Why only gravity is "geometrical"?
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sirix - 24 Jan 2007 17:03 GMT hey ho! What is the obstruction to developing a theory of - for example - electromagnetism, that would imply that electromagnetism is not a real force (like gravity in general relativity)?
Or maybe such a theory exists? If so, than why one can't find a "common geometric picture" for gravity and electromagnetism?
 Signature [ sirix ]------------sirix-at-univ-szczecin-pl------------- http://sirix.wordpress.com (my maths&physics-oriented blog)
Dirk Van de moortel - 24 Jan 2007 17:45 GMT > hey ho! > What is the obstruction to developing a theory of - for example - [quoted text clipped - 3 lines] > Or maybe such a theory exists? If so, than why one can't find a "common > geometric picture" for gravity and electromagnetism? Because the acceleration of an object under the influence of gravity does not depend on the any of the object's properties. The mass cancels out in F = m a = m M G / r^2 giving a = M G / r^2
Acceleration of an object under the influence of electromagnetic forces depends on charge and the mass of the body. F = m a = q ( E + vxB ) givig a = q/m ( E + vxB )
You see that with gravity the acceleration merely depends on the location, which suggest that it can be treated in a geometrical way. This clearly is not the case with electromagnetism.
Dirk Vdm
Dumbledore - 24 Jan 2007 18:26 GMT [anip]
http://users.telenet.be/vdmoortel/dirk/Physics/TwinsEvents.html "We use 3 inertial reference frames" [because Dorks can't get the result they want in two]. "In neither of these frames any form of acceleration is felt" [neither one of all three]. "In order for the travelling twin to make HIS trip, SHE must be in frame S' while going away". "if T = 5 years and v = 0.8c, then the stay at home twin will have aged 10 years".
Belgium is where the farts blow.
"Your conclusion is dead wrong. Start over, but skip the first part and the conclusion." -- Dork Van de fuckhead.
"You made a mistake" -- Dork Van de psychotic fumble mumbler.
ASSistant professor Paul B. Andersen, tusseladd:
"That is, we can reverse the directions of the frames which is the same as interchanging the frames, which - as I have told you a LOT of times, OBVIOUSLY will lead to the transform: t = (tau-xi*v/c^2)/sqrt(1-v^2/c^2) x = (xi - v*tau)/sqrt(1-v^2/c^2) or: tau = (t+xv/c^2)/sqrt(1-v^2/c^2) xi = (x + vt)/sqrt(1-v^2/c^2)"
Steve Lawrence (sal) the hypocrite: "In general I'd say there are three main reasons people ignore questions in this forum. 1) They accidentally overlook the question (not really ignoring it) 2) They think it's boring and don't want to discuss it 3) They can't answer it and don't want to admit that." Ref: news:pan.2007.01.14.14.05.37.850117@nospam.org.
sirix - 24 Jan 2007 19:08 GMT >> hey ho! >> What is the obstruction to developing a theory of - for example - >> electromagnetism, that would imply that electromagnetism is not a real >> force (like gravity in general relativity)?
> You see that with gravity the acceleration merely depends on > the location, which suggest that it can be treated in a geometrical > way. This clearly is not the case with electromagnetism. Simple answer to a simple question - thanks. Exactly what I needed. May one say that this observation was one of main motivations of Einstein?
 Signature [ sirix ]------------sirix-at-univ-szczecin-pl------------- http://sirix.wordpress.com (my maths&physics-oriented blog)
Dirk Van de moortel - 24 Jan 2007 19:20 GMT >>> hey ho! >>> What is the obstruction to developing a theory of - for example - [quoted text clipped - 7 lines] > Simple answer to a simple question - thanks. Exactly what I needed. > May one say that this observation was one of main motivations of Einstein? Yes, I think *the* motivation to create his general theory.
Dirk Vdm
Bob A - 24 Jan 2007 18:14 GMT > hey ho! > What is the obstruction to developing a theory of - for example - [quoted text clipped - 3 lines] > Or maybe such a theory exists? If so, than why one can't find a "common > geometric picture" for gravity and electromagnetism? study vector fields
Nathan Urban - 24 Jan 2007 19:01 GMT > What is the obstruction to developing a theory of - for example - > electromagnetism, that would imply that electromagnetism is not a real > force (like gravity in general relativity)?
