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Vector field A in R^3 with curl A = [radial outward]/R^2 ? Date: 1998/03/16
I need a vector field A(x,y,z) such that the curl of this field gives the field of a "point charge", that is the field is radial with a 1/R^2 dependence.
Re: Vector field A in R^3 with curl A = [radial outward]/R^2 ? Date: 1998/03/18
In article <6ek1le$5sb$1@newshost.nmt.edu> parendt@nmt.edu (Paul Arendt) writes:
> ale2 <ale2@NOSPAMpsu.edu> wrote: > >I need a vector field A(x,y,z) such that the curl of this field gives > >the field of a "point charge", that is the field is radial with a 1/R^2 > >dependence. > > Magnetic monopole, eh? Try: > A_x = -y/(r(r+z)) > A_y = x/(r(r+z)) > A_z = 0 > > where r = sqrt(x^2 + y^2 + z^2), of course.
I used Mathematica to take the curl of this**
In[1] Curl [ {-y/[[Sqrt[x^2+y^2+z^2][Sqrt[x^2+y^2+z^2]+z], x/[[Sqrt[x^2+y^2+z^2][Sqrt[x^2+y^2+z^2]+z], 0}, Cartesian[x,y,z]]
Out[1] {big mess}
and it spit out, in no time, a complicated expression. Only problem is I can't figure out now how to get Mathematica to convert that mess into spherical coordinates.
But the following field does (with the help of Mathematica and a suggestion to just look at the expression for the curl in spherical coordinates) have a curl that is radial with a 1/r^2 dependence;
A_phi = -Cot[theta]/r
For when its curl is evaluated with Mathematica,...
In[2] Curl[{0,0, - Cot[theta]/r}, Spherical[r,theta,phi]] Out[2] {1/r^2,0,0}
> > Now, it's singular on the -z axis, but whaddya expect? The > condition B = curl A follows from the equation div B = 0, > and some topological considerations. > > I hate it when monopoles pass through my SQUIDS during a brain scan! > >
** If I had a vote for a Nobel prize in physics, Stephen Wolfram would get it, for Mathematica is clearly dynamite *8^). Would he get your vote ?
Re: Vector field A in R^3 with curl A = [radial outward]/R^2 ? Date: 1998/03/18
In article <35102EC4.3720@physics.uc.edu> Ricardo Rademacher <nospam-ricardor-nospam@physics.uc.edu> writes:
> > > > ** If I had a vote for a Nobel prize in physics, Stephen Wolfram would > > get it, for Mathematica is clearly dynamite *8^). Would he get your > > vote ? > > Nice tool, but it has severe limitations for serious research.
Oh, I would bet that a lot of serious research has been churned out with Mathematica.
The number of books written about Mathematica speaks in part to the large number of people who have fallen in love with the software. To each his own (software).
Re: h - again ? Date: 1998/03/26
In article <6fc2ra$4df$1@nnrp1.dejanews.com> Neil.Haughey@bnfl.com writes:
> So far the replies to my original question are just the answers you would > expect from 99% of physics graduates.
I will try to take the viewpoint of the other 1% though the other 99% gave interesting answers.
Look at the function
where N is an integer, f is the cylindrical coordinate.
Here one can see how even though energy, w, can change the angular momentum remains the same. It is all in the shape, kind of.
Too bad its not quite a spinor?
Re: Relativistic particle spin questions. Date: 1998/03/27
In article <35269aab.16498769@aklobs.org.nz> rtomes@kcbbs.gen.nz (Ray Tomes) writes:
> I have heard that particles in accelerators tend to have their spin > lined up in the direction of motion. Is that correct? > > Is this just an expected relativistic effect due to contraction along > the axis of travel as seen by us?
I have had this question, think I have resolved it?
Consider a large number of letter O's scattered about near the origin of some rest frame. Let the letter O's also have a random distribution of orientations with respect to that rest frame such that if we form the vector sum of all the unit normals (normal to the plane that contains the letter O) then that vector sum would be approximately zero. Now consider how the letter O's appear in another frame that moves rapidly past the rest frame of the letter O's.
