gwyn@brl-tgr.ARPA (Doug Gwyn <gwyn>) (01/01/70)
> Assume that the energy of a "still" electron is ~ due to its electro- > static energy. ... Aw, I was hoping for something new. If you're going to assign a radius to an electron based on having pure electrostatic energy (== mass by special relativity), then you need to explain why its parts don't repel each other (in other words, why it is a single cohesive entity). The only semi-classical explanation for that seems to be that it has no parts, which is tricky if it has nonzero radius... This idea was dropped early in the 20th century. That doesn't prove that it's wrong, but people weren't happy with it.
williams@kirk.DEC (John Williams 223-3402) (08/15/85)
I have a theory somewhat similar, which I call Historical Relativity. This somewhat indirectly states that Matter is ejected from black holes when black holes form inside. Time being the orthagonal direction, it points differently inside a black hole. It would then be possible for time to reorient itself by the same mechanism that causes black holes inside the black holes. This would explain the cosmic jets we have observed in the distant regions of the universe. My intuition tells me that the universe is a continuous function. This would not necessitate a creator, where would a creator come from? A mathematical function simply exists. John Williams
cjh@petsd.UUCP (Chris Henrich) (08/17/85)
[] In article <3656@decwrl.UUCP> williams@kirk.DEC (John Williams 223-3402) writes: > My intuition tells me that the universe is a continuous function. >This would not necessitate a creator, where would a creator come from? >A mathematical function simply exists. As I remember the definition of "continuous function" from various mathematical courses and books, it is this: In an elementary context: f is continuous at x0 if the limit of f(x) as x approaches x0 exists, and is equal to f(x0). (Perfunctory apologies for a crude approximation to mathematical notation.) The function is continuous if it is "continuous at x0" for every x0 in its domain. Another definition, roughly equivalent to the first, is this: The function f is continuous at x0 if, for every Eps > 0, there exists a Del > 0 such that | x - x0 | < Del ==> |f(x) - f(x0)| < Eps. Or, if one has the notion of a "distance" or "metric" on the domain and another on the range, then The function f is continuous at x0 if, for every Eps > 0, there exists a Del > 0 such that dist(x, x0) < Del ==> dist( f(x), f(x0) ) < Eps. The most general definition known to me is like this. Let X and Y be topological spaces. (I.e. they are sets, and for each a class of "open" subsets is determined somehow.) Let f be a function whose domain is X and whose range is contained in Y. Then f is continuous if, for every open subset S of Y, the inverse image of S under f is an open subset of X. References are abundant. Books on "mathematical analysis" or "functional analysis" usually explain some or all of these definitions. (Good ones include _Analysis_I_ and _Analysis_II_ by S. Lang.) See also introductory books on "topology." There are good ones by Kelley and by Dugundji, and many more. If we try to apply these definitions to Mr. Williams's statements, nothing much happens. To call the universe a continunous function seems to me to be saying remarkably little. What, pray tell, is the domain, and what is the range? These questions being settled, can you tell us something about the values the function takes at various elements of the range? Or is there some completely different idea that is going by the name "continuous function"? If so, what is it? Regards, Chris -- Full-Name: Christopher J. Henrich UUCP: ..!(cornell | ariel | ukc | houxz)!vax135!petsd!cjh US Mail: MS 313; Perkin-Elmer; 106 Apple St; Tinton Falls, NJ 07724 Phone: (201) 758-7288
pmk@prometheus.UUCP (Paul M Koloc) (08/17/85)
> possible for time to reorient itself by the same mechanism that causes > black holes inside the black holes. This would explain the cosmic jets > we have observed in the distant regions of the universe. > John Williams Interesting! > My intuition tells me that the universe is a continuous function. Two things tell us that the universe isn't continuous. First, the "big bang", and second, the constant "h bar" or even the fact that particles are not points. Time can more understandably be viewed as as "unfolding" of sequential infor- mation arrays like the distinct frames of a moving picture. The framing rate for a particle like a neutron would be ~(m*c^2)/(<h bar>) where "m" is the mass of a neutron, "c" the speed of light, and "h" Planck's constant. The framing rate decreases with the increase in effective mass of a neutron due to its general and special relativity effects (its position in a dense gravitational field or in rapid motion "velocity space"). If space were continuous then an infinite number of points would exist along a path an "inch" long. Scanning this space with a "point" test particle would not discover any "spatial holes" or gaps where "points" aren't defined (exit). In fact all of the information known to man (and the angels) could be put into a binary code and stored in such a space. Our space is "grainy" and there are gaps and spaces, and nature has a special trick to make it "look" continuous. Mathematically it is a "delta function" and in reality it is "the particle" The trick is also used by physicists to smooth out grainy data on a film strip. It is simply to make the width of the film scanning aperture or "slit width" wide enough so that there is always a few grains within view. Making the aperture even wider reduces the fluctuations and makes the output even smoother and perhaps less exact. > My intuition tells me that the universe is a continuous function. > This would not necessitate a creator, where would a creator come from? > A mathematical function simply exists. > John Williams Energy is more or less proportional to the square of "grain density" or "information density". That means if we pack information into a smaller space, the energy density goes up and the time or framing rate goes down. That also implies that as the framing rate decreases each frame has more "persistence" There is obviously information in our 3 space and that and the operators that "process" it are together what constitute entities we observe as par- ticles. Information could also exist in two space and 1 space, independent- ly of whether or not three space exists. Of course, the "physics" of those spaces would be different than for three space". The idea is that informa tion could flow from a dense higher energy density form to a lower density form. Then it could flow from 1 space to two and from two to three. In the latter transition it would appear to create a big bang and condense into the preferred form of three space, namely, matter. Also as "existence" (or information) perculates down from one to two dimensions, time activates and then in thee dimensions passes at a faster rate or "speeds up" Since lines can cross in two space and in three space, points exit and areas (surfaces)/ volumes can be delineated. That means that a multiplicity of objects can exist in those two spaces. But in one space there can only be one object because location is absent. One can not cross two lines to produce a point, without moving out of that space. If the grain density is infinite there, then existence would be infinitely persistent and time would not pass. There would be only one direction. So the concept of space and time would be contradictory as we know it. Words like eternal and omni- presence can also be used to describe such a state. True that physics can not understand the creation of the universe YET, it may well do so in the future. The idea that time is quantized seen as the continuous discreet fading and replacement of information "frames" means that in a sense the process of creation is still going on. This would occur for each and every particle in the universe. Are we just an ensemble of information, a sort of rapidly exchanging three dimensional arrays of matter generated by billions of little information processors called particle.? If thats true then we too are "compound" entities which display and process information. As to where to find the CREATOR, I would vote for an infinitely dense and continuous independently existing one dimensional space as the place for the CREATOR to exist. This is perhaps a little net.religion, net.- cosmology, and net.metaphysics; but, what the hell. Oh "hell" by the way is .. . .. . maybe some other time. :-) - - NOTE: MAIL PATH MAY DIFFER FROM HEADER - - +-------------------------------------------------------+--------+ | Paul M. Koloc, President: (301) 445-1075 | FUSION | | Prometheus II Ltd., College Park, MD 20740-0222 | this | | pmk@prometheus.UUCP; ..seismo!prometheus!pmk.UUCP | decade | +-------------------------------------------------------+--------+
tmb@talcott.UUCP (Thomas M. Breuel) (08/18/85)
