<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no,scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>It is well known that the direction of Gravity is "instantaneous",\nThat is, towards the locations of where the object is instead of\nwhere it was "distance/lightspeed" ago.\n\nThis would presumably be solvable by the fact that at least the\nlinear speed of the attracting body is "know" by any gravitons\ntraveling away from it. In that case we don\'t need any superluminal\npropagation.\n\nBut now I\'m interested in the following:\n\nWhat is know, or measured, about the Amplitude of Gravity?\nSay we are 1000 km close to a very high density body traveling near\nlightspeed and the gravitons that reach us were emitted when the body\nwas still 10,000 km away.\n\nDo we "feel" an object 10,000 km away or has nature something equal\nin store and let us "feel" the gravity as if the object was 1000 km\naway?\n\nRegards, Hans\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>It is well known that the direction of Gravity is "instantaneous",
That is, towards the locations of where the object is instead of
where it was "distance/lightspeed" ago.
This would presumably be solvable by the fact that at least the
linear speed of the attracting body is "know" by any gravitons
traveling away from it. In that case we don't need any superluminal
propagation.
But now I'm interested in the following:
What is know, or measured, about the Amplitude of Gravity?
Say we are 1000 km close to a very high density body traveling near
lightspeed and the gravitons that reach us were emitted when the body
was still 10,000 km away.
Do we "feel" an object 10,000 km away or has nature something equal
in store and let us "feel" the gravity as if the object was 1000 km
away?
Regards, Hans
OG
Jul2-04, 05:32 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no,scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n"Hans de Vries" <hansdevries@chip-architect.com> wrote in message\nnews:3881ea8b.0406301635.65af6add@posting.google.com...\n> It is well known that the direction of Gravity is "instantaneous",\n> That is, towards the locations of where the object is instead of\n> where it was "distance/lightspeed" ago.\n\nI have seen nothing to suggest that that any information about gravity\npropagates at anything other than light speed. Please provide references to\nsupport a contrary view.\n\n> This would presumably be solvable by the fact that at least the\n> linear speed of the attracting body is "know" by any gravitons\n> traveling away from it. In that case we don\'t need any superluminal\n> propagation.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>"Hans de Vries" <hansdevries@chip-architect.com> wrote in message
news:3881ea8b.0406301635.65af6add@posting.google.com...
> It is well known that the direction of Gravity is "instantaneous",
> That is, towards the locations of where the object is instead of
> where it was "distance/lightspeed" ago.
I have seen nothing to suggest that that any information about gravity
propagates at anything other than light speed. Please provide references to
support a contrary view.
> This would presumably be solvable by the fact that at least the
> linear speed of the attracting body is "know" by any gravitons
> traveling away from it. In that case we don't need any superluminal
> propagation.
Hans de Vries
Jul4-04, 08:40 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no,scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n"OG" <owen@gwynnefamily.org.uk> wrote in message news:<2kjnpqF2bivnU1@uni-berlin.de>...\n> "Hans de Vries" <hansdevries@chip-architect.com> wrote in message\n> news:3881ea8b.0406301635.65af6add@posting.google.com...\n> > It is well known that the direction of Gravity is "instantaneous",\n> > That is, towards the locations of where the object is instead of\n> > where it was "distance/lightspeed" ago.\n>\n> I have seen nothing to suggest that that any information about gravity\n> propagates at anything other than light speed. Please provide references to\n> support a contrary view.\n>\n> > This would presumably be solvable by the fact that at least the\n> > linear speed of the attracting body is "know" by any gravitons\n> > traveling away from it. In that case we don\'t need any superluminal\n> > propagation.\n\nI\'m not suggesting superluminal speed here but Astronomers have to use\nthe instantaneous direction in their calculations to get the correct\nresults even for our own solar system. Our solar system would become\nhighly instable if the retarded directions are used (the directions where\nthe object was "distance/lightspeed" ago\n\nOne could argue that this should be interpreted as superluminal\npropagation. A proponent of this theory is for instance Tom van\nFlandern. A example of a counter argument based on what I mentioned\nas the influence of the linear speed of the object on the interaction\ncan be found here:\n\nhttp://www.vialattea.net/esperti/fis/velgravita/9909087.pdf\n\nI found there has been quite a debate here on this very group about the\nsubject (with Tom van Flandern). I found a compilation here at John Baez:\n\nhttp://math.ucr.edu/home/baez/PUB/debate\n\nWhat I actually want to know is if Astronomers also have to use\nthe instantaneous distance (as well as the direction) in order to\nget any observed results.\n\nRegards, Hans\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>"OG" <owen@gwynnefamily.org.uk> wrote in message news:<2kjnpqF2bivnU1@uni-berlin.de>...
> "Hans de Vries" <hansdevries@chip-architect.com> wrote in message
> news:3881ea8b.0406301635.65af6add@posting.google.com...
> > It is well known that the direction of Gravity is "instantaneous",
> > That is, towards the locations of where the object is instead of
> > where it was "distance/lightspeed" ago.
>
> I have seen nothing to suggest that that any information about gravity
> propagates at anything other than light speed. Please provide references to
> support a contrary view.
>
> > This would presumably be solvable by the fact that at least the
> > linear speed of the attracting body is "know" by any gravitons
> > traveling away from it. In that case we don't need any superluminal
> > propagation.
I'm not suggesting superluminal speed here but Astronomers have to use
the instantaneous direction in their calculations to get the correct
results even for our own solar system. Our solar system would become
highly instable if the retarded directions are used (the directions where
the object was "distance/lightspeed" ago
One could argue that this should be interpreted as superluminal
propagation. A proponent of this theory is for instance Tom van
Flandern. A example of a counter argument based on what I mentioned
as the influence of the linear speed of the object on the interaction
can be found here:
I found there has been quite a debate here on this very group about the
subject (with Tom van Flandern). I found a compilation here at John Baez:
http://math.ucr.edu/home/baez/PUB/debate
What I actually want to know is if Astronomers also have to use
the instantaneous distance (as well as the direction) in order to
get any observed results.
Regards, Hans
pervect
Jul9-04, 04:49 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no,scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\nOn Thu, 1 Jul 2004 21:46:45 +0000 (UTC),\nhansdevries@chip-architect.com (Hans de Vries) wrote:\n\n>It is well known that the direction of Gravity is "instantaneous",\n>That is, towards the locations of where the object is instead of\n>where it was "distance/lightspeed" ago.\n>\n>This would presumably be solvable by the fact that at least the\n>linear speed of the attracting body is "know" by any gravitons\n>traveling away from it. In that case we don\'t need any superluminal\n>propagation.\n>\n>But now I\'m interested in the following:\n>\n>What is know, or measured, about the Amplitude of Gravity?\n>Say we are 1000 km close to a very high density body traveling near\n>lightspeed and the gravitons that reach us were emitted when the body\n>was still 10,000 km away.\n>\n>Do we "feel" an object 10,000 km away or has nature something equal\n>in store and let us "feel" the gravity as if the object was 1000 km\n>away?\n\nUnfortunately, it\'s only approximately true that gravity points\ntowards the instantaneous position of a quickly moving source. When\nthe velocity approaches \'c\' as in your example, this approximation\nbreaks down.\n\nOne of the papers which discusses this issue arose from the old\nargument you mentioned\n\nhttp://arxiv.org/ftp/physics/papers/9910/9910050.pdf\n\n"Unlike the EM case however, there is no exact cancellation of the\nretardation effects to all orders of B, but only cancellation up to\nlinear terms in B."\n\nThere is a solution for the gravitational field of an extremely\nrapidly moving body, but it may not be intuitive. The\nAichelburg-Sexyl boost gives the limiting case for a very rapidly\nmoving body, for which the gravitational field is an impulsive plane\nwave.\n\nIt\'s a lot easier to talk about the electric field of a rapidly moving\nbody, and to point out how the Aichelburg-Sexyl boost is similar. As\nan electric charge moves at a higher and higher velocity, the electric\nfield lines, which were originally uniformly distributed, start to\nbecome concentrated more and more in a direction normal to the motion\nof the particle. (See for instance figure 2 in the previously cited\nreference).\n\nIn the limit of a very rapidly moving charge, the electric field\nexists only transverse to the particle\'s motion, and the electric\nfield looks like the electric field of an impulsive plane wave.\n\nThere\'s more on the Aichelburg-Sexl boost at\nhttp://arxiv.org/abs/gr-qc/0110032\n\nNote that while we have discussed the behavior of the electric\ncomponent of the electromagnetic field of a moving charge, a truly\ncomplete description also includes a magnetic component. The same can\nbe said for the complete description of the gravitational "field" of a\nmoving mass.\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>On Thu, 1 Jul 2004 21:46:45 +0000 (UTC),
hansdevries@chip-architect.com (Hans de Vries) wrote:
>It is well known that the direction of Gravity is "instantaneous",
>That is, towards the locations of where the object is instead of
>where it was "distance/lightspeed" ago.
>
>This would presumably be solvable by the fact that at least the
>linear speed of the attracting body is "know" by any gravitons
>traveling away from it. In that case we don't need any superluminal
>propagation.
>
>But now I'm interested in the following:
>
>What is know, or measured, about the Amplitude of Gravity?
>Say we are 1000 km close to a very high density body traveling near
>lightspeed and the gravitons that reach us were emitted when the body
>was still 10,000 km away.
>
>Do we "feel" an object 10,000 km away or has nature something equal
>in store and let us "feel" the gravity as if the object was 1000 km
>away?
Unfortunately, it's only approximately true that gravity points
towards the instantaneous position of a quickly moving source. When
the velocity approaches 'c' as in your example, this approximation
breaks down.
One of the papers which discusses this issue arose from the old
argument you mentioned
"Unlike the EM case however, there is no exact cancellation of the
retardation effects to all orders of B, but only cancellation up to
linear terms in B."
There is a solution for the gravitational field of an extremely
rapidly moving body, but it may not be intuitive. The
Aichelburg-Sexyl boost gives the limiting case for a very rapidly
moving body, for which the gravitational field is an impulsive plane
wave.
It's a lot easier to talk about the electric field of a rapidly moving
body, and to point out how the Aichelburg-Sexyl boost is similar. As
an electric charge moves at a higher and higher velocity, the electric
field lines, which were originally uniformly distributed, start to
become concentrated more and more in a direction normal to the motion
of the particle. (See for instance figure 2 in the previously cited
reference).
In the limit of a very rapidly moving charge, the electric field
exists only transverse to the particle's motion, and the electric
field looks like the electric field of an impulsive plane wave.
There's more on the Aichelburg-Sexl boost at
http://arxiv.org/abs/http://www.arxiv.org/abs/gr-qc/0110032
Note that while we have discussed the behavior of the electric
component of the electromagnetic field of a moving charge, a truly
complete description also includes a magnetic component. The same can
be said for the complete description of the gravitational "field" of a
moving mass.