> Or maybe such a theory exists? If so, than why one can't find a "common > geometric picture" for gravity and electromagnetism? Such a theory exists: it's a 5-dimensional spacetime theory called Kaluza-Klein theory, unifying gravity and electromagnetism. However, quantizing it is as difficult as quantizing gravity. Furthermore, we already know that electromagnetism is unified with the weak nuclear force in electroweak theory, part of the Standard Model. Witten showed that it is not possible to obtain the Standard Model in a Kalzua-Klein framework, at least in the context of compactifying on a spatial manifold. There are various ways to dodge this, and I don't know if anyone has looked at the orbifold compactifications that are popular in string theory. But most people working in the "unified field theories in extra dimensions" moved on to string theory.
Note that K-K theory is a unified theory of gravity and electromagnetism, and it needs an extra spacetime dimension. It has to be that way: electromagnetism itself can't be regarded as pure (spacetime) geometry like gravity can, because, as another poster pointed out, EM doesn't obey the equivalence principle. Thus, the trajectory of a charged particle depends on internal properties of the particle (its charge to mass ratio), not just on spacetime geometry.
The way K-K theory evades this consequence is by adding an extra dimension in such a way that all of the charge-to-mass information winds up being encoded in the particle's spacetime trajectory (specifically in its 5th-dimensional momentum). Then a particle's path is determined solely by 5D spacetime geometry, although its apparent 4D spacetime path does depend on its internal properties.
On the other hand, you can regard ordinary Maxwell electromagnetic theory as a geometric theory in the sense of Yang-Mills theory described on a fiber bundle. However, spacetime is not truly dynamical in this theory as it is in GR or K-K theory, and it involves geometry in something other than spacetime (namely, a fiber bundle over spacetime), so you might regard that as "cheating".
I have discussed this topic in some more detail here:
http://groups.google.com/groups?as_umsgid=6hoi5o$ko7$1@crib.bevc.blacksburg.va.us http://groups.google.com/groups?as_umsgid=i2h82$95q$1@crib.bevc.blacksburg.va.us http://groups.google.com/groups?as_umsgid=6i520i$biu$1@crib.bevc.blacksburg.va.us
Dirk Van de moortel - 24 Jan 2007 20:49 GMT >> What is the obstruction to developing a theory of - for example - >> electromagnetism, that would imply that electromagnetism is not a real [quoted text clipped - 29 lines] > path is determined solely by 5D spacetime geometry, although its > apparent 4D spacetime path does depend on its internal properties. *Very* nice intro :-)
Dirk Vdm
> On the other hand, you can regard ordinary Maxwell electromagnetic > theory as a geometric theory in the sense of Yang-Mills theory [quoted text clipped - 8 lines] > http://groups.google.com/groups?as_umsgid=i2h82$95q$1@crib.bevc.blacksburg.va.us > http://groups.google.com/groups?as_umsgid=6i520i$biu$1@crib.bevc.blacksburg.va.us Dumbledore - 24 Jan 2007 22:41 GMT [anip]
http://users.telenet.be/vdmoortel/dirk/Physics/TwinsEvents.html "We use 3 inertial reference frames" [because Dorks can't get the result they want in two]. "In neither of these frames any form of acceleration is felt" [neither one of all three]. "In order for the travelling twin to make HIS trip, SHE must be in frame S' while going away". "if T = 5 years and v = 0.8c, then the stay at home twin will have aged 10 years".
Belgium is where the farts blow.
"Your conclusion is dead wrong. Start over, but skip the first part and the conclusion." -- Dork Van de fuckhead.
"You made a mistake" -- Dork Van de psychotic fumble mumbler.
ASSistant professor Paul B. Andersen, tusseladd:
"That is, we can reverse the directions of the frames which is the same as interchanging the frames, which - as I have told you a LOT of times, OBVIOUSLY will lead to the transform: t = (tau-xi*v/c^2)/sqrt(1-v^2/c^2) x = (xi - v*tau)/sqrt(1-v^2/c^2) or: tau = (t+xv/c^2)/sqrt(1-v^2/c^2) xi = (x + vt)/sqrt(1-v^2/c^2)"
Steve Lawrence (sal) the hypocrite: "In general I'd say there are three main reasons people ignore questions in this forum. 1) They accidentally overlook the question (not really ignoring it) 2) They think it's boring and don't want to discuss it 3) They can't answer it and don't want to admit that." Ref: news:pan.2007.01.14.14.05.37.850117@nospam.org.