In article <166@prometheus.UUCP>, pmk@prometheus.UUCP (Paul M Koloc) writes: > > My intuition tells me that the universe is a continuous function. > > Two things tell us that the universe isn't continuous. First, the "big bang", > and second, the constant "h bar" or even the fact that particles are not > points. > [...] > If space were continuous then an infinite number of points would exist along > a path an "inch" long. Scanning this space with a "point" test particle > would not discover any "spatial holes" or gaps where "points" aren't defined > (exit). In fact all of the information known to man (and the angels) could > be put into a binary code and stored in such a space. Our space is "grainy" > and there are gaps and spaces, and nature has a special trick to make it > "look" continuous. Mathematically it is a "delta function" and in reality > it is "the particle" > [...] > True that physics can > not understand the creation of the universe YET, it may well do so in the > future. The idea that time is quantized seen as the continuous discreet > fading and replacement of information "frames" means that in a sense the > process of creation is still going on. This would occur for each and every Nice that you all have intuitions and feelings about the universe. I do too. Nevertheless, the only fact is that we don't know whether the universe is continuous or discrete in either time or space, whether it is finite of infinite, or whether it has discontinuities, even if it is a continuum. Modern physics has lots of theories about these questions, some of them proven to higher degrees of accuracy than others. None of them promise to be 'the final theory' of the universe. Your remark about QM and discreteness of time strikes me as odd. Time is, of course, treated as a real variable in QM, and you can't just go from differential equations in time to difference equations and still have a working QT (at least I have never seen such a theory... it would definitely be interesting, though). Your remark about QM and discreteness of space strikes me as even odder. If you know of a way of representing QM on a lattice, I would like to hear about it. What tells you, by the way, that you can't store infite amounts of data in a limited space, and by what means can you infer from that that space is organised as a lattice? Unless you have a better argument than you presented in your posting, I would be extremely careful in making such statements. Finally, the object of physics simply cannot be to find out the 'cause' for the existence of the universe. By definition, the creation of the universe took place outside the realm of the physical laws that govern our universe. Therefore, physics is just not applicable to what happened before the universe existed. Another way of stating the above is that any physical theory must be testable. A theory of the creation of the universe is not testable or verifyable. Don't misunderstand me: I love physics, and there are lots of extremely interesting questions to be answered. Like any other natural science, physics does not give final answers, though. Every theory, however well established, may always turn out to be incorrect after all. Physics can only describe the universe to better and better approximations, and we may eventually find a theory that describes our world better than we have means to test it. Nevertheless, it is only a theory. QM and GR do not even meet these criteria. There are serious conflicts between the two theories, and (at least) one of them needs a lot of fixing. But physics is also not a religion or a philosophy. Physics cannot tell you either *why* or *how* the universe was created, or what the *purpose* of life or intelligence is. Physical sciences can only tell you what probably happened right after the universe was created and what kinds of systems may give rise to life and intelligence. Purpose and reason, although often used euphemistically in physics courses, have no place in the sciences. (reason here not in the sense of logic or intelligence, of course). Thomas.
gwyn@brl-tgr.ARPA (Doug Gwyn <gwyn>) (08/18/85)
> Finally, the object of physics simply cannot be to find out the > 'cause' for the existence of the universe. By definition, the creation > of the universe took place outside the realm of the physical laws that > govern our universe. Therefore, physics is just not applicable to > what happened before the universe existed. One possibility, though, is that physics can clarify whether the concept of "before the universe existed" has any meaning. In some cosmologies, time (by any reasonable definition) runs infinitely backward and forward so there can be no "before the universe existed". A lot of the popularizations of "the first few seconds after the big bang" cavalierly use everyday notions of time to discuss what most certainly cannot be correctly described with such notions. I don't know why so many people think the universe needs an external cause. Just what good would that do? Perhaps the observation that the universe operates according to definite rules contributes to this. However, it is possible to make considerable progress in understanding (a) how the rules are interrelated and (b) how at least some of the rules could not be otherwise. It seems perfectly plausible to me that the fundamental laws are inherent in the nature of existence and do not need to be ascribed to capricious whims of an external agency.
