Talk:Fuzzball (string theory)

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The Start

Just started the article on Fuzzballs, gave the bare essential infomation concerning the idea. Any help is welcome as this can be quite an extensive article that delves into many different cosmology ideas, at the moment I am relying on outside links but in the future I would rather not. 11:25, 21 January 2005‎ Jordan14

Key assumptions used in article

• Schwarzschild radius, per $R_{s}={\frac {2GM}{c^{2}}}$, = 2953.25 ±0.07 meters per solar mass (M_☉) (updated 14 August, 2023)

where:

M = mass in kilograms and where solar mass = 1.988435(27)×10³⁰ kg (from Measurement of Newton’s Constant Using a Torsion Balance with Angular Acceleration Feedback, Jens H. Gundlach and Stephen M. Merkowitz, PHYSICAL REVIEW LETTERS, VOLUME 85, NUMBER 14, (hereinafter referred to as the "University of Washington" group), wherein their value for (M_☉) (for use as M) was derived from their measurement of Big G).

G = 6.674215(92)×10⁻¹¹ m³ kg⁻¹ s⁻² for the purposes here only of calculating Schwarzschild radius since the above value for solar mass was derived from this Big G value from the same group (from Measurement of Newton’s Constant Using a Torsion Balance with Angular Acceleration Feedback, Jens H. Gundlach and Stephen M. Merkowitz, PHYSICAL REVIEW LETTERS, VOLUME 85, NUMBER 14. When one measures Big G, one also measures the masses of the Sun and Earth, and the relationship is proportional since the uncertainties in Earth's orbital radius and the length of a year are far smaller than Big G's).

c = 299,792,458 m/s

Note that the latest CODATA value for G, 6.67430(15)×10⁻¹¹ m³ kg⁻¹ s⁻², is slightly different from the U-of-W value. Since measurements of G establishes the mass of the Sun by solving Kepler's third law of planetary motion, as follows:

$$M_{\odot }={\frac {(\mathrm {au} )^{3}\times \pi ^{2}4}{(\mathrm {yr} )^{2}\times G}}$$

…the CODATA value requires slightly different masses for both the Sun and Earth. However, due to the way solar masses (M_☉) and G are used in the formula for calculating the Schwarzschild radius (top formula), an increase in Big G (G) in papers under circumstances where G is used to calculate M_☉ (like the U-of-W paper) means a proportional decrease in solar mass—the two (G and M_☉) are reciprocals—and the net result is no effect at all on the Schwarzschild radius because G and M (M_☉) are multiplication factors on the same line.

Using the U-of-W value's for M_☉ and G, where both come from the same paper at the same time, has the effect of adopting the U-of-W values for the number of SI atomic seconds assumed for a sidereal year as well as the number of meters in an astronomical unit (Earth-Sun distance) that the authors elected to use while writing their journal paper; those two variables (the au and the length of a year) influence the equality between G to 1 M_☉. These values used for the length of a year and the au are central to establishing the value of M_☉ because other terms in the M_☉ formula—like pi and “4”—are either locked down by definition or can be accurately expressed to an arbitrarily excessive precision.

Note that the Earth's orbit is an ellipse and travels faster when closer to the sun than when further away. Per Kepler's second law of planetary motion, the orbits of planets sweep out equal areas in equal time. The Schwarzschild formula will return a radius for any arbitrary mass used for M. However, since the number of kilograms in M_☉ is determined by the measurement of G, the magnitude assigned to M_☉ (in kilograms) is equivalent to asking “What centripetal force is there between the Earth and Sun?” And this is the same as asking “What combination of solar mass and strength of gravity, where mass could be bigger if the strength of gravity is weaker, accounts for the centripetal force between the Earth and Sun?” And that question is effectively asks “What combination of Sun-Earth distance and length of sidereal year causes the Earth to sweep out 2.228×10¹⁵ m²/s in its orbit?” Ergo, the Schwarzschild radius produces any radius for any arbitrary inputed value of M, but if M is M_☉, which is the product of of Kepler’s third law, the value of R_s, in meters, is an abstracted value describing “the Earth’s motion around the sun” that is dependent upon two values: the au and length of sidereal year.

Critical point: According to the authors' October 2000 paper, they relied upon the Astronomical Almanac for 2001 (U.S. Government Publishing Office, Washington, D.C., 1999), p. k6 for those two astronomical values.

The U-of-W authors’ decision to use the Astronomical Almanac for 2001 was a professional move and a beyond-vast improvement over the ad hoc way amateur laypersons on the Internet use when calculating terms like the length of a year based on the number of days that are supposedly in a year (the length of a day, as measured in SI seconds, varies and has longterm drift). Moreover, many laypersons when attempting to calculate the mass of the sun from G use the length of a tropical year (how long it takes the sun to appear in the same place in the sky), which is doubly wrong. Note that the sidereal year and the au in epoch 2001 was before the 2012 redefinition of the au as being precisely fixed at 149,597,870,700 meters. Accordingly, as regards the values that Astronomical Almanac for 2001 used for the length of year and the au, which came from the U.S. Naval Observatory, it was crucial that the length of the sidereal year and the au be in harmony and were calculated at the same time using the same set of assumptions and methodology since the two measures are intimately linked.

