Talk:Magnetic monopole/Archive 2

SI
There are Maxwell's equations written in cgs system in the article. Can somebody include Maxwell's equations written in SI in the article? --78.1.23.137 (talk) 15:28, 12 January 2008 (UTC)


 * It's not cgs either (note the lack of c's), it's "nondimensionalized", as explained in the sentence immediately prior. My preference would be to take that one out, and put in both the cgs and the SI (I think the equations are sufficiently important in this article to warrant including two forms). The nondimensionalized can be generated easily enough from the cgs. Thoughts? --Steve (talk) 08:20, 14 January 2008 (UTC)


 * It would be a good idea to have both cgs and SI equations. --161.53.6.108 (talk) 16:28, 16 January 2008 (UTC)

Price's non-monopole
Regarding my recent revert, the source is quite aware of Price's "result":


 * "Since the revival of interest in monopoles in the 1970s, there have been two well-known announcements of their discovery: that of Price et al [163], who found an cosmic ray track etched in a plastic detector, and that of Cabrera [158], who reported a single event in a induction loop. The former interpretation was immediately refuted by Alvarez [164], while the latter has never been duplicated, so is presumed spurious."

I believe this represents the scientific consensus: Price found nothing. Melchoir (talk) 21:20, 17 January 2008 (UTC)

The section in the body should also be looked at for accuracy. Melchoir (talk) 21:20, 17 January 2008 (UTC)

The necessary reference is http://usparc.ihep.su/spires/find/hep/www?irn=93726 Melchoir (talk) 22:03, 17 January 2008 (UTC)

"Scientific consensus" is meaningless if the science community is unaware of the results. Price did not find "nothing". Price found the track of a highly anomalous cosmic ray that did not fit with any prior cosmic ray tracks he had been observing for more than a decade. Price was the acknowledged Dean of cosmic ray research at the time, with hundreds of published papers. That is a fact that is not in dispute. The finding was not only published in the scientific literature, it was also published in the lay press of the day [Time, August 25, 2005, full page story; front page headlines of numerous newspapers, including SF Chronicle]. The tracks themselves were subject to extreme criticism, but no plausible explanation [other than the monopole explanation] for them were put forward by anyone, including Alvarez. Alvarez used a twisted and contorted theory of a "doubly fractionating" normal nucleus, with wide variations on the error bars, to suggest a normal nucleus having traversed the particle detector, causing the 64+ tracks that were measured. One would have to wonder why the first such doubly-fractionating nucleus just happened to mimic a magnetic monopole, without any of the trillions of expected other tracks coming close to, but not mimicing, a magnetic monopole having been seen first. This article is not to "prove" the validity of the experiment. Rather, it is to direct the reader to the idea that anomalous cosmic rays are detected which suggest the validity of magnetic monopole theory. Please do not revert again. —Preceding unsigned comment added by Oldnoah (talk • contribs) 02:19, 21 January 2008


 * Okay, let's break this down:
 * Your edit replaces "never been observed" with "never been directly observed". This change strongly suggests that magnetic monopoles have been indirectly observed, a claim for which you do not provide a source. Per Verifiability, this claim should be removed until a source is found.
 * Your edit also introduces the explanation "However, Milton's review neglects the substantial discovery of an anomalous cosmic ray particle found by Walter L. Wagner and P. Buford Price in 1975...". This is false. Milton's review does not neglect Price's event.
 * I'm not nearly familiar enough with Price's experimental technique or body of data to independently evaluate either. I also can't comment on the plausibility of Alvarez's or others' explanations. This is consistent with No original research. However, I am perfectly comfortable citing reviews by modern authors who call Price's anouncement a mistake (and these include Price himself, a few years afterward).
 * If you just want to draw attention to the monopole candidates, that's fine: the lead of the article should cover its contents. But innuendo isn't going to get the job done. Start by finding some reliable sources to reference. Melchoir (talk) 04:41, 21 January 2008 (UTC)

OK, now that you've acknowledged your lack of exxpertise in the field, then perhaps we can reach a compromise, and at least include Price's event as a leading magnetic monopole candidate event that is as of yet unproven. While Price did subsequently "retract" his claim, he did not say that the event was not recorded. Rather, he suggested that it might not have been a magnetic monopole, as it would have had to have been exceptionally massive [and theory at the time did not lend credence to exceptionally massive monopoles, though they do nowadays]. Likewise, Milton's review neglects the importance of the event, even if making casual mention. Please note that the event was recorded some 64 different times [top and bottom of each sheet of plastic], and there is no question that a cosmic ray of exceptionally high ionization potential traversed the particle detector.

All efforts to identify the tracks as having been caused by a known particle [e.g. doubly fractionating heavy nucleus] have the difficulty of being exceptionally implausible. One would have expected to have seen Billions of such doubly fractionating nuclei coming close to, but not exactly, mimicing a magnetic monopole track before having the first one ever detected exactly mimic a magnetic monopole. Price himself acknowledged this, and his "retraction" did not attempt to identify the culprit that caused the tracks. Rather, he was under intense pressure from Alvarez and others to "retract" his claim, and without proof of a "live" magnetic monopole, he left it inconclusive.

I happened to have worked with the Price group at that time, and personally saw the tracks, and they indeed were quite anomalous compared to all other cosmic ray tracks [in the millions] observed. I am quite familiar with the track-etch technique, which has been used successfully by many other groups since Price et al. pioneered the technique in the late 1960s when he worked at GE.

Since Milton does make some mention, I will correct that part. Oldnoah (talk) 21:31, 21 January 2008 (UTC)Oldnoah


 * Well yes, clearly Price's event is a leading magnetic monopole candidate. In fact, I rather envy you for having seen the tracks! But the edits you keep restoring are more sensational and simplistic than your explanations here. Rather than force you to defend them again, I'll try something else. The current lead is, after all pretty short... Melchoir (talk) 04:14, 22 January 2008 (UTC)


 * Oldnoah, the crux of the issue is that we have a verifiable source (Alvarez's paper) that refutes Price's analysis, but we do not have a verifiable source that refutes Alvarez's refutation. What we have is your own refutation of Alvarez's refutation, but your comments on the discussion page of a Wikipeda article do not constitute a verifiable source. It seems to me, based on the verifiable sources we have available so far, that the physics community has long since given up on interpreting this event as a monopole. If that's incorrect, please point us to a verifiable source that says otherwise.--76.93.42.50 (talk) 03:05, 9 March 2008 (UTC)

Dirac quantization condition
In the text, it is mentioned that Dirac stated that the product of the electric charge and the magnetic pole units is an integer number, and therefore that these two entities have reciprocal units.

