Jack Sarfatti
Nov14-04, 11:59 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\nCORRECTED 2nd Draft\n\nOn Nov 13, 2004, at 1:05 PM, Jack Sarfatti wrote:\n\nFrom the published papers of STAIF and NASA BPP (now defunct) it is\napparent that many aerospace engineers do not understand the essentials\nof Einstein\'s theory of gravity in their attempts to come up with exotic\nadvanced propulsion systems. Hence the silly proposal to change "rest\nmass" (part of Hal Puthoff\'s PV program) for more efficient space-craft.\nIndeed, you might be able to do that, but it would be a disaster WMD to\ndo so as a reading of Sir Martin Rees\'s "Just Six Numbers" shows. (Also\nTipler & Barrow "The Anthropic Cosmological Principle).\n\nI only use 1916 plain vanilla GR with the Levi-Civita connection. No\nextended "Affine" connection etc.\n\nStart with\n\nds^2 = guvdx^udx^v\n\nSummation convention over repeated upper and lower indices.\n\nEquations in physics must be dimensionally consistent. Mathematicians\nsometimes flout this in differential geometry. One can do this virtually\nin intermediate steps as long as one checks that the final real output\nequations are physically consistent dimensionally. Similarly theoretical\nphysicists have a pure mathematician\'s Cargo Cult fetish and like to be\n"elegant" setting everything in sight = 1, e.g. h = c = G = 1 that\ncauses a lot of confusion and leads to them missing interesting\nconnections between seemingly disparate quantities. As Ludwig Boltzmann\nsaid "Elegance is for tailors."\n\nds is the local frame invariant differential length, dx^u is a\nframe-dependent coordinate differential length, therefore, the metric\ntensor components guv must be dimensionless pure numbers and the L-C\nconnection has dimension 1/(length). Therefore, c^2{L-C} is an\n"acceleration".\n\nExample 1. Global Inertial Frame GIF in really flat space-time.\n\nIn Cartesian coordinates\n\nds^2 = -(cdt)^2 + dx^2 + dy^2 + dz^2\n\ngoo = -1\n\ng11 = g22 = g33 = 1\n\nall off-diagonal components = 0.\n\nLook at (see below for proof)\n\n{LC}i00 = (1/2)(g0i,0 + gi0,0 - g00,i) = goi,0 - (1/2)goo,i\n\nObviously\n\n{LC}i00 = 0\n\nin GIF Cartesian coordinates.\n\n1a. Do a static orthogonal coordinate transformation to spherical polar\ncoordinates. This is not a local general coordinate transformation but a\nrigid global coordinate transformation.\n\nz = rcos(theta)\n\nx = rsin(theta)cos(phi)\n\ny = rsin(theta)sin(phi)\n\ndt = dt\'\n\ndz = drcos(theta) - rsin(theta)dtheta\n\ndx = drsin(theta)cos(phi) + rcos(theta)cos(phi)dtheta -\nrsin(theta)sin(phi)dphi\n\ndy = drsin(theta)sin(phi) + rcos(theta)sin(phi)dtheta +\nrsin(theta)cos(phi)dphi\n\nSubstitute to get\n\nds^2 = -(cdt)^2 + dr^2 + r^2[dtheta^2 + sin^2(theta)dphi^2]\n\nThe infinitesimal coordinate differentials in the little orthonormal\ntriad at (r,theta, phi) in space are\n\nder = erdr\ndetheta = ethetardtheta\ndephi = ephirsin(theta)dphi\n\nwhere er, etheta and ephi are an orthonormal 3-vector basis or LOCAL\nORTHOGONAL TRIAD FRAME in 3D space.\n\nObviously, the dimensionless metric tensor components in this static\northogonal coordinate transformation are for\n\n0 = t, 1 = x, 2 = y, 3 = z\n\n0\' = t, 1\' = r, 2\' = theta, 3\' = phi\n\nds^2 = gu\'v\'(de^u\')(de^v\')\n\ng0\'0\' = g00 = -1\n\ng1\'1\' = g11 = +1\n\ng2\'2\' = g22 = +1\n\ng3\'3\' = g33 = +1\n\nThat is, the individual metric tensor components under this restricted\nset of global static orthogonal coordinate transformations in globally\nflat space-time are invariants.