Descriptive Set Theory
I've been looking a little into what there is on-line about descriptive set theory, a relatively new field. It seems that with the questions about cardinality and descriptions on this list, that descriptive set theory (Polish spaces being an important element) would be useful, if not essential. A search of this list doesn't turn up any references to it. Does anyone have enough knowledge of it to give a brief note on how it ties in with this list's discussion? Tom Caylor
Fwd: Re: ROSS MODEL OF THE UNIVERSE - The Simplest Yet Theory of Everything
Note: forwarded message attached. ---BeginMessage--- Jesse and George: the cobbler apprentice speaketh: you, mathematically high-minded savants look for a primitive realization of 'negative mass' etc, while you find it natural to use negative numbers. If I was 185lb last week and now 180 lb, then I have 5 lb in negative. Of course I cannot physically identify the 'missing mass', but mathematically it exists and I can calculate with it, speak about it, think about it: it 'exists'. Not a piece of negaitive mass, of course. You got used to how much is minus 2 as a POSITIVE value, it is a matter of habit-speak, it means: missing from the rest. As compared to... washed away in routine talk. I wouldn't look for something positive in negative. What you are missing is the language to fit it into any theory made up for poitive items. Imagine the confusion when the zero was invented. Does zero exist? (Ask Hal) Have a good day John Mikes --- Jesse Mazer [EMAIL PROTECTED] wrote: George Levy wrote: Negative matter/energy however are different. If negative matter/energy could exist they would give space a negative curvature. The issue of negative curvature is somewhat separate from negative mass, though--if the density of matter/energy in our universe was below the critical density Omega, the universe would have negative curvature, no need for negative mass (see http://tinyurl.com/9ox67 ). It might be true that adding a certain density of negative mass/energy would have the same effect on spacetime curvature as subtracting the same amount from the density of positive mass/energy though, I'm not sure. Negative matter/energy may be identical to dark energy. I think dark energy has negative pressure (tension, basically), but not negative energy--see section 6 of the article at http://tinyurl.com/8kepb , the one titled Negative Pressure. But the Casimir effect that pulls two parallel plates together (see http://tinyurl.com/anoky ) might qualify as negative energy--at least, the energy density between the plates is lower than the energy of the ground state of the quantum vacuum, but whether this would actually have the same effect as negative energy in GR is probably something physicists can't be sure of without a theory of quantum gravity. Here's an article on negative mass/energy, and its relevance to keeping wormholes open in GR: http://www.physics.hku.hk/~tboyce/sf/topics/wormhole/wormhole.html Jesse ---End Message---
Re: ROSS MODEL OF THE UNIVERSE - The Simplest Yet Theory of Everything
On Thu, Oct 06, 2005 at 08:08:13PM -0400, Jesse Mazer wrote: This idea looks like it's pretty similar to LeSage's pushing gravity theory--there's an article on it at http://en.wikipedia.org/wiki/LeSage_gravity which points out fatal flaws in the the idea. It's also discussed in the second chapter of Richard Feynman's The Character of Physical Law, I'll quote the relevant section here: ... Very interesting. I had heard of this theory a couple of decades ago, but never new who originated it. Interestingly, something similar is being revived by Rueda and Haisch. see arXiv:gr-qc/0504061. I quote a recent New Scientist article on the topic: WHERE mass comes from is one of the deepest mysteries of nature. Now a controversial theory suggests that mass comes from the interaction of matter with the quantum vacuum that pervades the universe. The theory was previously used to explain inertial mass - the property of matter that resists acceleration - but it has been extended to gravitational mass, which is the property of matter that feels the tug of gravity. For decades, mainstream opinion has held that something called the Higgs field gives matter its mass, mediated by a particle called the Higgs boson. But no one has yet seen the Higgs boson, despite considerable time and money spent looking for it in particle accelerators. In the 1990s, Alfonso Rueda of California State University in Long Beach and Bernard Haisch, who was then at the California Institute for Physics and Astrophysics in Scotts Valley and is now with ManyOne Networks, suggested that a very different kind of field known as the quantum vacuum might be responsible for mass. This field, which is predicted by quantum theory, is the lowest energy state of space-time and is made of residual electromagnetic vibrations at every point in the universe. It is also called a zero-point field and is thought to manifest itself as a sea of virtual photons that continually pop into and out of existence. ?If particles are at rest, then the net effect of this jiggling is zero, but an accelerating particle would experience a net force? Rueda and Haisch argued that charged matter particles such as electrons and quarks are unceasingly jiggled around by the zero-point field. If they are at rest, or travelling at a constant speed with respect to the field, then the net effect of all this jiggling is zero: there is no force acting on the particle. But if a particle is