Can you set a reference and an explanation for that? I have the original work by Dirac in 1931 (Proc. Roy. Soc. A133, 60) and the later one from 1948 (Phys. Rev. 74, 817) right now on my table, which I read in the last day, and the quantization condition Dirac showed is quite different:

$$\hbar c / e\mu_0 = 2$$,

with the symbols being respectively Planck's constant, velocity of light, electrical charge and magnetic pole (he uses the symbol $$g$$, still used now, in the later work). In this picture, $$e$$ and $$\mu_0 (g)$$ should actually have the same units, since:

$$e^2 = (1/137) \hbar c$$.

Also the wiki explanation on how Dirac gets to his conclusion is not consistent with what written here in the original work. Maybe this is another way to get to the same results (which is actually not the same in this case), but the corresponding reference should be cited as the main source of the paragraph. As it is right now, it looks like Dirac made such statements, which is not true. —Preceding unsigned comment added by 213.100.42.209 (talk) 00:05, 8 February 2008 (UTC)

SI again
Will anybody add Maxwell's equations in SI units to the article? --83.131.70.167 (talk) 20:05, 9 February 2008 (UTC)


 * Done. I copied the SI straight out of a textbook (see the footnote I put in), but for the cgs, I just guessed that magnetic and electric charges would have the same units, and that the previous version on this page was correct in nondimensionalized form. It would be best if someone could check it against a reliable source, and cite it. Anyone?--Steve (talk) 06:28, 10 February 2008 (UTC)


 * Good jod! I did some fixings. You forgot to square the c's; I used such units for magnetic charge such that in static situation (no currents) it would be $$\nabla \cdot \mathbf{H}=\rho_{m_{free}}$$, just like units 99%+ times used for electric charge are such that $$\nabla \cdot \mathbf{D}=\rho_{e_{free}}$$. I did so because magnetic $$\ \mathbf{H}$$ analogous to electric $$\ \mathbf{D}$$ (both don't need $$\epsilon_0$$s and/or $$\mu_0$$s when being calculated). Because such units probably weren't used by Jackson, I've commented out your reference. --161.53.6.108 (talk) 10:04, 11 February 2008 (UTC)


 * Hello! I like the bold vectors. I'm not sure about the other changes though:
 * CGS: I don't think the c's should be squared in the cgs version of Faraday's and Ampere's. See for example or the article Maxwell's equations (section 5). (It should agree with the standard versions when rho_m and J_m are zero, of course.) Also, why did you put 1/c^2 in the cgs Gauss's law of magnetism? If E and B have the same units in cgs, wouldn't it be most likely that rho and rho_m have the same units too? Is there a source for this?
 * SI: I see how it's nice and symmetrical with a mu_0 multiplying the magnetic charge, but the article should have the equations in the most common and conventional way, not the best way. It's not our place to choose the units for magnetic charge; this is an encyclopedia, not a standards-committee. Now, Jackson purports to have the extended Maxwell's equations in SI units, and there's no mu_0. Do you have a comparably reliable source that has it with a mu_0? If so, great, we should put in a citation, and add a note that other unit conventions are also sometimes used. If not, I'm afraid we'll have to take the mu_0 back out. --Steve (talk) 17:57, 11 February 2008 (UTC)
 * I've now reverted these changes, but added a "citation needed" template to cgs to emphasize that we should have a reliable source on it. (More reliable than my educated guess.) --Steve (talk) 00:11, 12 February 2008 (UTC)

Emphasis here is to the symmetry!
This article is about monopoles, not about Maxwell's equations (and Extended and unit variants!).

It is important here emphasis in the symmetry, then simplified by nondimensionalization highlight the symmetry!

Please, REVERT TO http://en.wikipedia.org/w/index.php?title=Magnetic_monopole&oldid=190222242 —Preceding unsigned comment added by 143.107.230.53 (talk) 20:31, 11 February 2008 (UTC)


 * Well, the above anon asked me to comment here on my talk page. I don't hold a strong opinion on which presentation is best for the reader. If it's a big deal, one possible solution would be to expand on all possible forms in a new article, Symmetrized Maxwell equations, and leave just enough here to have something to refer back to. Melchoir (talk) 20:53, 11 February 2008 (UTC)


 * The cgs version displays the symmetry just as clearly as the nondimensionalized. The SI version does not, but is a widely-used, standard system of units, the inclusion of which was repeatedly requested. So we put in both. Seems like a perfect solution. Anyone interested in the nondimensionalized version will have no trouble reconstructing it from the cgs. We could even say explicitly, "for nondimensionalized, take out the c's from the cgs", but I don't see the need.
 * That said, if someone wants to make a separate article on symmetrized Maxwell equations, there are some other things to say about it, such as the extra transformations under which they're invariant (see Jackson, for example). But without the addition of new content, I don't think it would be appropriate to make a separate article just for three tables and two paragraphs of text. --Steve (talk) 22:12, 11 February 2008 (UTC)
 * Makes sense to me. In general, I tend to favor the creation of stubs in topics that have room to grow, but this one would really start out slim. Melchoir (talk) 22:32, 11 February 2008 (UTC)
 * I added a sentence immediately above the tables, saying that cgs displays the symmetry more clearly than SI. Does that help make the point? If not, other ideas? --Steve (talk) 00:08, 12 February 2008 (UTC)
 * About "The cgs version displays the symmetry just as clearly as the nondimensionalized" (from Steve 22:12), NO. It is not a kind of "personal taste", please compare objectively: nondimensionalized have
 * Where you see the largest tables?
 * Where you see more metric-dependent constants (4pi is universal mathematic)
 * Where reader can "see fast" the equations and symmetry?
 * About a lot of big metric-polluted tables and non-relevant information: it is visual pollution, the SI+CGI tables not add encyclopedic information. Wikipedia text must be simple, didactic, exact, etc. not polluted and so difficult to read (and to download!).

More than 1 year ago!
The "enhancing notation for show symmetries" edit, is from 03:33, 28 January 2007. For DELETE User:Sbyrnes321 MUST FIRST TALK HERE. See comparison bellow.

Nondimensionalized, SI, and CGI comparison
About visual pollution, please compare and vote (justify) for decide if change or not the article text. Important sugestion: only ONE table at the article.

About "visual pollution":
 * Where you see the largest table?
 * Where you see more metric-dependent constants?
 * Where reader can "see fast" the equations and symmetry?