We will no longer see a completely random distribution of orientations for the letter O's. To the observer rushing past the letter O's the unit normals will be "rotated" in alignment with our direction of travel, and at ultra relativistic velocities the unit normals will either point with or against our direction of travel.
At this point one only need to consider the letter O's to be spinning in the plane that contains them and one recovers the fact that an ultra relativistic electron has its spin with or against it direction of travel?
Link to thread of next article. Brooklyn bridge sits on wood?! Date: 1998/04/09
I was going through "A Picture History of the Brooklyn Bridge" by Mary J. Shapiro and if I read the book correct one or both of the main stone towers that holds up the bridge rests on a large platform of wood?
I would have thought that there would be problems with the wood rotting out and causing the bridge to settle. Obvious the bridge is still up. What keeps the wood from rotting?
"Toward an understanding of the spin-statistics theorem". Date: 1998/04/16
The latest issue of The American Journal of Physics (Am. J. Phys. 66 (4), April 1998, pages 284-303) has an article by Ian Duck and E. C. G. Sudarshan titled, "Toward an understanding of the spin-statistics theorem". My hat goes off to Duck and Sudarshan for their work on an issue I find more important than the unification of general relativity and quantum mechanics *8^)
"Why is it that particles with half-integral spin are Fermi particles whose amplitudes add with the minus sign, whereas particles with integral spin are Bose particles whose amplitudes add with the positive sign? We apologize for the fact that we cannot give you an elementary explanation. An explanation has been worked out by Pauli from complicated arguments of quantum field theory and relativity. He has shown that the two must necessarily go together, but we have not been able to find a way of reproducing his arguments on an elementary level... . This probably means that we do not have a complete understanding of the fundamental principle involved... ."
I'm afraid that Feyman, if he were alive today, would still make the above comment that ... "This probably means that we do not have a complete understanding of the fundamental principle involved... ."
Can any of you Weinbergs or Wittens out there come up with a more elementary explanation of the spin-statistics theorem?
Something James Clerk Maxwell wrote. Date: 1998/04/19
The following quote of Maxwell's is from: From: "Science-Week" <prismx@scienceweek.com> Date: Sat, 18 Apr 1998 16:10:15 -0600
Hope it was worth your time.
"Mathematicians may flatter themselves that they possess new ideas which mere human language is as yet unable to express. Let them make the effort to express these ideas in appropriate words without the aid of symbols, and if they succeed they will not only lay us laymen under a lasting obligation, but, we venture to say, they will find themselves very much enlightened during the process, and will even be doubtful whether the ideas as expressed in symbols had ever quite found their way out of the equations into their minds."
-- James Clerk Maxwell
Re: What did I see last night? Author: Gene.Handler <Gene.Handler@gcidqmsrv.gmd.trw.com> Date: 1998/06/26 Forum: sci.astro
ale2@NOSPAMpsu.edu (ale2) wrote: > > At about 2:56 a.m. Friday morning (Pennsylvania time) I went out > for some fresh air in looked to the night sky. A very bright > "star" was seen and then in a matter of a few seconds the star > dimmed and then disappeared. My first though was I had witnessed > some kind of nova but thinking that is a rare event I though > maybe it was a satellite, but this "star" was easily the > brightest object in the sky, several times brighter then Venus. > So not a nova?, not a satellite,.. a plane, but I did not notice > it move at all. Any thoughts on what I saw? > > Anyway the "star" was towards the south-south-east at about 160 > degrees and it was about 45 degrees above the horizon. > > Do astronomers record all of the night sky, say with a wide > field camera, all of the time to catch events like this? > > Thanks for any thoughts! >
Congratulations, you have witnessed an Iridium satellite flare. There are 60 some odd of these satellites and they have flat reflective antenna. Sun light bouncing off them produces flares that can be VERY bright. The flares are common (usually at least one a day for any one location). I checked the site www2.gsoc.dlr.de for flares this morning as seen from mid Pennsylvania, and found this flare: 2:56:58 EDT, mag -6, position 39 deg. alt, 145 deg az (SE), Iridium 33. This sounds like an exact match to what you saw. Good reporting.
