Talk:Quadrupole

Unclear terms

I would like to ask for some clarification on this article, particularly the mathematical formulas. Most of the variables are left undefined as far as what they are representing. In particular, the first equation given is extremely unclear. I can deduce that the Q_ij is the moment, that q_n is the individual charge and that r is the distance between two charges (charges i and j perhaps?), but what is the delta, the x_i, and the x_j? Thank you! 84.37.22.14 (talk) 07:49, 20 June 2008 (UTC)

I changed the notation and added more explicit definition of the terms for the first two equations. Best regards, DeMk9D76 (talk) 19:07, 8 May 2012 (UTC)

Whoops still!

Also regarding the section on quadrupoles in gravitation, I'm no expert, but I find it confusing how a rod, or a rod containing two lead balls on its ends, is considered a quadrupole rather than a dipole. I can imagine that each sphere might have two poles, but elsewhere it says the flattened-at-the-poles earth is, by itself, a quadrupole. If a sphere is a monopole, and a dumbbell is a quadrupole, what's a dipole? hkyriazi 04:52, 21 February 2007 (UTC) (forgot to sign this yesterday when I first posted it...)

Ah, I see now that I missed the mention that mass is always positive, and so massive objects cannot have a gravitational dipole. But then what does it mean for a massive object to have any pole at all? Is gravity now thought to be anisotropic in some way? hkyriazi 04:52, 21 February 2007 (UTC)

Whoops!

There are some errors in section on quadrupoles in gravitation. First, moments are taken relative to some point. Second, the vanishing of dipole moment is not described correctly; this really arises from conservation of linear momentum. Third, in general relativity, the quadrupole radiation formula derived by Albert Einstein says that systems with time varying quadrupole moments produce radiation. A disk which is spinning with constant angular velocity (about the axis of symmetry) has a nonzero but constant quadrupole moment, so it produces no quadrupole radiation. On the other hand, a rod which is spinning with constant angular velocity (about an axis orthogonal to the axis of symmetry) does have a time varying quadrupole moment, and it does produce quadrupole radiation.---CH (talk) 00:24, 11 July 2005 (UTC)

Salsb and everyone else

Your hot on this page! And do have fun! Whatever you do please don't mess up my Quad pic! LOL

Thanks Scott 20:53:59, 2005-09-09 (UTC)

Yeah, great work on this everyone! This article's been on my User:Laurascudder/To do forever (of course that list has a pathetic turnover rate). I think this could perhaps use a seperate mathematical formalism section at the end, which could include the formula in the intro along with perhaps a few ways of defining the quadrupole moment. It's a topic that could have a wide audience, so some I was thinking more math wouldn't be unwelcome, but might be a bit much at the start. What do you think?

If I recall correctly the "contested observation" of the magnetic monopole was from a researcher who set up the experiment on a back table just for kicks and let it run all the time. After a seriously long runtime he got one count, which doesn't mean he actually found one. It has of course not been reproduced, so a good cut. — Laura Scudder | Talk 06:45, 15 September 2005 (UTC)

This is my recollection as well, and since there wasn't a citation to anyone else, I figured it should get cut. I think this article still needs work, but we're making progress. cheers Salsb 11:40, 15 September 2005 (UTC)

---

It was not a honky-tonk experiment, and there are followups. See [1]. Blas Cabrera at Stanford got the one positive result. The issue is of some importance, I have read, because the existence of one (1) magnetic monopole, it is said, will quantize all electric charges. As to how many one expects - the inflationary cosmology people have ways to wipe out most of them. Since experiments are still in progress, it may be worth keeping some discussion.Pdn 18:27, 15 September 2005 (UTC)

I went and found the citation, which is PRL 48 (20). p1378-1382 (1982), and my recollection was correct. To further quote from the link you provided "

Cabrera's device never spotted another monopole. His group has built second- and third-generation detectors, the last of which was thousands of times more sensitive than the original. But they came up empty-handed. "We never again saw an event like this one in any of the individual instruments," he says. "It seemed less and less likely that the one event we saw was a monopole."" and " In the early 1990s, Cabrera switched to seeking other particles..." There was a nice review of the status of magnetic monopoles in 2002 in the International Journal of Modern Physics A vol 17 p732-747, and it also appears that the accelerator experiments stopped in the mid 1990's, although there is still some theoretical work ongoing. This should probably go into an article on magnetic monopoles, but I thinks it good not to appear here as the status, for now, is highly unlikly to exist. Salsb 18:57, 15 September 2005 (UTC)

R0

For calculating the nuclear quadrupole moment. I can't find the value of this anywhere - not in text books, not constants pages.. It is a constant right? 1.3E-15 ? if this is what i think it is, it might be useful to have this on here. Rog 12:10, 25 January 2006 (UTC)

