I'll copy this to PICLIst as much for fun as anything. Maths is in fact not dead but it has been dealt a blow very recently which spells disaster for mathematical research as we have known it to date. Everything which maths proves is still true but the certainty of being able to get from point A to B, even if they are similar and known, is now seen to be unknowable. This is not just a rehash of Godel - it is a new "discovery" of possibly greater import. > I have for many years maintained a passing interest in theoretical physics > etc. and have probably read most of the readily available "popular" > literature on the subject plus some less accessible material which I have > happened across. I don't pretend to understand all of it in detail but I > think I do have a reasonably good grasp of the basic theories and the issues > they are attempting to explain/confront. I try > I have become somewhat bemused by what I (and others) perceive as the > increasingly bizarre theories being put forward in an attempt to "explain" > and model/predict observable physical behaviour, I just laugh (quite literally.) "Let there be light" is often a fairly good target model, although understanding how we get from there to here is not always (ever?) straight forward. > and have come to wonder is > there are not some parallels between what is going on in thoretical physics > now and what was going on in the first quarter of last century in > mathematics. I refer to the ambitious plan of David Hilbert (and others > like Bertrand Russell) to formalise mathematics which was subsequently shown > by Kurt Godel (in 1931) to be complete folly. You need to read a recent New Scientist article that I have. It's the sort of material that you just have to accept that they probably know what they are doing while reserving judgement - could as likely be an April fools' hoax (not an April mag) but there is so much of that at the leading edge these days that one can feel uncomfortable about but cannot reject due to lack of adequate knowledge. A mathematical researcher has very recently demonstrated that mathematics is full of islands of fact which are not necessarily connected and the connectivity or otherwise is unknowable without trying to walk there and finding out. (Literally "you can't get there from here"). The chain of results of a series of events being connecrted is used to generate a 0/1 figure (this is tyhe solution to the Turing "halting problem" in each case and these are used to generate an unknowable number they call (naturally enough) Omega. They compare mathematics to field zoology - someone suspects that there is a new unknown primate in the Borneo jungle and goes to look for it. He/She may well find one but there is no formal logical basis for the expectation. This is one of THEIR examples. People doing mathematical research have expect3d that there is a change of connectivity between apparently similar "stuff" but it aint necessarily so and nobody can say why or why not or if or not any particlar apparently connected matrers really are connected. It feels to me somewhat akin to Fractal connectivity - two apparently connected physical points may or may not be - there is no *(known) numerical way of determining if they are in fact connected othe rthan stepping down the ever diminisghing dimensions of the fractal pattern - IF they both join then they join. If they don't join for as long as you serach then they MAY still jopin but you haven't found out yet. If they don't join you will never find out - just hunt forever. The physical connection corresponds to the Turing halting result being true. The APPARENT non joining corresponds to the it-hasn't-halted-yet case. They have a whole family of second order effects waiting in the wings once they start to get to grips with the implications of Omega. > Is it not just possible (probable ?) that there is not (and never can be) a > grand universal theory which explains everything in a self-consistent > manner. If one is prepared to consider this possibility, then theoretical > fantasies such as cosmic strings, 23-dimensional space, dark matter, > negative time, infinite divergence of parallel futures, and the like take on > a whole new light. AFAIK 10 dimensions is the normally acceoted figure. Interestinghly (and there's no reason that this is necessarily more than coincidence, but it may be) very ancient Jewish scholars (Achmonides?) deduced from studying the Torah that the universe was composed of 10 dimensions of which 4 were knowable and 6 were unknowable. Of the 10 we know of 4 and the other 6 insist, they tell me, in being "rolled up" ( Incidentally, whatever happened