Martin

Disappearance of Black Hole Singularity in Quantum Gravity Authors: Leonardo Modesto Comments: 8 pages "We apply techniques recently introduced in quantum cosmology to the Schwarzschild metric inside the horizon and near the black hole singularity at r = 0. In particular, we use the quantization introduced by Husain and Winkler, which is suggested by Loop Quantum Gravity and is based on an alternative to the Schrodinger representation introduced by Halvorson. Using this quantization procedure, we show that the black hole singularity disappears and spacetime can be dynamically extended beyond the classical singularity." http://arxiv.org/gr-qc/0407097 A singularity in Gen.Rel. is a point or region where the theory breaks down and fails to calculate (produces infinities or just nonsense). It is common for singularities in a classical theory to be fixed by quantizing the theory-------the classical atom would immediately decay, the Bohr atom didnt. for decades now it has been expected that a quantum theory of gravity (a quantization of the classical Gen.Rel.) would fix the Big Bang and Black Hole singularities-----this is what one expects quantizing to do. In LQC, the Big Bang singularity was fixed by Martin Bojowald, and no longer exists----our universe had a prior contracting phase----by now a halfdozen or more other researchers have confirmed Bojowald's result. bojowald is likely to have been working on resolving the BH singularity (I judge by appearances from his recent papers) and he probably will publish something about it. Doubtless Modesto's paper---tho it seems to be a scoop---is not the last word. Modesto's QG is allied with and similar to Bojowald's LQC model, but not identical. In Modesto's model of quantum gravity, anyway, spacetime does extend past where the classical BH singularity used to be.

John Baez was at the Dublin GR17 conference and gave one of the plenary talks, the day before Hawking's. Baez has a good physics website hosting the Usenet Physics FAQ and his own "this week's finds in mathematical physics" column Baez posted his report on the Dublin event today http://math.ucr.edu/home/baez/week207.html

Earlier I posted the Friedmann equations, this version includes the cosmological constant as "dark energy" in the rho term. this is how a lot of people do it nowadays, and the dark energy fraction is given as 73 percent of total energy density rho. [math](\frac{a'}{a})^2 = \frac{8\pi G}{3}\rho - \frac{k}{a^2}[/math] [math]\frac{a''}{a}= -\frac{4\pi G}{3}(\rho + 3p)[/math] Sometimes it's good to be able to separate the cosmological constant part out as Lamda, an inverse distance squared term. then rho is all the other stuff, not counting dark energy, and the equations are: [math](\frac{a'}{a})^2 = \frac{8\pi G}{3}\rho - \frac{k}{a^2} + \frac{\Lambda}{3}[/math] [math]\frac{a''}{a}= -\frac{4\pi G}{3}(\rho + 3p)+\frac{\Lambda}{3}[/math] BTW all this is according to Sean Carroll Living Review article http://relativity.livingreviews.org/Articles/lrr-2001-1/node3.html this is with c = 1 units, which simplifies things some. the scale factor of the metric (whose increase is the expansion of the universe) is denoted by the letter a. k is a spatial curvature parameter used to distinguish three cases k = -1, 0, +1 for negative curvature, spatially flat, positive curvature rho is an energy density, and easy to confuse with p pressure the universe appears to be spatially flat, the critical density rhocrit is that needed for it to be perfectly flat with k = 0 the Hubble parameter H is defined to be the time derivative a' of the scale parameter a, divided by a. [math]H^2 = (\frac{a'}{a})^2 [/math] for the time being assume we've included the Lambda term in rho as "dark energy, because this is a convenient way to set things up for calculating stuff, like the critical density. In the case of a spatially flat universe the first Friedmann equation boils down to [math]H^2 = \frac{8\pi G}{3}\rho_{crit}[/math] algebraically that turns into the formula for the critical density [math]\rho_{crit} = \frac{3}{8\pi G}H^2[/math] the Hubble parameter has been measured really accurately at 71 km/s per Mpc and this lets us calculate the critical density at 0.83 joule per cubic km.since the U tests out flat or very nearly so, this is taken to be the density of all the stuff, stars galaxies, light, dark matter, dust, dark energy etc. It all amounts to 0.83 joule per cubic km. And the dark energy being 73 percent (from supernova data) means that its share is 0.6 joule per cubic km. Sean Carroll is a blogger as well as one of the worlds foremost cosmologists. he's at chicago check out his blog sometime--it can be entertaining the name is "preposterousuniverse" the albert einstein institute near Berlin has charge of LivingReviews of Relativity and they asked Sean Carroll to do their article on Cosmological Constant---I chose to follow Carroll's notation because it's standard. Dont always like what Carroll says or agree with him but its an authoritative source,which reduces chances of confusion.