Nondimensionalized
 * {| class="wikitable"

! Name ! Without Magnetic Monopoles ! With Magnetic Monopoles (with Maxwell's extension):
 * Gauss's law:
 * $$\nabla \cdot \mathbf{E} = 4 \pi \rho_e $$
 * $$\nabla \cdot \mathbf{E} = 4 \pi \rho_e $$
 * Gauss' law for magnetism:
 * $$\nabla \cdot \mathbf{B} = 0 $$
 * $$\nabla \cdot \mathbf{B} = 4 \pi \rho_m $$
 * Faraday's law of induction:
 * $$-\nabla \times \mathbf{E} = \frac{\partial \mathbf{B}} {\partial t}$$
 * $$-\nabla \times \mathbf{E} = \frac{\partial \mathbf{B}}{\partial t} + 4 \pi\mathbf{J}_m$$
 * Ampère's law
 * $$-\nabla \times \mathbf{E} = \frac{\partial \mathbf{B}} {\partial t}$$
 * $$-\nabla \times \mathbf{E} = \frac{\partial \mathbf{B}}{\partial t} + 4 \pi\mathbf{J}_m$$
 * Ampère's law
 * Ampère's law
 * $$\nabla \times \mathbf{B} = \frac{\partial \mathbf{E}} {\partial t} + 4 \pi \mathbf{J}_e $$
 * $$\nabla \times \mathbf{B} = \frac{\partial \mathbf{E}} {\partial t} + 4 \pi \mathbf{J}_e $$
 * }

SI
 * {| class="wikitable"

! Name ! Without Magnetic Monopoles ! With Magnetic Monopoles (with Maxwell's extension):
 * Gauss's law:
 * $$\nabla \cdot \mathbf{E} = \rho_e / \epsilon_0 $$
 * $$\nabla \cdot \mathbf{E} = \rho_e / \epsilon_0 $$
 * Gauss's law:
 * $$\nabla \cdot \mathbf{E} = 4 \pi \rho_e $$
 * $$\nabla \cdot \mathbf{E} = 4 \pi \rho_e $$
 * Gauss' law for magnetism:
 * $$\nabla \cdot \mathbf{B} = 0 $$
 * $$\nabla \cdot \mathbf{B} = 4 \pi \rho_m $$
 * Faraday's law of induction:
 * $$-\nabla \times \mathbf{E} = \frac{\partial \mathbf{B}} {\partial t}$$
 * $$-\nabla \times \mathbf{E} = \frac{\partial \mathbf{B}}{\partial t} + 4 \pi\mathbf{J}_m$$
 * Ampère's law
 * Faraday's law of induction:
 * $$-\nabla \times \mathbf{E} = \frac{\partial \mathbf{B}} {\partial t}$$
 * $$-\nabla \times \mathbf{E} = \frac{\partial \mathbf{B}}{\partial t} + 4 \pi\mathbf{J}_m$$
 * Ampère's law
 * Ampère's law
 * $$\nabla \times \mathbf{B} = \frac{\partial \mathbf{E}} {\partial t} + 4 \pi \mathbf{J}_e $$
 * $$\nabla \times \mathbf{B} = \frac{\partial \mathbf{E}} {\partial t} + 4 \pi \mathbf{J}_e $$
 * }

CGS
 * {| class="wikitable"

! Name ! Without Magnetic Monopoles ! With Magnetic Monopoles (with Maxwell's extension):
 * Gauss's law:
 * $$\nabla \cdot \mathbf{E} = 4 \pi \rho_e $$
 * $$\nabla \cdot \mathbf{E} = 4 \pi \rho_e $$
 * Gauss' law for magnetism:
 * $$\nabla \cdot \mathbf{B} = 0 $$
 * $$\nabla \cdot \mathbf{B} = 4 \pi \rho_m $$
 * Faraday's law of induction:
 * $$-\nabla \times \mathbf{E} = \frac{1}{c}\frac{\partial \mathbf{B}} {\partial t}$$
 * $$-\nabla \times \mathbf{E} = \frac{1}{c}\frac{\partial \mathbf{B}} {\partial t} + \frac{4 \pi}{c}\mathbf{J}_m$$
 * Ampère's law
 * $$-\nabla \times \mathbf{E} = \frac{1}{c}\frac{\partial \mathbf{B}} {\partial t}$$
 * $$-\nabla \times \mathbf{E} = \frac{1}{c}\frac{\partial \mathbf{B}} {\partial t} + \frac{4 \pi}{c}\mathbf{J}_m$$
 * Ampère's law
 * Ampère's law
 * $$\nabla \times \mathbf{B} = \frac{1}{c}\frac{\partial \mathbf{E}} {\partial t} + \frac{4 \pi}{c} \mathbf{J}_e $$
 * $$\nabla \times \mathbf{B} = \frac{1}{c}\frac{\partial \mathbf{E}} {\partial t} + \frac{4 \pi}{c} \mathbf{J}_e $$
 * }


 * Second table is wrong since there should not be 4pi in SI equations. --193.198.16.211 (talk) 19:50, 17 February 2008 (UTC)


 * Yes, these tables have been edited since being posted on the talk page, and are now incorrect. Do not use them. The versions in the article should be watched more carefully, but I believe that they're correct at the moment. --Steve (talk) 06:04, 18 February 2008 (UTC)

Reply
Hello! I fully agree that the nondimensionalized version is the best single way to make the symmetry of the equations clear, with the smallest table and fewest metric-dependent constants.
 * Ok!

However, I strongly disagree that the SI and cgs, with their metric-dependent constants, are "non-relevant information" and do "not add encyclopedic information". Displaying the symmetry in Maxwell's extended equations is not, in my view, the only reason that the equations are in the article: The other important reason is so that people who want to do an electromagnetic calculation using monopoles can have a place where they can look up the equations they need. SI is the most common system of units in electromagnetism, used universally by engineers and often by physicists. So putting the equations in SI units is very relevent to many readers---and I think it's telling that there have been at least two independent requests on the talk page for the SI equations to be put in. It's certainly encyclopedic information.
 * Ok, SI vote. About "... other important reason is so that people who want to do an electromagnetic calculation using monopoles can have a place where they can look up the equations they need...", yes, I agree, but people have (here on Wikipedia) the Maxwell's equations (or complementar sections or articles if you prefer) for it (show "for utility" copy/paste not for simple, didactic, and exact explanation).

