Van Jacques
Sep27-04, 03:31 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>\nAs a student I was taught about MHD and plasmas as nonrelativistic\ntheories. I have always thought that this is a mistake from the start.\nHow can one have a non-relativistic theory of the EM field?\nIs not EM fundamentally relativistic, especially if one is going\nto have fields in moving coordinate sytems, as with an MHD flow.\nIt\'s important that we know what group the differential eqns. are\ninvariant under. In Newtonian physics, one has the Galilean\ntransformations,\nbut with an EM field, one must have Lorentz invariance.\n\nWhile one can construct Galilean invariant MHD eqs., using\nthem introduces errors that can\'t be dismissed as "small for small\nvelocities". Consider Alfven waves with v_p^2 = B^2/n (non-rel) and\nv_p^2 = B^2(nf + B^2) (relativistic), where f = 1 + e + p/n =\nrelativistic\nspecific enthalpy = index. When n --> 0, the non-rel expression --> oo,\nbut the relativistic expression has v_p^2 --> 1. There are other\nproblems, especially for the theory of waves in MHD and plasma.\n\nI think a system consisting of matter and an EM field should be done\nrelativistically from the start. This is especially true when doing\nwaves.\nI also think that the Lagrangian and canonical field theory is\nby far the best way to do this problem.\n\nI have written a paper on MHD and plasma waves from this\npoint of view, if any one want a copy, email me for it.\n\nVan\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>As a student I was taught about MHD and plasmas as nonrelativistic
theories. I have always thought that this is a mistake from the start.
How can one have a non-relativistic theory of the EM field?
Is not EM fundamentally relativistic, especially if one is going
to have fields in moving coordinate sytems, as with an MHD flow.
It's important that we know what group the differential eqns. are
invariant under. In Newtonian physics, one has the Galilean
transformations,
but with an EM field, one must have Lorentz invariance.
While one can construct Galilean invariant MHD eqs., using
them introduces errors that can't be dismissed as "small for small
velocities". Consider Alfven waves with v_p^2 = B^2/n (non-rel) and
v_p^2 = B^2(nf + B^2) (relativistic), where f = 1 + e + p/n =
relativistic
specific enthalpy = index. When n --> 0, the non-rel expression --> oo,
but the relativistic expression has v_p^2 --> 1. There are other
problems, especially for the theory of waves in MHD and plasma.
I think a system consisting of matter and an EM field should be done
relativistically from the start. This is especially true when doing
waves.
I also think that the Lagrangian and canonical field theory is
by far the best way to do this problem.
I have written a paper on MHD and plasma waves from this
point of view, if any one want a copy, email me for it.
Van
theories. I have always thought that this is a mistake from the start.
How can one have a non-relativistic theory of the EM field?
Is not EM fundamentally relativistic, especially if one is going
to have fields in moving coordinate sytems, as with an MHD flow.
It's important that we know what group the differential eqns. are
invariant under. In Newtonian physics, one has the Galilean
transformations,
but with an EM field, one must have Lorentz invariance.
While one can construct Galilean invariant MHD eqs., using
them introduces errors that can't be dismissed as "small for small
velocities". Consider Alfven waves with v_p^2 = B^2/n (non-rel) and
v_p^2 = B^2(nf + B^2) (relativistic), where f = 1 + e + p/n =
relativistic
specific enthalpy = index. When n --> 0, the non-rel expression --> oo,
but the relativistic expression has v_p^2 --> 1. There are other
problems, especially for the theory of waves in MHD and plasma.
I think a system consisting of matter and an EM field should be done
relativistically from the start. This is especially true when doing
waves.
I also think that the Lagrangian and canonical field theory is
by far the best way to do this problem.
I have written a paper on MHD and plasma waves from this
point of view, if any one want a copy, email me for it.
Van