accelerating, their calculations in 1994 showed that it would encounter more photons from the quantum vacuum in front than behind it (see Diagram). This would result in a net force pushing against the particle, giving rise to its inertial mass (Physical Review A, vol 49, p 678). But this work only explained one type of mass. Now the researchers say that the same process can explain gravitational mass. Imagine a massive body that warps the fabric of space-time around it. The object would also warp the zero-point field such that a particle in its vicinity would encounter more photons on the side away from the object than on the nearer side. This would result in a net force towards the massive object, so the particle would feel the tug of gravity. This would be its gravitational mass, or weight (Annalen der Physik, vol 14, p 479). ?If they could come up with a prediction, people would take notice. We're all looking for something we can measure? Rueda and Haisch say this demonstrates the equivalence of inertial and gravitational mass - something that Einstein argued for in his theory of general relativity. In place of having the particle accelerate through the zero-point field, you have the zero-point field accelerating past the particle, says Haisch. So the generation of weight is the same as the generation of inertial mass. The idea is far from winning wide acceptance. To begin with, there's a conundrum about the zero-point field that needs to be solved. The total energy contained in the field is staggeringly large - enough to warp space-time and make the universe collapse in a heartbeat. Obviously this is not happening. Also, the pair's work can only account for the mass of charged particles. Nobel laureate Sheldon Glashow of Boston University is dismissive. This stuff, as Wolfgang Pauli would say, is not even wrong, he says. But physicist Paul Wesson of Stanford University in California says Rueda and Haisch's unorthodox approach shows promise, though he adds that the theory needs to be backed up by experimental evidence. If Haisch [and Rueda] could come up with a concrete prediction, then that would make people sit up and take notice, he says. We're all looking for something we can measure. Journal reference: Annalen der Physik (vol 14, p 479) -- *PS: A number of people ask me about the attachment to my email, which is of type application/pgp-signature. Don't worry, it is not a virus. It is an electronic signature, that may be used to verify this email came from me if you have PGP
Re: ROSS MODEL OF THE UNIVERSE - The Simplest Yet Theory of Everything
Jesse wrote Well, you're free to define "negative mass" however you like, of course--but this is not how physicists would use the term. When you plug negative values of mass or energy into various physics equations it leads to weird consequences that we don't see in everyday life, such as the fact that negative-mass objects would be gravitationally repelled by positive-mass objects, rather than attracted to them. Jesse you are too quick. If you actually plug the right signs in Newton's equations: F=ma and F=Gmm'/r2 you'll discover that positive mass attracts everything including negative mass, and that negative mass repels everything including negative mass. The behavior is markedly different from that of matter and antimatter. So negative mass could never gravitationally form planets but could only exist in a gaseous or distributed form in the Universe and appear to cancel long range gravitational force (possibly what we are seeing with the Pioneer spacecrafts?) George Levy
Re: ROSS MODEL OF THE UNIVERSE - The Simplest Yet Theory of Everything
--- Jesse Mazer [EMAIL PROTECTED] wrote: John M wrote: Jesse and George: SNIP JeMa: Well, you're free to define negative mass however you like, of course--but this is not how physicists would use the term. When you plug negative values of mass or energy into various physics equations it leads to weird consequences that we don't see in everyday life, such as the fact that negative-mass objects would be gravitationally repelled by positive-mass objects, rather than attracted to them. Likewise, in general relativity only negative mass/energy would be able to hold open a wormhole, there'd be no way to arrange positive mass/energy to do that. Jesse JohnMi: There is a 'physicist-invented' system (a miraculous edifice) of the model physics, the explanatory ever modified quantitative treatment of the ever increasing knowledge (epistemically enriching cognitive inventory continually further-discovered) going through systems, all with equations including still holding and duly modified expressions (eg. entropy). (It is incredibly successful and productive to originate our technology.) The entire setup is based on positive mass (matter?) and energy. It is a balanced entity. Put a new patern into it and the whole order goes berzerk. The difficulty is the modelwise-reduced values and the APPLICATION of the results of math onto them. The beyond the model boundaries effects are disregarded. We have a balanced complexity and if we try to alter one segment the thing falls apart. We must not include e.g. negative mass into a complexity built on positive mass only. It has no provisions for a different vision. (Heliocentric constant orbiting could not fit into the planatary geocentric retrogradational image, it was deemed false. Maybe paradoxical. Astronomy had to be rewritten for the new concepts, it did not fit into the (then) Ptolemaic order. Heliocentric was wrong.) We