to theory of primordial black holes - > supposedly these have existed since the big bang and (according to theory) > are numerous, more or less uniformly distributed throughout the universe, > and readily account for the "missing mass". "Standard" / classical black holes have a minimum size of approx 3 stellar masses. As I understand it "quantum" black holes which were only able to be formed during the early stages after the putative big bang can be very small but may perhaps have a maximum upper size ?? A black hole has a number of parameters which are directly tied to its mass. These include size, temperature, radiation rate and lifetime. A BH looks lime an ideal black body. Hawking demonstarted that a BH radiates but a BH will suffer net growtgh if its mean environment is hotter than it's temperature. For classical back holes > 3ish stellar maases the temperature is well under 1 degree K and the background radiation left over from the (again, putative) big bang ensures that it is ALWAYS swimming in an energy soup that is hotter than it is so ALL classical black holes have a net growth. However, quantum BHs are smaller and will net radiate. As they radiate they shrink and their temperature rises so their radiation per area increasesso they get hotter and ... poof. However their very very very small physical size ensures that the radiation rate is very very small until they get very very hot. At the very end of a longish life they quite suddenly run away and explode in a shower of very very hard ganmma radiation. Quantum BHs from the pBB will in most cases suffered net radiation and will exterminate themselves. To survive the 15 billion years (+/- 14.999996 billion years :-) ) that they think the universe has been around a QBH needs to weigh a billion tonnes and be p[roton size - see figures below.. The point is that there are liable to be far fewer QBHs now than there were then if they ever existed AND if any are at the dying point abouty now then they should produce a very characteristic signature as they die. To put some figures on the "very"s I've added some rough stuff below of varying relevance which will have some errors in it. Some key points from below include - By the time a BH is a smassive as the sun its temperature is 10^-7K so it is a net grower. - A QBH mass 10^9 tonnes = 10^15 grams would be the size of a proton = trillion degrees K (!). Radiates gamma and photons. This would take 10 billion years to evaporate completely BUT in the last 0.1 second would liberate 10^6 megatonne Multi H-bomb output (!!!) - Tunguska "meteorite" was probably about 10 megatonne. From elsewhere: A 1 km comet strike would have about E22 megatonne energy ! - A QBH over moon mass and 0.1mm diamater has temperature under 2.7K and will grow 9and cool). +++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++ .BLACK HOLES: ++++++++++++ Black Holes. J P Luminet. CST 523.8 L95 Cambridge University Press. orig=French. 300 pages. Excellent . p210: SCHWARZCHILD BLACK HOLES HAVE TEMPERATURE INVERSELY PROPORTIONAL TO MASS. Mass same as sun - temperature is negligible. = 10^-7 degree Kelvin (!) Mini asteroid = 6000 K / Visible radiation. 10^9 tonnes = 10^15 grams = size of proton = trillion degrees K (!). Radiates gamma and photons. This would take 10 billion years to evaporate completely but in the last 0.1 second would liberate 10^6 megatonne Multi H-bomb output (!!!) The Lifetime of a black hole is proportional to the cube of its mass. 1 tonne in 10^-10 second. 10^6 tonnes in 10 years. (Note rapid increase in life but drop in radiation rate due to cube law. ( 1 million toness = 10 years) (1000 million tonnes = 10 billion years) Minimum mass to survive 15 billion years is a billion tonnes = mass of a mountain and radius = 10^-13 cm (!). = same size as a proton. V large BH lifetimes are very much in excess of universe lifetime. Rate for v large BH is very slow and is offset by growth rate. Cosmic background is 2.7K. BH smaller than the moon = 10^26 gram = 0.1 mm have temps over 2.7K. Larger holes are cooler and should suck energy from background. Therefore still extant radiating holes are 10^15 gram < x < 10^26 gram. Smaller have vanished. larger are growing. From above Life = M^3 x Kl Kl <> 10^-19 to 3 x 10^-19 M = Kilogram, L = Second Temperature = Kt/M Kt <> 10^21 T degrees Kelvin M Kilogram Added later: Black Body emissivity = 1.73 10^-7 Btu/mr ft^2 T^4 which should give radiation rate to a 0K sink. mr == hr ??? Schwarzchild radius R=2GM/c^2 = M/E27 Metre, Kilogram Based on the above a BH of mass 3*10^18 Kg would have a temperature of 300 K and would exert one gravity at about 6400m radius. The key