Note also that the U-of-W paper's uncertainty in the magnitude of 1 M_☉ equals the uncertainty in R_s; for both values it is a relative standard uncertainty of 1.4×10⁻⁵. The U-of-W's stated uncertainty in the magnitude of G has no effect on the uncertainty of R_s due, as mentioned above, to the way G and M are reciprocals of each other in all contexts where a measurement of G is used to establish the magnitude of M_☉. Since there is a linear and proportional equality between the magnitude of R_s and 1 M_☉, the uncertainty in R_s (a relative uncertainty of 1.4×10⁻⁵) therefore equals ±0.04 meters; ergo, R_s = 2953.25 ±0.04 m/M_☉.

However, the U-of-W measurement of G, while precise, is not the only high-precision measurement out there; other measurements of G have been done by other groups and they vary from the U-of-W's. The measurement of G is a modern mess in comparison to that of other fundamental constants of nature, which are known with precisions that are either many more orders of magnitude more precise or are locked down by definition. While the CODATA value of G was heavily influenced by the U-of-W paper, it incorporates measurements from other groups around the world and the resultant uncertainty in the CODATA value is a complex evaluation of competing uncertainties, some of which don’t overlap; it is a weighted assessment of all measurements of G. The CODATA value of 6.67430(15)×10⁻¹¹ m³ kg⁻¹ s⁻² is a relative standard uncertainty of 2.2×10⁻⁵. Thus, the proper value and uncertainty for R_s is 2953.25 ±0.07 m/M_☉. This article rounds the value to 2953 m/M_☉ so as to avoid excess precision.

Summary: Due to the simple and elegant (and sometimes reciprocal and self-nulling) nature of the formulas for calculating the mass of the sun (M_☉) and the Schwarzschild radius (R_s), the magnitude of R_s is strongly influenced by the values of two key astronomical values taken from the Astronomical Almanac for 2001 (U.S. Government Publishing Office, Washington, D.C., 1999), p. k6; and the uncertainty, or tolerance, of R_s comes from the CODATA value for G. Both sources are the most authoritative ones for the values of the length of a year and au (to calculate M_☉), and G to plug into the formulas for calculating R_s.

• Planck density: $\rho _{P}={\frac {m_{P}}{l_{P}^{3}}}$ = 5.15489(36)×10⁹⁶ kg/m³

where:

m_P is the Planck mass (CODATA value) with a relative standard uncertainty of 5.0×10⁻⁵

l_P is the Planck length (CODATA value) with a relative standard uncertainty of 5.0×10⁻⁵

