Question on infinity (singularity)
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From: kado on 16 Mar 2010 04:45 On Mar 15, 7:52 am, Uncle Al <Uncle...(a)hate.spam.net> wrote: > snip > > Don't you mean googleplex, i.e., google^google? However, even this is a finite number, and does not equate to infinity. D.Y. Kadoshima
From: Han de Bruijn on 16 Mar 2010 06:45 On 15 mrt, 08:34, MicroTech <henry.ko.nor...(a)gmail.com> wrote: > In physics (and cosmology) I quite often see references to > "singularities" (as inside "black holes" and as the origin of the so > called "big bang") as being "points with no size, of infinite mass, > infinite density, infinite temperature, and infinite pressure" (or > something to this effect). > > As I understand an "infinite quantity", it will stay infinite even if > one adds n, or subtracts n, or multiplies by n, or divides it by n <> > 0... > > I am told by science that "the universe is estimated to contain 10^80 > particles." This is a big number, for sure, but a far cry from an > infinite number of particles. It seems to me that if we subtract 10^80 > from an infinity of particles, the remaining number of particles would > still be infinite... So, if the "original singularity" indeed had > infinite mass, what in the "big bang" made it finite, suddenly? And > does not the same question equally apply to density, temperature, and > pressure? > > A related question is, if something has infinite density, how can > there be room for its constituent particles to freely move around (as > in temperature)? How can something with infinite density be infinitely > hot? > > Another related question is: if a "singularity" shows up in an > equation (as is claimed to happen in some of Einstein's equations), is > this not a sure sign that something in the equation is wrong? Like > dividing by zero, somewhere? > > As I am neither a mathematician nor a physicist, it may well be that > I've got the concept of "infinity" wrong. I would really appreciate it > if someone in this forum can point out to me where my understanding is > wrong (and provide correct interpretations of the term)! > > References to published papers (accessible on line), especially papers > showing what the "Einstein Singularities" are, would be very much > appreciated! > > Henry Norman In physics, roughly speaking, there are TWO kinds of singularities: those that can be renormalized and those that cannot be renormalized. Renormalization is the convolution (integral) of the singularity with a "hat" function, such as for example a Gaussian distribution. Which is actually the modelling of a how a singularity would be measured by a device with "finite aperture". Mathematical details are found in: http://hdebruijn.soo.dto.tudelft.nl/QED/singular.pdf Singularities that CAN be renormalized are NOT "physically serious". And there is no need to rule them out. The true (measured) outcome at a renormalized singularity is simply a (not always large) number which is not quite well defined. Singularities that can NOT be renormalized are physically impossible. They just indicate that the current physical modelling FAILS at those places. An example of a renormalizable singularity is the Coulomb field of an electron. An example of a non renormalizable singularity is the ideal gas law at volume zero. Indeed it is seen that the ideal gas law must be replaced by another law in that neighbourhood: the gas will become a fluid in the first place. Most interesting are cases where there exists a continuous as well as a discrete modelling of the _same_ physical phenomenon. In such cases, it can happen that the continuous model shows singularities while it is quite certain, from the discrete point of view, that singularities cannot exist at all. The only plausible explanation remaining is that the continuous modelling actually BREAKS DOWN at the singularities and the discrete model prevails there. An outstanding example is found at: http://hdebruijn.soo.dto.tudelft.nl/QED/index.htm#ft In an accompanying paper it is explained _how_ exactly the continuous model at hand breaks down. And it should be even possible in principle to measure the breakdown. The model predicts it to happen at "primary mass flow equal to a critical value of about 215.6 kg/s". Details in: http://hdebruijn.soo.dto.tudelft.nl/jaar2004/IHXTAK.pdf Han de Bruijn
From: Jeroen Belleman on 16 Mar 2010 09:03 Han de Bruijn wrote: > > In physics, roughly speaking, there are TWO kinds of singularities: > those that can be renormalized and those that cannot be renormalized. > > Renormalization is the convolution (integral) of the singularity with > a "hat" function, such as for example a Gaussian distribution. [...] Thank you for this. A very enlightening peek into a field outside my direct experience. It doesn't look so formidable after all. Jeroen Belleman
From: Han de Bruijn on 16 Mar 2010 09:58
On 16 mrt, 14:03, Jeroen Belleman <jer...(a)nospam.please> wrote: > Han de Bruijn wrote: > > > In physics, roughly speaking, there are TWO kinds of singularities: > > those that can be renormalized and those that cannot be renormalized. > > > Renormalization is the convolution (integral) of the singularity with > > a "hat" function, such as for example a Gaussian distribution. [...] > > Thank you for this. A very enlightening peek into a field outside > my direct experience. It doesn't look so formidable after all. > > Jeroen Belleman Renormalization is basically much simpler than most people think. Most theoretical physicists tend to exaggerate / mystify their achievements for rather mundane reasons: nice and easy is not rewarding these days, when counted in research money. Han de Bruijn |