There are challenging implications of the Curl of E from a charge in
acceleration or in a gravitational field, in cases where a co-moving
current-carrying loop is subjected to favorable net induction. I don't know
what previous work was done to resolve such problems, which could be known to
SHS users. Consider an insulated charge Q resting in a natural gravitational
field, with a relatively small current-carrying loop S nearby, lying in the
vertical plane connecting them. The Del cross E of the curved field lines will
provide favorable induction to the loop if current runs down nearest the
charge. (The rest of the E field should have no net effect, even if unshielded,
given the Curl.) This much should be uncontroversial (Correct me if I'm wrong
about the Curl E in gravity, but see explanation in Appendix. I think it is
accepted.) The problem is the implications of the induction. Even in a
gravitational field, the net extra voltage should keep adding energy to S.
Unlike the case of free acceleration, forces between Q and S can't compensate
for energy gain by opposing motion (not that it's clear to me how they would,
even in that case.)

If we agree that S conserves energy with no charge present nearby, how do we
deal with the extra push given charges as they move around the loop? Even
granting some quirks of transmitting force and energy in the gravity field, the
continuous Del cross E should allow us to keep depositing energy in the loop
that otherwise wouldn't be there. Since the field from Q is stable, this would
continue to indefinitely accumulate energy in the system without source. We are
not supposed to be able to do that, but just saying that gives no understanding
of the situation and how it works. We need analysis that shows *how* the energy
is conserved, assuming that it is. This problem is presumably of interest
regarding the relationship between gravity and electromagnetism.

As usual, I am interested in any prior reference and resolution of this or
similar cases. I know that _Gravitation_ (Wheeler, Thorne, et al.) may well
cover such things, but right now I can't butt my middle-brows against a copy,
with reasonable clarity, in reasonable time.

Appendix: Background development, as needed.

Momentarily accelerating a charge puts a sort of "kink" or bend in the field
lines, sloping away from the acceleration, and propagating at c in a vacuum.
Oscillation produces the familiar wavy patterns of radiation. Continuous
acceleration of a charge relative to an inertial observer generates curving
field lines, sloping away from the acceleration, and resembling a bloom of
fiber optic threads subjected to gravity. We are more familiar with the case
where charges are oscillated linearly within an antenna by other oscillating
charges, but there is net Del cross E around a uniformly accelerating charge.
By definition it will produce a net voltage around a loop. The bending of field
lines is similar for a charge "resting in a gravitational field," which is
essentially equivalent to having the observer move along with an accelerating
charge. (Since transformation of E and B is dependent only upon velocity, the
transformation by the comoving observer will yield the same local field - what
matters - as in the stay-behind case with momentarily stationary Q. If observer
accelerates but not the charge, observer sees no Curl - it matters whether
source or detector is doing the accelerating in EM as in other areas. See
Feynman Lectures II.) To a comoving observer in the equivalent gravitational
field, the lines follow the free fall paths that would be taken by light
emitted from the charge.

Neil Bates

Neil wrote:
There are challenging implications of the Curl of E from a charge in
acceleration or in a gravitational field, in cases where a co-moving
current-carrying loop is subjected to favorable net induction. I don't know
what previous work was done to resolve such problems, which could be known to
SHS users. Consider an insulated charge Q resting in a natural gravitational
field, with a relatively small current-carrying loop S nearby, lying in the
vertical plane connecting them. The Del cross E of the curved field lines will
provide favorable induction to the loop if current runs down nearest the
charge. (The rest of the E field should have no net effect, even if unshielded,
given the Curl.) This much should be uncontroversial (Correct me if I'm wrong
about the Curl E in gravity, but see explanation in Appendix. I think it is
accepted.) The problem is the implications of the induction. Even in a
gravitational field, the net extra voltage should keep adding energy to S.
Unlike the case of free acceleration, forces between Q and S can't compensate
for energy gain by opposing motion (not that it's clear to me how they would,
even in that case.)

If we agree that S conserves energy with no charge present nearby, how do we
deal with the extra push given charges as they move around the loop? Even
granting some quirks of transmitting force and energy in the gravity field, the
continuous Del cross E should allow us to keep depositing energy in the loop
that otherwise wouldn't be there. Since the field from Q is stable, this would
continue to indefinitely accumulate energy in the system without source. We are
not supposed to be able to do that, but just saying that gives no understanding
of the situation and how it works. We need analysis that shows *how* the energy
is conserved, assuming that it is. This problem is presumably of interest
regarding the relationship between gravity and electromagnetism.

As usual, I am interested in any prior reference and resolution of this or
similar cases. I know that _Gravitation_ (Wheeler, Thorne, et al.) may well
cover such things, but right now I can't butt my middle-brows against a copy,
with reasonable clarity, in reasonable time.

Appendix: Background development, as needed.