• With regard to how 6.8 solar masses is a “median-size” stellar-mass black hole, this is based on this list of black hole candidates. Excluding one useless entry with a mass range of 3–100 solar masses, the median value of all the rest of the candidates with known masses is 7.2 solar masses with a 3.1 standard deviation. I chose 6.8 solar masses (0.13 of a standard deviation off the median value) because its Schwarzschild radius produced a nice round value of 20 km and its density was also a nice round number.
• According to this article by Goddard Space Flight Center (NASA), the minimum mass for a black hole lies in the range of 1.7–2.7 solar masses and the smallest black hole discovered so far is 3.8 solar masses.
• Note: The neutron star density range of 3.7–5.9×10¹⁷ kg/m³, comes from Wikipedia’s article on the subject.
• The “70-story tall building” is the Four Seasons Hotel Miami, which is independently listed as “789 feet (240 meters)” tall.
• The Empire State Building is 1,453 ft–89⁄16 in (443.09 meters) tall (according to Wikipedia here in the article) and independently at Empire State Building Official Internet Site (although they erred with the metric conversion by 0.1 meter).
• With an area of 1430.4 square kilometers, Kauai has an equivalent radius of 21.338 km.
• Drop of water: Long-standing rule of thumb in science is 0.05 mL (20 drops per milliliter) [1], [2]
• Mean density of granite = 2.667 g/mL (used to be 2.75 g/mL) (Citation: Geological Society of America, Daly et al., 1966)
• Density of gold = 19.32 g/mL. Though gold’s density is often stated as 19.3 g/mL (Web Elements and Wikipedia), the customary, high-precision value is 10.18 troy ounces per cubic inch, which works out to 19.32 g/mL (Google search, World Gold Council, and hypertextbook)
• One astronomical unit = 1.49597870691(6)×10¹¹ m
• Our solar system’s termination shock radius was measured at 83.7 and 94 AU by Voyager 2 and 1 respectively [3]
• Planck density = 5.1×10⁹⁶ kg/m³
• Mass of Sagittarius A* is 4.31 ±0.06 million solar masses: Monitoring stellar orbits around the Massive Black Hole in the Galactic Center by S. Gillessen et al.
• With regard to 3.9 billion solar masses being “near the upper bounds for supermassive black holes”, the biggest known supermassive black hole is 18 billion solar masses. Cite: NewScientist.com, Biggest black hole in the cosmos discovered, which tells of a paper by Mauri Valtonen of Tuorla Observatory in Finland. I chose 3.9 billion solar masses because its density is equal to that of a fluid with which everyone is familiar: air.
• Range of mass of the universe = 10⁵³–10⁶⁰ kg [4] with 10⁵³–10⁵⁵ being common values.
• Rounded, high-end mass universe at 10⁵⁵ kg at the Planck density of 5.1×10⁹⁶ kg/m³ = volume of 1.96×10⁻⁴² m³ or radius of 7.76 fm, which is about the size of uranium nucleus.
• Rounded, low-end mass of the universe at 10⁵³ kg at the Planck density = volume of 1.96×10⁻⁴⁴ m³ or radius of 1.67 fm, which is the size of helium‑4 nucleus.
• Precision estimate: Assuming Guth’s Inflationary theory is correct and Ω is precisely 1, then the critical density of the universe is 1.8791×10⁻²⁹ g/cm³ (1.8791×10⁻²⁶ kg/m³) [5], (8.988×10¹⁶ J/m³) and assuming the universe has a radius of 46.5 billion light years, then the mass of the universe is 6.7×10⁵⁴ kg, which is close to two other commonly quoted masses for the universe (2×10⁵⁴ kg and 2.5×10⁵⁴ kg) (google search). At the Planck density of 5.1×10⁹⁶ kg/m³ = volume of 1.314×10⁻⁴² m³ = radius of 6.79 fm, which is about the size of a gold nucleus
• A total mass of 2×10⁵⁴ kg (a commonly cited mass) at the Planck density is a volume of 3.92×10⁻⁴³ m³ = radius of 4.54 fm, which is about 84% the diameter of an iron nucleus and 129% the size of an oxygen‑16 nucleus.
• Uranium nucleus radius = 7.4×10⁻¹⁵ m (7.4 fm) (rochester.edu)
• Gold nucleus radius is 6.5×10⁻¹⁵ m (6.5 fm) [6]
• Iron nucleus radius = 5.4×10⁻¹⁵ m (5.4 fm) [7].
• Oxygen-16 nucleus radius = 3.53×10⁻¹⁵ m (3.53 fm) [8]
• Helium-4 nucleus = 1.7×10⁻¹⁵ m (1.7 fm) [9]
• The most likely and plausible mass range for the universe (1×10⁵³ to 1×10⁵⁵ kg), when compacted to the Planck density results in radii equal to that of atomic nuclei ranging from helium‑4 to uranium (1.67–7.76 fm).
• (Added Aug. 14, 2023) With regard to …with a radiated power—for the entire black hole—of 1.2×10⁻²⁹ watt (12 billion-billion-billionths of one milliwatt). Such a minuscule signal is to one watt as ¹⁄₃₀₀₀th of a drop of water (about one-quarter the volume of a common grain of table salt) is to all the Earth's oceans, per NOAA, the volume of earth’s oceans is 1,335,000,000 cubic kilometers (1.335×10²⁴ milliliters). Moreover, 20 drops are assumed per milliliter (Excel Medical, confirmed via personal experiences decades ago). Ergo, (2.670×10²⁵ drops) in earth’s oceans × (1.2×10⁻²⁹ watt) = 3.204×10⁻⁴ of a drop = ¹⁄₃₁₂₁th of a drop, rounded to ¹⁄₃₀₀₀ so as to not exceed a precision of one part in twenty (drops per ml). The size of a grain of common table salt is taken to be a cube measuring 400 micrometers per side (my own value for common Morton-brand table salt using a video-measuring stereo microscope at work while taking photos of solder paste… and also after finding a wild range of values for salt on the Internet), thus, 0.2503 of a salt grain, rounded to "one-quarter." Greg L (talk)

Excess-precision values:

• 6.8 solar masses is Schwarzschild radius of 20.087 kilometers and is 3.98364×10¹⁷ kg/m³ and 0.05 mL (“one drop”) at that density has a mass of 19.918 million metric tons, which is equivalent to a sphere 242.517 meters in diameter at a density of 2.667 g/mL, and a teaspoon of such a fuzzball would have a mass of 1.9635 billion metric tons.
• Assuming a conservative lower limit of 2.7 solar masses for a black hole (maximum upper limit for a neutron star), a black hole can have a density of up to 2.5268×10¹⁸ kg/m³, and 0.05 mL (“one drop”) at that density has a mass of 126.340 million metric tons, which is equivalent to a sphere 448.924 meters in diameter at a density of 2.667 g/mL, and a teaspoon of such a fuzzball would have a mass of 12.454 billion metric tons.
• Cygnus X-1, 8.7‑solar-mass black hole, Schwarzschild diameter = 51.400 kilometers.
• Cross-sectional area of 51.400-kilometer-diameter is 2074.96 km² whereas Walker County, Texas is listed as 2,075 km² (Wikipedia and Census results).
• The neutron star density range of 3.7–5.9×10¹⁷ kg/m³, (1.8237–2.9081 billion metric tons per teaspoon) equates to fuzzballs with masses ranging from 7.056 to 5.588 solar masses
• 4.31 million solar masses = 9.91615×10⁵ kg/m³ = 51.326 times that of gold.
• 3.9 billion solar masses = 77.0104 astronomical units and 1.211068 kg/m³, which was contrasted to atmospheric density = 1.1968 kg/m³, which was taken at 13.94 °C (global mean temperature), 194 meters (median altitude of human habitation), and 9 °C dewpoint, (which is 1.16% molar concentration of water).

