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David Rutherford
Oct12-04, 10:49 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>\nI\'ve just posted an article on my webpage dealing with what I believe is\na companion law to the Biot-Savart law that has, until now, gone\nundiscovered, as far as I know. You can see it at\n\nhttp://www.softcom.net/users/der555/biotcomp.pdf\n\nPlease make all comments here in sci.physics.research (or under the\nthread "Biot-Savart\'s Companion (10/11/04)" in sci.physics or\nsci.physics.particle), since I don\'t discuss my theories by email.\n\n--\nDave Rutherford\n"New Transformation Equations and the Electric Field Four-vector"\nhttp://www.softcom.net/users/der555/newtransform.pdf\n\nApplications:\n"4/3 Problem Resolution"\nhttp://www.softcom.net/users/der555/elecmass.pdf\n"Action-reaction Paradox Resolution"\nhttp://www.softcom.net/users/der555/actreact.pdf\n"Energy Density Correction"\nhttp://www.softcom.net/users/der555/enerdens.pdf\n"Proposed Quantum Mechanical Connection"\nhttp://www.softcom.net/users/der555/quantum.pdf\n"Biot-Savart\'s Companion"\nhttp://www.softcom.net/users/der555/biotcomp.pdf\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">&nbsp;&nbsp;View this Usenet post in original ASCII form </a></div><P></jabberwocky>I've just posted an article on my webpage dealing with what I believe is
a companion law to the Biot-Savart law that has, until now, gone
undiscovered, as far as I know. You can see it at

http://www.softcom.net/users/der555/biotcomp.pdf

Please make all comments here in sci.physics.research (or under the
thread "Biot-Savart's Companion (10/11/04)" in sci.physics or
sci.physics.particle), since I don't discuss my theories by email.

--
Dave Rutherford
"New Transformation Equations and the Electric Field Four-vector"
http://www.softcom.net/users/der555/newtransform.pdf

Applications:
"4/3 Problem Resolution"
http://www.softcom.net/users/der555/elecmass.pdf
"Action-reaction Paradox Resolution"
http://www.softcom.net/users/der555/actreact.pdf
"Energy Density Correction"
http://www.softcom.net/users/der555/enerdens.pdf
"Proposed Quantum Mechanical Connection"
http://www.softcom.net/users/der555/quantum.pdf
"Biot-Savart's Companion"
http://www.softcom.net/users/der555/biotcomp.pdf
Danny Ross Lunsford
Oct13-04, 02:13 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\n\nDavid Rutherford &lt;drutherford@softcom.net&gt; wrote in message news:&lt;nY6dnQttq4z-wPbcRVn-iQ@softcom.net&gt;...\n&gt; I\'ve just posted an article on my webpage dealing with what I believe is\n&gt; a companion law to the Biot-Savart law that has, until now, gone\n&gt; undiscovered, as far as I know. You can see it at\n&gt;\n&gt; http://www.softcom.net/users/der555/biotcomp.pdf\n&gt;\n&gt; Please make all comments here in sci.physics.research (or under the\n&gt; thread "Biot-Savart\'s Companion (10/11/04)" in sci.physics or\n&gt; sci.physics.particle), since I don\'t discuss my theories by email.\n\nI looked at this ages ago - the change in momentum represented by such\na force happens, not via change of velocity (speed or direction) but\nby change of mass of the electron. Formally one can think of a\n(reducible) EM field living in the even subalgebra of the Dirac\nalgebra, with an additional scalar (and possibly pseudoscalar) field.\nSuch a field leads to a force law\n\nF = pE + JxB + NJ\n\nwhere N is the scalar field and (p,J) is the charge-current density.\nIf we assume a convected current J = pV we get your term. Putting this\nequal to the dotted momentum, and writing J in terms of electrons and\ndelta functions, you\'ll see that N acts on the mass of the electron.\n\nI seem to recall a Canadian guy named Watson who did some work in this\ndirection. No idea what journal.\n\nNote that in one interpretation, the new force distinguishes between\nmatter and antimatter - for the latter\n\nF = pE + JxB - NJ\n\nIt occured to me that the action on the mass may be one way of\nthinking about the relationship of the muon to the electron.\n\n-drl\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">&nbsp;&nbsp;View this Usenet post in original ASCII form </a></div><P></jabberwocky>David Rutherford <drutherford@softcom.net> wrote in message news:<nY6dnQttq4z-wPbcRVn-iQ@softcom.net>...
> I've just posted an article on my webpage dealing with what I believe is
> a companion law to the Biot-Savart law that has, until now, gone
> undiscovered, as far as I know. You can see it at
>
> http://www.softcom.net/users/der555/biotcomp.pdf
>
> Please make all comments here in sci.physics.research (or under the
> thread "Biot-Savart's Companion (10/11/04)" in sci.physics or
> sci.physics.particle), since I don't discuss my theories by email.