Momentarily accelerating a charge puts a sort of "kink" or bend in the field
lines, sloping away from the acceleration, and propagating at c in a vacuum.
Oscillation produces the familiar wavy patterns of radiation. Continuous
acceleration of a charge relative to an inertial observer generates curving
field lines, sloping away from the acceleration, and resembling a bloom of
fiber optic threads subjected to gravity. We are more familiar with the case
where charges are oscillated linearly within an antenna by other oscillating
charges, but there is net Del cross E around a uniformly accelerating charge.
By definition it will produce a net voltage around a loop. The bending of field
lines is similar for a charge "resting in a gravitational field," which is
essentially equivalent to having the observer move along with an accelerating
charge. (Since transformation of E and B is dependent only upon velocity, the
transformation by the comoving observer will yield the same local field - what
matters - as in the stay-behind case with momentarily stationary Q. If observer
accelerates but not the charge, observer sees no Curl - it matters whether
source or detector is doing the accelerating in EM as in other areas. See
Feynman Lectures II.) To a comoving observer in the equivalent gravitational
field, the lines follow the free fall paths that would be taken by light
emitted from the charge.

Neil Bates


Hold a book out at arm's length.
After 2 minutes, ask yourself, "Am I doing work?"
Your aching muscles say, "Yes!"
Our gravity theory says, "No."
Because where does the energy come from
that is opposing your muscles?
Where does gravitational energy come from?
John

Neil wrote in message
...
There are challenging implications of the Curl of E from a charge in
acceleration or in a gravitational field, in cases where a co-moving
current-carrying loop is subjected to favorable net induction. I don't know

I believe I have the resolution to the paradox. It is rather subtle and unlike
customary effects, but it will do the job. The work done by the current charges
as they are pushed across the bottom of the loop, by the field from the nearby
charge Q, accumulates mass-energy at a low potential. The input work required
to push the current charges against the field from Q, across the top of the
loop, uses up mass-energy at a higher potential. The rate of change of
difference in potential energy mgy, at the rates gy dm/dt = gy dE/c^2 dt, (one
positive, the other negative, at two different heights y1 and y2) compensates
for the extra work done by the Curl of E. Not at all intuitive or easy to
visualize, but work on it and it will come through. I thought of this a few
years ago, but forgot about it. It does show that gravity and electromagnetism
cooperate, like all forces, to conserve certain quantities like energy.

Neil

"Starblade Darksquall" wrote in message
om...
"Neil" wrote in message
...
Neil wrote in message
...
There are challenging implications of the Curl of E from a charge in
acceleration or in a gravitational field, in cases where a co-moving
current-carrying loop is subjected to favorable net induction. I don't
know

I believe I have the resolution to the paradox. It is rather subtle and
unlike
customary effects, but it will do the job. The work done by the current
charges
snip
years ago, but forgot about it. It does show that gravity and
electromagnetism
cooperate, like all forces, to conserve certain quantities like energy.

Neil

I figured it was that the mean system will fall according to gravity,
and that will correspond to the problem of changing curl, so that
relative to free fall there is no increase in curl. Is this what
you're saying, or am I misreading you somehow?

(...Starblade Riven Darksquall...)

Sorry for the delay, but I hope this answer is meaty enough to make up. The
answer is similar to what you have said, but let me make it more clear:
Normally, if a system falls in a gravitational field, it does actual work in
proportion to the change in potential energy: W = -mg Delta y, or of course
E/c^2 = m. Then, the net combined actual and potential energy remain constant.
What we need instead, is a way to compensate for the work done in the current
loop by the curl E, caused by accelerating the charge. That is done by the
overall E field, which does positive work (F dot v, +) along the bottom of the
loop, and negative work (F dot v, -) along the top. Mass-energy is redistributed
downward without "doing the work of falling", to compensate for (not nullify)
the loop circulation. I don't know just how this would actually manifest in a
real current loop, say powered by a battery, exposed to a strong linear external
E field. Would one side get warmer? I don't know, and it would/did make for a
good experiment.

Side note 1: This compensation depends on Faraday's law having the correct
value. It does (Del cross E = -@B/@t) in our 3-D space. However, I found that in
spaces of other dimensions, it does not. We can find the curl E by looking at
two parts of the E field: Coulombic E_c (parallel to projection radius r) and
radiative E_r (perp. to r). Ironically, it is the time-delay of E_c that causes
curl from a uniformly accelerating charge, not the radiative field! Consider:
each point in space right now is receiving signals from the charge (say, pos.)
at different times in the past. Pick a reference distance r_0, at which the
charge's *retarded* position (signal is now received from when it was at ...) is
"zero," at velocity zero. At a slightly greater distance r1, the charge was
actually a bit higher (this falls out in the limit), but it's velocity projects
it to a point below zero. The field received at r1 is tilted a bit upwards, and
more so as we move out along r. This gives the correct curl E. The radiative
field that ironically *looks* appropriate isn't: just consider that the integral
around the appropriate "polar wedge" cancels out, since the weaker 1/r at the
far side of the wedge has to go around a proportionately longer leg.