Cool endeavor

Cool endeavor from yours, a task which I would not be capable of myself. However, wanting to read the article to discover cool stuff, I stumble upon the first highlighted paragraph. The information paradox is not the fact that anything that went passt the horizon is doomed to "crash" on the singularity (which in fact nobody knows what it is exactly they are talking about) but is a quantum problem. It involves Hawking radiation, and the fact that unitarity is apparently lost when the BH evaporates, because of the no-hair theorem. Namely, all the information that was trapped in, as long as it stays inside somehow does not pose a serious problem, but as soon as it is radiated back into an observer's frame, the information is supposed to be totally scrambled i.e. thermalized. Quantum mechanics forbid that. Several attempts at solving the issue are still not entirely convincing. I will stop here since I fall short of being a specialist. But please, make amendments on this first paragraph. — Preceding unsigned comment added by 194.199.1.52 (talk) 14:59, 25 November 2017 (UTC)

Thanks for the attaboy… and I apologize for the over-five-year delay in responding (I was incredibly busy at work).

As for information paradox section—as you pointed out—quantum theory and general relativity don’t play nice with each other and the experts in both fields can’t agree to this day. So the subject is at my personal ability to grasp it.

Note that while I was writing this article, I took care to exchange many emails with Dr. Mathur and spoke with him over the phone on occasion. Dr. Mathur even offered the assistance of one of his graduate students to add a math section to the article (which I declined as I feel those abstruse math sections are wholly unnecessary for a general-interest encyclopedia). He read the article as well as the information paradox section, which was central to his theory. He provided his feedback, I incorporated his feedback, and at the end of the back & forth, he declared my original 2010 version to be sound. As for what others may have done to this article since then, I’m not sure but I’ll take a gander soon. Greg L (talk) 21:09, 2 August 2023 (UTC)

References needed

This article currently has just two real references, neither of which does much to support the bulk of the material in the article. Although there has been a {{more citations needed}} template since 2013, a lot of new material is being added with zero references to support it. I'm especially concerned about @Greg L's statements above that he wrote the article based on unpublished personal communication with Dr. Mathur. An editor with as much tenure as Greg should know that unpublished communication is not an acceptable source for an article. Some of the recent material added, such as this, which explicitly contradicts other sources and claims that they are incorrect, needs very strong sourcing, yet it has none at all. As it stands, this article's sourcing is quite abysmal. CodeTalker (talk) 20:10, 3 August 2023 (UTC)

Dilemmas like this frequently occur with abstruse scientific articles, CodeTalker, where Popular Science-grade publications mangle science and then volunteer 9th-grader Wikipedians further mangle things as they try their hand at authoring for the very first time. There is a wild diversity in the technical scope of our articles so a “one size fits all” rule cannot apply; that’s precisely whey Wikipedia has so many policies and rules. And if one is prone to quote rules when complaining that an article isn’t to your liking, it’s incumbent to properly understand those rules and policies.

First off, you are misinterpreting Wikipedia’s policies on sourcing when you write unpublished communication is not an acceptable source for an article. I have no citations in the article—though maybe I should—referencing my collaboration with the Ph.D. author of the paper on fuzzballs, Dr. Mathur and how he approved everything; I mentioned that only in this talk page, which is wholly appropriate so Wikipedians can better collaborate. Still, as you correctly point out, that doesn't address the issue of the article having a dearth of citations.

Importantly, WP:SCHOLARSHIP reads as follows regarding primary sources, Prefer secondary sources – Articles should rely on secondary sources whenever possible. For example, a paper reviewing existing research, a review article, monograph, or textbook is often better than a primary research paper. When relying on primary sources, extreme caution is advised. Wikipedians should never interpret the content of primary sources for themselves. Note the “whenever possible” part; our current rule allows primary sources where necessary without the need to invoke WP:IGNORE for this outlier-abstruse article. In this article, the original author of the paper, Dr. Mathur, after many discussions, reviewed the article—and signed off on everything—so in the final analysis I interpreted nothing by myself, as required by WP:SCHOLARSHIP.

Many more of our abstruse scientific articles could wildly benefit from such collaborations. Why? Even well-respected secondary sources like this article in Quanta Magazine, which ludicrously stated Indeed, at the horizon of the humongous black hole at the center of galaxy M87, the first black hole to be imaged directly, gravity doesn’t pull all that much harder than it does on Earth. Such errors are the product of using Newtonian formulas for gravitation rather than Einstein’s. The more scientifically abstruse the subject matter, the more one must be exceedingly cautions when looking towards secondary RSs and the greater is the imperative for there to be a close collaboration between an experienced wikipedian and an expert on the subject.

It’s a simple reality that some articles, like List of Bewitched episodes, are more straightforward for an all-volunteer army of regular contributors to create and maintain with few errors versus a highly scientific and complex topic like string theory. If you are able to find excellent secondary sources to add to the article, please have at it yourself and improve this article with citations. But given the abysmal quality of secondary sources on such an abstruse subject, I suggest that you elicit the assistance of an expert in the field to ensure you are properly interpreting what you read… or, failing that, contact Dr. Mathur yourself to ensure you you’ve got things nailed.

I’ve dealt with Ph.D.s experts before when writing on Wikipedia. When I told them what I was doing (writing on Wikipedia), one of them thought I was nuts for writing in a venue where some kid can wade in right after me and undo everything; ergo, you’ll very seldom see an original authoring expert willing to write on Wikipedia; it takes a collaboration where an experienced wikipedian is willing to do the heavy lifting and have the expert review it. And as an expert in PEM-based fuel cells (I have a dozen patents to my name in fuel cells and hydrogen sensing), I can attest first hand that experts wan’t nothing to do with Wikipedia’s articles on the subject. I think I once spent about 60 seconds looking at our Proton-exchange membrane fuel cell article before backing out, loath to get into edit wars and flame wars with people who got something out of Popular Mechanics.