The nuclear quadrupole moment is not a constant. It depends on the individual atoms and isotopes. —Preceding unsigned comment added by 141.5.13.135 (talk) 15:14, 11 March 2009 (UTC)

Clarity of introduction

Guys, the introduction of this article is not clear to someone who is not familiar with the field. For example, compare the other entries on Google:define. I am not an expert, and I do not know if they are completely accurate. But I'm sure that it is possible to write an equally (or more) clear and concise yet accurate introduction (definition). Ideally, it should be no longer than a couple of sentences. -Pgan002 02:54, 9 June 2006 (UTC)

Article title

Is the article about quadrupoles or rather about multipoles? If "quadr" is part of the word, I strongly suspect that a quadrupole has something to do with "four". Yet "four" is mentioned only once in passing, towards the bottom of the article. It seems that the article needs be renamed. -Pgan002 03:00, 9 June 2006 (UTC)

not a very good description

This page only mentions the electric quadrupole as part of the multipole expasion-this can be found on the multipole expansion page. How is it derived? what are some of its properties? just some thoughts.

I seem to remember that the multipole expansion is derived by Laurent expanding $V(\mathbf {r} )=-{\frac {1}{4\pi \epsilon _{0}}}\sum _{i}{\frac {q_{i}}{|\mathbf {r_{i}} -\mathbf {r} |}}$ and then identifying various bits as the multipole. The derivation is more messy than enlightening, something to really only be done once in one's career, but can be found in J. D. Jackson. — Laura Scudder ☎ 16:33, 8 June 2007 (UTC)

Gravitational multipoles

What is written in the section is essentially correct. -- 213.140.18.136 11:01, 28 September 2007 (UTC)

Effect on the Moon orbit

The article says that the quadrupole from the flattened Earth is less important for distand satellites like the Moon. Hovewer, I've found out that there is indeed an important effect if precise ephemeris calculation is desired. From the JPL's Horizon project the precise positions and velocities of all known solar system bodies can be retrieved for any time between -3000 and 3000 AD. I retrieved the dates for 2000 and 2020 and did an N-body calculation (with all 8 planets, Pluto, the biggest three asteroids Ceres, Pallas and Vesta, and the Moon), using a high-precision Bulirsch-Stoer algorithm (actually that one from Numerical Recipes, but the free ODEX2 algorithm by Ernst Hairer is of equivalent precision). While there are obvious errors in the inner solar system from the neglection of relativistic effects (a position error of the planets themselves that is approx. three times larger than their relativistic perihelion precession), there are unexpectedly large errors for the Moon, about 400 km within 20 years. The error accumulates to about 1600 to 1700 km (i.e. about one Moon radius) within a century. It came out that the real Moon is feeling a slightly (about 0.5 ppm) larger force than from Newton's law of gravity. From an older calculation I made for the local gravity on Earth using centrifugal force and quadrupole moment, I could extrapolate the difference to the Moon's distance, and it is of precisely the same order of magnitude (if a mean geocentric latitude of about 15 degrees is assumed) required to fix the orbit error.

I am trying to find some third-party references to this to get this issue out of the fog of original research. Then it may be added to the article that quadrupole moments of planets (and maybe even of the Sun) have to be taken into account for precise solar system simulations.--SiriusB (talk) 09:42, 30 July 2010 (UTC)

gravitation graphic

I guess it was easier to find graphics for the others than for the gravitational quadrupole? 4.249.63.91 (talk) 22:54, 30 December 2010 (UTC)

Clarity of the Maths

Can I echo the comments above about the Maths being presented unhelpfully here. Is it really necessary to stick to tensor notation throughout? I'm a Maths graduate and I (along with most Maths graduates) don't really know much about tensors. Would be nice to see the equations presented in more traditional format, so everyone can access them. — Preceding unsigned comment added by 138.253.156.11 (talk) 00:29, 7 February 2016 (UTC)

please check

I do not really understand

Still higher multipoles, e.g. of order 2^l, would be obtained by dipolar (quadrupolar, octopolar, ...) arrangements of point dipoles (quadrupoles, octopoles, ...), not point monopoles, of lower order, e.g. 2^l-1

My math is poor and the phrase might be correct, but I would write

Still higher multipoles may be obtained by arrangements of lower order point ones, e.g. that of order 2^l by dipolar arrangements of 2^(l-1) multipoles, quadrupolar of 2^(l-2) ones ...

May someone explain me why my mouse is unable to move here 2^l and 2^(l-1) from the article?

I remember that in the Jackson the multipoles were defined using the spherical harmonics so that a factor 1/sqr(4*pi) appeared in the formulae ... but I am aged and have no more access to the library to check my memory.

thanks. pietro. 151.29.78.113 (talk) 09:33, 29 April 2024 (UTC)