Hans de Vries
Jul11-04, 03:57 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no,scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\n\npervect <pervect@invalid.invalid> wrote in message news:<dbeoe0hon25h69ddqbe4onjit674n91459@4ax.com>...\n\n> >Do we "feel" an object 10,000 km away or has nature something equal\n> >in store and let us "feel" the gravity as if the object was 1000 km\n> >away?\n>\n> Unfortunately, it\'s only approximately true that gravity points\n> towards the instantaneous position of a quickly moving source. When\n> the velocity approaches \'c\' as in your example, this approximation\n> breaks down.\n>\n> One of the papers which discusses this issue arose from the old\n> argument you mentioned\n>\n> http://arxiv.org/ftp/physics/papers/9910/9910050.pdf\n>\n> "Unlike the EM case however, there is no exact cancellation of the\n> retardation effects to all orders of B, but only cancellation up to\n> linear terms in B."\n>\n> There is a solution for the gravitational field of an extremely\n> rapidly moving body, but it may not be intuitive. The\n> Aichelburg-Sexyl boost gives the limiting case for a very rapidly\n> moving body, for which the gravitational field is an impulsive plane\n> wave.\n>\n> It\'s a lot easier to talk about the electric field of a rapidly moving\n> body, and to point out how the Aichelburg-Sexyl boost is similar. As\n> an electric charge moves at a higher and higher velocity, the electric\n> field lines, which were originally uniformly distributed, start to\n> become concentrated more and more in a direction normal to the motion\n> of the particle. (See for instance figure 2 in the previously cited\n> reference).\n>\n> In the limit of a very rapidly moving charge, the electric field\n> exists only transverse to the particle\'s motion, and the electric\n> field looks like the electric field of an impulsive plane wave.\n\nSometimes called the "Lorentz Pancake" I saw. It arises because almost\n100% of the field is emitted in the forward direction of motion. The flat\n"Pancake" field normal to the particle\'s motion propagates parallel to\nthe particle and originated from the particle far backwards.\n\nI found an illustration of the purely geometric effect that causes the\nemission of the field to be more and more concentrated in the forward\ndirection with increasing speed here: (on page 5)\n\nhttp://www.pas.rochester.edu/~dmw/phy218/Lectures/Lect_66b.pdf\n\nIt is used here to derive the Lienard Wiechert potentials from a\nmoving charge with retarded sources. Actually it is this effect which\n\'de-skews\' the cone-like field from a moving charge which has\n"more field" trailing behind it than it has in front of it.\n\nThe field becomes front/back symmetric again because "more field"\nis propagated forwards than backwards. It looks to me that this should\nwork exactly the same for a classical mass, but then it is GR that\nintroduces these higher order terms of B that "do not fit".\n\n>\n> There\'s more on the Aichelburg-Sexl boost at\n> http://arxiv.org/abs/gr-qc/0110032\n>\n> Note that while we have discussed the behavior of the electric\n> component of the electromagnetic field of a moving charge, a truly\n> complete description also includes a magnetic component. The same can\n> be said for the complete description of the gravitational "field" of a\n> moving mass.\n\nThanks,\n\nRegards, Hans\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>pervect <pervect@invalid.invalid> wrote in message news:<dbeoe0hon25h69ddqbe4onjit674n91459@4ax.com>...
> >Do we "feel" an object 10,000 km away or has nature something equal
> >in store and let us "feel" the gravity as if the object was 1000 km
> >away?
>
> Unfortunately, it's only approximately true that gravity points
> towards the instantaneous position of a quickly moving source. When
> the velocity approaches 'c' as in your example, this approximation
> breaks down.
>
> One of the papers which discusses this issue arose from the old
> argument you mentioned
>
> http://arxiv.org/ftp/physics/papers/9910/9910050.pdf
>
> "Unlike the EM case however, there is no exact cancellation of the
> retardation effects to all orders of B, but only cancellation up to
> linear terms in B."
>
> There is a solution for the gravitational field of an extremely
> rapidly moving body, but it may not be intuitive. The
> Aichelburg-Sexyl boost gives the limiting case for a very rapidly
> moving body, for which the gravitational field is an impulsive plane
> wave.
>
> It's a lot easier to talk about the electric field of a rapidly moving
> body, and to point out how the Aichelburg-Sexyl boost is similar. As
> an electric charge moves at a higher and higher velocity, the electric
> field lines, which were originally uniformly distributed, start to
> become concentrated more and more in a direction normal to the motion
> of the particle. (See for instance figure 2 in the previously cited
> reference).
>
> In the limit of a very rapidly moving charge, the electric field
> exists only transverse to the particle's motion, and the electric
> field looks like the electric field of an impulsive plane wave.
Sometimes called the "Lorentz Pancake" I saw. It arises because almost
100% of the field is emitted in the forward direction of motion. The flat
"Pancake" field normal to the particle's motion propagates parallel to
the particle and originated from the particle far backwards.
I found an illustration of the purely geometric effect that causes the
emission of the field to be more and more concentrated in the forward
direction with increasing speed here: (on page 5)
It is used here to derive the Lienard Wiechert potentials from a
moving charge with retarded sources. Actually it is this effect which
'de-skews' the cone-like field from a moving charge which has
"more field" trailing behind it than it has in front of it.
The field becomes front/back symmetric again because "more field"
is propagated forwards than backwards. It looks to me that this should
work exactly the same for a classical mass, but then it is GR that
introduces these higher order terms of B that "do not fit".
>
> There's more on the Aichelburg-Sexl boost at
> http://arxiv.org/abs/http://www.arxiv.org/abs/gr-qc/0110032
>
> Note that while we have discussed the behavior of the electric
> component of the electromagnetic field of a moving charge, a truly
> complete description also includes a magnetic component. The same can
> be said for the complete description of the gravitational "field" of a
> moving mass.
Thanks,
Regards, Hans
tessel@tum.bot
Jul13-04, 03:37 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no,scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>On Thu, 1 Jul 2004, Hans de Vries wrote:\n\n> It is well known that the direction of Gravity is "instantaneous",\n> That is, towards the locations of where the object is instead of\n> where it was "distance/lightspeed" ago.\n\nYou probably meant that in Newtonian gravitation, changes in the\ndistribution of matter HERE results in an -instantaneous- "update" of the\ngravitational potential THERE.\n\nI\'ll try to give a rough answer under the assumption that you are an\nadvanced undergraduate physics student familiar with Maxwell\'s theory of\nEM and Newtonian gravitation. If not, you should probably read the FAQ:\n\nhttp://www2.corepower.com:8080/~relfaq/relativity.html\n\nOK, here\'s my rough answer:\n\nEngrave upon your heart the often useful and very close formal analogy\nbetween Newtonian gravitation (treated as a classical field theory, i.e.\nin terms of a potential which obeys a field equation, the Laplace\nequation) and electrostatics in Maxwell\'s theory of EM.\n\nIn electrostatics, we should expect that when we pass to charge\ndistributions which are evolving over time, the effect (on the EM field)\nof changes in the charge distribution HERE will propagate at the speed of\nlight from HERE to THERE. This expectation is correct, but as someone\napparently already mentioned, if you\'ve read Feynman\'s Lectures on\nPhysics, you know that there is a surprise lurking here! If not, it would\nbe a good idea to go study his discussion of retarded potentials in EM.\n\nNow, in the analogous situation in gtr, there is a -further- surprise! I\nwon\'t say more because you need to understand "Maxwell\'s surprise" first.\nIn fact, if you\'ve never read Landau & Lifschitz, this would be a good\npoint to read at least the first two thirds or so of this classic:\n\nauthor = {L. D. Landau and E. M. Lifshitz},\ntitle = {The Classical Theory of Fields},\nseries = {Course of Theoretical Physics},\nvolume = 2,\nedition = {Fourth},\npublisher = {Pergamon},\nyear = 1975}\n\nAs you can see, this book offers a unified presentation of the two golden\nexemplars of relativistic classical field theories, namely Maxwell\'s\ntheory of EM and Einstein\'s theory of gravitation. But LL\'s treatment of\ngtr is dated, so you can pass over that lightly for now and study instead\na modern gtr textbook; in this context I\'d recommend one of these:\n\nauthor = {Sean Carroll},\ntitle = {Spacetime and geometry: an introduction to general relativity},\npublisher = {Addison-Wesley},\nyear = 2004}\n\nauthor = {Bernard F. Schutz},\ntitle = {A First Course in General Relativity},\npublisher = {Cambridge University Press},\nyear = 1985}\n\n(These are UG textbooks with excellent chapters on gravitational\nradiation.) Finally, you can skim a paper by Steve Carlip:\n\nauthor = {S. Carlip},\ntitle = {Aberration and the Speed of Gravity},\njournal = {Phys. Lett. A},\nvolume = 267,\nyear = 2000,\npages = {81--87},\nnote = {gr-qc/9909087}}\n\n> This would presumably be solvable by the fact that at least the linear\n> speed of the attracting body is "know" by any gravitons traveling away\n> from it.\n\nThis sounds about as far from the spirit of gtr as can be imagined--- so\nprobably I guessed wrong above about your background! But if so, see in\nparticular the FAQ article on "how does gravity get out of a black hole?".\n\nBTW, be aware if you start talking here about gravitation, and don\'t\nspecify a theory, readers are likely to assume you mean gtr or possibly\nNewtonian theory unless you state otherwise. Also, gtr is a purely\nclassical relativistic field theory of gravitation, and thus does not\nrequire the some problematic notion of a "graviton".\n\n> What is know, or measured, about the Amplitude of Gravity?\n\nAssuming you are asking about gtr, this question probably needs to be\nquantified in at least two essential ways:\n\n1. by "amplitude" do you mean "field strength", as in "typical component\nof Riemann tensor?"--- presumably you want generally applicable\ninformation about how such a "field strength" scales with distance from\nthe source of the field,\n\n2. what kind of field are you interested in: "Coulomb" or "radiative" or\nsomething else?\n\nIn more detail:\n\nIf by "amplitude" you mean "field strength", then be aware that in both\nEinstein\'s theory of gravity and Maxwell\'s theory of EM "the field" is\ngenerally taken to be the "curvature" of a certain "connection". This is\nnot a single numerical field but a "tensor field". You may also encounter\nformulations in terms of differential forms (scalar valued, for Maxwell;\noperator valued, for Einstein).\n\nIn Maxwell\'s theory of EM, "the field" in this sense can be regarded as an\nantisymmetric tensor field on spacetime; wrt a particular observer\'s\nmotion, this can be "split" into two spatial vector fields, the electric\nand magnetic field vectors. One way of understanding the profound\ndistinction between elecrostatic fields and EM wave fields in Maxwell\'s\ntheory is that in the former case, the magnetic vector can be "transformed\naway" by passing to a suitable "adapted observer", but this is not\npossible in the latter case.