Perhaps a compromise would be to display the nondimensionalized version at the top of the section (where both charts are now),
 * Can you do this, I not well-come here, they delete may edits...

adding a note that this is equivalent to the cgs version, but with the factors of c removed. Then, at the end of the section, after all the text, say "The equations take on a different, less-obviously symmetric form in SI:" and put in the SI units. That way, someone reading the article from start to finish would get the pedagogical presentation of the nondimensionalized version, while the people trying to look up cgs or SI would be able to find it. I don't think two five-row charts overwhelms the section, so I don't see why it's necessary to just choose one. What do other people think? --Steve (talk) 17:08, 12 February 2008 (UTC)


 * It is better to use SI (and cgs) units because more people are familiar with those units than with non-dimensionalized ones.
 * Ok, SI vote.
 * And bold vectors used in SI and cgs tables are better than those used in non-dimensionalized ones.
 * OK, se here (up) the non-dimensionalized in bold face (exchanged \vec to \mathbf).

The anon who is against SI and cgs, and is for use of non-dimensionalized units seems to be the opposite of some editors who had complained that this article is pro-monopole biased. Perhaps this anon wants that article would be biased in such way as much as possible, but better to AFG first before jumping to conclusions.
 * The anon, am I? Sorry! No I not want bias this article.
 * However, there is no need for as hard as possible emphasis on symmetry, as this anon would probably like. I am going to revert to SI/cgs version now. --193.198.16.211 (talk) 00:08, 13 February 2008 (UTC)
 * Ops, ok, but the VOTE is to SI, then, we need revert ONLY SI.

Hi again! Thanks for contributing, and you certainly are welcome here :-) One note on style is: In the future, could you please reply in a single block of text, after all the previous text of that discussion? Inserting line-by-line comments, and editing your own text, works well in some places (like usenet, where readers can easily access the previous posts), but makes talk-pages very hard to read on Wikipedia. See WP:TALK.

Maxwell's equations with monopoles are not on any other Wikipedia page in SI or cgs units. So it's not a matter of "copy/paste for utility", it's making them available when they wouldn't be otherwise. Also, why are you so insistent on having only one form of the equations? If you look at other articles, for example Maxwell's equations, you'll find the equations written in 10 forms (by my count). "Magnetic monopole" is not an especially long article (see WP:SIZE), and I think it has plenty of room for two forms of these very important equations.

If no one objects, I'll implement the "compromise" I suggested above, with cgs first (for didactic reasons) and SI at the end of the section. Does anyone have comments, pro or con? --Steve (talk) 19:13, 17 February 2008 (UTC)
 * Ok, Thanks for your "third opinion", and sorry about WP:TALK. About "complete set of Maxwell's equations variants", yes, the place is there, not need all copies here... but your solution was good. --anon (talk) 12:01, 19 February 2008 (UTC)
 * I find myself liking this idea. Looking at the current state of the article, it seems strange to have the SI version presented alone or even first. I don't have statistics, but it seems like very few authors make that choice when discussing monopoles.
 * We could even try a meta-compromise where the SI table contains only the symmetrized equations (since the point of comparison has already been made) and is condensed into a 2x2 format instead of 1x4. This way they take up less space, and the visual effect of redundancy is reduced. Melchoir (talk) 19:24, 17 February 2008 (UTC)


 * I tried to edit accordingly. Thoughts? --Steve (talk) 06:06, 18 February 2008 (UTC)


 * Looks good to me! Melchoir (talk) 08:24, 18 February 2008 (UTC)
 * Final comment about SI vs cgi: SI is the international standard, not cgi... "didactic cgs", is "didactic for USA". At en.Wikipedia people adopting SI. --anon (talk) 12:01, 19 February 2008 (UTC)

PS: it was, for discuss this little point ("how to display equations"), a lot of "discuss work" (!), but it result in a final consensus. I it was very good! --anon (talk) 12:01, 19 February 2008 (UTC)

units of the quantum of magnetic monopole charge?
The "Dirac's quantization" section ends up by saying that q_e q_m is an integer. However, it's not at all clear to me what units this would be in. In SI, the product of q_e and q_m has units of (C)(T.m2)=(J.s), i.e., angular momentum. In cgs, E and B have the same units, q_e and q_m have the same units, and therefore the product q_e q_m is not dimensionless. I can see two possible interpretations of the article as it stands: Anyway, I think the article should state what the quantum of magnetic charge comes out to be in both cgs units (statcoulombs) and SI (T.m2). In SI, I think it should equal a*hbar/e=(a)(4.1*10^-15 T.m2), where a is some unitless constant.--76.93.42.50 (talk) 21:02, 8 March 2008 (UTC)
 * 1) The article states Maxwell's equations in cgs and SI, but then states the quantization condition in some other, unspecified system of units in which charges are dimensionless.
 * 2) The article states Maxwell's equations in cgs and SI, and the statement of the quantization condition incorrectly omits some constants.


 * I fixed the quantization condition, using SI from a textbook. Your unit calculation was correct, by the way, you divide by hbar times unitless constants. I don't have a reference for what the condition is in cgs.


 * If you want to calculate the quantized unit of magnetic charge, that's fine with me, but will you use the electron quantum of charge e, or the quark quantum e/3? I don't know which is right, so unless you have a good argument or a reliable source for one or the other, you should be careful about your wording, and may want to just not include that bit of trivia. --Steve (talk) 17:48, 9 March 2008 (UTC)


 * Thanks, I think that's a big improvement! I think the current statement of the quantization condition, with an explicit statement of the system of units as SI, is sufficient -- nothing would really be added by giving a number for the quantum of magnetic charge. I do think, however, that the question of whether it should be based on e or e/3 is an important one (it occurred to me, too), and should be discussed in the article. My personal opinion would be that it should be e, not e/3 (since I don't think the quantization argument succeeds with e/3 unless there is a free quark somewhere in the universe), but that would be original research; we need a source, and it may be that there are subtleties involved that I don't understand.--76.93.42.50 (talk) 05:41, 14 March 2008 (UTC)

I think it would also be helpful if the article presented the equation for the force exerted by a magnetic field on a monopole, in cgi and SI. I believe in SI, in a system where q_m is defined by the form of Maxwell's equations given in the article, it should be F=(c^2/k)q_mB, where k is the Coulomb constant. (The c^2/k can also be expressed as 4pi/mu0.)--76.93.42.50 (talk) 18:49, 15 March 2008 (UTC)


 * Yea, that would be part of the "Lorentz Force equation with and without monopoles", which would be a nice inclusion, paralleling the Maxwell's equations. Sadly, it's not given in Jackson. The cgs version is given in a semi-reliable source here (see eqn (38)). For SI, I'm willing to believe that your rendition is correct, but it would be even better if there was a source for it, and I can't find any. You could put it in and flag it with "citation needed" maybe, like I did for the cgs Maxwell's equations? Or just put it in.... Or only put in the cgs, I dunno. The above-linked paper surprised me, in that it's as recent as 2001, and yet claims to be original. It could be that the symmetrized Lorentz force just isn't well-established in the physics literature yet, and maybe no one's even written down the SI version yet. --Steve (talk) 23:29, 15 March 2008 (UTC)