Martin Hogbin - 24 Jan 2007 21:46 GMT > > What is the obstruction to developing a theory of - for example - > > electromagnetism, that would imply that electromagnetism is not a real [quoted text clipped - 5 lines] > Such a theory exists: it's a 5-dimensional spacetime theory called > Kaluza-Klein theory, unifying gravity and electromagnetism. Good to see you back Nathan. It is pretty grim here now.
Martin Hogbin
Mitchell Jones - 30 Jan 2007 20:02 GMT > > > What is the obstruction to developing a theory of - for example - > > > electromagnetism, that would imply that electromagnetism is not a real [quoted text clipped - 9 lines] > > Martin Hogbin ***{What's grim is this ceaseless flame war between academic irrationalists and mostly unschooled people who reject academic nonsense based on common sense. Here is the way it came about:
(1) The advent of government funding created a system of punishments and rewards that benefitted irrationalists who worshipped the state.
(2) Said irrationalists, being the preferred beneficiaries of government funding, filled the chairs formerly occupied by rationalists, as they became vacated due to age and/or attrition.
(3) In the fullness of time, every field of academic endeavor became polluted by howling nonsense that flew in the face of common sense.
(4) The aforesaid howling nonsense was shielded from public view by a cloak of academic jargon, and subject to direct public contact only within classrooms, where the instructor was always in the power position, able to silence intelligent critics without dealing with their arguments, by exuding hostility, by refusing to permit questions during class or, for critics who were persistent, by handing out bad grades.
(5) With the advent of the internet, with its open discussion groups where everyone could take part, academic nonsense lost its protection. Academics who posted in open groups discovered that intelligent members of the general public recoiled from nonsense, and that when such doctrines were discussed in open groups, they had to deal with the criticisms that they had so easily avoided in their classrooms. Result: they employed scathing sarcasm, blatant evasion, ad hominem attacks, "crank lists," and other non-substantive rejoinders, in the hope of driving the critics out of the supposedly open groups.
(6) Most of the critics were successfully intimidated into silence (they became lurkers) or else driven out of the supposedly "open" groups entirely. Some, however, adopted the same techniques as those employed by the academics, and worse: to the scathing sarcasm, evasion, and ad hominem attacks, they added gutter language of the foulest sort, and they dug in their heels and refused to be silenced.
(7) The situation became "grim." A perpetual flame war became established in open ("unmoderated") groups, to the utter disgust of any sensible person who bothered to read the groups in question, and reasoned discussion became an endangered species.
What is the solution?
Short term, an individual can transform any group into what he wants by simply killfiling those who introduce ad hominems into discussions. Stop using web browsers to read usenet. Get a newsreader with a good killfile capability, and use it instead.
Longer term, the solution would be to end government funding of "education," on the grounds that when government funding is provided, education is automatically transformed into religion. Hence government funding of "education" is a direct violation of the principle of separation of church and state.
Of course, it ain't gonna happen. There is no way to turn back the clock. What's done is done. Government funding of "education," growing slowly in America for more than a hundred years, has affected the culture of the country in much the same way as a gradual accumulation of plaque affects the brain of an Alzheimer's patient. The disease is now terminal, because the patient has become too stupid to take the actions needed to save himself. Americans are no longer proud, independent minded, honorable, self-sufficient individualists. Now they are whining, begging, thieving, resentful, government worshipping collectivists, and there is no power of persuasion or force of logic that can rectify that state of affairs before economic collapse and social disintegration take the country down.
All living things, whether considered as individuals or as groups, age, grow old, and die. Civilizations are not exempt from the rules, and Western Civilization, the highest achievement of which was the United States of America, is very old, very senile, and in its death throes as we speak.
--Mitchell Jones}***
***************************************************************** If I seem to be ignoring you, consider the possibility that you are in my killfile. --MJ
G=EMC^2 Glazier - 30 Jan 2007 20:06 GMT Michael Quantum gravity is not based on GR Bert
sirix - 25 Jan 2007 14:00 GMT >> What is the obstruction to developing a theory of - for example - >> electromagnetism, that would imply that electromagnetism is not a real [quoted text clipped - 6 lines] > Kaluza-Klein theory, unifying gravity and electromagnetism. However, > quantizing it is as difficult as quantizing gravity. 1) Why not go further and introduce additional dimension for other forces?