How about, proton-->positron(like) as strong force-->infinity? Date: 1998/08/31
I will probably regret this post latter...
As the strong force gets stronger and stronger the "size" of the proton must get smaller and smaller? So if we take the limit where the strong force approaches infinity the three quarks will sit on top of each other? So we have
spin up, up quark + spin down, up quark + spin up or down, down quark.
Except for the mass we have a positron like particle?
And similar for the neutron,
neutron-->neutrino(like) as strong force-->infinity?
electron-->neutrino(like) as strength of electromagnetic force -->0
neutrino--> ? as strength of weak force --> 0
Thanks for any ideas and thoughts (please don't be too critical)!
Torsion bars and gears, how does this system work. Date: 1998/08/19
I have a (imaginary) mechanical system in mind and I am not sure of several of its motions, maybe you can help.
The system is a rather simple combination of torsion bars and transmissions. Let our mechanical system have the symmetry of a 2-dimensional square lattice. At each lattice point there is a "transmission" of sorts to which the ends of four torsion bars are attached. Each transmission shares four torsion bars so there are roughly twice as many torsion bars as transmissions. The operation of the transmissions is such that all four torsion bars share the same motion, for example, if the one torsion bar rotates an angle theta in the clockwise direction then the other three torsion bars will under go the same rotation and in the same sense. Each transmission, the ith transmission say, has a little pointer on top to indicate the angular position (theta_i) of the ends of the torsion bars.
Now consider such a system of large but finite extent put together such that there is no torsional energy stored in the system. Assume all components to be frictionless.
The following I think to be true of this system:
1- If one torsion bar is grabbed and rotated all other torsion bars will rotate the same amount but half of the transmissions will rotate in one sense and the other half will rotate in the opposite sense, that is the little pointers at every other transmission will rotate with the same sense?
2- Consider what happens when one torsion bar is removed from this system, given some twist (storing potential energy) and reattached (while holding the twist) to our system. After the torsion bar is reattached the twist on it is slowly released. What happens as the hold of the torsion bar is released is the potential energy of the single torsion bar is reduced while the potential energy of the rest of the system (all the other torsion bars) is increased. [The Lagrangian for this system is simply the sum of all the potential energies for all the torsion bars. The potential for the torsion bar between adjacent transmissions, say i and j, goes as (theta_i + theta_j)^2 assume no higher order terms needed unlike real torsion bars).]
3_ Consider the system in 2_ above. If my hunch is right the energy stored in the torsion bars will approximate the energy stored in a 2-dimensional dipole field? The greatest potential energy will be in a small area.
3_ (most interesting question?) It is also a hunch that the ground state is localized in position but for a potential barrier equivalent ground states exist located at neighboring lattice sites?
4_ For the above system at rest the sum of the four torques applied to each transmission is zero for otherwise the transmission would not be at rest?
Re: Theory of Everything (was New discoveries in physics). Date: 1998/09/06
In article <YgrI1.438$he1.951991@newse2.tampabay.rr.com> "Rex Bennett" <rbennet2@tampabay.rr.com> writes:
> Tom Davidson wrote in message <6stcfi$oa2$1@supernews.com>... > >"The Theory if Everything," as I learned it early in my struggles with > >computer programming, was that the more you tried to accomplish with a > >single program, the less satisfactorily it accomplished anything, so that a > >program designed to do everything would accomplish nothing. > > > >Tom Davidson > >(former government scientist) > > > > Even nature breaks its activities down into separate programs. > Perhaps we should learn from nature. (g)
The "software" for an ant or any simple insect may be distributed throughout the insect but that is just a matter of the hardware. You still have only one program that "runs" the bug?
Anybody have the "wiring" diagram for an ant or any simple animal they might like to email me?
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