stark@sbcs.UUCP (Eugene Stark) (08/19/85)
> Time can more understandably be viewed as as "unfolding" of sequential infor- > mation arrays like the distinct frames of a moving picture. The framing rate > for a particle like a neutron would be ~(m*c^2)/(<h bar>) where "m" is the > mass of a neutron, "c" the speed of light, and "h" Planck's constant. The > framing rate decreases with the increase in effective mass of a neutron due > to its general and special relativity effects (its position in a dense > gravitational field or in rapid motion "velocity space"). I have by now read several descriptions by Paul Koloc of the universe as evolving by "unfolding of sequential information arrays," "grainy time," etc. I wonder if he or some other reader could post some references to published work in this area, so that those of us who can't follow the description can perform the necessary "paradigm shift"? Gene Stark
pmk@prometheus.UUCP (Paul M Koloc) (08/20/85)
> Modern physics has lots of theories about these questions {the > nature of physical universe}, some of them proven to higher degrees > of accuracy than others. None of them promise to be 'the final > theory' of the universe. That was b. k. (before Koloc) :-) Precise accuracy is secondary to being comprehensive and coherent. > Your remark about QM and discrete time strikes me as odd. > Your remark about QM and discrete space strikes me as even odder. By the way didn't mention Quantum Mechanics. Matter certainly isn't continuous, consider the atomic theory, and I believe that the theory was "invented" before it could be directly verified by electric field microscope. Particles aren't points. They have a "delta function" over a discrete distribution width in space, and if there is an symmetry then there is a "delta function distribution" in time as well. That implies framing. Of course, if the framing rate (~10**25/sec) is fast enough, time "looks" very nearly continuous. Seems 1+1=2 to me, therefore. not so odd :-) > What tells you, by the way, > that you can't store infinite amounts of data in a limited space, Well, I tried to print the New York times on a neutron and gave up because I wasn't able to get my pencil sharp enough. :-) > and by what means can you infer from that that space is organized > as a lattice? Unless you have a better argument than you presented > in your posting, I would be extremely careful in making such statements. Huh? I didn't say and I didn't intend to imply anything related to a "lattice". In fact, quite the contrary. > Finally, the object of physics simply cannot be to find out the > 'cause' for the existence of the universe. By definition, the creation > of the universe took place outside the realm of the physical laws that > govern our universe. Therefore, physics is just not applicable to > what happened before the universe existed. Nonsense! Physics will go where ever the search for the nature of matter takes it. What more exciting place than that state it existed in before it was released into 3 space manifold and took on the its material form. My guess is that some formulations of physics could be made which would be applicable both to the matter of three space and the herein proposed hypo- matter of two space. Maybe micro chunks of hypo-matter are still "decaying" into matter and thereby generating the phenomena we observe as quasars. That's not quite as spectacular as "the big bang" but it's still pretty impressive. > Another way of stating the above is that any physical theory must > be testable. A theory of the creation of the universe is not > testable or verifiable. .. . . physics does not give final answers Why not?? ? I'm sure that we could get the defense department to fund an experiment to locally decay a micro chunk of hypo-matter but if we did it would be hazardous to our health, as according to one theory of Sagan, it has been for thousands of previously existing intelligent more technologically developed life in our universe. If hypo space exists and if our space is grainy and point wise not continuous, then it should be possible to "test" the theory in the following way. Since we live one the three space "side of the tracks" we can't observe hypo-matter. (this stuff doesn't have volume). However, if our matter was previously hypo-matter then we might be able to cause a chunk of "matter" to be put back into the "hypo matter" state. Now that would be a test, because we could demonstrate that the effected matter would "vanish". Of course, that's a no no. How can this be done? Glad you asked! Accelerate the matter to the speed of light. But, the theory says that before that happens the matter will become contracted so much that it will "slip between the grains" and our transitioned matter can't interact with it. It would essentially become so "thin" that it would "jump" to two space. (A quantum jump, of course!) Now if space is point wise continuous then it can't "fall through the fingers" and transitioned matter would not disappear. BUT for all you