2) What, for simple mathematics student, quantization is and why I should want to do it to gravity?
> force in electroweak theory, part of the Standard Model. Witten > showed that it is not possible to obtain the Standard Model in a [quoted text clipped - 3 lines] > popular in string theory. But most people working in the "unified > field theories in extra dimensions" moved on to string theory. I dunno whatch ya talkin' to me :-) I guess you say there's something wrong with K-K-theory? (I don't know what SM and what compactness has to do with it, but please don't answer here as my next topic will concern it :-)
> On the other hand, you can regard ordinary Maxwell electromagnetic > theory as a geometric theory in the sense of Yang-Mills theory > described on a fiber bundle. However, spacetime is not truly > dynamical in this theory as it is in GR or K-K theory, and it involves > geometry in something other than spacetime (namely, a fiber bundle > over spacetime), so you might regard that as "cheating". Oh! It's cool you mention this. In my differential geometry course lecturer said something and I'd love to know if I got it right and why it's cool.
(Please consider that I have no idea what Yang-Mills theory is)
1) There's a Maxwell's equation that comes from a god, and which can be summarized (possibly when there is no mass around?) by saying that electromagnetic force is a closed 2-form.
2) Every closed 2-form gives element of second cohomology group. Now, one postulates that this two form is in 2nd cohomology group with integer coefficients actually and one says that is has to do with the fact that charge is quantized (?)
3) So we can build a complex line bundle whose Chern class is precisely above form.
4) From now on, it's possible I say something very stupid. We want to do quantum mechanics on this bundle? That is, instead of taking wave functions we take "wave sections"? If it's so than is there any reason why we do it (except for "it works")?
5) Now, in a magic way we get a connection on this bundle, also from Maxwell's equation. How we do that?
6) What we do with this connection now? (Please, use as simple words as possible. Main reason I write here is because when I try to speak with physicists where I live, I have a very numb feeling that there's big glass wall between me and said physicists)
http://groups.google.com/groups?as_umsgid=6hoi5o$ko7$1@crib.bevc.blacksburg.va.us
You say here that extra dimension in K-K theory must be small and actually compact. Why? If you say that it's a ratio of charge to mass than shoudn't it be noncompact?
http://groups.google.com/groups?as_umsgid=i2h82$95q$1@crib.bevc.blacksburg.va.us
I get an error when trying get this one.
http://groups.google.com/groups?as_umsgid=6i520i$biu$1@crib.bevc.blacksburg.va.us If I ever understand what is chiral fermion problem, I'll be very happy :-)
 Signature [ sirix ]------------sirix-at-univ-szczecin-pl------------- http://sirix.wordpress.com (my maths&physics-oriented blog)
carlip-nospam@physics.ucdavis.edu - 25 Jan 2007 21:11 GMT
>>> What is the obstruction to developing a theory of - for example - >>> electromagnetism, that would imply that electromagnetism is not a real >>> force (like gravity in general relativity)?
>>> Or maybe such a theory exists? If so, than why one can't find a "common >>> geometric picture" for gravity and electromagnetism?
>> Such a theory exists: it's a 5-dimensional spacetime theory called >> Kaluza-Klein theory, unifying gravity and electromagnetism. However, >> quantizing it is as difficult as quantizing gravity.
> 1) Why not go further and introduce additional dimension for other forces? This can be done. As far as I know, the possibility first appeared in print as an "exercise for students" in Bryce DeWitt's 1963 Les Houches lectures. In fact, you can get out the Standard Model interactions from seven extra dimensions with the right geometry. There was a lot of interest in this in the early 1980s, but apart from the problem of quantization, it turns out that it's very difficult to get "chiral" fermions -- that is, elementary spin 1/2 particles whose "left-handed" versions are different from their "right-handed" versions -- from a higher dimensional theory, and chiral fermions are what we observe in Nature.
Incidentally, while string theory is certainly not just Kaluza-Klein theory, it has extra dimensions, and it's routine to get extra "geometric" interactions from these in the same fashion as Kaluza-Klein theory.