It is always unseemly to stand at the top of a ditch and holler down at someone nine feet down digging away at it that you are displeased with their progress and the manner in which they do it. Greg L (talk) 21:44, 3 August 2023 (UTC)

The WP:SCHOLARSHIP section that you cite does indeed say that editors should not interpret primary sources themselves. That does not mean they should personally contact experts to interpret it for them. In any case, this article has neither secondary nor primary sources, except for one paper by Mathur. This is not acceptable. It's fine if you disagree with Wikipedia's sourcing policies for "abstruse scientific articles", and you are more than welcome to open a discussion to change those policies in the appropriate place (probably WP:VPP). But as long as the policies stand as they are, editors are required to abide by them. That means providing sources for what you write here. It's nice that you have patents; I have several myself, but that doesn't give you or I authority to disregard policy. Surely the rather voluminous information you have added to this article didn't all come from personal communication with Mathur, so all I'm asking is wherever you obtained it from, you should add citations to those sources, in accordance with policy. Or are you saying you intend to continue editing this article without providing any sources? CodeTalker (talk) 23:18, 3 August 2023 (UTC)

Quoting you: That does not mean they should personally contact experts to interpret it for them. You’ve misstated the situation. I had Dr. Mathur interpret and correct what I wrote before publishing. And I seriously doubt there is a rule anywhere telling volunteer wikipedians that—given the dearth of reliable and accurate secondary sources on arcane maters like string theory—that they mustn’t contact actual experts to see if what they are writing is correct or not. As if a ninth-grader blindly parroting what they read in Popular Mechanics is extra-good chicken.

Abiding by this approach for highly technical topics like string theory is far better than falling hook, line, and sinker for nonsense like this article in Quanta Magazine, which incorrectly stated Indeed, at the horizon of the humongous black hole at the center of galaxy M87, the first black hole to be imaged directly, gravity doesn’t pull all that much harder than it does on Earth. So… people are to believe that a photon can’t escape an imaginary upwards-pointing flashlight at the event horizon of a black hole (where the escape velocity of gravity equals the speed of light) but a Saturn V rocket with a 1.15:1 thrust-to-weight ratio can liftoff from an event horizon and do what light beams cannot. The known laws of physics and the very notions of “time” and “space” break down at event horizons, matter is theorized to degenerate beyond individual quarks and dissolve into strings, but a rocket can supposedly not only exist at an event horizon (without being squashed entirely out of existence) but launch from an event horizon! Misinformation like this—and believing it without giving it even cursory reflection—only reinforces what John F. Kennedy once observed: “Too often we enjoy the comfort of opinion without the discomfort of thought.”

I can only conjecture that the author at Quanta Magazine was really thinking about the magnitude of gravitational tides near supermassive black holes. But he wrote what he wrote, which is unambiguous and preposterously incorrect. It’s especially notable that Quanta Magazine is an editorially independent online publication launched by the Simons Foundation in 2012 to enhance public understanding of science. The Simons Foundation behind Quanta is like the Annenberg Foundation and accepts no advertising.

Editors who blindly buy into what they read on secondary sources on ultra-arcane scientific topics are bound to add incorrect material to Wikipedia and should proceed with great caution. Greg L (talk) 23:55, 3 August 2023 (UTC)

P.S. I added a dozen citations as of this writing.

While trying to write this article at a reading-difficulty level akin to ‘Scientific American’, which would be appropriate for the general-interest encyclopedia that is Wikipedia, I was (trying to) study up on Killing vector field, which is central to Steven Hawking's theory of Hawking radiation. The lead of the article—what is supposed to be the “accessible” initial part of an article—read as follows today:

---

“ In mathematics, a Killing vector field (often called a Killing field), named after Wilhelm Killing, is a vector field on a Riemannian manifold (or pseudo-Riemannian manifold) that preserves the metric. Killing fields are the infinitesimal generators of isometries; that is, flows generated by Killing fields are continuous isometries of the manifold. More simply, the flow generates a symmetry, in the sense that moving each point of an object the same distance in the direction of the Killing vector will not distort distances on the object. ”

---

Following just one of those links, Isometry, added no clarity—even after reading the clarifying note:

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“ In mathematics, an isometry (or congruence, or congruent transformation) is a distance-preserving transformation between metric spaces, usually assumed to be bijective.^[a]

^a. "We shall find it convenient to use the word transformation in the special sense of a one-to-one correspondence $\ P\to P'\$ among all points in the plane (or in space), that is, a rule for associating pairs of points, with the understanding that each pair has a first member P and a second member P' and that every point occurs as the first member of just one pair and also as the second member of just one pair...

In particular, an isometry (or "congruent transformation," or "congruence") is a transformation which preserves length ..." — Coxeter (1969) p. 29

”

---

Not surprisingly, I elected to not mention “Killing vector field” since linking to it would serve no possible purpose except, perhaps, to make the author seem extra-sciencey and smart-smart beyond all comprehension. Parroting language straight out of scientific papers originally written for publish-or-perish Ph.D.s is easy; understanding it well enough to then convey the concept in simple terms appropriate for a ‘Scientific American’-level readership is far harder. Prose that calls attention to itself or poorly communicates to the target readership is poor prose.