However, compute the fields in N-D space using reasonable assumptions: E =
qr^(1-N), and the radiative field is whatever is needed to get the correct
inertia increase of collected charges, given integral of the first equation from
infinity to r. (This rules out 2-D spaces, which seems to have passed by
"Planiverse" enthusiasts unnoticed.) BTW, consider that inertia calculation
transverse to acceleration, or you'll run into all that "wrong factor" stuff.
What we find is that the radiative field is no longer 1/r, but (N-1)/2c^2(2-N)
qar^(2-N). (It doesn't make much sense anymore for the sake of "radiation" in
those spaces, either.) The curl of the coulombic field follows the same logic as
before, and gives the correct value (given B is still proportional to q, v, in
the usual way, but no longer a simple cross product.) However, the radiative
field now really does have a curl. For 4-D space, the Faraday's law must be
adjusted to Del cross E = -1.75 @B/@t [in higher spaces, the curl *is* the
oriented plane containing the circulation, not the vector perp. to that plane.]
This wreaks all kinds of havoc, not just on my gravity example, but on the whole
need for motional and current-change induction to match up, etc. Higher spaces
don't work out right, for other reasons as well, despite prevalent insinuations
about the accidental nature of only three spaces unfolding from a compactified
state.

Side note 2: You may be wondering, what if we co-accelerated charge and loop in
inertial space instead of setting them up in "real" gravity. Then, there isn't
(?) a true gravitational potential and it seems we could siphon off the energy
from the circulation voltage. Well, without going into details: taking the
linear case, any attempt to recycle the process and get a PM machine is foiled
by various interactions. However, set up a charge and an adjacent tiny loop at
the rim of a rotating disk, and it isn't so clear how energy would cancel out.
In some orientations, with a simple loop, changing A field pushes against the
charge's motion. However, in other orientations, and especially with a
field-compensating (*but inert to induction effects....*) magnetized plate
contained in the loop, I can't find any way to make up for the voltage in the
loop. That doesn't mean there isn't, but it would be an interesting problem for
someone to work on. I haven't seen this sort of problem, or even discussion of
continuous curl E from co-accelerating charges, in textbooks. It may be
mentioned, or implied, in _Gravitation_, Wheeler, Thorne, et al.

Neil Bates

Neil wrote:
There are challenging implications of the Curl of E from a charge in
acceleration or in a gravitational field, in cases where a co-moving
current-carrying loop is subjected to favorable net induction. I don't know
what previous work was done to resolve such problems, which could be known to
SHS users. Consider an insulated charge Q resting in a natural gravitational
field, with a relatively small current-carrying loop S nearby, lying in the
vertical plane connecting them. The Del cross E of the curved field lines

Hold it: why are the field lines curved? Because of the
gravitational field? How much are they curved in, say, 1 G,
neglecting electrostatic interaction with "nearby" charges?
Is the gravitating body charged or not?

If the rest of your exposition is correct, you should be
able to oppose gravity _directly_ with a properly oriented
current-carrying coil (of non-cylindrical cross-section or
something?).

Mark L. Fergerson

Mark Fergerson wrote in message
...
Neil wrote:
There are challenging implications of the Curl of E from a charge in
acceleration or in a gravitational field, in cases where a co-moving
current-carrying loop is subjected to favorable net induction. I don't know
what previous work was done to resolve such problems, which could be known
to
SHS users. Consider an insulated charge Q resting in a natural gravitational
field, with a relatively small current-carrying loop S nearby, lying in the
vertical plane connecting them. The Del cross E of the curved field lines

Hold it: why are the field lines curved? Because of the
gravitational field? How much are they curved in, say, 1 G,
neglecting electrostatic interaction with "nearby" charges?
Is the gravitating body charged or not?

If the rest of your exposition is correct, you should be
able to oppose gravity _directly_ with a properly oriented
current-carrying coil (of non-cylindrical cross-section or
something?).

Mark L. Fergerson


No, because gravity affects electric field lines to a slight degree, and
electric charges affect gravity only due to their own mass-energy (including
field energy via
energy density = (E field)^2.) You might as well just put a mass under or over
the object you want to affect, but technically adding current to a coil
increases its energy and thus gives it a bit more gravity. The effect however is
tiny, but I've heard that scientists at Georgia Tech, and/or NASA have been
working on effects of superconductors on gravity.

Neil wrote in message
...

"Starblade Darksquall" wrote in message
om...
"Neil" wrote in message
...
Neil wrote in message
...
........

This whole induction process works only if we contrive to have charges move
around the path like cars on a race track, since otherwise redistribution of
charge within a natural conductor would cancel out the effect.