sci-fi fans, if it DOES jump then we have a little problem .. . the problem .. . . is that hypo-space might "tear" and dump some hypo-matter on us, which as it generates a "white hole" and transforms into matter, transforming us into a supernova fragment. > But physics is also not a religion or a philosophy. > Physics can not tell you .. . *how* the universe was created.. . Physics is a natural philosophy (and occasionally is catachismic). What are they teaching you up there at Harvard?? The Bible says God made the world and with a little help and a lot of work physics will tell us how. Gosh, you mean we're NOT the center of the universe! Aw Shucks! - - NOTE: MAIL PATH MAY DIFFER FROM HEADER - - +-------------------------------------------------------+--------+ | Paul M. Koloc, President: (301) 445-1075 | FUSION | | Prometheus II Ltd., College Park, MD 20740-0222 | this | | ..umcp-cs!seismo!prometheus!pmk.UUCP | decade | +-------------------------------------------------------+--------+
pmk@prometheus.UUCP (Paul M Koloc) (08/20/85)
Doug Gwyn writes: > that physics can clarify whether the concept > of "before the universe existed" has any meaning. In some cosmologies, > time (by any reasonable definition) runs infinitely backward and forward > so there can be no "before the universe existed". I agree! Without matter time runs at an "infinite rate" and no information is altered. So reality is empty. However, with the injection of existence, which then takes on material forms in our three space, time is clamped "slowed greatly". So it does make sense to look at that moment when 3space became "non empty". Further assume the material state represents the "debris" of a decay of a two space "hypo-matter". Then time had meaning, even "before" our (three dimensional) portion of the universe became non-empty, because time had already existed for hypomatter. > A lot of the popularizations of "the first few seconds after the big > bang" cavalierly use everyday notions of time to discuss what most > certainly cannot be correctly described with such notions. Maybe not in a precisely measurable physics sense, but in terms of time being sequential framing of "information arrays" it still makes sense to contemplate it. That means that we may be able to reason to the maximum peak densities and minimum framing rates and that could give us some understanding of what the state of hypo-matter is. > I don't know why so many people think the universe needs an external > cause. Just what good would that do? Energy can't be created nor destroyed so it must have transformed from a non-three dimentsional manifold. Two space is the nearest adjacent manifold that satisfies the need for a hyper compressed and ultra high energy density state sufficient to power a "big-bang" 3d injection. It then transforms to the much fluffier (almost cotton candy-like state, by comparison) material state. This scenario conserves energy for the multi-manifold universe for one thing. Of course, the next step is to deal with the existence state of one dimensional space. If that state is infinitely dense then we are sort of 1/4 th of the way between absolute void and God, between an infinitely persistent time frame and an infinitely high framing rate. What good did it do to find out that the cosmos didn't have the earth as its center? For one it was humbling. More intelligent creatures then we? I have little doubt. > Perhaps the observation that the universe operates according to definite > rules contributes to this. However, it is possible to make considerable > progress in understanding (a) how the rules are interrelated and (b) how > at least some of the rules could not be otherwise. It seems perfectly > plausible to me that the fundamental laws are inherent in the nature of > existence and do not need to be ascribed to capricious whims of an > external agency. Yes, half of particle duality is that they function as "logic operators". Let's face it we write software that becomes the filter to transform information, why can't the physical universe be the software read-out of some two space net wizards (accomplished programmers - angels?)
sra@oddjob.UUCP (Scott R. Anderson) (08/23/85)
In article <166@prometheus.UUCP>, pmk@prometheus.UUCP (Paul M Koloc) writes: >> Two things tell us that the universe isn't continuous. First, the "big bang", >> and second, the constant "h bar" or even the fact that particles are not >> points. And in another article, >> Particles aren't points. They have a "delta function" >> over a discrete distribution width in space, and if there is an >> symmetry then there is a "delta function distribution" in time as well. So far as we know, the "fundamental" particles (quarks, leptons, etc.) ARE points. Experiments have yet to determine any finite extent for these particles. I believe that the current upper limit on the radius of the electron is 10^(-18) meters or 0.001 fermi. Such particles are described by wave functions, which under appropriate conditions (i.e. the particle