\n\nIn Einstein\'s theory of gravity (gtr), the "field" corresponds to the\nRiemann tensor, a fourth rank tensor field on spacetime; wrt a particular\nobserver\'s motion, a vacuum field can be "split" into two second rank\n"spatial tensors"; the one analogous to the electric vector in the Maxwell\nsplitting then corresponds neatly to the "tidal force field" (a symmetric\nsecond rank spatial tensor) of Newtonian gravity. One way to understand\nthe profound distinction between Coulomb and radiative fields in\nEinstein\'s theory is that in the former case, the second tensor (the\nmagnetogravitic tensor) can be "transformed away" by passing to a suitable\n"adapted observer", but this is not possible in the latter case.\n\nThe formulation I just sketched is very useful for understanding formal\nanalogies between Maxwell and Einstein which are very useful. But other\nformulations are also very useful. In particular, in some contexts (e.g.\ndiscussions of "gravitational radiation"; see below), "amplitude" may\nrefer to a "gravitational strain" which is read off the metric tensor; in\na weak slowly changing field, the Newtonian potential can be read off the\n-metric-, not the connection. If this sounds confusing, well, there are\nvery good reasons for all of these different formulations!\n\nOK, now let\'s consider the question: "how does field strength scale with\ndistance?"\n\nWell, this question still needs to be qualified, because in most\ninteresting field theories, "field updating information" is carried by\nradiation. For example, in Maxwell\'s theory of EM the field is updated by\nthe arrival of EM radiation from a distant place where the charge\ndistribution is changing. In Einstein\'s theory of gravitation, the field\nis updated by the arrival of gravitational radiation from a distant place\nwhere the mass/momentum distribution is changing; in such theories, there\nis a distinction between "radiative fields" and the slowly changing field\nproduced by same a moving charge (Maxwell) or a moving massive body\n(Einstein). A particularly simple case is the spherically symmetric field\nproduced by a suitable static object, which I\'ll somewhat inaccurately\ncall a "Coulomb field". Again comparing Maxwell and Einstein, roughly\nspeaking, Coulomb field magnitudes of static fields scale like this\n\nMaxwell q/r^2\n\nEinstein m/r^3\n\nThe amplitude of typical radiative fields falls off much less rapidly with\ndistance, however. So, the answer depends upon what kind of field (e.g.\n"Coulomb" or "plane wave") you have in mind.\n\nIf the m/r^3 rather than m/r^2 surprises you, see this expository post\n(archived on Relativity on the World Wide Web):\n\nhttp://math.ucr.edu/home/baez/PUB/tidal\n\nIn the case of gtr, there is an additional subtlety lurking here, which I\npointed out here recently (not for the first time): the obvious assumption\nthat the fields scale linearly with mass or charge is not correct--- or at\nleast highly misleading! This is part of a more general general\nobservation: we must be far more sophisticated in how we think about\nconcepts like "mass", "momentum", etc., which we want to use to\ncharacterize "the field of an isolated object", when we pass from flat\nspacetime to curved spacetimes. Advanced readers intrigued by this remark\ncan look for a fairly recent post on "point symmetries" and the family of\n"Weyl vacuums" (all -static- axisymmetric vacuum solutions to the EFE).\n\n> Say we are 1000 km close to a very high density body traveling near\n> lightspeed and the gravitons that reach us were emitted when the body\n> was still 10,000 km away.\n>\n> Do we "feel" an object 10,000 km away or has nature something equal\n> in store and let us "feel" the gravity as if the object was 1000 km\n> away?\n\nAs someone apparently already told you, according to gtr, while the tidal\nforce field on a test particle which is produced by an isolated slowly\nmoving massive object is approximately Coloumb, the tidal force field on a\ntest particle which is produced by an isolated "ultrarelativistic" massive\nobject is approximately modeled by a kind of "Gaussian pulse"\ngravitational wave (a special case of the "Ehlers/Kundt class 4 pp wave").\nIn the standard "harmonic chart" this exact vacuum solution can be written\n\nds^2 = -2m exp(-U^2/2/a^2) log(R)/a/sqrt(pi) dU^2\n\n- 2 dU dV + dR^2 + R^2 dTheta^2,\n\n-infty < U,V < infty, 0 < R < infty, -pi < Theta < pi\n\nRoughly speaking, you can think of this as the field being almost entirely\nconcentrated in the intersection of\n\n(a) a planar wavefront moving at the speed\nof light\n\n(b) the axis of cylindrical symmetry R = 0,\n\nand with the tidal force field on a typical initially static test particle\nscaling like exp(-U^2)/R^2. IOW, the tidal force field, as measured by a\ntypical slowly moving observer ("slowly moving" wrt the "very quickly\nmoving" massive object!) is "Gaussian" in -time- and "inverse square" in\ndistance from the `axis\' along which the ultrarelativistic object is\ntraveling. As you can see, this doesn\'t look anything like the tidal force\nfield of the Schwarzschild solution, which, as measured by a very slowly\nmoving observer, is essentially static, spherically symmetric and roughly\n"inverse cube" in "distance" from the massive object!\n\nJust to be clear, the solution I wrote down above is an exact vacuum\nsolution, but its -interpretation- as modeling the field produced by a\nvery rapidly moving Schwarzschild object involves an approximation. In a\nsuitable limit, this "Gaussian pulse wave", a special "type EK4 pp wave",\nbecomes the well-known Aichelburg-Sexl "ultrarelativistic boost of a\nSchwarzshild mass" solution, in which--- to abuse terminology--- "the\nGaussian pulse turns into a Dirac delta".\n\nAdvanced readers can look for past posts to this group which very\nextensively discussed ultrarelativistic fields in great detail, including\n"light bending" and other phenomena. Note that there are of course\ngeneralizations to "ultrarelativistic boosts" of Kerr masses and of\ncompact bodies with nonzero multipole moments, and to combined\ngravitational and EM fields, etc. Another concept which is relevant here\n(and important for advanced students) is "Penrose limit".\n\nOne last comment: the AS "ultrarelativistic boost" is ideally suited as an\ningredient for "colliding plane wave" (CPW) models in gtr. The methods of\nsoliton theory which I am discussing in the "Solitons in One Post"\nthread then apply to constructing such solutions, because the Ernst\nequation (as I already mentioned in that thread) admits soliton solutions.\n\n"T. Essel" (hiding somewhere in cyberspace)\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>On Thu, 1 Jul 2004, Hans de Vries wrote:
> It is well known that the direction of Gravity is "instantaneous",
> That is, towards the locations of where the object is instead of
> where it was "distance/lightspeed" ago.
You probably meant that in Newtonian gravitation, changes in the
distribution of matter HERE results in an -instantaneous- "update" of the
gravitational potential THERE.
I'll try to give a rough answer under the assumption that you are an
advanced undergraduate physics student familiar with Maxwell's theory of
EM and Newtonian gravitation. If not, you should probably read the FAQ:
Engrave upon your heart the often useful and very close formal analogy
between Newtonian gravitation (treated as a classical field theory, i.e.
in terms of a potential which obeys a field equation, the Laplace
equation) and electrostatics in Maxwell's theory of EM.
In electrostatics, we should expect that when we pass to charge
distributions which are evolving over time, the effect (on the EM field)
of changes in the charge distribution HERE will propagate at the speed of
light from HERE to THERE. This expectation is correct, but as someone
apparently already mentioned, if you've read Feynman's Lectures on
Physics, you know that there is a surprise lurking here! If not, it would
be a good idea to go study his discussion of retarded potentials in EM.
Now, in the analogous situation in gtr, there is a -further- surprise! I
won't say more because you need to understand "Maxwell's surprise" first.
In fact, if you've never read Landau & Lifschitz, this would be a good
point to read at least the first two thirds or so of this classic:
author = {L. D. Landau and E. M. Lifshitz},
title = {The Classical Theory of Fields},
series = {Course of Theoretical Physics},
volume = 2,
edition = {Fourth},
publisher = {Pergamon},
year = 1975}
As you can see, this book offers a unified presentation of the two golden
exemplars of relativistic classical field theories, namely Maxwell's
theory of EM and Einstein's theory of gravitation. But LL's treatment of
gtr is dated, so you can pass over that lightly for now and study instead
a modern gtr textbook; in this context I'd recommend one of these:
author = {Sean Carroll},
title = {Spacetime and geometry: an introduction to general relativity},
publisher = {Addison-Wesley},
year = 2004}
author = {Bernard F. Schutz},
title = {A First Course in General Relativity},
publisher = {Cambridge University Press},
year = 1985}
(These are UG textbooks with excellent chapters on gravitational
radiation.) Finally, you can skim a paper by Steve Carlip:
author = {S. Carlip},
title = {Aberration and the Speed of Gravity},
journal = {Phys. Lett. A},
volume = 267,
year = 2000,
pages = {81--87},
note = {http://www.arxiv.org/abs/gr-qc/9909087}}
> This would presumably be solvable by the fact that at least the linear
> speed of the attracting body is "know" by any gravitons traveling away
> from it.
This sounds about as far from the spirit of gtr as can be imagined--- so
probably I guessed wrong above about your background! But if so, see in
particular the FAQ article on "how does gravity get out of a black hole?".
BTW, be aware if you start talking here about gravitation, and don't
specify a theory, readers are likely to assume you mean gtr or possibly
Newtonian theory unless you state otherwise. Also, gtr is a purely
classical relativistic field theory of gravitation, and thus does not
require the some problematic notion of a "graviton".
> What is know, or measured, about the Amplitude of Gravity?
Assuming you are asking about gtr, this question probably needs to be
quantified in at least two essential ways:
1. by "amplitude" do you mean "field strength", as in "typical component
of Riemann tensor?"--- presumably you want generally applicable
information about how such a "field strength" scales with distance from
the source of the field,
2. what kind of field are you interested in: "Coulomb" or "radiative" or
something else?
In more detail:
If by "amplitude" you mean "field strength", then be aware that in both
Einstein's theory of gravity and Maxwell's theory of EM "the field" is
generally taken to be the "curvature" of a certain "connection". This is
not a single numerical field but a "tensor field". You may also encounter
formulations in terms of differential forms (scalar valued, for Maxwell;
operator valued, for Einstein).
In Maxwell's theory of EM, "the field" in this sense can be regarded as an
antisymmetric tensor field on spacetime; wrt a particular observer's
motion, this can be "split" into two spatial vector fields, the electric
and magnetic field vectors. One way of understanding the profound
distinction between elecrostatic fields and EM wave fields in Maxwell's
theory is that in the former case, the magnetic vector can be "transformed
away" by passing to a suitable "adapted observer", but this is not
possible in the latter case.