\n\nTherefore {L-C}i\'0\'0\' = 0 as well in GIF static orthogonal spherical\npolar coordinates.\n\nThis result is intuitively obvious, but needs to be shown formally as well.\n\nLet\'s call these trivial coordinate transformations.\n\n1b. The simplest non-trivial coordinate transformation to a non-inertial\nframe with the appearance of an "inertial force" (mis-named\n"non-inertial force" is more precise) is the global Galilean\ntransformation along the z axis\n\nt -> t\' = t\n\nx -> x\' = x\n\ny -> y\' = y\n\nz -> z\' = z - (1/2)gt^2\n\nwhere gt/v << 1\n\ntherefore,\n\ndz = dz\' + gt\'dt\'\n\nSubstitute into\n\nds^2 = -(cdt)^2 + dx^2 + dy^2 + dz\'^2\n\nto get\n\nds^2 = -(cdt\')^2 + dx\'^2 + dy\'^2 + (dz\' + gt\'dt\')^2\n\n= -(cdt\')^2 + dx\'^2 + dy\'^2 + dz\'^2 + (gt\')^2dt\'^2 + 2gt\'dt\'dz\'\n\n= [(gt\')^2 - c^2]dt\'^2 + 2gt\'dt\'dz\' + dx\'^2 + dy\'^2 + dz\'^2\n\n= [(gt\'/c)^2 - 1](cdt\')^2 + 2(gt\'/c)cdt\'dz\' + dx\'^2 + dy\'^2 + dz\'^2\n\nTherefore, the dimensionless GLOBAL NONINERTIAL FRAME (GNIF) metric\ntensor components are\n\ng0\'0\' = [(gt\'/c)^2 - 1]\n\ng0\'3\' = g3\'0\' = 2(gt\'/c)\n\nNote that this off-diagonal space-time metric tensor component is a\n3-vector Lense-Thirring "frame drag" gravimagnetic field in the sense of\nRay Chiao\'s "gravity radio" superconducting transducer proposal.\n\nFinally notice that in this GNIF as the rest frame for object of rest mass m\n\n(1/2)g0\'^3\',0\' = g/c^2\n\nTherefore, the translational "weight" as an inertial force in this\nparticular GNIF is simply\n\n(Weight 3-Vector)3\' = mc^2(1/2)g0\'^3\',0\'= mc^2{LC}3\'0\'0\'/2 since goo,3\'\n= 0 in this case.\n\nTherefore, this particular case simplifies to\n\nW = mg along the z axis.\n\nNote that a non-gravity force is causing the frame to accelerate.\n\nLocally this is equivalent to a gravity "g-force", but globally it does\nnot fall off to zero as does a real gravity field from a compact source.\nSee Chap 10 of Landau & Lifshitz "Classical Theory of Fields".\n\nNote that there are no inertial forces in inertial frames (either global\nor local).\n\nThe plain vanilla L-C connection has no GCT tensor part.\n\nThat is the L-C connection in 1916 GR is 100% inertial force, no GCT\ntensor force component.\n\nExtended connections with torsion and non-metricity dynamical fields do\nhave GCT tensor pieces, but they are not part of 1916 GR.\n\nThe not-GCT tensor Levi-Civita connection for parallel transport of\ngeometric objects in curved space-time is\n\n{LC}wuv = (1/2)(gvw,u + gwu,v - guv,w)\n\nu,v,w,l = 0,1,2,3\n\nNote that indices ij,k = 1,2,3 confined to the 3D spacelike surface in a\ngiven 3+1 foliation of the manifold.\n\nTherefore,\n\n{LC}i00 = (1/2)(g0i,0 + gi0,0 - g00,i) = goi,0 - (1/2)goo,i\n\n\nFirst look only at the ordinary partial time derivative of the\ngravimagnetic field\n\n(1/2)gi0,0\n\n\nComma means ordinary partial derivative.