is at point x) are delta functions. A delta function has no width, as it is non-zero only at x. This is how one describes a point particle quantum-mechanically. In article <490@talcott.UUCP> tmb@talcott.UUCP (Thomas M. Breuel) writes: > >Time is, of course, treated as a real variable in QM, and you >can't just go from differential equations in time to difference >equations and still have a working QT (at least I have never seen >such a theory... it would definitely be interesting, though). >.... >Your remark about QM and discreteness of space strikes me >as even odder. If you know of a way of representing QM on >a lattice, I would like to hear about it. This is done on a regular basis in field theories, although only as a calculation technique. The procedure uses the path integral formulation of QM and discretizes space-time onto a lattice with some lattice spacing 'a'. After everything is all said and done, the limit a -> 0 is taken. Lurking nearby, however, is the question of the distinguishability of small a (e.g. Planck Length) from a = 0. At this point, we can't tell the difference because the energies required are so enormous. If space were discretized, though, there would be some probability of "Umklapp" processes occurring, in which a particle could change it's momentum for no apparent reason. Scott Anderson ihnp4!oddjob!kaos!sra
pmk@prometheus.UUCP (Paul M Koloc) (08/25/85)
> > Time can more understandably be viewed as as "unfolding" of sequential > > information arrays like the distinct frames of a moving picture. The > > framing rate for a particle like a neutron would be ~(m*c^2)/(<h bar>) > > .... . . > I have by now read several descriptions by Paul Koloc of the universe as > evolving by "unfolding of sequential information arrays," "grainy time," > etc. I wonder if he or some other reader could post some references to > published work in this area, so that those of us who can't follow the > description can perform the necessary "paradigm shift"? > Gene Stark Eugene, My view of the universe comes from notions gathered from Lucretius, Feynmann, Einstein, . and Wheeler. The concept is a sort of generalized "information theory", which includes considering the dynamics of operator and array aspects "particles" to be the basis for what the physical universe is all about. The question is "If nature is unified and we discover the element of unification, then what word would best describe that entity?". It seems to me that "information" would be an excellent candidate. The difference between existence and non-existence is the presence of "grains". What's interesting is that most physicsl laws seem to apply, and some new stuff seems to be falling out. For example, it allows the existence of "antimatter of charge 1" but prohibits antimatter particles from being "stable" with charge two or more. (Sorry folks no "antimatter galaxy" floating around some place.) It also generates a basis for the description of gravity, electric fields, magnetic fields in a way which clearly unifies them in terms of a grainy information. As a result, the generation of magnetic fields by massive spinning and precessing objects is allowed and is a calculable artifact of a "time distortion" due to the mass induced distortion of the "local metric". Current efforts are directed in a completely different area of research, namely, controlled thermnuclear fusion. However, in about three to four years, that project should be successful enough (or will be shown not to be feasible), that I can devote time to working out a more concise and comprehensive description of the theory. I'm sure that the "mind set" of billard ball elementary particle theory is about to crumble, and a more operator/array duality along the lines of information theory will emerge whether or not I'm successful. ~ - - NOTE: MAIL PATH MAY DIFFER FROM HEADER - - +-------------------------------------------------------+--------+ | Paul M. Koloc, President: (301) 445-1075 | FUSION | | Prometheus II Ltd., College Park, MD 20740-0222 | this | | ..umcp-cs!seismo!prometheus!pmk.UUCP | decade | +-------------------------------------------------------+--------+
pmk@prometheus.UUCP (Paul M Koloc) (08/25/85)
> In articles <166@prometheus.UUCP>, pmk@prometheus.UUCP (Paul M Koloc) writes: >>> Two things tell us that the universe isn't continuous. First, "big bang", >>> Particles aren't points. They have a "delta function" > > Scott Anderson (ihnp4!oddjob!kaos!sra) <3656@decwrl.UUCP> answers: > So far as we know, the "fundamental" particles (quarks, leptons, etc.) ARE > points. Experiments have yet to determine any finite extent for these > particles. I believe that the current upper limit on the radius of the > electron is 10^(-18) meters or 0.001 fermi. If you had said kilometers. Actually, electron radius is ~ e^2/(m*c^2) which comes to about 3 * 10^(-15) meters. Still infinitely larger than a point radius. --"e" is charge; "m" is electron mass; and "c" is light speed. They are represented as points, for convenience. > Such