 * I added the cgi version of the Lorentz force. I'm not confident enough that I have the SI version right to put it in. I think there's some material in the back of Jackson on how to convert cgi equations into SI...?--76.93.42.50 (talk) 03:56, 19 March 2008 (UTC)


 * Hehe, I think you mean "cgs" not "cgi". Jackson's appendix doesn't appear to discuss the units for monopoles. I think just having it in cgs is fine. :-) --Steve (talk) 14:29, 20 March 2008 (UTC)


 * UPDATE: The Lorentz force for monopoles (in SI) was in Jackson after all, as an exercise. I also found another publication with the cgs version, and cited it. That publication cites a book from 1952 as another place the law is discussed. It's funny that the recent arxiv paper seemingly didn't bother to find and cite the prior derivations of the law, given such a long history of it. It's nice, though, that everyone agrees on the end result. --Steve (talk) 16:55, 15 April 2008 (UTC)

properties, searches
IMO the article could use a more thorough and systematic discussion of the experimental and theoretical work that has been done on monopoles. The review paper by Milton has quite a bit of information.--76.93.42.50 (talk) 05:50, 14 March 2008 (UTC)

Lorentz force in SI
Can anybody put generalized Lorentz force equation in SI units in terms of E and B? This would be required because everything else in this article is expressed in terms of E and B as it should be. --193.198.16.211 (talk) 12:09, 15 April 2008 (UTC)


 * Done. Doesn't look quite as pretty, but I suppose there's something to be said for being consistent. --Steve (talk) 16:47, 15 April 2008 (UTC)

Uses?
Can we put in a new section that would detail the possible applications of a monopole? Right now I don't see the point in one. ScienceApe (talk) 03:53, 7 June 2008 (UTC)


 * I find it hard to imagine that there will ever be technological uses for magnetic monopoles, mainly because they're either nonexistent or extremely rare. Technological applications are certainly not why physicists are interested in them. Physicists are also interested in neutron stars and lots of things that don't likely having technological applications.


 * That said, if anything notable has been said about technological applications of monopoles (other than by kooks and science-fiction writers), I'm all for it. :-) --Steve (talk) 04:46, 7 June 2008 (UTC)


 * Magnetic monopoles would catalyze proton decay (if they exist and proton decay actually happens [like in SU(5)]). This could then be used to convert ordinary matter into an energy just like in case with annihilation of matter and antimatter, only that antimatter is not needed, which would make some things easier. However, can anybody find any sources about that? --193.198.16.211 (talk) 05:25, 10 June 2008 (UTC)
 * That is very interesting. I think I'll go to the reference desk on this one. ScienceApe (talk) 18:52, 12 June 2008 (UTC)

Point that could use clarification
The article says: "'Some current models suggest that while magnetic monopoles could exist, they are so massive that they may never be observed in practice.'" Could anyone knowledgeable please clarify this? It's not clear to me why this implication (massive implies unobservable) should make sense, and certainly wouldn't be clear to a non-physicist. Does massive imply (1) Hard to create? (2) Hard to detect? (3) Rare? (4) Unstable? I can't imagine (2) is true, since it should have a clear electromagnetic signal. (1) is true but doesn't rule out observational studies with big underground detectors, or something like that. Whatever the answer is, this could be a lot clearer. --Steve (talk) 06:15, 10 June 2008 (UTC)

"Fake" monopoles
Does anyone have info about fake monopoles? I'm talking about, for example, 6 square current loops arranged in a box, with currents ran in such direction, that all the fields go in the cube, or out of it. Of course it's not a perfect monopole, and magnetic fields will leak through. 84.250.37.116 (talk) 01:12, 17 June 2008 (UTC)


 * That turns out to be mathematically impossible, without "real" monopoles. If the magnetic field pointed into the cube on all sides, then you can apply Gauss' law for magnetism with the cube as a Gaussian surface, to say that the cube must contain actual magnetic monopoles. You can't do it with just currents, no matter how creatively you arrange them. Try it yourself! --Steve (talk) 01:26, 17 June 2008 (UTC)


 * true, unless you bring in all the excess flux in a solenoid. This is Sidney Coleman's "monopole hoax", a funny way of describing Dirac's string. The string is the location of the solenoid, in the limit that the solenoid is made infinitely thin. When the flux is a multiple of the dirac unit, the solenoid is truly undetectible by particles whose charge is an integer multiple of the electron charge.Likebox (talk) 21:03, 19 July 2008 (UTC)

Likebox's recent edit
Hi Likebox, I have a few concerns about your recent edit:
 * "hypothetical particle" was changed to "unobserved particle". Most people would, I think, interpret "unobserved" as meaning that it's 100% known that they exist, just they haven't been directly observed. On the other hand, I think most people would interpret "hypothetical" meaning that it's hypothesized that it might exist, but no one knows (cf. Hypothetical protein, for example). The latter seems much more in tune with the consensus of the physics community, as far as I've seen. For example, Jackson's E&M textbook says "At the present time there is no experimental evidence for the existence of magnetic charges or monopoles" (my emphasis). Do you have a reliable source that expresses 100% confidence in their existence?
 * You say GUTs and string theories "firmly predict" and "absolutely require" monopoles. Could you please find a reference for that? Are you really saying that no physicist, no matter how clever, will ever come up with a GUT or string-theory model of the universe in which there are no magnetic monopoles? If that's what you're saying, it's a very bold statement, which demands a very reliable reference.
 * You should read WP:lead. Terms like "topologically nontrivial" and "U(1) gauge group" do not belong in the introduction of an article, especially one which we know has many non-specialist readers. With only a little more effort, you could instead put that information later in the article, where it belongs (make a new section, if there isn't already an appropriate place for it).
 * "By tying monopoles to electric charge quantization, Dirac showed that monopoles should be expected in nature." I'm skeptical of this, and not just because you provided no source. In fact, I took a graduate QM course taught by a reasonably-well-known mathematical physicist (Berkeley professor Robert Littlejohn), and he summarized a lecture on Dirac monopoles in the following words: "Dirac's argument: If a monopole exists anywhere in the universe, then electric charge is quantized. In fact, electric charge is quantized. Is this the explanation? No one knows". If you read the lecture notes, I think you'll agree that he understands Dirac's argument plenty well.
 * "Some current models have magnetic monopoles that are so massive that they may never be observed." I know you're not responsible for this statement, but maybe you happen to understand it, in which case could you please put in a better explanation? See the above section where I explain why it's confusing as written. :-) --Steve (talk) 18:36, 20 July 2008 (UTC)