\n\nHere I prove that the "translational" "Weight" actually measured in the\n"rest LNIF" of the object of rest mass m being weighed is\n\n(Weight 3-Vector)^i = mc^2{LC}^i00/2 -> mc^2(1/2)gi0,0 when g00,i = 0\n\nThis comes from the "ma = F" of Einstein\'s 1916 GR:\n\nd^2xl/ds^2 + (1/2){LC}lvw(dx^v/ds)(dx^w/ds) = Fl(non-gravity)/mc^2\n\nIn the special LNIF REST FRAME of the center of mass of object of rest\nmass m where\n\nd^2x^i/ds^2 = 0, i = 1,2,3\n\ndx^i/ds = 0\n\ndx^0/ds = 1\n\nd^2x0/ds^2 = 0\n\n(1/2){LC}i00 = Fi(non-gravity)/mc^2\n\n(1/2){LC}000 = F0(non-gravity)/mc^2\n\n\nHomework Problem\n\nShow what combination of {LC} connection field components give the\ncentrifugal and Coriolis forces under what kind of non-trivial\ncoordinate transformations of the globally flat metric field.\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>CORRECTED 2nd Draft
On Nov 13, 2004, at 1:05 PM, Jack Sarfatti wrote:
From the published papers of STAIF and NASA BPP (now defunct) it is
apparent that many aerospace engineers do not understand the essentials
of Einstein's theory of gravity in their attempts to come up with exotic
advanced propulsion systems. Hence the silly proposal to change "rest
mass" (part of Hal Puthoff's PV program) for more efficient space-craft.
Indeed, you might be able to do that, but it would be a disaster WMD to
do so as a reading of Sir Martin Rees's "Just Six Numbers" shows. (Also
Tipler & Barrow "The Anthropic Cosmological Principle).
I only use 1916 plain vanilla GR with the Levi-Civita connection. No
extended "Affine" connection etc.
Start with
ds^2 = guvdx^udx^v
Summation convention over repeated upper and lower indices.
Equations in physics must be dimensionally consistent. Mathematicians
sometimes flout this in differential geometry. One can do this virtually
in intermediate steps as long as one checks that the final real output
equations are physically consistent dimensionally. Similarly theoretical
physicists have a pure mathematician's Cargo Cult fetish and like to be
"elegant" setting everything in sight = 1, e.g. h = c = G = 1 that
causes a lot of confusion and leads to them missing interesting
connections between seemingly disparate quantities. As Ludwig Boltzmann
said "Elegance is for tailors."
ds is the local frame invariant differential length, dx^u is a
frame-dependent coordinate differential length, therefore, the metric
tensor components guv must be dimensionless pure numbers and the L-C
connection has dimension 1/(length). Therefore, c^2{L-C} is an
"acceleration".
Example 1. Global Inertial Frame GIF in really flat space-time.
In Cartesian coordinates
ds^2 = -(cdt)^2 + dx^2 + dy^2 + dz^2
goo = -1
g11 = g22 = g33 = 1
all off-diagonal components = .
Look at (see below for proof)
{LC}i00 = (1/2)(g0i,0 + gi0,0 - g00,i) = goi,0 - (1/2)goo,i
Obviously
{LC}i00 =
in GIF Cartesian coordinates.
1a. Do a static orthogonal coordinate transformation to spherical polar
coordinates. This is not a local general coordinate transformation but a
rigid global coordinate transformation.
z = rcos(\theta)x = rsin(\theta)cos(\phi)y = rsin(\theta)sin(\phi)dt =[/itex] dt'
dz = drcos(\theta) - rsin(\theta)dthetadx = drsin(\theta)cos(\phi) + rcos(\theta)cos(\phi)dtheta -rsin(\theta)sin(\phi)dphidy = drsin(\theta)sin(\phi) + rcos(\theta)sin(\phi)dtheta +rsin(\theta)cos(\phi)dphi
Substitute to get
ds^2 = -(cdt)^2 + dr^2 + r^2[dtheta^2 + sin^2(\theta)dphi^2]
The infinitesimal coordinate differentials in the little orthonormal
triad at (r,\theta, \phi) in space are
der = erdr
detheta = ethetardtheta
dephi = ephirsin(\theta)dphi
where er, etheta and ephi are an orthonormal 3-vector basis or LOCAL
ORTHOGONAL TRIAD FRAME in 3D space.