In Einstein's theory of gravity (gtr), the "field" corresponds to the
Riemann tensor, a fourth rank tensor field on spacetime; wrt a particular
observer's motion, a vacuum field can be "split" into two second rank
"spatial tensors"; the one analogous to the electric vector in the Maxwell
splitting then corresponds neatly to the "tidal force field" (a symmetric
second rank spatial tensor) of Newtonian gravity. One way to understand
the profound distinction between Coulomb and radiative fields in
Einstein's theory is that in the former case, the second tensor (the
magnetogravitic tensor) can be "transformed away" by passing to a suitable
"adapted observer", but this is not possible in the latter case.
The formulation I just sketched is very useful for understanding formal
analogies between Maxwell and Einstein which are very useful. But other
formulations are also very useful. In particular, in some contexts (e.g.
discussions of "gravitational radiation"; see below), "amplitude" may
refer to a "gravitational strain" which is read off the metric tensor; in
a weak slowly changing field, the Newtonian potential can be read off the
-metric-, not the connection. If this sounds confusing, well, there are
very good reasons for all of these different formulations!
OK, now let's consider the question: "how does field strength scale with
distance?"
Well, this question still needs to be qualified, because in most
interesting field theories, "field updating information" is carried by
radiation. For example, in Maxwell's theory of EM the field is updated by
the arrival of EM radiation from a distant place where the charge
distribution is changing. In Einstein's theory of gravitation, the field
is updated by the arrival of gravitational radiation from a distant place
where the mass/momentum distribution is changing; in such theories, there
is a distinction between "radiative fields" and the slowly changing field
produced by same a moving charge (Maxwell) or a moving massive body
(Einstein). A particularly simple case is the spherically symmetric field
produced by a suitable static object, which I'll somewhat inaccurately
call a "Coulomb field". Again comparing Maxwell and Einstein, roughly
speaking, Coulomb field magnitudes of static fields scale like this
Maxwell q/r^2
Einstein m/r^3
The amplitude of typical radiative fields falls off much less rapidly with
distance, however. So, the answer depends upon what kind of field (e.g.
"Coulomb" or "plane wave") you have in mind.
If the m/r^3 rather than m/r^2 surprises you, see this expository post
(archived on Relativity on the World Wide Web):
http://math.ucr.edu/home/baez/PUB/tidal
In the case of gtr, there is an additional subtlety lurking here, which I
pointed out here recently (not for the first time): the obvious assumption
that the fields scale linearly with mass or charge is not correct--- or at
least highly misleading! This is part of a more general general
observation: we must be far more sophisticated in how we think about
concepts like "mass", "momentum", etc., which we want to use to
characterize "the field of an isolated object", when we pass from flat
spacetime to curved spacetimes. Advanced readers intrigued by this remark
can look for a fairly recent post on "point symmetries" and the family of
"Weyl vacuums" (all -static- axisymmetric vacuum solutions to the EFE).
> Say we are 1000 km close to a very high density body traveling near
> lightspeed and the gravitons that reach us were emitted when the body
> was still 10,000 km away.
>
> Do we "feel" an object 10,000 km away or has nature something equal
> in store and let us "feel" the gravity as if the object was 1000 km
> away?
As someone apparently already told you, according to gtr, while the tidal
force field on a test particle which is produced by an isolated slowly
moving massive object is approximately Coloumb, the tidal force field on a
test particle which is produced by an isolated "ultrarelativistic" massive
object is approximately modeled by a kind of "Gaussian pulse"
gravitational wave (a special case of the "Ehlers/Kundt class 4 pp wave").
In the standard "harmonic chart" this exact vacuum solution can be written
ds^2 = -2m \exp(-U^2/2/a^2) log(R)/a/\sqrt(\pi) dU^2- 2 dU dV + dR^2 + R^2 dTheta^2,-\infty <[/itex] U,V [itex]< \infty,< R < \infty, -\pi < \Theta < \pi
Roughly speaking, you can think of this as the field being almost entirely
concentrated in the intersection of
(a) a planar wavefront moving at the speed
of light
(b) the axis of cylindrical symmetry R = 0,
and with the tidal force field on a typical initially static test particle
scaling like \exp(-U^2)/R^2. IOW, the tidal force field, as measured by a
typical slowly moving observer ("slowly moving" wrt the "very quickly
moving" massive object!) is "Gaussian" in -time- and "inverse square" in
distance from the `axis' along which the ultrarelativistic object is
traveling. As you can see, this doesn't look anything like the tidal force
field of the Schwarzschild solution, which, as measured by a very slowly
moving observer, is essentially static, spherically symmetric and roughly
"inverse cube" in "distance" from the massive object!
Just to be clear, the solution I wrote down above is an exact vacuum
solution, but its -interpretation- as modeling the field produced by a
very rapidly moving Schwarzschild object involves an approximation. In a
suitable limit, this "Gaussian pulse wave", a special "type EK4 pp wave",
becomes the well-known Aichelburg-Sexl "ultrarelativistic boost of a
Schwarzshild mass" solution, in which--- to abuse terminology--- "the
Gaussian pulse turns into a Dirac \delta".
Advanced readers can look for past posts to this group which very
extensively discussed ultrarelativistic fields in great detail, including
"light bending" and other phenomena. Note that there are of course
generalizations to "ultrarelativistic boosts" of Kerr masses and of
compact bodies with nonzero multipole moments, and to combined
gravitational and EM fields, etc. Another concept which is relevant here
(and important for advanced students) is "Penrose limit".
One last comment: the AS "ultrarelativistic boost" is ideally suited as an
ingredient for "colliding plane wave" (CPW) models in gtr. The methods of
soliton theory which I am discussing in the "Solitons in One Post"
thread then apply to constructing such solutions, because the Ernst
equation (as I already mentioned in that thread) admits soliton solutions.
"T. Essel" (hiding somewhere in cyberspace)
Hans de Vries
Jul14-04, 03:52 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no,scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\ntessel@tum.bot wrote in message news:<40f39146\\$1@news.sentex.net>...\n> On Thu, 1 Jul 2004, Hans de Vries wrote:\n>>\n>>\n\nThank you for your extensive response.\n\nA little summary for so far of the various responses and some\nother things I figured out:\n\n==================================================================\nCOULOMB FIELDS - NON ULTRA RELATIVISTIC - CONSTANT SPEED\n==================================================================\n\nA first "Lienard Wiechert type" approach based on retarded q/r and m/r\npotentials combined with the Doppler effect produces fields directed\nto the instantaneous position. An observer behind a screen with a\nsmall opening will experience a field directed towards the instanta-\nneous source but the opening has to be on the line between the retarded\nsource and the observer.\n\nMore detailed approaches however show that the direction towards the\ninstantaneous source is not exact, not for GR and also not for EM.\n\nTwo papers, One from Steve Carlip [1] and one from Michael Ibison,\nHarold E. Puthoff and Scott R. Little [2] derive that the direction of\nmaximal stretching tidal force is not exactly to the instantaneous\nsource but differs in a second order term of Beta.\n\nBoth papers are maybe somewhat premature in their statements about the\nEM field. The Lienard Wiechert approach neglects the effects caused by\nMaxwell\'s Displacement Current. Radiation from an oscillating Lienard\nWiechert charge through a small opening in an absorbing screen does not\ndiffract but continues to propagate in the same direction. A charge\nwith constant speed has an electric field with non-zero second order\nderivatives which produces extra electrical terms. These terms are\nnon radiative since the charge has a constant speed.\n\nI\'ve not found anything which handles Lienard Wiechert + Displacement\nCurrent. (I guess it probably complicates math in a way similar to a\ntheory which assumes that gravitation energy is itself a source of\ngravity)\n\n\n==================================================================\nRADIATION/LIGHT - NON ULTRA RELATIVISTIC - CONSTANT SPEED\n==================================================================\n\nThe observed origin of Light/EM radiation or gravitational radiation\ndepends on the speed of the observer. An observer at rest observes\nthe radiation as coming from the retarded source while an observer\nwith the same speed as the source observes the radiation as coming\nfrom the instantaneous direction.\n\nIt\'s simply the time base shift of SR which is responsible for\nrotating the phase front of the radiation from one direction to\nthe other.\n\n==================================================================\nCOULOMB & RADIATION - ULTRA RELATIVISTIC - CONSTANT SPEED\n==================================================================\n\nAll fields are basically propagating parallel to the source due to\nthe Doppler effect and are highly concentrated in the plane parallel\nto the source. The Coulomb fields are deviating from direction\ntowards the instantaneous source.\n\n\nFor so far.\n\nRegards, Hans.\n\n\n[1] Aberration and the Speed of Gravity\nSteve Carlip.\nhttp://www.vialattea.net/esperti/fis/velgravita/9909087.pdf\n\n[2] The speed of gravity revisited.\nMichael Ibison, Harold E. Puthoff, Scott R. Little\nhttp://arxiv.org/ftp/physics/papers/9910/9910050.pdf\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>tessel@tum.bot wrote in message news:<40f39146$1@news.sentex.net>...
> On Thu, 1 Jul 2004, Hans de Vries wrote:
>>
>>
Thank you for your extensive response.
A little summary for so far of the various responses and some
other things I figured out:
A first "Lienard Wiechert type" approach based on retarded q/r and m/r
potentials combined with the Doppler effect produces fields directed
to the instantaneous position. An observer behind a screen with a
small opening will experience a field directed towards the instanta-
neous source but the opening has to be on the line between the retarded
source and the observer.
More detailed approaches however show that the direction towards the
instantaneous source is not exact, not for GR and also not for EM.
Two papers, One from Steve Carlip [1] and one from Michael Ibison,
Harold E. Puthoff and Scott R. Little [2] derive that the direction of
maximal stretching tidal force is not exactly to the instantaneous
source but differs in a second order term of \Beta.
Both papers are maybe somewhat premature in their statements about the
EM field. The Lienard Wiechert approach neglects the effects caused by
Maxwell's Displacement Current. Radiation from an oscillating Lienard
Wiechert charge through a small opening in an absorbing screen does not
diffract but continues to propagate in the same direction. A charge
with constant speed has an electric field with non-zero second order
derivatives which produces extra electrical terms. These terms are
non radiative since the charge has a constant speed.
I've not found anything which handles Lienard Wiechert + Displacement
Current. (I guess it probably complicates math in a way similar to a
theory which assumes that gravitation energy is itself a source of
gravity)
==================================================================
RADIATION/LIGHT - NON ULTRA RELATIVISTIC - CONSTANT SPEED
==================================================================
The observed origin of Light/EM radiation or gravitational radiation
depends on the speed of the observer. An observer at rest observes
the radiation as coming from the retarded source while an observer
with the same speed as the source observes the radiation as coming
from the instantaneous direction.