It may help visualize dark energy to know how much of it is in a cubic km. It is about half a joule---more exactly 0.6 joule a joule is the amount of energy it takes to lift a kilogram up by about 10 centimeters. it is less than the amount of energy involved in lifting a pound weight up one foot---but in the same ballpark. so a joule is very roughly a harmless smallish amount of energy like a footpound. And the dark energy, by the best measurements so far, in a cubic kilometer is about 0.6 joule. It is supposed to be constant and uniformly distributed. there's other stuff but that's a start

Starting another thread Admiral J asked an interesting question "What is the highest(heat) possible temperature? It's interesting that while the lowest possible temp has a value(absolute zero) even though it has never yet been reached. What about the highest or hottest temp possible. The biggest number I've seen is 100Million degrees C, or are there even higher temps?" this thread got a lot of posts but became involved in personality issues and lost contact with the starting question one way to address questions like this is to think about what is the natural scale of temperature---one that makes the formulas clean and simple. And nowadays there is increasing use of Planck scales (length, energy, time, temperature, mass...) because they impress people as comparatively "natural". Planck actually defined the Planck temperature in 1899 and calculated it in Centigrade (now Celsius) to approximately the temp we use today. And you could say that he "predicted the temperature of the Big Bang" because right at the beginning cosmologists postulate a "Planck era" during which the U had Planck temperature and planck density (one planck mass unit per cubic planck length) etc etc. And particles were whizzing around with essentially their kinetic energies being around the Planck energy unit. So cool, but it is ridiculous to say that max planck predicted the temperature of the big bang because he didnt even think about that, he just calculated the temperature as one of his "natural units" but just like the speed of light is an extreme speed, some of the units he calculated turned out to in some way extreme-----extremely short, extremly brief, extremely hot, extremely dense, extremely powerful in ter ms of wattage, extremely strong in terms of force. they didnt even have the Big Bang back in 1899. He was just trying to think up some units which were more universal and "natural" to his way of thinking than the metric ones and whatever else people had come up with so far. but it did happen the temperature he calculated back then, namely 1.4 x 1032 kelvin is the temp that cosmologists like to talk about existing right at first and then of course things expanded and cooled and it has never been that hot again. at least they used to. Now there are all these inflation scenarios and it is hard to keep track of the latest Big Bang fashions Furthermore it doesnt matter--we dont know what the BB was like and it was a long time ago. what about Planck temperature NOW. Well it is easy to define and using it, and other "natural unit" scales, makes formulas simple, and practically speaking it works as a Top End of the temp scale with absolute zero being Bottom End, for the simple reason that nobody talks about any temps higher than Planck----BECAUSE the laws of physics melt at that temperature. If you have a box with atoms in it and heat the box then as you approach that temp the matter comes apart into quarks which collide with each other hard enough to form microscopic black holes and it is a realm of the unknown---when things reach those energies and that temperature it is so abnormal as to be beyond reasonable conjecture. (there is a lively interest in inventing planck-scale physics these days but it has not been done, it is no exageration to say that it is an unknown realm, and I for one think of it as the Planck Temperature being the Melting Point of the Laws of Physics, and leave it at that) Another nice thing about planck temp is it has a simple formula there is this basic formula in physics E = kT where k is Boltzmann constant that connects temp scale with energy scale. at some T, the kT is the energy that is characteristic of things happening at that temp.------like air molecules kinetic energy is 3/2 kT ------like the jiggling energy of atoms in a crystal of metal is 3 kT----like the thermal glow from a hot thing has a mix of photon energies and a rather typical one is kT. So if you look at all the photons flooding in from the sun, a typical energy for one of them to have is kT, where T is the temp at the surface of the sun. Now Planck defined a natural unit of energy and the Planck temperature is simply that temperature for which kT is one unit of energy in his units, k is equal to one. there is a one-for-one correspondence between temp and energy. and Planck made it so that in his units the hbar constant (that relates frequency and energy) is also one. so Planck energy is just that amount of energy which correponds to a unit of frequency that is, one over his time unit----not "one per second" but one per Planck time unit. so the formulas are real basic well that's enough for now