particles are described by wave functions, which under appropriate > conditions (i.e. the particle is at point x) are delta functions. A > delta function has no width, as it is non-zero ONLY AT x. This is how > one describes a point particle quantum-mechanically. I think "point" in quantum mechanics means "smudge". And certainly, you are right provided your mesh isn't too fine. Now reads: "only at (smudge) 'x'". > In article <490@talcott.UUCP> tmb@talcott.UUCP (Thomas M. Breuel) writes: > >. ..Your (Koloc) remark about QM and discreteness of space strikes me > >as even odder. If you know of a way of representing QM on > >a lattice, I would like to hear about it. > > This is done on a regular basis in field theories, although only as > a calculation technique. The procedure uses the path integral... . > formulation of QM and discretizes space-time onto a lattice with > some lattice spacing 'a'. After everything is all said and done, > the limit a -> 0 is taken. Thanks for the help. Consequently, a --> 0 approximates a --> "smudge x" It usually is considered to be the other way around! > Lurking nearby, however, is the question of the distinguishability of > small a (e.g. Planck Length) from a = 0. At this point, we can't tell > the difference because the energies required are so enormous. If space > were discretized, though, there would be some probability of "Umklapp" > processes occurring, in which a particle could change it's momentum for > no apparent reason. It does "change" and the reason is its lack of infinite "information density"; so it "jiggles" a little in "momentum space". Wish I could claim that as an excuse to get out of paying off a speeding ticket. - - NOTE: MAIL PATH MAY DIFFER FROM HEADER - - +-------------------------------------------------------+--------+ | Paul M. Koloc, President: (301) 445-1075 | FUSION | | Prometheus II Ltd., College Park, MD 20740-0222 | this | | ..umcp-cs!seismo!prometheus!pmk.UUCP | decade | +-------------------------------------------------------+--------+
gwyn@brl-tgr.ARPA (Doug Gwyn <gwyn>) (08/26/85)
> Actually, electron radius is ~ e^2/(m*c^2)
Oh, really? How did you determine this?pmk@prometheus.UUCP (Paul M Koloc) (08/26/85)
In an earlier article I corrected an estimate of electron radius: > > Actually, electron radius is ~ e^2/(m*c^2) ~ 3*10^15 meters In article <966@brl-tgr.ARPA> (Doug Gwyn gwyn@brl-tgr.ARPA Organization: Ballistic Research Lab challenges: > Oh, really? Yep! An electron is neato because its the ground state of "THE" elementary half particle. A pure information annihilator. Enough for the commercials. > How did you determine this? Assume that the energy of a "still" electron is ~ due to its electro- static energy. If that's a reasonable approximation then, its energy can be measured by its still mass. So Energy(mass) = Energy(electric field). Then m*c^2 = e^2/r; e is proportional to charge, m is mass and c is light speed. Then r (its smallest smudge radius) is as above! Happy? :-) - - NOTE: MAIL PATH MAY DIFFER FROM HEADER - - +-------------------------------------------------------+--------+ | Paul M. Koloc, President: (301) 445-1075 | FUSION | | Prometheus II Ltd., College Park, MD 20740-0222 | this | | ..umcp-cs!seismo!prometheus!pmk.UUCP | decade | +-------------------------------------------------------+--------+
sra@oddjob.UUCP (Scott R. Anderson) (08/28/85)
>> So far as we know, the "fundamental" particles (quarks, leptons, etc.) ARE >> points. Experiments have yet to determine any finite extent for these >> particles. I believe that the current upper limit on the radius of the >> electron is 10^(-18) meters or 0.001 fermi. In article <171@prometheus.UUCP> pmk@prometheus.UUCP (Paul M Koloc) writes: >If you had said kilometers. Actually, electron radius is ~ e^2/(m*c^2) >which comes to about 3 * 10^(-15) meters. Still infinitely larger than >a point radius. --"e" is charge; "m" is electron mass; and "c" is light >speed. They are represented as points, for convenience. This is what is known as the classical electron radius; it can be derived in several ways based on classical electrodynamics (ref. Jackson, Classical Electrodynamics). However, an electron is a quantum mechanical object, and as one might expect the above expression is only valid in certain regimes (e.g. when the experimental probe has a wavelength much greater than the c.e.r.). Current experimental results make clear that the c.e.r. has nothing to do with the true electron radius, assuming it has one. Note that I am not saying that the electron doesn't have a finite radius, just that experiments have set a limit on what it can be. And ascribing a finite size to electrons (or muons or quarks) is an unnecessary complication for most field theories (recall Occum's Razor!). >I think "point" in quantum mechanics means "smudge". If you choose to know nothing at all about a particle's momentum, "point" means "point" in the mathematical sense. This is the delta function. Scott Anderson ihnp4!oddjob!kaos!sra