And no, no target readership for Wikipedia is legitimately Ph.D.s; they seldom come here. Greg L (talk) 23:58, 24 September 2023 (UTC)

A public thank-you to a valued behind-the-scenes contributor to this article

I want to give a well-deserved public shout-out to Viktor T. Toth, who created the Hawking radiation calculator cited frequently in the article. Mr. Toth provided invaluable feedback while I struggled with this article.

It's worth noting that I independently calculated (which is to say, double-checked) many of the values cited to his online calculator until it was clear that the calculator A) uses correct formulas, and B) of course, isn’t capable of occasional calculation mistakes like I am.

During our many email exchanges, it’s clear that Mr. Toth not only truly and deeply understands the direct and tangential theories underlying the formulas of black holes and Hawking radiation, but also has an uncanny ability to use plain-speak when communicating arcane scientific issues. In particular, Mr. Toth utterly shamed me into diverging from a near-exclusive particle-based treatment of Hawking radiation towards a wave-based treatment. Without connecting the dots between waves and particles, one would be doing a disservice to our readership.

Thank you, Viktor.

Greg L (talk) 01:46, 4 October 2023 (UTC)

An interesting picture of everything in the Universe that is or ever was

I didn’t want to lose this scientific paper and a fascinating graph in the paper that shows every size and mass of object in the universe that ever existed. It is beyond the scope of this article, but many people who are interested enough in this article to visit this talk page will find this interesting.

• GRAPH OF EVERYTHING: Masses, sizes, and relative densities of objects in our Universe. I find it interesting that according to fuzzball theory, all portions of a fuzzball lie precisely on the diagonal “black hole” line along the top of the graph. This is unlike a classic black hole where the void between the event horizon and the singularity occupies the forbidden zone at top and where the singularity is way beyond the top of the graph.

• JOURNAL ARTICLE: That image comes from the journal paper, “All objects and some questions” at the American Journal of Physics.

• NEWS STORIES ABOUT THE ARTICLE: Two simplified synopses of the journal paper are available at “A new view of all objects in the universe” at Phys.org, and at “Astrophysicists Put All Objects in Universe into One Pedagogical Plot” at Sci.News.

In the graph, the white “instanton” dot at the intersection of “quantum uncertainty” and “forbidden by gravity” (general relativity) is the Planck mass (2.176×10⁻⁵ g, or the mass of a cubic salt crystal measuring 0.216 mm on a side) compressed into a volume of one Planck length cubed, at the Planck density. And, as the paper says, the temperature of the Hawking radiation emitted from the instanton is the Planck temperature. At the upper right-hand corner of the graph, the big black dot is the Universe, which fits on the “black hole” line.

I hope others find this helpful in connecting the dots between general relativity and quantum physics. Greg L (talk) 03:07, 19 October 2023 (UTC)

Pronunciation of Chandrasekhar

@Phantom Hoover:

With regard to your deletion (∆ edit here) of the pronunciation of “Chandrasekhar” claiming that it is “superfluous and inaccurate,” I’d have to agree with you that I may not have chosen the best option (there are many different pronunciation guides). But given that a Goggle search on “pronounce Chandrasekhar” yields scores of websites and YouTube videos on how to pronunce it, this clearly demonstrates a long-felt need for an easy-to-follow pronunciation guide. One of the websites alone had 18 different ways of pronouncing it.

And I dare estimate that fewer than one in a hundred people know how to follow the IPA pronunciation guide (/ˌtʃændrəˈʃeɪkər/), so those IPA guides aren’t useful for 99+ percent of our readership. Between the abstruse IPA guides and given the scores of on-line pronunciation guides, I see no foundation for stating that including a pronunciation in the English-language version of Wikipedia is, as you alleged, “superfluous.”

Given though, that there are many different ways for English-speaking people to pronounce his name, the pronunciation given preference at the top by Google, chaan·druh·say·kr is A) properly formed and B) now authoritatively cited. You may find the newly formed and properly cited form, in the second paragraph, here in the article.

Greg L (talk) 00:11, 1 December 2023 (UTC)

I actually had second thoughts about whether the pronunciation was correct and so I also looked it up, and ended up correcting the pronunciation at both Subrahmanyan Chandrasekhar and Chandrasekhar limit to an IPA rendition that matches what you'd written, sourced against an English-language Indian documentary. I'm removing your pronunciation guide from this page again simply because the normal practice is to put the pronunciation guide for a name or term at the start of its own article to avoid clutter. But yes, I was wrong about the pronunciation being incorrect. Phantom Hoover (talk) 00:42, 1 December 2023 (UTC)

@Phantom Hoover:

We need a non-IPA pronunciation on Wikipedia on things related to Chandrasekhar to make the pronunciation accessible to a greater number of readers. There are lousy practices all over Wikipedia, but using obscure practices because they’re extra-sciency is poor encyclopedic practices.

The amount of clutter here is beyond minimal. English-speaking readers aren’t expected to employ an alveolar trill when pronouncing the Hindi/Urdu “ra” sound. If, as you say, my original phonetic was correct all along (and after my own further digging, I am finding that to be the case too), then it serves a useful purpose here.

