Talk:Fuzzball (string theory)

message: * Schwarzschild radius, per R_{s} = \frac{2GM}{c^{2}}, = 2953.25 ±0.07 meters per solar mass () (updated 14 August, 2023)
::where:
::M = mass in kilograms and where solar mass =  (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 () (for use as M) was derived from their measurement of Big G).
::G =  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, , 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 () 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  (like the U-of-W paper) means a proportional decrease in solar mass—the two (G and ) are reciprocals—and the net result is no effect at all on the Schwarzschild radius because G and M () are multiplication factors on the same line.
:Using the U-of-W value's for  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 . These values used for the length of a year and the au are central to establishing the value of  because other terms in the  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  is determined by the measurement of G, the magnitude assigned to  (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  in its orbit?” Ergo, the Schwarzschild radius produces any radius for any arbitrary inputed value of M, but if M is , which is the product of of Kepler’s third law, the value of Rs, 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  equals the uncertainty in Rs; for both values it is a relative standard uncertainty of . The U-of-W's stated uncertainty in the magnitude of G has no effect on the uncertainty of Rs 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 .  Since there is a linear and proportional equality between the magnitude of Rs and , the uncertainty in Rs (a relative uncertainty of ) therefore equals ±0.04 meters; ergo, Rs = 2953.25 ±0.04 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  is a relative standard uncertainty of . Thus, the proper value and uncertainty for Rs is 2953.25 ±0.07 m/. This article rounds the value to  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 () and the Schwarzschild radius (Rs), the magnitude of Rs 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 Rs 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 ), and G to plug into the formulas for calculating Rs.
* Planck density:  \rho_P = \frac{m_P}{l_P^3} = 
:where:
:mP is the Planck mass  (CODATA value) with a relative standard uncertainty of 
:lP is the Planck length (CODATA value) with a relative standard uncertainty of 
* 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  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–8 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) , 
* 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 = 
* Our solar system’s termination shock radius was measured at 83.7 and 94 AU by Voyager 2 and 1 respectively 
* Planck density = 
* Mass of Sagittarius A* is  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  with 1053–1055  being common values.
* Rounded, high-end mass universe at 1055 kg at the Planck density of  = volume of  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  or radius of  1.67 fm, which is the size of helium4 nucleus.
* Precision estimate: Assuming Guth’s Inflationary theory is correct and Ω is precisely 1, then the critical density of the universe is  () , () and assuming the universe has a radius of 46.5 billion light years, then the mass of the universe is , which is close to two other commonly quoted masses for the universe ( and ) (google search). At the Planck density of   = volume of  = radius of 6.79 fm, which is about the size of a gold nucleus
* A total mass of  (a commonly cited mass) at the Planck density is a volume of  = radius of 4.54 fm, which is about 84% the diameter of an iron nucleus and 129% the size of an oxygen16 nucleus.
* Uranium nucleus radius =  m (7.4 fm) (rochester.edu)
* Gold nucleus radius is  m (6.5 fm) 
* Iron nucleus radius =  (5.4 fm) .
* Oxygen-16 nucleus radius =  (3.53 fm) 
* Helium-4 nucleus =   (1.7 fm) 
* The most likely and plausible mass range for the universe ( to ), when compacted to the Planck density results in radii equal to that of atomic nuclei ranging from helium4  to uranium (1.67–7.76 fm).
* (Added Aug. 14, 2023) With regard to …, per NOAA, the volume of earth’s oceans is 1,335,000,000 cubic kilometers (). Moreover, 20 drops are assumed per milliliter (Excel Medical, confirmed via personal experiences decades ago). Ergo, () in earth’s oceans × () =  of a drop =  of a drop, rounded to  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  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 , 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, 8.7solar-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  (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 =  = 51.326 times that of gold.
* 3.9 billion solar masses =  astronomical units and , 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).  — Preceding unsigned comment added by Greg L (talk • contribs) 21:21, 19 August 2023 (UTC)
thread_title:  Key assumptions used in article 

message: 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)
thread_title:  A public thank-you to a valued behind-the-scenes contributor to this article 

message: 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 (, 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)
thread_title:  An interesting picture of everything in the Universe that is or ever was 

message: === 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…
# First carefully examine those other articles,
# Correct any errors of fact, as there will be many,
# Ensure all necessary citations are present and truly support the statement,
# Correct the presentation to ensure it is given an encyclopedic treatment, including grammar, and
# 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  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,  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)
thread_title:  Scope of this article (the information is not properly duplicated elsewhere) 

message: 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  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,  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)
thread_title:  Proper citations on arcane scientific articles that are difficult to cite 

message: 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)
thread_title:  Interior structure of a classical black hole 

message: What you’ve done on this article is a demonstrably clear combination of Wikipedia:Vandalism () 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)
replies: text: 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)
thread_title:  Vandalism 

message: Maybe add back a very few that are not already linked, that will be eventually worked into the article per seealso, thank you, Malerooster (talk) 14:54, 5 December 2023 (UTC)
thread_title:  See also section 

message: The "Picture of a Black Hole" over the Hawaiian island is extremly misleading to non-scientific readers, as it makes one think that a Black Hole is a normal sphere sitting in a flat space with a euclidean shape, volume etc. That is clearly not the case, if you know anything about general relativity, and leads to misconceptions amongst laypeople. 159.205.161.203 (talk) 09:02, 3 April 2024 (UTC)
replies: text: It’s another leftover from the old version of the article, which was deeply flawed and needed a ground-up rewrite that I found difficult to approach given the lack of sources that could be easily summarised into an encyclopaedic article (which I have no experience writing). I keep telling myself I’ll get back to it one day. Phantom Hoover (talk) 23:11, 7 April 2024 (UTC)
thread_title:  Picture of Black Hole Misleading