It's simply the time base shift of SR which is responsible for
rotating the phase front of the radiation from one direction to
the other.
All fields are basically propagating parallel to the source due to
the Doppler effect and are highly concentrated in the plane parallel
to the source. The Coulomb fields are deviating from direction
towards the instantaneous source.
For so far.
Regards, Hans.
[1] Aberration and the Speed of Gravity
Steve Carlip.
http://www.vialattea.net/esperti/fis/velgravita/9909087.pdf
[2] The speed of gravity revisited.
Michael Ibison, Harold E. Puthoff, Scott R. Little
http://arxiv.org/ftp/physics/papers/9910/9910050.pdf
pervect
Jul15-04, 04:57 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no,scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\nOn 14 Jul 2004 03:52:53 -0400, hansdevries@chip-architect.com (Hans de\nVries) wrote:\n\n>\n>==================================================================\n> COULOMB FIELDS - NON ULTRA RELATIVISTIC - CONSTANT SPEED\n>==================================================================\n>\n>A first "Lienard Wiechert type" approach based on retarded q/r and m/r\n>potentials combined with the Doppler effect produces fields directed\n>to the instantaneous position. An observer behind a screen with a\n>small opening will experience a field directed towards the instanta-\n>neous source but the opening has to be on the line between the retarded\n>source and the observer.\n>\n>More detailed approaches however show that the direction towards the\n>instantaneous source is not exact, not for GR and also not for EM.\n\nIt\'s fairly well known that the direction of the electric field is\ntowards the source for a charged particle moving at _constant speed_,\nregardless of whether the motion is ultra-relativistic or not.\n\nThe Lienard Wiechart analysis you mention was for the more complex\ncase of an accelerating particle.\n\nFor the case of a particle moving at constant velocity see\n\nhttp://www.phys.ufl.edu/~rfield/PHY2061/images/relativity_14.pdf\n\nwhich starts with the relation E = KQ/r^2 R>, where R> is the unit\nradial vector, and derives the result that the E field for a charge\nmoving with velocity v=B/c is\n\nE = KQ(1-B^2) / (r^2(1-B^2sin^2(theta))^3/2) R>\n\nOther notable points of this function are that the E field in the\ndirection transverse to the motion (theta=90) is multiplied by gamma =\n1/sqrt(1-B^2), and that the Gauss intergal for the total charge is\nconserved.\n\nIt would help to know about the Faraday tensor to follow the\nderivation, otherwise the transformation properties of E utilized in\nthis derivation may appear a bit mysterious.\n\nThe moving charge will also generate a B field, of course. However a\nB field will not exert a force on a stationary test particle (only on\na moving test particle). So as long as all the test particles are\nstationary, there will not be any forces due to the B field. Of\ncourse, if one is interested in questions like the force on a\nco-moving particle, the B field becomes extremely important.\n\nFor gravity, things are not so simple, and I\'ve never seen a detailed\ndescription of the field of a moving mass in spite of having an\ninterest in the topic - except for the special case where the mass is\nmoving very close to the speed of light, where the Aichelberg-Sexl\nboost analysis will apply.\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>On 14 Jul 2004 03:52:53 -0400, hansdevries@chip-architect.com (Hans de
Vries) wrote:
>
>==================================================================
> COULOMB FIELDS - NON ULTRA RELATIVISTIC - CONSTANT SPEED
>==================================================================
>
>A first "Lienard Wiechert type" approach based on retarded q/r and m/r
>potentials combined with the Doppler effect produces fields directed
>to the instantaneous position. An observer behind a screen with a
>small opening will experience a field directed towards the instanta-
>neous source but the opening has to be on the line between the retarded
>source and the observer.
>
>More detailed approaches however show that the direction towards the
>instantaneous source is not exact, not for GR and also not for EM.
It's fairly well known that the direction of the electric field is
towards the source for a charged particle moving at _constant speed_,
regardless of whether the motion is ultra-relativistic or not.
The Lienard Wiechart analysis you mention was for the more complex
case of an accelerating particle.
For the case of a particle moving at constant velocity see
which starts with the relation E = KQ/r^2 R>, where R> is the unit
radial vector, and derives the result that the E field for a charge
moving with velocity v=B/c is
E = KQ(1-B^2) / (r^2(1-B^{2sin}^2(\theta))^3/2) R>
Other notable points of this function are that the E field in the
direction transverse to the motion (\theta=90) is multiplied by \gamma =1/\sqrt(1-B^2), and that the Gauss intergal for the total charge is
conserved.
It would help to know about the Faraday tensor to follow the
derivation, otherwise the transformation properties of E utilized in
this derivation may appear a bit mysterious.
The moving charge will also generate a B field, of course. However a
B field will not exert a force on a stationary test particle (only on
a moving test particle). So as long as all the test particles are
stationary, there will not be any forces due to the B field. Of
course, if one is interested in questions like the force on a
co-moving particle, the B field becomes extremely important.
For gravity, things are not so simple, and I've never seen a detailed
description of the field of a moving mass in spite of having an
interest in the topic - except for the special case where the mass is
moving very close to the speed of light, where the Aichelberg-Sexl
boost analysis will apply.
Arnie King
Jul15-04, 03:23 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no,scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\nhansdevries@chip-architect.com (Hans de Vries) wrote in message news:<3881ea8b.0407132133.7f11301e@posting.google.com>...\n>\n> Both papers are maybe somewhat premature in their statements about the\n> EM field. The Lienard Wiechert approach neglects the effects caused by\n> Maxwell\'s Displacement Current. >\n\nI don\'t understand this. The L-W potentials give fields that satisfy\nthe full Maxwell equations. References [1] and [2] you cited, also\nsuch standard sources as Jackson, don\'t say anything about the L-W\npotentials being deficient in any way. Correct me if I am wrong, but\nthe displacement current is a handwavy pedagogic idea used to motivate\nto beginners the addition of the dE/dt term into the Ampere\'s law\nequation.\n\nArnie\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>hansdevries@chip-architect.com (Hans de Vries) wrote in message news:<3881ea8b.0407132133.7f11301e@posting.google.com>...
>
> Both papers are maybe somewhat premature in their statements about the
> EM field. The Lienard Wiechert approach neglects the effects caused by
> Maxwell's Displacement Current. >
I don't understand this. The L-W potentials give fields that satisfy
the full Maxwell equations. References [1] and [2] you cited, also
such standard sources as Jackson, don't say anything about the L-W
potentials being deficient in any way. Correct me if I am wrong, but
the displacement current is a handwavy pedagogic idea used to motivate
to beginners the addition of the dE/dt term into the Ampere's law
equation.
Arnie
Hans de Vries
Jul16-04, 09:19 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no,scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\nPanSynthesis@netscape.net (Arnie King) wrote in message news:<41400681.0407150628.7c35567f@posting.google.com>...\n> hansdevries@chip-architect.com (Hans de Vries) wrote in message news:<3881ea8b.0407132133.7f11301e@posting.google.com>...\n> >\n> > Both papers are maybe somewhat premature in their statements about the\n> > EM field. The Lienard Wiechert approach neglects the effects caused by\n> > Maxwell\'s Displacement Current. >\n>\n> I don\'t understand this. The L-W potentials give fields that satisfy\n> the full Maxwell equations. References [1] and [2] you cited, also\n> such standard sources as Jackson, don\'t say anything about the L-W\n> potentials being deficient in any way. Correct me if I am wrong, but\n> the displacement current is a handwavy pedagogic idea used to motivate\n> to beginners the addition of the dE/dt term into the Ampere\'s law\n> equation.\n>\n> Arnie\n\n---------------------------------------------------\n\nLienard-Wiechert potentials are propagated in straight lines away from\nthe "point" source with the speed of light. That is the right approach\nas far as the propagation speed is concerned: c. No discussion here.\n\nA number of unresolved problems with L-W might indicate that it\'s\nnot yet a complete theory. (These problems are: runaways and pre-\nacceleration. See for instance here)\n\nhttp://www.pas.rochester.edu/~dmw/phy218/Lectures/Lect_70b.pdf\n\nMy issue is: Shouldn\'t the EM Field itself be also a source from which\nEM fields propagates away in all directions with the speed of light.\nIt does complicate mathematics considerably since each point of the field\nbecomes a source.\n\n( I could find a very simple way to actually prove the above with the help\nof the diffraction example further below )\n\nIn Maxwell\'s EM each point of the field has an energy of (E^2 + B^2)/2\nand a change in E or B will have an influence on it\'s environment.\nThat\'s at least how it\'s presented in each and every text book.\n\nOf course. There\'s always the question of what is the result of what.\nA = B can mean that A is the result of B or visa versa, B is the result\nof A, or they can be both the result of C but do not influence each\nother. (the = character is basically ambiguous)\n\nIn L-W the fields propagate in straight lines away through the vacuum\nwithout interacting with it\'s wider neighborhood anymore. This gives it\nan almost corpuscular character.\n\nIt would suggest that the vacuum could for instance support very narrow\nbeams of low frequency radio waves which can travel a significant distance\nthrough space without spreading out.\n\nThis would actually be highly desirable for the huge mobile telecommuni-\ncation market which has large networks of point to point radio connections.\nOr imagine a spacecraft at the outside of the solar system which would\nneed only a fraction of the energy to send it\'s information back to earth.\n\nCoherent laser light doesn\'t spread out much because the wave fronts add\nin the forward direction and cancel each other in other directions. The\nsmaller the wavelength the smaller the spread for a given beam-width.\n\n\nAnother example where L-W can\'t explain what we see is the diffraction\nof radiation which goes through a small hole in a screen. Each textbook\nexplains this effect in terms of wave-fronts originating from the vacuum\nwithin the hole.\n\nThe radiation spreads out as a function of the wavelength. The larger the\nwavelength/hole-radius ratio the more it spreads out. A ratio >>1 will\nresult in a full half circle. The energy which enters the whole is\nbasically the total energy spreading out in 180 degrees.\n\nL-W can only explain this by assuming that the radiation at an angle\noriginates from the sides of the hole of the screen and that the reduction\nof radiation on the centerline is caused by cancellation with radiation\nof opposite phase with the same frequency and in the same direction.\n\nBut, the centerline goes through the center of the hole. So there\'s\nnothing which can radiate according to L-W!\n\nI think this is enough to safely say that L-W in it\'s current form is\nincomplete even though it\'s an improvement over Maxwell because it\nintroduces c as the general propagation speed of the field.\n\n--------------------------------------------------\n\nThere are two practical problems in the generation of the mathematics\nof a theory which includes fields propagating away with c from each\npoint of the field. A point source emits a field and each point\nit reaches becomes a new source which emits a field and each point\nit reaches becomes a new source which ..... et-cetera.\n\nA small enough "coupling constant" may allow us to cut off the calculation\nafter a few iterations.\n\nA second problem stems from the 1/r2 character of the field. We must\nassume some very small radius where the field stops otherwise we end up\nwith infinities. One such radius is the "classical radius" of the\nelectron but we know nothing for sure here.\n\n\n--------------------------------------------------\n\nRegards, Hans\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>PanSynthesis@netscape.net (Arnie King) wrote in message news:<41400681.0407150628.7c35567f@posting.google.com>...