Please don’t delete it unless you can find a more compelling encyclopedic purpose than it “introduces” clutter… particularly when there are no phonetic pronunciations available elsewhere on this project. Greg L (talk) 00:55, 1 December 2023 (UTC)

(Also the manual of style is clear-cut on the IPA being the single preferred way to transliterate pronunciations, and for good reason. Everyone has their own idea of a respelling system for English and they all end up foundering on the total inconsistency of English orthography; and 'Chandrasekhar' is in any case not an English name.) Phantom Hoover (talk) 00:52, 1 December 2023 (UTC)

@Phantom Hoover: The MOS was intended to have a single standard pronunciation technique right after the name in the lead for consistency; it wasn’t intended to proscribe a helpful parenthetical buried in referencing text. To avoid still more tedious do-da like this over something helpful to readers but unwelcome by wikipedians who think like you, fine. You get your way; I won’t include a helpful parenthetical for the 99% of people who have no clue what /ˌtʃændrəˈʃeɪkər/ means. The argument that “Well… they should know the IPA” is a lousy reason for an encyclopedia that is supposed to educate and use prose that doesn’t call attention to itself.

This reminds me of the passion that a handful of editors had years ago trying to get Wikipedia to use “mebibytes” and “kibibytes” instead of “megabytes” and “kilobytes” for RAM capacities… and a couple of those editors are still active, trying to slip the practice into Wikipedia through back-door tricks even though the 100% of the commercial computer world doesn’t use those proposed units. Just because something is fancy, doesn’t make it better prose and a sound encyclopedic practice. Greg L (talk) 01:05, 1 December 2023 (UTC)

Okay, looking at the article and this talk page it's clear to me that you're treating this article as your personal fiefdom, and that your approach to pronunciation guides is far from the only departure from normal encyclopaedic content you've introduced. I'll have to find time to review this article more thoroughly, because it currently reads like an attempt at writing a textbook, containing large amounts of redundant detail on subjects that have their own articles, rather than a focused entry on a specific subject as part of a cross-referenced encyclopaedia. Phantom Hoover (talk) 03:40, 1 December 2023 (UTC)

Well, that’s not even a thinly veiled threat. You clearly threatened to be disruptive and vindictive after someone pushed back at an edit that you yourself admitted was in error. Moreover, looking at your contributions history, it appears your specialty is deleting large swaths from articles, accompanied by edit comments like “Because it's part of the proof, you dolt.”

I suggest you try contributing to Wikipedia in a more useful manner (like adding well cited material that makes articles truly better), cool your jets, and think long and hard about what a collaborative writing environment is about. Contributing to Wikipedia is not threatening to do more of your delete-large-swaths-of-articles treatment to projects others have labored on for months. Greg L (talk) 04:05, 1 December 2023 (UTC)

Scope of this article (the information is not properly duplicated elsewhere)

TL;DR

I’d like to share a thought about this article. Someone mentioned that they could find some of the information mentioned here elsewhere on Wikipedia. Well… sure. Since fuzzballs are a type of black hole, there is obviously overlap. But, no; for the most part, the impression is false because the implementations and focus points differ greatly. Also, since many people learn visually, I created five static images and one animation for this article. As with all images, the wikipedian community is welcome to use these new images across the project.

Before contemplating deleting sections of this article in the erroneous belief that a given bit of information is properly and accurately given an encyclopedic treatment elsewhere on Wikipedia, please…

1. First carefully examine those other articles,
2. Correct any errors of fact, as there will be many,
3. Ensure all necessary citations are present and truly support the statement,
4. Correct the presentation to ensure it is given an encyclopedic treatment, including grammar, and
5. Ensure that every key point of fact mentioned here is also mentioned there.

Keen attention must be given to citations that purportedly support assertions of fact but don’t. Some editors might even be purposely using wholesale fakes to make unsuspecting wikipedians accept on face value that the “cited” assertion is correct and correctly cited. This phenomenon is endemic across Wikipedia’s science-related articles.

Details

For the most part, this article (Fuzzballs) is focused on the distinctive properties of fuzzballs and how they differ from classic black holes and neutron stars. I’ve endeavored to delve into very specific aspects of fuzzballs, such as how their mean densities differ from those of neutron stars. Such points of fact are either poorly covered elsewhere on Wikipedia or are not covered at all.

Importantly, while laboring on this article, I noted glaring and wildly incorrect assertions in articles I linked to, such as this version of "Neutron star", which falsely asserted as follows:

---

Neutron stars that can be observed are extremely hot and typically have a surface temperature of around 600,000 K.^{[9] [10] [11] [12] [a]}

---

This is, of course, nonsense. Neutron stars have no “typical” temperature. Neutron stars are left-over cinders that don’t generate heat through fusion; they are like a spatter ball of hot metal from a welder’s torch that start out exceedingly hot and rapidly cool. Neutron stars can be tens of millions of kelvin immediately after formation and inexorably cool down to hundreds of thousands of kelvin after millions of years.

Critically, none of the five citations (simulated in the above quotation) that supposedly “cite” that statement supported it. Most of them were cited to books that are hard to access without inter-library loans, but two of the citations were to websites that didn’t even have temperature as an attribute being discussed. Click here to explore the actual “citations.”

Errors like these tend to start a vicious circle where nonsense on Wikipedia is regurgitated on science-related websites and then wikipedians turn around and use those websites as citations to support the falshood!

It’s easy for a non-scientific, all-volunteer army of contributors on Wikipedia to introduce errors—particularly in science- and math-related articles. The false information regarding temperature was introduced 26 December 2013 and at that time cited a scientific paper on ArXiv, "The Neutron Star Mass Distribution", that didn’t discuss temperatures at all.