I find alpha = 1/137 a lot more interesting than e because alpha tells you how strong the electrodynamic coupling is It tells you about nature. Quantum Electrodynamics (QED) is a theory based on this one parameter alpha and everything is calculated from formulas and powerseries in alpha. So you plug in alpha and you find the periodic table of elements and you find chemistry and you find how hot stars are and how fast they burn their fuel and a lot of interesting stuff. but e = 2.71828 has to exist by mathematical necessity and it has to be what it is. You dont have to measure it experimentally it just comes out of human mathematics. It occurs in lots of formulas because it is dictated by human custom how we shall write hour formulas and it is in accordance to the conventions to use e. But I do not think that e tells very much interesting stuff about nature. It could not be different however different nature was. Whereas if alpha was a few percent different nature would be radically changed. Intuitively the number contains information. So I went and put May 17 (the 137th day of the year) on the SFN calendar for next year, so as to have an Alpha Day

there is only one non-zero function which is equal to its own slope that is, f'(x) = f(x) for all real numbers x from minus infinity to plus infinity. mathematicians have a special name for f(1) they call it e. and the value is 2.71828... it is also called "base of the natural logarithms" which is fine if you know what base means and natural means and logarithm means but the main thing is that in the whole universe of mathematics there is only this one unique nontrivial real-valued function f(x) which equals its own slope, i.e. its derivative. and BTW all its derivatives are the same, f = f' = f" = f"' and so on and e is just a conventional symbol for the value this function has at 1: e = f(1)

Alpha Day is May 17, the 137th day of the year. The constant alpha is the basic constant in all electro-magnetic interactions and determines among other things why we have the elements we do and what their chemical properties are. So its being the right size and not a few percent different makes life possible. And keeps the sea from blowing up in an H-bomb fusion reaction and makes it so there are stable elements heavier than helium, and so on. It is fundamental to the universe. Alpha reciprocal is about 137.036..., so very close to 137. So a good approximation for alpha is 1/137. Alpha is better than PI

When is the day for the fine structure constant alpha? this number is as important and universal as pi the approximate value (analogous to 22/7 for pi) is [math]\frac{1}{137}[/math]

In French the acronym is OIN Organisation Internationale de Normalisation the choice of the acronym was a "compromise" or friendly merger between French and English In english the natural way to form the acronym would say IOS International Organization for Standardisation the "history of the name" paragraph at the official ISO website says that because it was different (OIN != IOS) they chose to make a veiled reference to the Greek word ISOS meaning EQUAL and to make the acronym neither exactly French or exactly english but rather ISO Here is what the French ISO site says: "Parce que le nom de l'Organisation internationale de normalisation donnerait lieu à des abréviations différentes selon les langues ("IOS" en anglais et "OIN" en français), il a été décidé d'emblée d'adopter un mot dérivé du grec isos, signifiant "égal". La forme abrégée du nom de l'organisation est par conséquent toujours ISO." (American engineers would have been happy with it because they would naturally want to say "international standards organization" in any case)

Again, this is not a math fact but something physical. It is about the Casimir effect, the energy of the vacuum and the force of attraction it causes between two conducting plates To make it simple suppose we are working in Planck units, there is a unit of force and a unit of distance to measure the separation d of the plates, and a Planck unit of area to measure the area A of the plates. The Casimir attraction force turns out to be proportional to [math] \frac{1}{d^4}[/math] and the constant of proportionality involves pi, so the force per unit area is: [math]\frac{F}{A} = \frac{\pi^2}{240} \frac{1}{d^4}[/math]

this is not a math fact but something about black body radiation at some given temperature T if you work in Planck units (c = G = hbar = k = 1) then there is a unit energy and unit length and area and temperature and so on and you can ask what is the radiant heat power per unit area of a generic surface at temperature T [math] \frac{\pi^2}{60} T^4[/math] thats the radiant heat brightness of something at temp T the fraction pi-square over 60 is the value of the Stefan-Boltzmann constant in natural, or Planck, units.

Right, many of the classical mediterannean people were well aware of earth being round and the greek mathematician Eratosthenes even calculated its circumference---and got the right answer within a few percent (if one allows for the weird oldfashione units of measurement he used). Dante was circa 1300, that is before Galileo (circa 1600) and Dante was merely a poet---but he used a spherical Earth, not a flat one, in his poem. Round earth has been a normal view for literate people since at least as far back as 200 BC (Archimedes, Eratosthenes time) in the Mediterranean and European cultures------about other places like Chinese and Mayan and Hindu and Inca and all that stuff I do not know maybe they also had round earth concept. Even Snorri the Icelander who wrote around 1200 referred to the "circle" of the earth, but those vikings up there were just barely literate so it is hard to be sure about what they thought. Tho far from being an expert in history and such questions, I strongly agree with you Mr. Ed 84, that it is a big mistake to suppose old people all thought earth was flat. (but some old maps look as if it was flat or maybe just a patch on a sphere, not the whole ball)

Martin Bojowald (Berlin) is preparing to quantize the standard black hole model and get rid of the infinite density business. (but he and colleagues have not accomplished this yet, as you point out it is not yet done) His track record is good, in 2001 Bojowald quantized the big bang singularity and got rid of the infinite density there, his 2001 paper was "Absence of singularity in Loop Quantum Cosmology" the work has been confirmed and extended by a lot of other people by now----a recent paper (with references to earlier work) is online http://arxiv.org/gr-qc/0407074 Bojowald's two most recent papers were setting up the machinery to quantize gravity in the context of black holes. You can find them online at arxiv.org. Or if you want ask me and I can easily get the links.