> 2) What, for simple mathematics student, quantization is and why I should > want to do it to gravity? Quantization means taking a classical physical theory and making it into a quantum mechanical one (with wave functions, observables as operators, probabilistic predictions, etc.). If you want to unify gravity with other interactions, you *must* do this, since the other interactions are observed to be quantum mechanical. If you're not trying to unify things, there is no completely conclusive proof that gravity must be quantized, but it turns out to be extremely hard to consistently couple nonquantum gravity to quantum matter (where "extremely hard" should be understood as "no one has a clue how to do it").
Steve Carlip
Nathan Urban - 26 Jan 2007 19:20 GMT Steve Carlip already fielded a few of your questions, I will try a few more.
> > Witten showed that it is not possible to obtain the Standard Model > > in a Kalzua-Klein framework, at least in the context of [quoted text clipped - 3 lines] > > people working in the "unified field theories in extra dimensions" > > moved on to string theory.
> I dunno whatch ya talkin' to me :-) I guess you say there's something wrong > with K-K-theory? The problem is that nobody knows how to make K-K theory compatible with chiral fermions in a nice way.
> (I don't know what SM and what compactness has to do with it, but > please don't answer here as my next topic will concern it :-) In extra-dimensional theories you usually postulate that the extra dimensions are compact and small. Your choice of compact manifold produces different interactions when projected down onto the four large dimensions.
> > [gauge theory on fiber bundles]
> Oh! It's cool you mention this. In my differential geometry course lecturer > said something and I'd love to know if I got it right and why it's cool. Ok, my cohomology theory is too rusty to answer that, but perhaps you could get John Baez to tell you either on sci.physics.research or on his blog, The n-Category Cafe. You can also read his book, _Gauge Fields, Knots, and Gravity_, although that takes mostly an associated vector bundle approach and avoids principal bundles.
I can tell you that the connection (i.e. the electromagnetic or Yang-Mills field), gives you the phase shift of a quantum mechanical particle when it is transported along a path.
> (Please consider that I have no idea what Yang-Mills theory is) If you take a G-connection A where G is a Lie group, then Yang-Mills theory is the equation of motion you obtain from finding the stationary point of the action \int tr(F^*F), where F is the curvature 2-form ("field strength") associated with A, ^ is the wedge product, and * is the Hodge dual. A is the Yang-Mills field. Maxwell's equations for electromagnetism obtain when G=U(1). You get extra terms in the Yang-Mills field equations (equations of motion) beyond what appear in Maxwell's equations when G is non-Abelian.
Note the key point: the field strength is not any old 2-form, but the curvature associated with a G-connection, which is the field itself. The field strength is automatically closed from the Bianchi identities.
> You say here that extra dimension in K-K theory must be small and actually > compact. Why? If you say that it's a ratio of charge to mass than shoudn't > it be noncompact? The charge-to-mass ratio is encoded in 5th-dimensional momentum. Momentum is a tangent (or really cotangent) vector and classically can have any magnitude, even on a compact manifold.
> > http://groups.google.com/groups?as_umsgid=i2h82$95q$1@crib.bevc.blacksburg.va.us
> I get an error when trying get this one. I elided a 6 at the beginning. It should be:
http://groups.google.com/groups?as_umsgid=6i2h82$95q$1@crib.bevc.blacksburg.va.us
> If I ever understand what is chiral fermion problem, I'll be very happy :-) As Steve said, it's the incompatibility of the theory with the experimental fact that that left-handed and right-handed fermions can be different. (Left-handed and right-handed refers to spinning clockwise or counterclockwise.. really it comes from spinor representations.)
