έτσι:
ds² = dx² + dy² + dz² - c²dt²
Όμως
στην Πεδιακή Κβαντική Θεωρία του Μικρόκοσμου
η υπογραφή της Μετρικής
είναι + - - -
οπότε
η Μετρική γράφεται έτσι:
ds² = c²dt² - dx² - dy² - dz²








- Μία διαδικασία.
Ετυμολογία[]
Η ονομασία "Υπογραφή" σχετίζεται ετυμολογικά με την λέξη "γραφή".
Εισαγωγή[]
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.
Relativity[]
Metric signature[]
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 mΠρότυπο:Sup = pΠρότυπο:IsuppΠρότυπο:Sub as the relationship between mass and four momentum
whereas the signature (−,+,+,+) corresponds to:
and gives mΠρότυπο:Sup = −pΠρότυπο:IsuppΠρότυπο:Sub.
Curvature[]
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 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).
Other sign conventions[]
- The sign choice for time in frames of reference and proper time: + for future and − for past is universally accepted.
- The choice of in the Dirac equation.
- The sign of the electric charge, field strength tensor in gauge theories and classical electrodynamics.
- Time dependence of a positive-frequency wave (see, e.g., the electromagnetic wave equation):
- (mainly used by physicists)
- (mainly used by engineers)
- The sign for the imaginary part of permittivity (in fact dictated by the choice of sign for time-dependence).
- The signs of distances and radii of curvature of optical surfaces in optics.
- The sign of work in the first law of thermodynamics.
- The sign of the weight of a tensor density, such as the weight of the determinant of the covariant metric tensor.
- The active and passive sign convention of current, voltage and power in electrical engineering.
- A sign convention used for curved mirrors assigns a positive focal length to concave mirrors and a negative focal length to convex mirrors.
It is often considered good form to state explicitly which sign convention is to be used at the beginning of each book or article.
Spacelike, Lightlike, and Timelike Intervals[]
Another absolute quantity in special relativity is the spacetime interval between two events, which is defined as follows:
spacetime interval = d2 – c2t2
where d is the distance between the events (according to a given reference frame),
t is the time between the events (in that frame),
and c is the speed of light.
Remarkably, all inertial reference frames agree about this quantity, even though they disagree about distance d and time t.
The spacetime interval indicates how two events are related to each other in space and time.
It can be positive (spacelike), negative (timelike), or zero (lightlike):
1) Spacelike intervals: If the spacetime interval is positive, this means you’d have to travel faster than the speed of light to get from one event to the other. As we’ll see, reference frames may disagree about the order in which these events occurred. (In other words, one observer may think event A happened first, while another observer thinks event B happened first, and yet another may think the two events were simultaneous. And according to Einstein, there’s no fact of the matter who’s right!) But all reference frames will agree that the events occurred at different locations, hence the events are said to have spacelike separation.
2)Timelike intervals: If the spacetime interval is negative, this means it’s possible to get from one event to the other traveling slower than the speed of light. Reference frames may disagree about whether these events happened at the same location. But all reference frames will agree that the events occurred at different times, and they’ll also agree about the order in which these events occurred, hence the events are said to have timelike separation.
3) Lightlike intervals: If the spacetime interval is zero, this means a beam of light could travel directly from one event to the other. All reference frames will agree that the two events are lightlike separated, and they’ll also agree about the order in which these events occurred. Events are said to have lightlike separation when they are related in this way.
In the special theory of relativity, the distances and times between events are relative matters, depending on the observer’s frame of reference. However, the spacetime interval between two events is the same for all inertially moving (non-accelerated) observers: it is an absolute quantity. In other words, whether two events have timelike, lightlike, or spacelike separation is an absolute matter, independent of the observer’s reference frame.
Υποσημειώσεις[]
Εσωτερική Αρθρογραφία[]
- Μετρικός Τανυστής Minkowski
- Μετρικός Τανυστής
- Μετρική Συνάρτηση
- Orientation (vector space), also known as "handedness"
- Symmetry (physics)
- Gauge theory
Βιβλιογραφία[]
Ιστογραφία[]
- Ομώνυμο άρθρο στην Βικιπαίδεια
- Ομώνυμο άρθρο στην Livepedia
- Conversion of Notations from ( -1, +1, +1, +1 ) to ( +1, -1, -1, -1 ) versions, biglobe.ne.jp
- [ ]
![]() ![]() |
---|
Αν και θα βρείτε εξακριβωμένες πληροφορίες "Οι πληροφορίες αυτές μπορεί πρόσφατα Πρέπει να λάβετε υπ' όψη ότι Επίσης, |
- Μην κάνετε χρήση του περιεχομένου της παρούσας εγκυκλοπαίδειας
αν διαφωνείτε με όσα αναγράφονται σε αυτήν
- Όχι, στις διαφημίσεις που περιέχουν απαράδεκτο περιεχόμενο (άσεμνες εικόνες, ροζ αγγελίες κλπ.)