 * I share these concerns (but was waiting to see if somebody else was going to take up the issue) --catslash (talk) 15:19, 22 July 2008 (UTC)


 * Well, I've wholesale reverted this edit, at least for the time being. I'm amenable to the reincorporation of some or all of it, as long as the seemingly-implausible claims are properly referenced and balanced, and the overly-technical descriptions are moved out of the introduction. :-) --Steve (talk) 17:23, 22 July 2008 (UTC)


 * Ok, Ok, maybe I was too bold. What I was getting at was three things: 1. in any GUT with no U(1) factor (it wouldn't really be a GUT otherwise) which reduces by Higgs mechanism to our world (to a U(1)) at long distances, there are monopoles (a simple topological proof is in Coleman's "Aspects of Symmetry") 2. A lattice gauge theory of a compact U(1) has finite-mass monopoles, and black holes can carry compact U(1) magnetic charge without getting infinite mass (folklore, the second follows from a black hole being able to carry any magnetic charge, and then it can Hawking radiate down to extremal state where Q=M) 3. Holographic quantum gravity and string theory do not allow U(1)'s to decompactify without extra geometry opening up (this type of thing is codified in Vafa's swampland program, although I'm not sure if he explicitly talks about this one).


 * So all short-distance completions of compact U(1) gauge theory have monopoles, and in string theory you know the U(1) is compact, that charge is quantized (although the experimental evidence is overwhelming anyway). It's nice to be able to say that there are magnetic monopoles, because I think that is one of the few unequivocal prediction of modern theoretical physics.Likebox (talk) 20:21, 22 July 2008 (UTC)


 * I'm afraid some of that went over my head, but I'm glad you understand it :-). I think what would be really great is
 * If you made sure that the article discusses these things well (the sections "Mathematical approach to Dirac monopole" and "Grand Unified Theories" discuss them to some extent, but for example there's nothing whatsoever about string theory outside a mention in the introduction).
 * If you could help me find some reliable-source quotes regarding the status of the theoretical prediction of monopoles. For example, here, Polchinski says: "the existence of magnetic monopoles seems like one of the safest bets that one can make about physics not yet seen", and suggests "In any theoretical framework that requires charge to be quantized, there will exist magnetic monopoles", but says it's not a theorem but an "aesthetic principle based on experience with a rather wide range of examples". I'm sure other quotes could be found that are stronger or weaker, and it would probably be worth looking. I'm thinking a sentence in the intro like:


 * I think something to that effect would get across the strength of the theoretical prediction without improperly implying 100% confidence, which of course is impossible in physics. But it would be better if the first sentence in that box also had a specific source. --Steve (talk) 06:46, 23 July 2008 (UTC)


 * I'm sorry--- I was too terse. The argument for monopoles is this:


 * A gauge field configuration is a map from loops to a Lie group. In EM, the group is the complex numbers of size 1 under multiplication, U(1). The map is called the "holonomy" or the "wilson loop", and it is specified completely by associating an infinitesimal group element to each infinitesimal path, that's called the gauge field. The total holonomy along a path or a loop is the ordered product of the infinitesimal elements along the way. The gauge field associated to an infinitesimal loop is always near the identity.
 * If you imagine a big sphere, you can deform an infinitesimal loop which starts and ends at the north pole in the following way: stretch out the loop over the western hemisphere until it becomes a great circle (which still starts and ends at the north pole) then let it shrink back to a little loop while going over the eastern hemisphere. This is called "lassoing" the sphere. It is a sequence of loops, so the holonomy takes it to a sequence of group elements, a continuous path in the lie group. Since the loop at the beginning of the lassoing is the same as the loop at the endand at the end, the path in the group is closed.
 * If the group path associated to the lassoing procedure winds around the U(1), the sphere contains magnetic charge. This is easy to see because the holonomy in a U(1) group is exp(i\int A dt) and \int A dt is \int B dA by Stokes theorem. The total magnetic charge must be quantized because the Holonomy at the end must be the identity because the loop is small. The total winding is given by the total magnetic charge, and since winding is quantized, the magnetic charge is quantized.
 * If charge is quantized in units of e you can think of 1/e as the radius of the U(1), and to go around requires a magnetic flux 1/e. This is the Dirac condition, revealed to be a statement that you can go around a U(1) gauge group.
 * If the U(1) comes from breaking a compact Lie group, the path which winds around the U(1) is topologically trivial in the big group (sometimes you have to go around the U(1) more than once to get it to be trivial, but you always can do it after a small number of windings). This means that there is a gauge-field configuration in the big group which is continuous and allows the monopole configuration to unwind itself at short distances, but at the cost of not staying in the U(1). In order to do this with as little energy as possible, you should do it only near one point inside the sphere, the center of the monopole.
 * If you don't have a gut, you stay inside the U(1) and the price you pay is that you get a singular point--- the center of the monopole has shrunk to a point.


 * So that explains why monopoles occur in GUTs--- the monopole field is consistent at long distances, and at short distances, a GUT regulator will allow the topology to relax itself. The principle is this: if you have quantized charge, then you can make a monopole but it's a singularity, and in a field theory, the singularity might have infinite mass. But if you make a cutoff, like a lattice or a GUT, the singularity has a finite mass. In gravity theories, the singularity can be an ordinary black hole, and for large charges, the mass of the black hole is equal to the charge (classically), so that when quantum gravity provides the cutoff, you can be confident that the monopoles are there. What you can't be completely confident about is whether they have the minimum magnetic charge, or maybe twice that or three times that. You can also put a reasonable bound on their mass, although unfortunately it's on the order of the Planck mass.Likebox (talk) 03:35, 24 July 2008 (UTC)


 * This is a beautiful explanation, although I wish you would have put it into the article and not the talk page. :-) Anyway, I just added a paragraph to the intro to try to get at the thrust of your previous edit. If you get a chance, could you take a look and correct anything that's not right? Plus, to add any relevant quotes or sources to back up or correct the claims made. Thanks for this enlightening conversation, --Steve (talk) 06:55, 24 July 2008 (UTC)


 * This is the argument in Coleman, it might be his or it might be 70s folklore. The argument is already sort of in the article, but written overly formally. "Aspects of Symmetry" is the source, but I don't know a good source for the string theoretic argument, it's sort of modern folklore based on black hole decay. The swampland papers give you that the monopole is finite mass.Likebox (talk) 20:21, 24 July 2008 (UTC)


 * I put it in the article. The definition of gauge fields as connections always annoyed me a little bit, because the mathematical notion of bundle contains a whole bunch of topology which is just not there in the gauge field. There is some topology, but the type is slightly different because bundles can be glued using discrete symmetries, in which case if you wanted to interpret the bundle as a gauge field configuration you would need a discrete gauge field and singularities.Likebox (talk) 22:40, 25 July 2008 (UTC)

Hi again! I hate to snipe at your productive edits, but again I want to make sure the language in the introduction isn't stronger than appropriate. In particular, you write "the existence of magnetic monopoles is regarded by conservative physicists as an open question." This sentence implies that there are many physicists who do not regard it as an open question. Maybe this is true, but can you please find one or more quotes or sources that testify to this fact?