After that wildly false bit about temperature had been on the Neutron star article for 3612 days (10 years!), I finally corrected it. I spotted far too many other errors on the Neutron star article for me to address; it’s a mess right now and suffers from thousands of small drive-by shootings over more than a decade. The community must do its part to correct it and the many other science-related articles on this project. That Wikipedia’s articles are a mess should come as no surprise to any wikipedian who’s been around for any length of time.

Proper citations on arcane scientific articles that are difficult to cite

To address the problem of incorrect or false citations, the community should consider requiring that all citations must reference the specific part of the website or the specific chapter, figure number, or table number in a scientific paper. An example of this is as follows:

^[14] "Magnetic Hydrogen Atmosphere Models and the Neutron Star RX J1856.5−3754" (PDF), Wynn C. G. Ho et al., Monthly Notices of the Royal Astronomical Society, 375, pp. 821-830 (2007), submitted December 6, 2006, ArXiv:astro-ph/0612145. The authors calculated what they considered to be "a more realistic model, which accounts for magnetic field and temperature variations over the neutron star surface as well as general relativistic effects," which yielded an average surface temperature of 4.34+0.02
−0.06×10⁵ K at a confidence level of 2𝜎 (95%); see §4, Fig. 6 in their paper for details.

Of course, citations should ideally be from secondary sources but this isn’t always possible on arcane scientific subjects. Note that WP:SCHOLARSHIP reads as follows regarding primary sources, Prefer secondary sources – Articles should rely on secondary sources whenever possible. For example, a paper reviewing existing research, a review article, monograph, or textbook is often better than a primary research paper. When relying on primary sources, extreme caution is advised. When adding citations referencing scientific papers, “caution,” I think, means pointing out precisely where to look in the paper and what one can expect to read when they get there. This is demonstrated in the above example. Doing so will make lives easier for all wikipedians; expecting this practice to be the norm will improve the project.

Greg L (talk) 04:36, 3 December 2023 (UTC)

Interior structure of a classical black hole

Some of the more salvageable material on this page is the comparisons between qualitative properties of a fuzzball and that of a classical Schwarzschild black hole, but unfortunately a lot of it rests on misconceptions about the latter. A Schwarzschild black hole is not a spherical event horizon enclosing an empty spherical volume with a tiny grain of infinite density (the 'singularity') at the centre. Spacetime is incredibly distorted near the Schwarzschild radius and gets even more distorted inside; the interior volume and radius of the black hole are at best extremely difficult to describe; and the singularity is not a massive object that exists in space, it's a region in the future of the interior of the hole where general relativity breaks down. Almost all physicists agree that the singularity is unphysical and that a complete theory of quantum gravity should take over before it arises; the interesting aspect of the fuzzball seems to be that it takes over at the event horizon during formation of the hole. Phantom Hoover (talk) 13:07, 3 December 2023 (UTC)

Vandalism

@Phantom Hoover: What you’ve done on this article is a demonstrably clear combination of Wikipedia:Vandalism (On Wikipedia, vandalism has a very specific meaning: editing (or other behavior) deliberately intended to obstruct or defeat the project's purpose, which is to create a free encyclopedia, in a variety of languages, presenting the sum of all human knowledge) and Wikipedia:Disruptive editing. The record of everything you’ve done here cannot be erased for all to see and unambiguous and the end result makes your intentions clear as glass.

I’ll be taking you to Wikipedia:Administrators' noticeboard/Incidents if you engage in any more of this. Greg L (talk) 14:57, 3 December 2023 (UTC)

I would appreciate you doing so immediately, as I don't think this dispute is going anywhere without neutral arbitration. I intend to continue editing the pre-August version of the page, importing material from the far longer version from a few days ago when it's appropriate and relevant. I would be surprised if anyone agrees with your accusation that this constitutes vandalism. Phantom Hoover (talk) 15:31, 3 December 2023 (UTC)

Evidence of intent of vandalism

@Phantom Hoover: What you’ve done on this article is a demonstrably clear combination of Wikipedia:Vandalism (On Wikipedia, vandalism has a very specific meaning: editing (or other behavior) deliberately intended to obstruct or defeat the project's purpose, which is to create a free encyclopedia, in a variety of languages, presenting the sum of all human knowledge) and Wikipedia:Disruptive editing.

The record of everything you’ve done here cannot be erased and is there for all to see. The intent of your actions is clear and unambiguous.

Several days ago, after the looked at your contributions history. Seeing your proclivity at deleting large swaths from articles (accompanied by edit comments like “Because it's part of the proof, you dolt.”), I tried to avoid your promised disruption, I rolled the article back to this version dating to 13:59, 5 August 2023 except I deleted a {More citations needed|date=July 2013} from it. That version of the article had errors and didn’t have a single citation.

I left that version up for a couple of days in hopes that you would settle down and lose interest in vandalism and violations of Wikipedia:Do not disrupt Wikipedia to illustrate a point.

Here’s what you did: all you did just now was to roll it back to the August version (the one with zero citations except with minor changes to the lead) to falsely make it appear that you had made edits in earnest to add value.

I hadn’t intended to set a trap for you; I merely wanted to avoid needless wikidrama and allow you time to cool down.

I’ll be taking you to Wikipedia:Administrators' noticeboard/Incidents if you engage in any more of this.

Greg L (talk) 15:43, 3 December 2023 (UTC)