Obviously, the dimensionless metric tensor components in this static
orthogonal coordinate transformation are for
= t, 1 = x, 2 = y, 3 = z0' = t, 1' = r, 2' = \theta, 3' = \phids^2 = gu'v'(de^u')(de^v')
g0'0' = g00 = -1
g1'1' = g11 = +1
g2'2' = g22 = +1
g3'3' = g33 = +1
That is, the individual metric tensor components under this restricted
set of global static orthogonal coordinate transformations in globally
flat space-time are invariants.
Therefore {L-C}i'0'0' = as well in GIF static orthogonal spherical
polar coordinates.
This result is intuitively obvious, but needs to be shown formally as well.
Let's call these trivial coordinate transformations.
1b. The simplest non-trivial coordinate transformation to a non-inertial
frame with the appearance of an "inertial force" (mis-named
"non-inertial force" is more precise) is the global Galilean
transformation along the z axis
t -> t' = tx -> x' = xy -> y' = yz -> z' = z - (1/2)gt^2
where gt/v << 1
therefore,
dz = dz' + gt'dt'
Substitute into
ds^2 = -(cdt)^2 + dx^2 + dy^2 + dz'^2
to get
ds^2 = -(cdt')^2 + dx'^2 + dy'^2 + (dz' + gt'dt')^2= -(cdt')^2 + dx'^2 + dy'^2 + dz'^2 + (gt')^2dt'^2 + 2gt'dt'dz'
= [(gt')^2 - c^2]dt'^2 + 2gt'dt'dz' + dx'^2 + dy'^2 + dz'^2= [(gt'/c)^2 - 1](cdt')^2 + 2(gt'/c)cdt'dz' + dx'^2 + dy'^2 + dz'^2
Therefore, the dimensionless GLOBAL NONINERTIAL FRAME (GNIF) metric
tensor components are
g0'0' = [(gt'/c)^2 - 1]
g0'3' = g3'0' = 2(gt'/c)
Note that this off-diagonal space-time metric tensor component is a
3-vector Lense-Thirring "frame drag" gravimagnetic field in the sense of
Ray Chiao's "gravity radio" superconducting transducer proposal.
Finally notice that in this GNIF as the rest frame for object of rest mass m
(1/2)g0'^3',0' = g/c^2
Therefore, the translational "weight" as an inertial force in this
particular GNIF is simply
(Weight 3-Vector)3' = mc^2(1/2)g0'^3',0'= mc^2{LC}3'0'0'/2 since goo,3'
= in this case.
Therefore, this particular case simplifies to
W = mg along the z axis.
Note that a non-gravity force is causing the frame to accelerate.
Locally this is equivalent to a gravity "g-force", but globally it does
not fall off to zero as does a real gravity field from a compact source.
See Chap 10 of Landau & Lifshitz "Classical Theory of Fields".
Note that there are no inertial forces in inertial frames (either global
or local).
The plain vanilla L-C connection has no GCT tensor part.
That is the L-C connection in 1916 GR is 100% inertial force, no GCT
tensor force component.
Extended connections with torsion and non-metricity dynamical fields do
have GCT tensor pieces, but they are not part of 1916 GR.
The not-GCT tensor Levi-Civita connection for parallel transport of
geometric objects in curved space-time is
{LC}wuv = (1/2)(gvw,u + gwu,v - guv,w)
[itex]u,v,w,l = 0,1,2,3
Note that indices ij,k = 1,2,3 confined to the 3D spacelike surface in a
given 3+1 foliation of the manifold.
Therefore,
{LC}i00 = (1/2)(g0i,0 + gi0,0 - g00,i) = goi,0 - (1/2)goo,i
First look only at the ordinary partial time derivative of the
gravimagnetic field
(1/2)gi0,0
Comma means ordinary partial derivative.
Here I prove that the "translational" "Weight" actually measured in the
"rest LNIF" of the object of rest mass m being weighed is
(Weight 3-Vector)^i = mc^2{LC}^i00/2 -> mc^2(1/2)gi0,0 when g00,i =
This comes from the "ma = F" of Einstein's 1916 GR:
d^{2xl}/ds^2 + (1/2){LC}lvw(dx^v/ds)(dx^w/ds) = Fl(non-gravity)/mc^2
In the special LNIF REST FRAME of the center of mass of object of rest
mass m where
d^{2x}^i/ds^2 = 0, i = 1,2,3dx^i/ds = dx^0/ds = 1d^{2x0}/ds^2 = (1/2){LC}i00 = Fi(non-gravity)/mc^2(1/2){LC}000 = F0(non-gravity)/mc^2
Homework Problem
Show what combination of {LC} connection field components give the
centrifugal and Coriolis forces under what kind of non-trivial
coordinate transformations of the globally flat metric field.