I looked at this ages ago - the change in momentum represented by such
a force happens, not via change of velocity (speed or direction) but
by change of mass of the electron. Formally one can think of a
(reducible) EM field living in the even subalgebra of the Dirac
algebra, with an additional scalar (and possibly pseudoscalar) field.
Such a field leads to a force law

F = pE +[/itex] JxB + NJ

where N is the scalar field and (p,J) is the charge-current density.
If we assume a convected current J = pV we get your term. Putting this
equal to the dotted momentum, and writing J in terms of electrons and
\delta functions, you'll see that N acts on the mass of the electron.

I seem to recall a Canadian guy named Watson who did some work in this
direction. No idea what journal.

Note that in one interpretation, the new force distinguishes between
matter and antimatter - for the latter

F = pE + JxB [itex]- NJ

It occured to me that the action on the mass may be one way of
thinking about the relationship of the muon to the electron.

-drl
David Rutherford
Oct14-04, 11:07 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\nDanny Ross Lunsford wrote:\n&gt;\n&gt; I looked at this ages ago - the change in momentum represented by such\n&gt; a force happens, not via change of velocity (speed or direction) but\n&gt; by change of mass of the electron.\n\nLet me see if I understand you correctly. The change in momentum is\n\ndp/dt = d(mv)/dt\n= mdv/dt + vdm/dt\n= ma + vdm/dt\n\nSince m = Energy/c^2, we can write the last term as\n\nvdm/dt = (v/c^2)d(Energy)/dt\n\nThe time component of the force, classically, is\n\nd(Energy)/dt = qv.E\n\nso vdm/dt = (1/c^2)qv(v.E) and\n\ndp/dt = ma + (1/c^2)qv(v.E)\n\nThus the classical equation of motion can be written\n\ndp/dt = ma + (1/c^2)qv(v.E) = qE + qvxB\n\nor\n\nma = qE + qvxB - (1/c^2)qv(v.E)\n\nI assume you are referring, in your comment, to the last term\n(1/c^2)qv(v.E), where v is the velocity of the test particle q. This is\n_not_ the same as my term (1/c^2)qv(v\'.E), where v is the velocity of\nthe test particle q, and v\' is the velocity of the _source_ q\' of E (I\'d\nlike to point out that my term (1/c^2)qv(v\'.E) is from actreact.pdf not\nbiotcomp.pdf).\n\nIf my assumption is incorrect, please let me know.\n\n&gt; Formally one can think of a\n&gt; (reducible) EM field living in the even subalgebra of the Dirac\n&gt; algebra, with an additional scalar (and possibly pseudoscalar) field.\n&gt; Such a field leads to a force law\n&gt;\n&gt; F = pE + JxB + NJ\n&gt;\n&gt; where N is the scalar field and (p,J) is the charge-current density.\n&gt; If we assume a convected current J = pV we get your term.\n\nAre you saying that N = (1/c^2)v\'.E? If so, how is N derived?\n\n--\nDave Rutherford\n"New Transformation Equations and the Electric Field Four-vector"\nhttp://www.softcom.net/users/der555/newtransform.pdf\n\nApplications:\n"4/3 Problem Resolution"\nhttp://www.softcom.net/users/der555/elecmass.pdf\n"Action-reaction Paradox Resolution"\nhttp://www.softcom.net/users/der555/actreact.pdf\n"Energy Density Correction"\nhttp://www.softcom.net/users/der555/enerdens.pdf\n"Proposed Quantum Mechanical Connection"\nhttp://www.softcom.net/users/der555/quantum.pdf\n"Biot-Savart\'s Companion"\nhttp://www.softcom.net/users/der555/biotcomp.pdf\n\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">&nbsp;&nbsp;View this Usenet post in original ASCII form </a></div><P></jabberwocky>Danny Ross Lunsford wrote:
>
> I looked at this ages ago - the change in momentum represented by such
> a force happens, not via change of velocity (speed or direction) but
> by change of mass of the electron.

