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Importance to math students: One of the first steps on graduate level. Importance in General: Between important fill & specialized knowledge (mid/lowmid) Two References have been added. The corresponding german wikipage has a non-english link. Maybe a link to Wolfram would be better
Phi0618 ( talk) 17:55, 21 November 2007 (UTC)
The first sentence gets it backwards: it is gradient which is the more general concept. We take gradient, retrict it to four dimensions and space-time metric and only then get the usual four-gradient used in physics. — Preceding unsigned comment added by 149.156.47.235 ( talk) 13:00, 7 September 2012 (UTC)
As there seems to be some doubt about this, here are four works plucked from Google books which use and for the 4-gradient and d'Alembertian respectively.
Admittedly these authors do seem to be in a minority. -- catslash ( talk) 12:49, 23 February 2010 (UTC)
This also goes against the notation I've seen elsewhere in Wikipedia (e.g. D'Alembert operator, Klein-Gordon equation). It seems to me we should add a parenthetical to clarify this. What do you think? Gneisss ( talk) 15:52, 25 July 2016 (UTC)
There seems to be a bit more notational difference in the use of 4-vectors than in a lot of other physics. I will simply add the same note here that is in the article... It applies to the use of the box symbol as well.
Regarding the use of scalars, 4-vectors and tensors in physics, various authors use slightly different notations for the same equations. For instance, some use for invariant rest mass, others use for invariant rest mass and use for relativistic mass. Many authors set factors of and and to dimensionless unity. Others show some or all the constants. Some authors use for velocity, others use . Some use as a 4-wavevector (to pick an arbitrary example). Others use or or or or or , etc. Some write the 4-wavevector as , some as or or or or or . Some will make sure that the dimensional units match across the 4-vector, others don't. Some refer to the temporal component in the 4-vector name, others refer to the spatial component in the 4-vector name. Some mix it throughout the book, sometimes using one then later on the other. Some use the metric (+---), others use the metric (-+++). Some don't use 4-vectors, but do everything as the old style E and 3-vector p. The thing is, all of these are just notational styles, with some more clear and concise than the others. The physics is the same as long as one uses a consistent style throughout the whole derivation. 208.104.19.227 ( talk) 15:57, 1 August 2016 (UTC)
There are several references in the article to the use of the "gradient" in QM. IMO, this (a) is completely out of place in an article that is intrinsically about a classical operator, and (b) is making a leap based on the similarity of notation, but in QM it is not appropriate to call it a gradient operator, as it operates on a (wave)function that is not a scalar function of the point in spacetime. Aside from the WP:OR aspects. I'm not likely to engage much here (if I did, I would delete it all, considering my opinion), but I thought I'd bring some attention to this. — Quondum 01:42, 5 August 2017 (UTC)
References
Something is amiss. I found a website claiming that although is allowed, isn't and in principle, one is actually using a covariant derivative in Minkowski space. Some precision or clarification on that issue would be helpful. TonyMath ( talk) 15:17, 11 July 2015 (UTC)
208.104.19.227 ( talk) 15:32, 2 August 2016 (UTC)
This article is rated C-class on Wikipedia's
content assessment scale. It is of interest to the following WikiProjects: | ||||||||||||||
|
Importance to math students: One of the first steps on graduate level. Importance in General: Between important fill & specialized knowledge (mid/lowmid) Two References have been added. The corresponding german wikipage has a non-english link. Maybe a link to Wolfram would be better
Phi0618 ( talk) 17:55, 21 November 2007 (UTC)
The first sentence gets it backwards: it is gradient which is the more general concept. We take gradient, retrict it to four dimensions and space-time metric and only then get the usual four-gradient used in physics. — Preceding unsigned comment added by 149.156.47.235 ( talk) 13:00, 7 September 2012 (UTC)
As there seems to be some doubt about this, here are four works plucked from Google books which use and for the 4-gradient and d'Alembertian respectively.
Admittedly these authors do seem to be in a minority. -- catslash ( talk) 12:49, 23 February 2010 (UTC)
This also goes against the notation I've seen elsewhere in Wikipedia (e.g. D'Alembert operator, Klein-Gordon equation). It seems to me we should add a parenthetical to clarify this. What do you think? Gneisss ( talk) 15:52, 25 July 2016 (UTC)
There seems to be a bit more notational difference in the use of 4-vectors than in a lot of other physics. I will simply add the same note here that is in the article... It applies to the use of the box symbol as well.
Regarding the use of scalars, 4-vectors and tensors in physics, various authors use slightly different notations for the same equations. For instance, some use for invariant rest mass, others use for invariant rest mass and use for relativistic mass. Many authors set factors of and and to dimensionless unity. Others show some or all the constants. Some authors use for velocity, others use . Some use as a 4-wavevector (to pick an arbitrary example). Others use or or or or or , etc. Some write the 4-wavevector as , some as or or or or or . Some will make sure that the dimensional units match across the 4-vector, others don't. Some refer to the temporal component in the 4-vector name, others refer to the spatial component in the 4-vector name. Some mix it throughout the book, sometimes using one then later on the other. Some use the metric (+---), others use the metric (-+++). Some don't use 4-vectors, but do everything as the old style E and 3-vector p. The thing is, all of these are just notational styles, with some more clear and concise than the others. The physics is the same as long as one uses a consistent style throughout the whole derivation. 208.104.19.227 ( talk) 15:57, 1 August 2016 (UTC)
There are several references in the article to the use of the "gradient" in QM. IMO, this (a) is completely out of place in an article that is intrinsically about a classical operator, and (b) is making a leap based on the similarity of notation, but in QM it is not appropriate to call it a gradient operator, as it operates on a (wave)function that is not a scalar function of the point in spacetime. Aside from the WP:OR aspects. I'm not likely to engage much here (if I did, I would delete it all, considering my opinion), but I thought I'd bring some attention to this. — Quondum 01:42, 5 August 2017 (UTC)
References
Something is amiss. I found a website claiming that although is allowed, isn't and in principle, one is actually using a covariant derivative in Minkowski space. Some precision or clarification on that issue would be helpful. TonyMath ( talk) 15:17, 11 July 2015 (UTC)
208.104.19.227 ( talk) 15:32, 2 August 2016 (UTC)