> hansdevries@chip-architect.com (Hans de Vries) wrote in message news:<3881ea8b.0407132133.7f11301e@posting.google.com>...
> >
> > Both papers are maybe somewhat premature in their statements about the
> > EM field. The Lienard Wiechert approach neglects the effects caused by
> > Maxwell's Displacement Current. >
>
> I don't understand this. The L-W potentials give fields that satisfy
> the full Maxwell equations. References [1] and [2] you cited, also
> such standard sources as Jackson, don't say anything about the L-W
> potentials being deficient in any way. Correct me if I am wrong, but
> the displacement current is a handwavy pedagogic idea used to motivate
> to beginners the addition of the dE/dt term into the Ampere's law
> equation.
>
> Arnie
Lienard-Wiechert potentials are propagated in straight lines away from
the "point" source with the speed of light. That is the right approach
as far as the propagation speed is concerned: c. No discussion here.
A number of unresolved problems with L-W might indicate that it's
not yet a complete theory. (These problems are: runaways and pre-
acceleration. See for instance here)
My issue is: Shouldn't the EM Field itself be also a source from which
EM fields propagates away in all directions with the speed of light.
It does complicate mathematics considerably since each point of the field
becomes a source.
( I could find a very simple way to actually prove the above with the help
of the diffraction example further below )
In Maxwell's EM each point of the field has an energy of (E^2 + B^2)/2
and a change in E or B will have an influence on it's environment.
That's at least how it's presented in each and every text book.
Of course. There's always the question of what is the result of what.
A = B can mean that A is the result of B or visa versa, B is the result
of A, or they can be both the result of C but do not influence each
other. (the = character is basically ambiguous)
In L-W the fields propagate in straight lines away through the vacuum
without interacting with it's wider neighborhood anymore. This gives it
an almost corpuscular character.
It would suggest that the vacuum could for instance support very narrow
beams of low frequency radio waves which can travel a significant distance
through space without spreading out.
This would actually be highly desirable for the huge mobile telecommuni-
cation market which has large networks of point to point radio connections.
Or imagine a spacecraft at the outside of the solar system which would
need only a fraction of the energy to send it's information back to earth.
Coherent laser light doesn't spread out much because the wave fronts add
in the forward direction and cancel each other in other directions. The
smaller the wavelength the smaller the spread for a given beam-width.
Another example where L-W can't explain what we see is the diffraction
of radiation which goes through a small hole in a screen. Each textbook
explains this effect in terms of wave-fronts originating from the vacuum
within the hole.
The radiation spreads out as a function of the wavelength. The larger the
wavelength/hole-radius ratio the more it spreads out. A ratio >>1 will
result in a full half circle. The energy which enters the whole is
basically the total energy spreading out in 180 degrees.
L-W can only explain this by assuming that the radiation at an angle
originates from the sides of the hole of the screen and that the reduction
of radiation on the centerline is caused by cancellation with radiation
of opposite phase with the same frequency and in the same direction.
But, the centerline goes through the center of the hole. So there's
nothing which can radiate according to L-W!
I think this is enough to safely say that L-W in it's current form is
incomplete even though it's an improvement over Maxwell because it
introduces c as the general propagation speed of the field.
There are two practical problems in the generation of the mathematics
of a theory which includes fields propagating away with c from each
point of the field. A point source emits a field and each point
it reaches becomes a new source which emits a field and each point
it reaches becomes a new source which ..... et-cetera.
A small enough "coupling constant" may allow us to cut off the calculation
after a few iterations.
A second problem stems from the 1/r2 character of the field. We must
assume some very small radius where the field stops otherwise we end up
with infinities. One such radius is the "classical radius" of the
electron but we know nothing for sure here.
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no,scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\nArnie King <PanSynthesis@netscape.net> wrote in message\nnews:41400681.0407150628.7c35567f@posting.google.com...\n>\n>\n> hansdevries@chip-architect.com (Hans de Vries) wrote in message\nnews:<3881ea8b.0407132133.7f11301e@posting.google.com>...\n> >\n> > Both papers are maybe somewhat premature in their statements about the\n> > EM field. The Lienard Wiechert approach neglects the effects caused by\n> > Maxwell\'s Displacement Current. >\n>\n> I don\'t understand this. The L-W potentials give fields that satisfy\n> the full Maxwell equations. References [1] and [2] you cited, also\n> such standard sources as Jackson, don\'t say anything about the L-W\n> potentials being deficient in any way. Correct me if I am wrong, but\n> the displacement current is a handwavy pedagogic idea used to motivate\n> to beginners the addition of the dE/dt term into the Ampere\'s law\n> equation.\n\nThat wasn\'t Maxwell\'s purpose for the displacement current in his original\nderviation of "Maxwell\'s equations" (On Physical Lines of Force, 1861),\nproposition 14. Maxwell\'s purpose was "To correct the equations of electric\ncurrents for the effect due to the elasticity of the medium."\n\nhttp://www.google.com/groups?selm=vcq714l2obfe7e%40corp.supernews.com\n\nSince \'modern\' EM theory has abandoned Maxwell\'s medium (keeping only the\nresulting equations), it is not surprising that displacement current looks a\nlittle "handwavy."\n\n--\ngreywolf42\nubi dubium ibi libertas\n{remove planet for return e-mail}\n\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Arnie King <PanSynthesis@netscape.net> wrote in message
news:41400681.0407150628.7c35567f@posting.google.com...
>
>
> hansdevries@chip-architect.com (Hans de Vries) wrote in message
news:<3881ea8b.0407132133.7f11301e@posting.google.com>...
> >
> > Both papers are maybe somewhat premature in their statements about the
> > EM field. The Lienard Wiechert approach neglects the effects caused by
> > Maxwell's Displacement Current. >
>
> I don't understand this. The L-W potentials give fields that satisfy
> the full Maxwell equations. References [1] and [2] you cited, also
> such standard sources as Jackson, don't say anything about the L-W
> potentials being deficient in any way. Correct me if I am wrong, but
> the displacement current is a handwavy pedagogic idea used to motivate
> to beginners the addition of the dE/dt term into the Ampere's law
> equation.
That wasn't Maxwell's purpose for the displacement current in his original
derviation of "Maxwell's equations" (On Physical Lines of Force, 1861),
proposition 14. Maxwell's purpose was "To correct the equations of electric
currents for the effect due to the elasticity of the medium."
Since 'modern' EM theory has abandoned Maxwell's medium (keeping only the
resulting equations), it is not surprising that displacement current looks a
little "handwavy."
--
greywolf42
ubi dubium ibi libertas
{remove planet for return e-mail}
Arnie King
Jul20-04, 04:25 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no,scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\nhansdevries@chip-architect.com (Hans de Vries) wrote in message news:<3881ea8b.0407152304.36406309@posting.google.com>...\n>\n\n> A number of unresolved problems with L-W might indicate that it\'s\n> not yet a complete theory. (These problems are: runaways and pre-\n> acceleration. See for instance here)\n>\n\n> Another example where L-W can\'t explain what we see is the diffraction\n> of radiation which goes through a small hole in a screen. Each textbook\n> explains this effect in terms of wave-fronts originating from the vacuum\n> within the hole.\n>\n\nThe L-W potentials give a specific solution to Maxwell\'s equations.\nNamely, the solution when a point charge moves in a prescibed (known a\npriori) manner, and there are no surfaces anywhere on which boundary\nconditions have to be satisfied. The L-W potentials yield E and B\nfields that exactly satisfy Maxwell\'s equations in this special case.\n\nIn some situations, you may not know a priori the trajectory of the\npoint charge. For example, you may have prescibed a\nnon-electromagnetic force that acts on the point charge. In this case,\nthe charge will accelerate because of that force. The acceleration\nwill produce radiation, and the radiative part of the particle\'s\nfields will act on the particle, adding additional forces ("radiation\ndamping") which you won\'t know explicitly since the radiation depends\non the total acceleration. Thus you won\'t be in a position to apply\nthe L-W solution directly. (One imagines that a successive\napproximation and iteration approach will work.) But this is no\ninadequacy of the L-W solution, which you should look on more narrowly\nas a solution to a rather particlular problem, not a general theory.\n\nIt is true that the theory of the radiation damping of a point charge\nis in a bad state. This points to some inadequacy of the point charge\nas a valid concept in classical physics. The approaches that have been\ntried are somewhat ad hoc, (integral equations based on the iteration\nreferred to above) and lead to runaways and preaccelerations.\nJackson\'s book has a discussion.\n\nIn principle, the trajectory of a charge could be determined by\nobservation. The radiation damping effects on the accelaration would\nthen be included in the observation, one would know the correct\ntrajectory, and the L-W formulas would then yield the correct fields.\n\nTo treat your diffraction problem, you have to go back to Maxwell\'s\nequations and apply the appropriate boundary conditions on the screen.\nThe L-W formulas, at least in the form one finds in textbooks, have\nbeen worked out in a situation where there are no boundaries.\n\n-Arnie\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>hansdevries@chip-architect.com (Hans de Vries) wrote in message news:<3881ea8b.0407152304.36406309@posting.google.com>...
>
> A number of unresolved problems with L-W might indicate that it's
> not yet a complete theory. (These problems are: runaways and pre-
> acceleration. See for instance here)
>
> Another example where L-W can't explain what we see is the diffraction
> of radiation which goes through a small hole in a screen. Each textbook
> explains this effect in terms of wave-fronts originating from the vacuum
> within the hole.
>
The L-W potentials give a specific solution to Maxwell's equations.
Namely, the solution when a point charge moves in a prescibed (known a
priori) manner, and there are no surfaces anywhere on which boundary
conditions have to be satisfied. The L-W potentials yield E and B
fields that exactly satisfy Maxwell's equations in this special case.
In some situations, you may not know a priori the trajectory of the
point charge. For example, you may have prescibed a
non-electromagnetic force that acts on the point charge. In this case,
the charge will accelerate because of that force. The acceleration
will produce radiation, and the radiative part of the particle's
fields will act on the particle, adding additional forces ("radiation
damping") which you won't know explicitly since the radiation depends
on the total acceleration. Thus you won't be in a position to apply
the L-W solution directly. (One imagines that a successive
approximation and iteration approach will work.) But this is no
inadequacy of the L-W solution, which you should look on more narrowly
as a solution to a rather particlular problem, not a general theory.