Let me see if I understand you correctly. The change in momentum is

dp/dt = d(mv)/dt= mdv/dt + vdm/dt= ma + vdm/dt

Since m = Energy/c^2, we can write the last term as

vdm/dt = (v/c^2)d(Energy)/dt

The time component of the force, classically, is

d(Energy)/dt = qv.E

so vdm/dt = (1/c^2)qv(v.E) and

dp/dt = ma + (1/c^2)qv(v.E)

Thus the classical equation of motion can be written

dp/dt = ma + (1/c^2)qv(v.E) = qE + qvxB

or

ma = qE + qvxB - (1/c^2)qv(v.E)

I assume you are referring, in your comment, to the last term
(1/c^2)qv(v.E), where v is the velocity of the test particle q. This is
_not_ the same as my term (1/c^2)qv(v'.E), where v is the velocity of
the test particle q, and v' is the velocity of the _source_ q' of E (I'd
like to point out that my term (1/c^2)qv(v'.E) is from actreact.pdf not
biotcomp.pdf).

If my assumption is incorrect, please let me know.

> Formally one can think of a
> (reducible) EM field living in the even subalgebra of the Dirac
> algebra, with an additional scalar (and possibly pseudoscalar) field.
> Such a field leads to a force law
>
> F = pE + JxB + NJ
>
> where N is the scalar field and (p,J) is the charge-current density.
> If we assume a convected current J = pV we get your term.

Are you saying that N = (1/c^2)v'.E? If so, how is N derived?

--
Dave Rutherford
"New Transformation Equations and the Electric Field Four-vector"
http://www.softcom.net/users/der555/newtransform.pdf