So Fischer beat Spassky in 1972 then forfit the rematch in 1975 then beat Spassky again in 1992 (ten games to five) and announced in 1996 he's out of chess and prefers "Fisher random" where the chess pieces are arranged randomly at the start of the game---I guess you have to think more creatively that way and cant go on having memorized past games and chessbook analysis---who knows it could be fun and beautiful. Maverick. what if Mozart lived to 61 years old and was on the run for having played a sonata for Napoleon when he was a non-person exiled to St Helena island what if Michelangelo was on the run for refusing to finish the ceiling for the Pope? but it never happened, Mozart as we all know finished painting the ceiling under the popes orders and as we all know Michelangelo died young never dedicated a sonata to that monster Bonaparte. but Fischer insisted on going to Belgrade and kicking Spassky's butt. thereby earning the displeasure of the US state department. I didnt realize what an unpleasant person he is! Also the first 11 games were in a Montenegrin town of Sveti-Stefan, I guess on the coast. And then after one or the other won 5 games the plan was to move the match to Belgrade. So it was continued in Belgrade after game #11. Also Fischer, whose mother was jewish (which I guess makes him nominally jewish) speaks scathingly of Jews! Also he is reported to have said that the United States should be destroyed.

What YT is asking for is what he calls "Cognitive" devices (rhymes, sentences etc) to aid in remembering science stuff. in American english we call such things "mnemonics" you have a mnemonic sentence or mnemonic rhyme to help recall something. More and more these days people are using the Planck length But there is no mnemonic to remember the formula there is a formula for it in terms of hbar, c, and G the gravitational constant. can anyone come up with a mnemonic for the formulas defining the Planck length or the Planck area? the area is another useful quantity and it is the square of the length. the Planck length and area are examples of natural units---ones cropping up more and more these days.

The spectral types of stars, from hottest down to coolest OBAFGKM Oh be a fine girl, kiss me! the sun, as luck would have it, is a medium size and medium hot star and it happen to be G type (where the word girl comes in the sentence) and that rhymes with G-spot so it is all easy enough to remember

Somebody at the Dublin conference made a transcript of the much-anticipated talk Stephen Hawking gave today on his proposal to resolve the black hole information paradox. They got the transcript to Sean Carroll a cosmologist/blogger at University of Chicago, who posted it here: http://pancake.uchicago.edu/%7Ecarroll/hawkingdublin.txt As you can see from the final paragraphs of the transcript, Hawking conceded his bet with John Preskill in style----the stakes being an encyclopedia, Hawking offered Preskill an Encyclopedia of Cricket. However Cricket is an obcure English pastime unknown to people in Preskill's part of the world---where they do more surfing and such. Preskill had, however, heard of baseball (which bears a superficial resemblance to Cricket) so Hawking in a grand gesture had the Encyclopedia of Baseball flown across the Atlantic so that he could present it as he conceded the bet. there are some interesting things to discuss about the paradox, and it helps to read what hawking actually said, instead relying on a journalistic interpretation.

http://pancake.uchicago.edu/%7Ecarroll/hawkingdublin.txt this is a transcript of the talk Hawking gave today wednesday 21 July at Dublin GR17 conference describing his idea of how to resolve the BH info puzzle

A lot of these are Hong Kong films in Cantonese dialect and contain plenty of martial arts kick and hack-work Siunin Wong Fei-hung tsi titmalau is "Iron Monkey" in the english version I gather it can be pretty grim unless one really likes Martial Arts. there are some japanese too Shinobi no mono is indeed Ninja and i think also Saiyuki

screen plays are good I didnt know til now that so many are available online

this is not odd it is a great screenplay a friend of mine was trying to break into the screenwriting business and she owns a copy of Get Shorty and I borrowed it for about 6 months one time. It is really beautiful several times i watched the DVD with the language turned on to be French and english subtitles I like how French gangsters talk. It was very good in french as well. Maybe everybody in Hollywood should be made to talk french and the world would be better

Phi, Glad you like it too, please tell me if a particularly memorable scene comes back to you. with the script we can find passages of good dialog. I got interested in what other films have the script available online. Maybe they all do! I didnt realize that, if its true. In "favorite movies" thread, tesseract mentioned Pulp Fiction. here is the script: http://www.godamongdirectors.com/scripts/pulp.shtml somebody else mentioned Get Shorty. I wonder if the script is online--- it is Elmore Leonard, should be especially good writing. Yes! here is the Get Shorty script: http://www.allmoviescripts.com/scripts/6432623013f3d75190272f.html