In particular, saying something is an "Open question" does not imply that one has no guess or opinion about whether it's true or false; for example the Riemann hypothesis article describes it as an "open question" despite near-unanimous opinion among mathematicians that it's true. (See also here.) If you read Polchinski's arxiv paper, you'll see that he makes it clear that he doesn't regard the existence of monopoles as a fact or theorem, but rather as merely a "safe bet" "based on experience". So would you call him a "conservative physicist"? And where are the physicists who are not conservative? --Steve (talk) 00:01, 26 July 2008 (UTC)


 * The comments may be biased, but I was trying to be fair. If you don't like it, just edit it and we can go back-and-forth on the wording until we agree. By conservative physicists in this case I just meant experimental physicists, who do not (and should not) lace experiment too much with theory. The term includes experimentally grounded theorists, who do not accept anything as sure until there is quantitative lab data to support it. The not-so-conservative physicists means high energy theorists, who unanimously believe in monopoles. They don't agree about everything--- for example, with low energy supersymmetry, some people think its there and some people think its not, and they frame it in terms of probability. But with monopoles, they'll take any odds, as Polchinski says.


 * The reason I removed the open question box is because I really don't think its that productive to try to make a model without monopoles. You're not going to do it in string theory, that's for sure. The productive questions about monopoles probably are something like: what is the mass of the monopole? What is the dyon spectrum in different compactifications? How do monopoles become light when their quantum of charge gets small? How do dyons change identity when you move around the space of vacua? blah blah blah. All of these just take monopoles for granted.Likebox (talk) 04:28, 26 July 2008 (UTC)


 * Can you find a quote from anyone (experimentalist or theorist) that says that monopoles are not an open question, but rather a certain fact? Show me a physicist who has said "There is no doubt that there are monopoles in our universe." Until you find that quote (and you won't find it in Polchinski's paper), I'm changing it back to "open question in physics". :-) --Steve (talk) 05:36, 29 July 2008 (UTC)


 * There is always doubt, the question is how much. I tried a new wording.Likebox (talk) 21:53, 29 July 2008 (UTC)

Classical Vs. Quantum Mechanical Monopoles
It is important to note that the classical idea of adding a magnetic charge and current to the Maxwell equations, although presented in textbooks as "adding monopoles" has only an indirect relation to Dirac's monopoles, which are the ones people believe exist.

Dirac quantization has an hbar in it, so that Dirac monopoles disappear completely in the classical limit. Classical sources of magnetic charge and current are just two separate sources interacting by the same field. Dirac monopoles are topological partners of quantized electric charge, and they are a different idea altogether. I think the only way to give proper credit to Dirac for the topological monopole (which I think is the first topological defect in physics, but maybe fluid vortex lines count) is to assert prominently that Dirac's idea is not related in any obvious way to the doubling of current and charge sources.

Anyway, I was ok with the other wording, so if you change again, I'll let it be.Likebox (talk) 21:53, 29 July 2008 (UTC)


 * Sorry I was wrong about that. I guess what I meant was, take a Dirac monopole (or a 't Hooft monopole or whatever) and calculate the expectation-value electric and magnetic fields. As I understand it these fields will satisfy "Maxwell's equations with monopoles" (if they didn't, how would you know it's a monopole??) When I think of a classical monopole, I think of some object defined by how it relates to "Maxwell's equations with monopoles". So I wouldn't say that there's a well-defined thing called a classical monopole, which is different from a well-defined thing called a Dirac monopole. I would say there's a classical notion of a monopole, and Dirac found a quantum thing that corresponds to this classical notion. Do you agree with this?


 * Anyway, I appreciate that you're trying to draw a contrast between the first sentence and the following one, but I think what you're getting at goes without saying, and by saying it you're potentially confusing people. Saying that the classical monopole mandates "no relation" between magnetic and electric charges is misleading: for one thing, they interact with each other by attracting and repelling! Likewise you call them "separate fluids", but there's nothing about the classical notion of a monopole that says that a single particle can't have both electric and magnetic charge, so again readers will be misled. I think the classical notion of monopole makes no claims about how electric and magnetic charges do or don't relate, it just says there's two source terms in Maxwell's equations. Dirac didn't negate this classical notion, rather he added important details to it. Is this in agreement with your understanding? All this is somewhat above my education level in physics theory, so please correct me if I'm wrong. I hope you're having fun, cause otherwise I'd feel guilty taking so much of your time. :-) --Steve (talk) 00:46, 30 July 2008 (UTC)


 * It's not like I'm doing anything else. Anyway, you're right--- the classical monopole charge density and current density is a fluid of Dirac monopoles all moving together. The point I was making was that if you start thinking of charge as a continuous fluid, as you do classically, you can think of the electron as some negative fluid all concentrated at one point. But if you do, then Dirac's monopole can't be thought of as a separate fluid of magnetic charge which happens to be concentrated at one point, because a fluid has a continuous amount of charge, and the theory doesn't make sense unless charge comes in lumps.


 * Another way of saying this more formally: if you add magnetic charge density and current to the maxwell equation, you can't find a vector potential description with a single vector potential. If B is the curl of A, it would have zero divergence. Dirac's insight was that, when charge is quantized at point singularities, the divergence of B could also be quantized at point singularities without contradiction, so long as the quantum of magnetic charge is inverse to the quantum of electric charge. So in the classical limit, when the electric charge becomes a continuous fluid, the Dirac monopoles disappear completely.


 * What about the extended Maxwell equations? Well, you can introduce two vector potentials $$A_1$$ and $$A_2$$ and define E_1 and E_2 and B_1 and B_2 in the usual way, then write the "real" E and B as a mix of the two different interactions:


 * $$ E= \cos(\theta)E_1 + \sin(\theta)B_2 $$
 * $$ B= -\sin(\theta)E_2 + \cos(\theta)B_1 $$


 * And then you have continuous fluid monopole charge, but what you have really done is introduced a bigger gauge group U(1) cross U(1) with two separate sources, you have doubled the photon. That's what happens if you naively try to quantize Maxwell's equations with magnetic charge. The reason is that the magnetic interaction is just completely separate from the electric in the absence of the charge quantization condition. You need topology and charge in points to make a Dirac monopole.