question is, what is the energy radiation RATE? ANSWER: (I think) - very wimpy. Radiation rate is the same as for any black body at the same temperature. As a BH of this mass would be super-microscopic and only at 300K its radiation would be minimal. Even a 1000 K pinhead will not put out much heat. Therefore probably need multiple smaller BH's at raised temperature and same overall mass to get enough radiation. The temperature would be rather high to get the energy out through such a small size and would be in very nasty particles. Some means of nicely and safely converting these to heat would be needed. A star CAN have a quantum black hole at its core and function virtually unchanged. The radiation and absorption rates would adjust itself to match. This has been postulated as a reason for the Sun's neutrino deficit but more conventional mechanisms with a better fit have since been proposed. Tunguska meteorite was equivalent of 1500 Hiroshima bombs. NO crater !. Best theory is a meteor/comet fragment hundreds of metres across falling contra to planet's rotation and vapourising in atmosphere. Two astronomers proposed the passage of a mini black hole right through planet (exit in Atlantic ocean) but this would have caused seismic and atmospheric shock waves on exit which were not observed. Positional uncertainty Electron 1cm if velocity is measured to within 1cm/sec Proton 5um if velocity is measured to within 1cm/sec Proton is 2000 times more massive than electron. NB: While 5um is much less than for an electron the diameter of the Proton is a billion times smaller than the uncertainty ! (Dia Proton = 5 x 10^-15 ? Vacuum fluctuations: Electron - positron 10^-21 seconds Proton - antiproton 5 x 10^-25 seconds ie 2000 times less as 2000 times more massive. Photon is its own anti-particle (?) Hot metal radiates photon-photon but at a Trillion degrees K = electron/positron pairs (ie Terra + watt lasers concentrated into a small area will generate matter/antimatter pairs in free space (space would not be very free with that much energy there)). ============================================================================ BARYON NUMBERS - conserved in creation/destruction reactions (except where a black hole is involved) Photon # = 0 Neutron 1 Anti-neutron -1 So a photon can be converted to a pair of N/An but not vice versa BUT !!! Black holes do not conserve Baryon number ! They are formed from either positive or negative baryon number material but radiate on average matched pairs of positive and negative B # particles. Einstein - God does not play dice. Hawkings - Not only does God play dice but he throws them where we cannot see them. LUMINET Object Mass Radius Schwarzchild radius Atom 1m26Kg 1m8 cm 1m51cm Person 100Kg 1 metre 1m23 cm Mountain 1E12 Kg 1 Km 1m13 cm Earth 1E25 Kg 1E4 Km 1 cm Sun 1E30 Kg = 1M 1E6 Km 1 Km White dwarf 1M 1E4 km 1 km Neutron Star 1M 10 km 1 km Galaxy 1E11 M 1E5 ly 1m2 ly (light year) Universe 1E23 M 1E10 ly 1 E10 ly ie Rs = M/E27 Metre, Kilogram ++++++++++++++++++++++++++++++++++++++++++++++++++ Black Body temperatures: Name WaveLength Photon Energy Black Body temp cm EV K Radio >10 1m5 3m2 Microwave .01-10 1m5-1m2 3m2-30 Infrared 1m4-1m2 1m2-1 30-3000 Visible 2m5-1m4 1-6 3000-15000 UV 1m7-2m5 6-1000 15,000-3,000,000 X ray 1m9-1m7 1000-100,000 3p6-3p8 Gamma ray <1m9 >100,000 >3p8 Illuminated black holes produce a halo when viewed from the direction of the illumination source. Also a series of points in space at 2.96 radii when viwed at 90 degrees to the illumination. (These affects due to curving of light around the hole (other less bright patterns exist due to curvature around hole many times with decreasing energy). A BH with an acretion disk would allow distorted images of the bottom of the disk to be seen due to light bending. An acretion disk is stable only outside 3 Schwarzchild radii - below this distance it plunges directly into the hole without emitting em radiation. 1 electron volt = 1.602m12 erg = 1.602m19 joule. Einstein: Photon energy = 1.24m4 Ev/Lambda (L in cm) eg 7.35cm microwave photon energy = 1.7m5 Ev Visible light (lambda = 5m5 cm) = 2.5 Ev Chemical reaction energies are typically around 1 Ev. (eg removing electron from Hydrogen = 13.6 eV - a very violent reaction) I even recall that there was at > one time thought to be good evidence of them from observations of apparent > gravitational lensing. Sounded an eminently sensible idea to me - guess > that's why it never stood a chance. > > Regards, > > Ken Mardle > > > -- http://www.piclist.com hint: PICList Posts must start with ONE topic: [PIC]:,[SX]:,[AVR]: ->uP ONLY! [EE]:,[OT]: ->Other [BUY]:,[AD]: ->Ads