It is true that the theory of the radiation damping of a point charge
is in a bad state. This points to some inadequacy of the point charge
as a valid concept in classical physics. The approaches that have been
tried are somewhat ad hoc, (integral equations based on the iteration
referred to above) and lead to runaways and preaccelerations.
Jackson's book has a discussion.
In principle, the trajectory of a charge could be determined by
observation. The radiation damping effects on the accelaration would
then be included in the observation, one would know the correct
trajectory, and the L-W formulas would then yield the correct fields.
To treat your diffraction problem, you have to go back to Maxwell's
equations and apply the appropriate boundary conditions on the screen.
The L-W formulas, at least in the form one finds in textbooks, have
been worked out in a situation where there are no boundaries.
-Arnie
carlip@no-physics-spam.ucdavis.edu
Aug4-04, 02:25 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no,scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>pervect <pervect@invalid.invalid> wrote:\n\n[...]\n\n> For gravity, things are not so simple, and I\'ve never seen a detailed\n> description of the field of a moving mass in spite of having an\n> interest in the topic - except for the special case where the mass is\n> moving very close to the speed of light, where the Aichelberg-Sexl\n> boost analysis will apply.\n\nTo get a consistent description in general relativity, if a moving\nmass is accelerating, you have to include the field of whatever is\ncausing the acceleration as well. One exact solution along these\nlines is Kinnersley\'s ``photon rocket,\'\' which describes a mass with\nan arbitrary acceleration caused by the emission of electromagnetic\nradiation. See Kinnersley, Phys Rev 186 (1969) 1335; Damour, Class.\nQuant. Grav. 12 (1995) 725; Bonnor, Class. Quant. Grav. 11 (1994) 2007.\nIn Phys. Lett. A267 (2000) 81, I work out the acceleration of a test\nparticle in the field of such a source, expanded in powers of v/c.\n\nSteve Carlip\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>pervect <pervect@invalid.invalid> wrote:
[...]
> For gravity, things are not so simple, and I've never seen a detailed
> description of the field of a moving mass in spite of having an
> interest in the topic - except for the special case where the mass is
> moving very close to the speed of light, where the Aichelberg-Sexl
> boost analysis will apply.
To get a consistent description in general relativity, if a moving
mass is accelerating, you have to include the field of whatever is
causing the acceleration as well. One exact solution along these
lines is Kinnersley's ``photon rocket,'' which describes a mass with
an arbitrary acceleration caused by the emission of electromagnetic
radiation. See Kinnersley, Phys Rev 186 (1969) 1335; Damour, Class.
Quant. Grav. 12 (1995) 725; Bonnor, Class. Quant. Grav. 11 (1994) 2007.
In Phys. Lett. A267 (2000) 81, I work out the acceleration of a test
particle in the field of such a source, expanded in powers of v/c.
Steve Carlip
Oz
Aug7-04, 06:04 PM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no,scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>Hans de Vries <hansdevries@chip-architect.com> writes\n>A little summary for so far of the various responses and some\n>other things I figured out:\n\n<snip>\n\nI have been passingly introduced to the faraday tensor.\n\nIf I had to consider the effects of a relativistic charged particle at\nconstant speed I would (in my utterly naive viewpoint) set up a static\nfield in F for a charged particle. I wonder if someone would correct my\nprocedure.\n\n1) The field will be entirely electrostatic (ie no B terms).\n2) I imagine this to be a radial field in the space directions,\nemulating the classic point charge.\n3) The field at any point points perpendicular to the time direction.\n\n4) I set this in motion by applying a 4D lorentz transform.\n\n5) I ought then to be able to map between the two frames (and any other)\nusing the lorentz transform.\n\n6) I expect the B\'s to be non-zero as seen from the moving frame.\n\n7) I *think* the effect of the lorentz transform is to rotate the\noriginal E-fields into partly B-fields noting that the force on a test\ncharge should always be centre to centre in all frames. Well, I think\nthat\'s right, but this doesn\'t seem very comfortable.\n\nThat said (though probably wrong), I\'m worried about these second order\nterms that have been mentioned.\n\n\n\n--\nOz\nThis post is worth absolutely nothing and is probably fallacious.\n\nBTOPENWORLD address about to cease. DEMON address no longer in use.\n>>Use oz@farmeroz.port995.com<<\nozacoohdb@despammed.com still functions.\n\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Hans de Vries <hansdevries@chip-architect.com> writes
>A little summary for so far of the various responses and some
>other things I figured out:
<snip>
I have been passingly introduced to the faraday tensor.
If I had to consider the effects of a relativistic charged particle at
constant speed I would (in my utterly naive viewpoint) set up a static
field in F for a charged particle. I wonder if someone would correct my
procedure.
1) The field will be entirely electrostatic (ie no B terms).
2) I imagine this to be a radial field in the space directions,
emulating the classic point charge.
3) The field at any point points perpendicular to the time direction.
4) I set this in motion by applying a 4D lorentz transform.
5) I ought then to be able to map between the two frames (and any other)
using the lorentz transform.
6) I expect the B's to be non-zero as seen from the moving frame.
7) I *think* the effect of the lorentz transform is to rotate the
original E-fields into partly B-fields noting that the force on a test
charge should always be centre to centre in all frames. Well, I think
that's right, but this doesn't seem very comfortable.
That said (though probably wrong), I'm worried about these second order
terms that have been mentioned.
--
Oz
This post is worth absolutely nothing and is probably fallacious.
BTOPENWORLD address about to cease. DEMON address no longer in use.
>>Use oz@farmeroz.port995.com<<
ozacoohdb@despammed.com still functions.
Hans de Vries
Aug12-04, 09:29 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no,scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\n\n\nOz <oz@farmeroz.port995.com> wrote in message news:<\\$0QAl7BZj3EBFwKD@farmeroz.port995.com>...\n> Hans de Vries <hansdevries@chip-architect.com> writes\n> >A little summary for so far of the various responses and some\n> >other things I figured out:\n>\n> <snip>\n>\n> I have been passingly introduced to the faraday tensor.\n>\n> If I had to consider the effects of a relativistic charged particle at\n> constant speed I would (in my utterly naive viewpoint) set up a static\n> field in F for a charged particle. I wonder if someone would correct my\n> procedure.\n>\n> 1) The field will be entirely electrostatic (ie no B terms).\n> 2) I imagine this to be a radial field in the space directions,\n> emulating the classic point charge.\n> 3) The field at any point points perpendicular to the time direction.\n>\n> 4) I set this in motion by applying a 4D lorentz transform.\n>\n> 5) I ought then to be able to map between the two frames (and any other)\n> using the lorentz transform.\n>\n\nYou can do this in basically two (three) ways with the same results:\n\n========================== 1 ====================================\n\n1) The (more abstract) way is the Lorentz transformation as you say.\nIt will turn the radial field into a pancake like field which you\ncan either derive via the EM field tensor:\n\n1a) The E field increases with 1/sqrt(1-v^2/c^2) in the directions\nwhich are at 90 degrees angles with the speed.\n\nor derive it more "geometrically" with:\n\n1b) The Lorentz contraction of sqrt(1-v^2/c^2) in the direction of\nthe speed combined with an apparent increase of the potential energy\nin all directions with a factor of 1/sqrt(1-v^2/c^2).\n\nThe pointers of the electrostatic force keep pointing towards the\nactual position of the charge (They don\'t point to the position were\nthe charge was when the field "left" the charge)\n\n\n========================== 2 ====================================\n\n\n2) The physical laws of electromagnetism have to be compatible with\nSR and should give the same result without "knowing" anything about\nSpecial Relativity. Doing it this way gives you more insight into\nwhat is actually happening.\n\nThe Lienard Wiechert approach build the field of moving/accelerating\ncharges up from spheres emitted from the charge during it\'s motion\nand spreading out with C.\n\nThis generates the same results if you take into account that there\nis more field propagated in the forward direction than in the back-\nward direction because of a geometrical effect explained here:\n(at page 5)\n\nhttp://www.pas.rochester.edu/~dmw/phy218/Lectures/Lect_66b.pdf\n\nYou\'ll see that the pancake field at 90 degrees angles of the ultra\nrelativistic particle is propagating in almost the same direction\nas the charge and "left" the charge at a position far behind the\ncurrent position.\n\nThe field spreads in the form of a narrow cone. It propagates with C\nbut the speed at which it propagates away from the charge at 90\ndegrees angles is only sqrt(1-v^2/c^2).\n\nThis factor is the same the time dilation factor for somebody moving\nalong with the particle at the same speed. Result: both terms cancel\nand the speed becomes C again for the observer in the moving frame.\n\nAgain, the electric field pointers keep pointing to the actual\nposition of the charge and not to the position were the charge was\nwhen the field left it.\n\n(Sometimes this causes the erroneously conclusion that the electro-\nstatic field must propagate with a speed >> C because the pointers\nstay directed towards the actual position of the charge.\nIt\'s actually to the position were it would be when its speed doesn\'t\nchange in the mean time)\n\n=====================================================================\n\n\n> 6) I expect the B\'s to be non-zero as seen from the moving frame.\n>\n> 7) I *think* the effect of the lorentz transform is to rotate the\n> original E-fields into partly B-fields noting that the force on a test\n> charge should always be centre to centre in all frames. Well, I think\n> that\'s right, but this doesn\'t seem very comfortable.\n>\n\n=====================================================================\n\nI do prefer the view were the magnetic field is a relativistic site\neffect of electrostatics. So a B is only "seen" by >moving< parti-\ncles which are again in a different reference frame with a different\nE field which then explains the "magnetic" force.\n\nThe magnetic force is extremely small compared to the electrostatic\nforce with a ratio of v^2/c^2 It is acounted for by the tiny change\nof the E field because of a change in speed.\n\n=====================================================================\n\n\n> That said (though probably wrong), I\'m worried about these second order\n> terms that have been mentioned.\n\n=====================================================================\n\n\n\nWhat is said for the electric charge is also true for a particle\nwith mass m. Again you\'ll get a pancake like field as long as you\nuse SR.\n\nThe second order terms seems to occur if GR becomes involved. The\nforce (to be GR compliant: the direction of maximal stretching tidal\nforce ) does not point exactly anymore to the position where the mass\nwould be if it continued with constant speed, because of the 2nd order\nterms.\n\nI\'ve expressed some worries that the EM field also has 2nd order terms\nhere:\n\nhttp://groups.google.com/groups?hl=en&lr=&ie=UTF-8&c2coff=1&safe=off&selm=3881ea8b.0407132133.7f11301e%40posting.google.com\n\nThat might cause some problems with SR which would be bad or\nalternatively maybe could show that the EM field theory has\nsomehow GR build in it in a similar fashion that it has SR\nbuild into it. It would be actually very nice if one could\nprove this. (Nothing but pure speculation here!!!)\n\nBut also, Lienard Wiechert doesn\'t seem to be complete in the fact\nthat it doesn\'t allow the EM field itself to be the source of an\nEM field. As far as I can tell: It generally generates the right\nresults under those conditions were the EM field propagates in\nstraight lines. It can\'t explain effects found in diffraction.\nEven in vacuum there is a finite amplitude for non-straight propa-\ngation which becomes larger with longer wavelenghts.\n\n\nRegards, Hans\n</UL></PRE></font></td></tr></table></BODY><HTML>');"> <IMG SRC=/images/buttons/ip.gif BORDER=0 ALIGN=CENTER ALT="View this Usenet post in original ASCII form"> View this Usenet post in original ASCII form </a></div><P></jabberwocky>Oz <oz@farmeroz.port995.com> wrote in message news:<$0QAl7BZj3EBFwKD@farmeroz.port995.com>...