mmeron@cars3.uchicago.edu - 25 Jan 2007 00:09 GMT >hey ho! >What is the obstruction to developing a theory of - for example - [quoted text clipped - 3 lines] >Or maybe such a theory exists? If so, than why one can't find a "common >geometric picture" for gravity and electromagnetism? Well, if you take the lagrangian formalism (I know from your other posts that you're quite familiar with it) with any fields and use it to derive trajectory equations (instead of the usual equations of motion) you get results which formally looks just like geodesics equations (that's covered in Goldstein, as I recall). So you could say that motion within any field can be represented as following geodesics in appropriate geometry. Only (and this is a big only) the metric of said geometry depends on the mass so you end up not with a single geometry but with a potential infinity of such (different geometry for each mass) which rather disagrees with our notions of what geometry is, and is of little use besides. The exception is when the force itself (or the potential, if you wish) is proportional to the mass of the particle. In this case the mass cancels out in the metric and we're left with a single geometry. And, we've forces like this. In classical mechanics the ones that fit the bill are the inertial forces (centrifugal and coriolis), where the geometric transformation is trivial, and, of course gravity, where you've to abandon euclidean geometry but other than this no problem. When the force is not proportional to mass, though, such simple "geometrization of the field" doesn't work.
A more physical way to express the above is: you can geometrize the field when two different particles starting with the same initial conditions will follow same trajectory. Gravity is like this, EM isn't (just assume two particles, one charged and the other neutral, and you see that it doesn't work).
But, all is not lost. One can say "well, these two have same initial conditions in the dimensions we track, but perhaps there are some additional dimensions involved which we're not aware of, and a differnce in the initial conditions in those dimensions is what causes the differnece in the trajectories. In other words, a field which cannot be geometrized in our 4D spacetime, may be "geometrizable" in a larger dimensional space containing the 4D spacetime. Attempts along these lines were made, you may check on the Kaluza-Klein theory. As far as I know (and here I'm rapidly approaching the limits of what I can say without a refresher course), such attempts run into various difficulties but the topic is still open.
Mati Meron | "When you argue with a fool, meron@cars.uchicago.edu | chances are he is doing just the same"
PD - 25 Jan 2007 03:23 GMT On Jan 24, 6:09 pm, mme...@cars3.uchicago.edu wrote:
> In article <ep84ud$v2...@news.onet.pl>, sirix <s...@poczta.onet.pl> writes: > >hey ho! [quoted text clipped - 44 lines] > Mati Meron | "When you argue with a fool, > m...@cars.uchicago.edu | chances are he is doing just the same" Stitch together Mati's and Nathan's responses, and you've got yourself a nice little package. Well done!
PD
cliff wright - 25 Jan 2007 10:10 GMT > On Jan 24, 6:09 pm, mme...@cars3.uchicago.edu wrote: > [quoted text clipped - 53 lines] > > PD Cor Blimey! does that mean I've been communicating through "Hyperspace" for all these years. Cliff Wright ZL1BDA
Pmb - 25 Jan 2007 12:32 GMT > hey ho! > What is the obstruction to developing a theory of - for example - [quoted text clipped - 3 lines] > Or maybe such a theory exists? If so, than why one can't find a "common > geometric picture" for gravity and electromagnetism? Many therories use geometry in one sense or another. E.g. EM uses geometry, even pre-Einstein EM does. Einstein had something to say about this point. I'll dig it up and post it soon.
Pete
zzbunker@netscape.net - 25 Jan 2007 22:11 GMT > hey ho! > What is the obstruction to developing a theory of - for example - [quoted text clipped - 3 lines] > Or maybe such a theory exists? If so, than why one can't find a "common > geometric picture" for gravity and electromagnetism? The best reason is that the w.nks doing gravity research have passed a law that gravity is not a force, and that electromagnetism is subfield of the holistic quantum wave.
> -- > [ sirix ]------------sirix-at-univ-szczecin-pl------------- > http://sirix.wordpress.com(my maths&physics-oriented blog) Pmb - 26 Jan 2007 11:01 GMT >> hey ho! >> What is the obstruction to developing a theory of - for example - [quoted text clipped - 9 lines] > and that electromagnetism is > subfield of the holistic quantum wave. Who said that the theory of GR was geometrical?? It sure wasn't Einstein for he once wrote in a letter to Lincoln Barnett
"General remarks: I do not agree with the idea that the general theory of relativity is geometrsixing the gravitational field. The concepts of Physics have always been geometrical concepts and I cannot see why the g_ik field should be called geometrical than f.i. the electromagnetic field or the distance of bodies in Newtonian theory. The notion comes probably from the fact that the mathematical origin off the g_ik field is the Gauss-Riemann theory of the metrical contiuum which we are wont to look at as part of geometry, I am convinced, however, that the distinction between geometrical and other kinds of fields is not logically founded."
Pete
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