Applications:
"4/3 Problem Resolution"
http://www.softcom.net/users/der555/elecmass.pdf
"Action-reaction Paradox Resolution"
http://www.softcom.net/users/der555/actreact.pdf
"Energy Density Correction"
http://www.softcom.net/users/der555/enerdens.pdf
"Proposed Quantum Mechanical Connection"
http://www.softcom.net/users/der555/quantum.pdf
"Biot-Savart's Companion"
http://www.softcom.net/users/der555/biotcomp.pdf
Danny Ross Lunsford
Oct15-04, 01:54 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\nDavid Rutherford &lt;drutherford@softcom.net&gt; wrote in message news:&lt;MJSdnYeWj76HnPPcRVn-gw@softcom.net&gt;...\n\n&gt; If my assumption is incorrect, please let me know.\n\nEssentially dm Am is promoted to a dynamical field alongside dmAn -\ndnAm. Maxwell\'s eqns are now\n\ndiv E - dN/dt = rho\n\ncurl B - dE/dt + grad N = J\n\ndiv B = 0\n\ncurl E + dB/dt = 0\n\nor in 4-d notation\n\n(Fmn + gmn N),n = Jm\n\n\nIn terms of potentials\n\nE = -grad phi - dA/dt\nB = curl A\nN = -div A - d phi/dt\n\nThe current J is no longer directly conserved:\n\ndiv J + d rho/dt = (del^2 - dt^2) N\n\nNote that we still have the usual equation for A in terms of the\ncurrent:\n\n(del^2 - dt^2) Am = Jm\n\nso the new field measures the extent to which charge is not conserved.\nNow the Lorentz 4-force is\n\n(Fmn + gmn N) Jn\n\nand so\n\nFk = pE + JxB + NJ\nF4 = J.E + Np\n\nOne can restore the conservation of charge by introducing a second\ncurrent\n\nKn = (Fmn + gmn N),m\n\nand so (Jm + Km) is conserved. One then ends up with a theory with two\ncurrents whose sum alone is conserved, suggesting that one is matter\nand the other antimatter and that they can mutually annihilate - but\nis it a hollow theory because the field is reducible to the bivector\nF, which has its source in the conserved current, and the scalar N,\nwhich has its source in the rate of creation-annihilation of matter\nand antimatter.\n\nThe force on matter is\n\nd/dtau (M Vm) = (Fmn + gmn N) Jn\n\n= dM/dtau Vm + M dVm/dtau\n\nwhere M is the mass density.\n\nAssuming that Jn is convected p Vn and so proportional to the momentum\ndensity,\n\ndM/dtau Vm + M dVm/dtau = Fmn p Vn + p Vm N\n\nContracting with Vm\n\ndM/dtau = p N\n\nand for antimatter,\n\ndM/dtau = -p N\n\nIn short, the idea of div A being a dynamical field is partially\nseaworthy, but runs aground on the shore of reducibility. It actually\namounts to a grafting of the usual theory of the bivector field with\nthat of a new scalar field whose source is the rate of\ncreation-annihilation of matter-antimatter. The idea can be rescued by\nenlarging the transformation group so that F and N are themselves\nparts of an irreducible whole, and N is only a 4-scalar from the\nperspective of the restricted set of transformations that correpsond\nto the Lorentz group.\n\n(Apologies for any sign errors in the above :)\n\n-drl\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">&nbsp;&nbsp;View this Usenet post in original ASCII form </a></div><P></jabberwocky>David Rutherford <drutherford@softcom.net> wrote in message news:<MJSdnYeWj76HnPPcRVn-gw@softcom.net>...

> If my assumption is incorrect, please let me know.

Essentially dm Am is promoted to a dynamical field alongside dmAn -
dnAm. Maxwell's eqns are now

div E - dN/dt = \rho

curl B - dE/dt + grad N = Jdiv B =

curl E + dB/dt =

or in 4-d notation

(Fmn + gmn N),n = Jm


In terms of potentials

E = -grad \phi - dA/dt[/itex]
B = curl A
N = -div A - d \phi/dt

The current J is no longer directly conserved:

div J + d \rho/dt = (del^2 - dt^2) N

Note that we still have the usual equation for A in terms of the
current:

(del^2 - dt^2) Am = Jm

so the new field measures the extent to which charge is not conserved.
Now the Lorentz 4-force is

(Fmn + gmn N) Jn

and so

Fk = pE + JxB + NJF4 = J.E + Np

One can restore the conservation of charge by introducing a second
current

Kn = (Fmn + gmn N),m

and so (Jm + Km) is conserved. One then ends up with a theory with two
currents whose sum alone is conserved, suggesting that one is matter
and the other antimatter and that they can mutually annihilate - but
is it a hollow theory because the field is reducible to the bivector
F, which has its source in the conserved current, and the scalar N,
which has its source in the rate of creation-annihilation of matter
and antimatter.

The force on matter is

d/dtau (M Vm) = (Fmn + gmn N) Jn

= dM/dtau Vm + M dVm/dtau

where M is the mass density.

Assuming that Jn is convected p Vn and so proportional to the momentum
density,

dM/dtau Vm + M dVm/dtau = Fmn p [itex]Vn + p Vm N

Contracting with Vm

dM/dtau = p N

and for antimatter,

dM/dtau = -p N

In short, the idea of div A being a dynamical field is partially
seaworthy, but runs aground on the shore of reducibility. It actually
amounts to a grafting of the usual theory of the bivector field with
that of a new scalar field whose source is the rate of
creation-annihilation of matter-antimatter. The idea can be rescued by
enlarging the transformation group so that F and N are themselves
parts of an irreducible whole, and N is only a 4-scalar from the
perspective of the restricted set of transformations that correpsond
to the Lorentz group.

(Apologies for any sign errors in the above :)

-drl