are skewed by the past 26 centuries into seeing only the positive side of matter and energy. All the math equations are built on that. Of course they reject another view. Gravitation - or whatever we DON'T know about it - is no proof for rejecting a new idea which is outside of the existing ignorance about it. Equations or not. The fantasy of a wormhole ditto. Phlogiston neither(haha). Equational 'matching' within the same system and its values is not too impressive. The values are captive to the present (and past??) instrumentation and their calculative evaluation. If something does not match: it is wrong a priori. Alter the experimental conditions! Observations are rejected because some theory prohibits them. (Of course the 'observations' are also interpreted). I am not advocating the negative mass and energy idea, just fight the 'methods for their rejection' before we look into a possibility to use them right. Nobody took a second explanation for the redshift seriously, because Hubble's ingenious idea was so impressive. And today, after millions of so slanted experiments, we all expand. Irrevocably. And selectively only. Thanks for a serious reply. I did not intend to go that deeply into it. John M
Re: ROSS MODEL OF THE UNIVERSE - The Simplest Yet Theory of Everything
I'm not really confusing the two, but the idea is so imprecisely put it probably seems as though I do. The Dirac equation has both positive and negative energy solutions. The Dirac solution to the negative energy solutions was that they are all present as an unobservable Dirac sea. If you pop a particle out of the sea, the resulting hole has positive mass, and opposite charge - what we conventionally call antimatter. The problem is that this idea only works for fermions, obeying the Pauli exclusion principle. Feynman's solution goes one better, and talks about particles travelling backwards in time, which also works for bosons. What I was speculating was what impact embedding the Dirac equation into a curved spacetime might have. Might it lead to a net imbalance between matter and antimatter, or even just an imbalance between positive and negative energy solutions. I don't know - I haven't done the maths. It also wouldn't surprise me if someone has done the maths in the 75 years since the Dirac equation was written down, and found it doesn't work. Cheers On Wed, Oct 05, 2005 at 08:11:16PM -0700, George Levy wrote: Russell Standish wrote: Incidently, here's my own theory on the origin of matter. (Special) relativistic quantum mechanics delivers the prediction of matter being in perfect balance with antimatter - this is well known from Dirac's work in the 1930s. However, if spacetime had a nonzero curvature, is this not likely to bias the balance between matter and antimatter, giving rise to the net presence of matter in our universe. It strikes me that mass curves spacetime is the wrong way of looking at General Relativity - causation should be seen the other way - curved spacetime generates mass. As I mentioned above, it is not surprising that spacetime is curved, what is surpising is that it is so nearly flat. Russell, you are confusing antimatter with negative matter/energy. According to convention antimatter has inverted electrical charge and therefore when the amount of matter and antimatter are in equal amount, the net charge is zero. Antimatter, however, has positive mass corresponding to positive energy in the sense of E=mc^2 . Consequently, antimatter as well as matter give space a positive curvature. Negative matter/energy however are different. If negative matter/energy could exist they would give space a negative curvature. Negative matter/energy may be identical to dark energy. George Levy -- *PS: A number of people ask me about the attachment to my email, which is of type application/pgp-signature. Don't worry, it is not a virus. It is an electronic signature, that may be used to verify this email came from me if you have PGP or GPG installed. Otherwise, you may safely ignore this attachment. A/Prof Russell Standish Phone 8308 3119 (mobile) Mathematics0425 253119 () UNSW SYDNEY 2052 [EMAIL PROTECTED] Australiahttp://parallel.hpc.unsw.edu.au/rks International prefix +612, Interstate prefix 02 pgp6N05gRyCfC.pgp Description: PGP signature
Re: ROSS MODEL OF THE UNIVERSE - The Simplest Yet Theory of Everything
George Levy wrote: Jesse wrote Well, you're free to define negative mass however you like, of course--but this is not how physicists would use the term. When you plug negative values of mass or energy into various physics equations it leads to weird consequences that we don't see in everyday life, such as the fact that negative-mass objects would be gravitationally repelled by positive-mass objects, rather than attracted to them. Jesse you are too quick. If you actually plug the right signs in Newton's equations: F=ma and F=Gmm'/r2 you'll discover that positive mass attracts everything including negative mass, and that negative mass repels everything including negative mass. You're right, I got it backwards, I was just going from memory there. The negative-mass object will be attracted to the positive-mass one, while the positive-mass object will be repelled by the negative-mass one. So if you have two masses of equal and opposite magnitude, they'll accelerate continuously in the direction of the positive-mass object, with the distance between them never changing (at least according to Newtonian mechanics, it might not work quite the same way in GR). Jesse