> Hans de Vries <hansdevries@chip-architect.com> writes
> >A little summary for so far of the various responses and some
> >other things I figured out:
>
> <snip>
>
> I have been passingly introduced to the faraday tensor.
>
> If I had to consider the effects of a relativistic charged particle at
> constant speed I would (in my utterly naive viewpoint) set up a static
> field in F for a charged particle. I wonder if someone would correct my
> procedure.
>
> 1) The field will be entirely electrostatic (ie no B terms).
> 2) I imagine this to be a radial field in the space directions,
> emulating the classic point charge.
> 3) The field at any point points perpendicular to the time direction.
>
> 4) I set this in motion by applying a 4D lorentz transform.
>
> 5) I ought then to be able to map between the two frames (and any other)
> using the lorentz transform.
>
You can do this in basically two (three) ways with the same results:
1) The (more abstract) way is the Lorentz transformation as you say.
It will turn the radial field into a pancake like field which you
can either derive via the EM field tensor:
1a) The E field increases with 1/\sqrt(1-v^2/c^2) in the directions
which are at 90 degrees angles with the speed.
or derive it more "geometrically" with:
1b) The Lorentz contraction of \sqrt(1-v^2/c^2) in the direction of
the speed combined with an apparent increase of the potential energy
in all directions with a factor of 1/\sqrt(1-v^2/c^2).
The pointers of the electrostatic force keep pointing towards the
actual position of the charge (They don't point to the position were
the charge was when the field "left" the charge)
2) The physical laws of electromagnetism have to be compatible with
SR and should give the same result without "knowing" anything about
Special Relativity. Doing it this way gives you more insight into
what is actually happening.
The Lienard Wiechert approach build the field of moving/accelerating
charges up from spheres emitted from the charge during it's motion
and spreading out with C.
This generates the same results if you take into account that there
is more field propagated in the forward direction than in the back-
ward direction because of a geometrical effect explained here:
(at page 5)
You'll see that the pancake field at 90 degrees angles of the ultra
relativistic particle is propagating in almost the same direction
as the charge and "left" the charge at a position far behind the
current position.
The field spreads in the form of a narrow cone. It propagates with C
but the speed at which it propagates away from the charge at 90
degrees angles is only \sqrt(1-v^2/c^2).
This factor is the same the time dilation factor for somebody moving
along with the particle at the same speed. Result: both terms cancel
and the speed becomes C again for the observer in the moving frame.
Again, the electric field pointers keep pointing to the actual
position of the charge and not to the position were the charge was
when the field left it.
(Sometimes this causes the erroneously conclusion that the electro-
static field must propagate with a speed >> C because the pointers
stay directed towards the actual position of the charge.
It's actually to the position were it would be when its speed doesn't
change in the mean time)
> 6) I expect the B's to be non-zero as seen from the moving frame.
>
> 7) I *think* the effect of the lorentz transform is to rotate the
> original E-fields into partly B-fields noting that the force on a test
> charge should always be centre to centre in all frames. Well, I think
> that's right, but this doesn't seem very comfortable.
>
I do prefer the view were the magnetic field is a relativistic site
effect of electrostatics. So a B is only "seen" by >moving< parti-
cles which are again in a different reference frame with a different
E field which then explains the "magnetic" force.
The magnetic force is extremely small compared to the electrostatic
force with a ratio of v^2/c^2 It is acounted for by the tiny change
of the E field because of a change in speed.
What is said for the electric charge is also true for a particle
with mass m. Again you'll get a pancake like field as long as you
use SR.
The second order terms seems to occur if GR becomes involved. The
force (to be GR compliant: the direction of maximal stretching tidal
force ) does not point exactly anymore to the position where the mass
would be if it continued with constant speed, because of the 2nd order
terms.
I've expressed some worries that the EM field also has 2nd order terms
here:
That might cause some problems with SR which would be bad or
alternatively maybe could show that the EM field theory has
somehow GR build in it in a similar fashion that it has SR
build into it. It would be actually very nice if one could
prove this. (Nothing but pure speculation here!!!)
But also, Lienard Wiechert doesn't seem to be complete in the fact
that it doesn't allow the EM field itself to be the source of an
EM field. As far as I can tell: It generally generates the right
results under those conditions were the EM field propagates in
straight lines. It can't explain effects found in diffraction.
Even in vacuum there is a finite amplitude for non-straight propa-
gation which becomes larger with longer wavelenghts.
Regards, Hans
Oz
Aug13-04, 06:41 AM
<jabberwocky><div class="vbmenu_control"><a href="jabberwocky:;" onClick="newWindow=window.open('','usenetCode','toolbar=no,location=no,scrollbars=yes,resizable=yes,status=no,width=650,height=400'); newWindow.document.write('<HTML><HEAD><TITLE>Usenet ASCII</TITLE></HEAD><BODY topmargin=0 leftmargin=0 BGCOLOR=#F1F1F1><table border=0 width=625><td bgcolor=midnightblue><font color=#F1F1F1>This Usenet message\'s original ASCII form: </font></td></tr><tr><td width=449><br><br><font face=courier><UL><PRE>\n\n\nHans de Vries <hansdevries@chip-architect.com> writes\n\n>>Oz:\n>> 5) I ought then to be able to map between the two frames (and any other)\n>> using the lorentz transform.\n>>\n>\n>You can do this in basically two (three) ways with the same results:\n>\n>========================== 1 ====================================\n>\n>1) The (more abstract) way is the Lorentz transformation as you say.\n>It will turn the radial field into a pancake like field\n\nActually this hasn\'t really been discussed here using the faraday\ntensors. So really I have no idea.\n\n>which you\n>can either derive via the EM field tensor:\n>\n>1a) The E field increases with 1/sqrt(1-v^2/c^2) in the directions\n>which are at 90 degrees angles with the speed.\n>\n>or derive it more "geometrically" with:\n>\n>1b) The Lorentz contraction of sqrt(1-v^2/c^2) in the direction of\n>the speed combined with an apparent increase of the potential energy\n>in all directions with a factor of 1/sqrt(1-v^2/c^2).\n>\n>The pointers of the electrostatic force keep pointing towards the\n>actual position of the charge (They don\'t point to the position were\n>the charge was when the field "left" the charge)\n\nOK. That\'s what I had guessed should be the answer.\n\n>========================== 2 ====================================\n>\n>\n>2) The physical laws of electromagnetism have to be compatible with\n>SR and should give the same result without "knowing" anything about\n>Special Relativity. Doing it this way gives you more insight into\n>what is actually happening.\n\nInsight is what I need as a substitute for maths I don\'t know and\ncouldn\'t do.\n\n>The Lienard Wiechert approach build the field of moving/accelerating\n>charges up from spheres emitted from the charge during it\'s motion\n>and spreading out with C.\n\nI\'m not sure I quite see this. However once we get into acceleration\nthen there will be a new (and from memory horribly complex) description\nthat can be derived from SR. God only knows what the operator is that\nwould now replace the lorentz transform operator.\n\nHmm. I guess, on a quick \'off the top of my head\' thought, we would have\nan infinitesimal lorentz operator (full of dv/dt\'s) that we could\nmultiply by a generalised LO and somehow integrate to give an\naccelerating frame. Hmm, that seems (by better people than me) quite\ndoable and then we should with luck be able to take a limit.\n\n<shudder>\n\n>You\'ll see that the pancake field at 90 degrees angles of the ultra\n>relativistic particle is propagating in almost the same direction\n>as the charge and "left" the charge at a position far behind the\n>current position.\n\nnnggth....\n\nOk, I think I see what you are saying. In effect the field propagates at\nc, but the source is \'behind\' the generating particle and like \'just\ncaught up\'. Now you bring in the words \'almost the same direction as the\ncharge\', I am imagining that this is due (somehow) to the difference in\nangle between the particle (now) and the apparent source of the field\n\'left far behind\'.\n\nIts delightfully mindbending ....\n\n>The field spreads in the form of a narrow cone. It propagates with C\n>but the speed at which it propagates away from the charge at 90\n>degrees angles is only sqrt(1-v^2/c^2).\n\nOK, that feels good.\nI\'m rather thinking of it backwards (to preserve my sanity).\nI\'m setting up a static charge, and imagining the observer approaching\nat ultrarelativistic speeds. I think this would be more fruitful as the\nsymmetry is better preserved. Unfortunately my brain isn\'t very good in\n(3+1) geometry. I\'ll need a bit more time.\n\n>This factor is the same the time dilation factor for somebody moving\n>along with the particle at the same speed. Result: both terms cancel\n>and the speed becomes C again for the observer in the moving frame.\n\nToo much to take in in one go......\n\n>Again, the electric field pointers keep pointing to the actual\n>position of the charge and not to the position were the charge was\n>when the field left it.\n\nThat\'s what I expected from my \'reverse view\' model.\nNow I\'m hugely confused....\n\n>=====================================================================\n>\n>\n>> 6) I expect the B\'s to be non-zero as seen from the moving frame.\n>>\n>> 7) I *think* the effect of the lorentz transform is to rotate the\n>> original E-fields into partly B-fields noting that the force on a test\n>> charge should always be centre to centre in all frames. Well, I think\n>> that\'s right, but this doesn\'t seem very comfortable.\n>>\n>\n>=====================================================================\n>\n>I do prefer the view were the magnetic field is a relativistic site\n>effect of electrostatics.\n\nI think its the most gorgeous thing I have come across.\nI was never intuitive with B, simply because I had a gut feeling that\nmaxwell was concealing a deeper symmetry. The relativistic approach\nfixed that, and now I can see it for what it really is in a highly\nsimple an intuitive manner.\n\n>So a B is only "seen" by >moving< parti-\n>cles which are again in a different reference frame with a different\n>E field which then explains the "magnetic" force.\n>\n>The magnetic force is extremely small compared to the electrostatic\n>force with a ratio of v^2/c^2 It is acounted for by the tiny change\n>of the E field because of a change in speed.\n\nYup.\n\n>=================================