On Nov 13, 2004, at 1:05 PM, Jack Sarfatti wrote:
From the published papers of STAIF and NASA BPP (now defunct) it is
apparent that many aerospace engineers do not understand the essentials
of Einstein's theory of gravity in their attempts to come up with exotic
advanced propulsion systems. Hence the silly proposal to change "rest
mass" (part of Hal Puthoff's PV program) for more efficient space-craft.
Indeed, you might be able to do that, but it would be a disaster WMD to
do so as a reading of Sir Martin Rees's "Just Six Numbers" shows. (Also
Tipler & Barrow "The Anthropic Cosmological Principle).
I only use 1916 plain vanilla GR with the Levi-Civita connection. No
extended "Affine" connection etc.
Start with
ds^2 = guvdx^udx^v
Summation convention over repeated upper and lower indices.
Equations in physics must be dimensionally consistent. Mathematicians
sometimes flout this in differential geometry. One can do this virtually
in intermediate steps as long as one checks that the final real output
equations are physically consistent dimensionally. Similarly theoretical
physicists have a pure mathematician's Cargo Cult fetish and like to be
"elegant" setting everything in sight = 1, e.g. h = c = G = 1 that
causes a lot of confusion and leads to them missing interesting
connections between seemingly disparate quantities. As Ludwig Boltzmann
said "Elegance is for tailors."
ds is the local frame invariant differential length, dx^u is a
frame-dependent coordinate differential length, therefore, the metric
tensor components guv must be dimensionless pure numbers and the L-C
connection has dimension 1/(length). Therefore, c^2{L-C} is an
"acceleration".
Example 1. Global Inertial Frame GIF in really flat space-time.
In Cartesian coordinates
ds^2 = -(cdt)^2 + dx^2 + dy^2 + dz^2
goo = -1
g11 = g22 = g33 = 1
all off-diagonal components = .
Look at (see below for proof)
{LC}i00 = (1/2)(g0i,0 + gi0,0 - g00,i) = goi,0 - (1/2)goo,i
Obviously
{LC}i00 =
in GIF Cartesian coordinates.
1a. Do a static orthogonal coordinate transformation to spherical polar
coordinates. This is not a local general coordinate transformation but a
rigid global coordinate transformation.
z = rcos(\theta)x = rsin(\theta)cos(\phi)y = rsin(\theta)sin(\phi)dt =[/itex] dt'
dz = drcos(\theta) - rsin(\theta)dthetadx = drsin(\theta)cos(\phi) + rcos(\theta)cos(\phi)dtheta -rsin(\theta)sin(\phi)dphidy = drsin(\theta)sin(\phi) + rcos(\theta)sin(\phi)dtheta +rsin(\theta)cos(\phi)dphi
Substitute to get
ds^2 = -(cdt)^2 + dr^2 + r^2[dtheta^2 + sin^2(\theta)dphi^2]
The infinitesimal coordinate differentials in the little orthonormal
triad at (r,\theta, \phi) in space are
der = erdr
detheta = ethetardtheta
dephi = ephirsin(\theta)dphi
where er, etheta and ephi are an orthonormal 3-vector basis or LOCAL
ORTHOGONAL TRIAD FRAME in 3D space.
Obviously, the dimensionless metric tensor components in this static
orthogonal coordinate transformation are for
= t, 1 = x, 2 = y, 3 = z0' = t, 1' = r, 2' = \theta, 3' = \phids^2 = gu'v'(de^u')(de^v')
g0'0' = g00 = -1
g1'1' = g11 = +1
g2'2' = g22 = +1
g3'3' = g33 = +1
That is, the individual metric tensor components under this restricted
set of global static orthogonal coordinate transformations in globally
flat space-time are invariants.
Therefore {L-C}i'0'0' = as well in GIF static orthogonal spherical
polar coordinates.