 * I got confused about this when I was first learning Maxwell's equations. And I am not alone--- every few years somebody publishes a silly paper along the lines of "Monopoles don't exist because they lead to a doubling of the photon". And these people usually confuse their continuous U(1) cross U(1) faux-electromagnetism with the topological monopole.Likebox (talk) 19:19, 30 July 2008 (UTC)

More edits
Hi Likebox, sorry it took me so long before I took another look. I still found that I wanted to make changes to the intro, although I think we're gradually converging. Hope all is well! :-) --Steve (talk) 04:01, 20 August 2008 (UTC)
 * First, for the reasons described above, I think describing electric and magnetic charge as "separate fluids" is probably technically correct, but nonsensical to a non-expert reader. Remember, this is an article which we know has interest to non-physicists, and the intro section is supposed to be the most accessible part of the article.
 * Second, I rephrased it in such a way as to not make any particular claims about the relation between classical and quantum magnetic charge. Again, I'm sure it was technically correct before, but it's incidental to the article, and anyway was phrased in a way that non-specialists would misunderstand. I hope it's clearer now, and still correct.
 * Third, it was phrased in such a way as to imply (A) "quantization of charge implies monopoles" and not (B) "monopoles implies quantization of charge". While (B) is a universally accepted fact which is stated clearly in every source on monopoles, (A) is a bold claim which even Polchinsky describes as basically an educated guess. I'm not saying (A) is necessarily wrong, but it misleads readers about our state of knowledge. Remember No Original Research: the article has no sources that advocate for monopoles as forcefully as you do. If you found a source that does, it would be a useful addition.
 * Fourth, I added some "citation needed" templates. I'm not implying these are not true (I take your word for it that they are), but if they are true it shouldn't be too hard to find a reliable source that makes the claim clearly and explicitly and without a shred of doubt. It would be even better if you could put the precise quote into the footnote along with the source.
 * Fifth, I took out what I saw as gratuitous mentions of the topological nature of the Dirac monopole. Remember, the intro is supposed to be the most accessible part of the article, and just saying monopoles have something to do with topology confuses many readers and helps very few. This is already covered at length in the body of the article. However, I could imagine ways that it could be put back in the intro without alienating readers, if you feel strongly.
 * Sixth, experimental monopole searches didn't and don't just search for Dirac's monopoles, they search for any monopole, at least as I understand it.


 * It reads fine now--- thanks for cleaning it up.Likebox (talk) 05:05, 20 August 2008 (UTC)


 * responses to your points (although I have no problem with the current wording):


 * 1) Separate fluids--- bad terminology. I just wanted to get across the idea that you need charge in point sources for there to be monopoles.
 * 2) You kept the quantum/classical distinction clear enough for me.
 * 3) Your harping on "quantization of charge implies monopoles" vs. "monopoles imply charge quantization" is one that many people repeat a lot, but its not useful at all. Dirac said it, and it caught on, but it doesn't get the meaning of the thing across.
 * 4) I gave a string theory reference. Coleman's article discusses GUTs.
 * 5) The "gratuitous mention" of topology is not gratuitious--- I think you are assuming that other people are going to have a harder time understanding something which you, yourself have no trouble understanding. That's just ridiculous--- if it is written clearly and properly linked, anybody can understand anything which is already understood by somebody. If you are going to argue that something should be removed, say "I found it confusing", not "someone else will find it confusing". That somebody else can speak for him or herself.
 * 6) The experiments which look for monopoles are always calibrated to look for Dirac monopoles. Perhaps there are experiments looking for non-quantized monopoles, but they would be as fringe as free-quark searches. The Valentine day monopole was a Dirac flux quantum in size, for example, which is why they thought it wasn't noise.Likebox (talk) 19:28, 20 August 2008 (UTC)


 * 3. The distinction may very well be useless, I wouldn't know. But this is Wikipedia, and the policy is that if "many [reliable sources] repeat it a lot", it belongs in the article. As your view of monopoles becomes more and more widespread (and I personally believe that it will, eventually), eventually we'll be able to change the article accordingly. :-)
 * 4. Nice references, thanks.
 * 5. It was neither explained nor linked in the introduction, only mentioned, and moreover mentioned in a way that implied that the reader ought to already understand it. I did, actually, personally find it confusing, but perhaps was too shy to say so. :-) Again, if the phrasing is changed, I'm fine including this information, e.g.


 * Is this on the right track?
 * 6. You're equating "dirac monopole" with "monopole quantized into units of (whatever)/e". I'm not sure that's right. For example, the article 't Hooft-Polyakov monopole says it's "similar" to the Dirac monopole, not "a special case of". I imagine there's multiple definitions though. --Steve (talk) 20:38, 20 August 2008 (UTC)


 * "Similar too" means "at long distances equivalent" but at short distances it's continuous, not a singular point. You are right, I was using "Dirac monopole" to mean anything quantized in reciprocal amounts, and that includes various 'tHooft Polyakov monopoles, some of which can be big and floppy. There's a beautiful classical example due to Montonen and Olive where the Higgs field has zero potential exactly (you need a lot supersymmetry to make sure that this property is not destroyed in a quantum theory) and then the monopoles can be massless objects. I see what you mean though--- just because it is quantized like Dirac doesn't mean that the core is a point. I'm sorry for being snippy, I just guess my feelings were hurt when you said that the intro was confusing for non-specialists. Cheers, or as you say :).Likebox (talk) 04:53, 21 August 2008 (UTC)

Stars as monopoles
The sun is East. Polaris, the North Star, is North. The earth is like a lump of iron, and so turns the Eastern influence of the sun into a western one - likewise with Polaris and the southern polarity. Can you consider that every star is a monopole? 74.195.28.79 (talk) 23:46, 4 November 2008 (UTC)


 * There's a very precise, mathematical, scientific definition of a magnetic monopole. This definition has nothing to do with astrology, or the earth, or the directions of stars in the sky, or anything like that. So basically the answer to your question is no. If there are monopoles in astrology, then they have nothing to do with the magnetic monopoles being discussed in this article.


 * Perhaps they would belong in another article (assuming that they meet Wikipedia guidelines for inclusion of content). :-) --Steve (talk) 23:58, 4 November 2008 (UTC)