This result is intuitively obvious, but needs to be shown formally as well.
Let's call these trivial coordinate transformations.
1b. The simplest non-trivial coordinate transformation to a non-inertial
frame with the appearance of an "inertial force" (mis-named
"non-inertial force" is more precise) is the global Galilean
transformation along the z axis
t -> t' = tx -> x' = xy -> y' = yz -> z' = z - (1/2)gt^2
where gt/v << 1
therefore,
dz = dz' + gt'dt'
Substitute into
ds^2 = -(cdt)^2 + dx^2 + dy^2 + dz'^2
to get
ds^2 = -(cdt')^2 + dx'^2 + dy'^2 + (dz' + gt'dt')^2= -(cdt')^2 + dx'^2 + dy'^2 + dz'^2 + (gt')^2dt'^2 + 2gt'dt'dz'
= [(gt')^2 - c^2]dt'^2 + 2gt'dt'dz' + dx'^2 + dy'^2 + dz'^2= [(gt'/c)^2 - 1](cdt')^2 + 2(gt'/c)cdt'dz' + dx'^2 + dy'^2 + dz'^2
Therefore, the dimensionless GLOBAL NONINERTIAL FRAME (GNIF) metric
tensor components are
g0'0' = [(gt'/c)^2 - 1]
g0'3' = g3'0' = 2(gt'/c)
Note that this off-diagonal space-time metric tensor component is a
3-vector Lense-Thirring "frame drag" gravimagnetic field in the sense of
Ray Chiao's "gravity radio" superconducting transducer proposal.
Finally notice that in this GNIF as the rest frame for object of rest mass m
(1/2)g0'^3',0' = g/c^2
Therefore, the translational "weight" as an inertial force in this
particular GNIF is simply
(Weight 3-Vector)3' = mc^2(1/2)g0'^3',0'= mc^2{LC}3'0'0'/2 since goo,3'
= in this case.
Therefore, this particular case simplifies to
W = mg along the z axis.
Note that a non-gravity force is causing the frame to accelerate.
Locally this is equivalent to a gravity "g-force", but globally it does
not fall off to zero as does a real gravity field from a compact source.
See Chap 10 of Landau & Lifshitz "Classical Theory of Fields".
Note that there are no inertial forces in inertial frames (either global
or local).
The plain vanilla L-C connection has no GCT tensor part.
That is the L-C connection in 1916 GR is 100% inertial force, no GCT
tensor force component.
Extended connections with torsion and non-metricity dynamical fields do
have GCT tensor pieces, but they are not part of 1916 GR.
The not-GCT tensor Levi-Civita connection for parallel transport of
geometric objects in curved space-time is
{LC}wuv = (1/2)(gvw,u + gwu,v - guv,w)
[itex]u,v,w,l = 0,1,2,3
Note that indices ij,k = 1,2,3 confined to the 3D spacelike surface in a
given 3+1 foliation of the manifold.
Therefore,
{LC}i00 = (1/2)(g0i,0 + gi0,0 - g00,i) = goi,0 - (1/2)goo,i
First look only at the ordinary partial time derivative of the
gravimagnetic field
(1/2)gi0,0
Comma means ordinary partial derivative.
Here I prove that the "translational" "Weight" actually measured in the
"rest LNIF" of the object of rest mass m being weighed is
(Weight 3-Vector)^i = mc^2{LC}^i00/2 -> mc^2(1/2)gi0,0 when g00,i =
This comes from the "ma = F" of Einstein's 1916 GR:
d^{2xl}/ds^2 + (1/2){LC}lvw(dx^v/ds)(dx^w/ds) = Fl(non-gravity)/mc^2
In the special LNIF REST FRAME of the center of mass of object of rest
mass m where
d^{2x}^i/ds^2 = 0, i = 1,2,3dx^i/ds = dx^0/ds = 1d^{2x0}/ds^2 = (1/2){LC}i00 = Fi(non-gravity)/mc^2(1/2){LC}000 = F0(non-gravity)/mc^2
Homework Problem
Show what combination of {LC} connection field components give the
centrifugal and Coriolis forces under what kind of non-trivial
coordinate transformations of the globally flat metric field.