I was reading up about the magnetic vector potential (A) on Wikipedia
(http://en.wikipedia.org/wiki/Magnetic_vector_potential) , and got
myself confused about something that I'm hoping y'all can help me
with.

That article says that there is a big guage choice in defining the
vector potential because the divergence doesn't affect the magnetic
field, and could therefore be anything at all. It seems to me,
however, that:

- The E field is directly measurable, and has a -dA/dt term
- A at every point is a linear function of nearby currents
- We can create an oscillating current element (not a loop) and
correlate dE/dt at nearby points to ddJ/dtdt in that current element.
- this would tell us exactly how the vector potential is generated by
currents, including its divergence.

So how can the divergence be a guage choice?

Mr. Entropy wrote:
I was reading up about the magnetic vector potential (A) on Wikipedia
(http://en.wikipedia.org/wiki/Magnetic_vector_potential) , and got
myself confused about something that I'm hoping y'all can help me
with.

That article says that there is a big guage choice in defining the
vector potential because the divergence doesn't affect the magnetic
field, and could therefore be anything at all. It seems to me,
however, that:

- The E field is directly measurable, and has a -dA/dt term
- A at every point is a linear function of nearby currents
- We can create an oscillating current element (not a loop) and
correlate dE/dt at nearby points to ddJ/dtdt in that current element.
- this would tell us exactly how the vector potential is generated by
currents, including its divergence.

So how can the divergence be a guage choice?

The mathematical operation of an indefinite integral always includes
the addition of an "arbitrary" integration constant. That means that
the potential isn't fixed but can take any value depending upon the
constant of integration. One must set the arbitrary constant to some
agreed-upon standard to achieve consistency.

This thing holds for the Magentic Vector potential because as you
note, the E field is determined by induction which relates to -dA/dt.
So to find A one must integrate dA/dt. Once again there is an
arbitrary constant of integration that can be added because there are
many solutions to the differential equation in question. The choice
of that constant is what sets the gauge.

So then the "real" question becomes what should one set the constant
to such that values of "A" correspond to it's absolute values as
measured in space. But A is very difficult to measure directly and yet
Feynman and others have observed that A rather than B seems to be the
"real" field. (in other words quantum expressions etc. seem to work
with A but become a mess if one tries to use B) So. Classical E&M
guys have long regarded A as only a mathematical "trick" useful for
calculation but not fundamental because the value of A seems to be
quite arbitrary. Quantum physicists on the other hand look at their
equations and find A more fundamental than B.

So what gives? What gives is that nobody has quite figured it all out
yet. The key, would be some kind of "A" meter which could read A
directly and therefore set the arbitrary constant by imposing this
"absolute" value as some kind of "boundary condition" to be matched. I
don't think that anyone is quite there yet.

This thing holds for the Magentic Vector potential because as you
note, the E field is determined by induction which relates to -dA/dt.
So to find A one must integrate dA/dt. Once again there is an
arbitrary constant of integration that can be added because there are
many solutions to the differential equation in question. The choice
of that constant is what sets the gauge.

Thanks for the reply, Benj, but:

The divergence of A, which is the supposed guage choice, is a spatial
function and is not the integration constant of the time derivative
above.

The purpose of the experiment I outlined is not to directly measure A,
but to determine how A is created by currents. It assumes that, when
E isn't changing, A = some_kernel convolved with J, which is very
likely, and then measures the kernel directly by modulating J and then
measuring the correlated oscillations in dA/dt at various points in
the surrounding space.

Finding that kernel allows us to calculate A from J, including the
divergence. The ability to determine that kernel experimentally,
then, makes me think the the divergence of A has easily measurable,
physical consequences instead of being an arbitrary guage choice.

Mr. Entropy wrote:
Thanks for the reply, Benj, but:

The divergence of A, which is the supposed guage choice, is a spatial
function and is not the integration constant of the time derivative
above.

Actually the time derivative IS a spatial function, but be that as it
may...

Any vector field is defined by both its curl and divergence. A is no
different. The defining relation for A is that B is given by the Curl
of A. But that leaves divergence of A to be set any way we wish. One
such "usual" "gauge" is to set the divergence of A equal to zero. this
gives the usual relationship between J (current density) and A. But
actually an arbitrary divergence value can be picked because no matter
what we choose it does not change our definition that the Curl of A
gives B.

The purpose of the experiment I outlined is not to directly measure A,
but to determine how A is created by currents. It assumes that, when
E isn't changing, A = some_kernel convolved with J, which is very
likely, and then measures the kernel directly by modulating J and then
measuring the correlated oscillations in dA/dt at various points in
the surrounding space.

I'm not sure that your experiment which to me seems to be nothing more
than creating a varying current and measuring the resultant induction
(E) will determine an "absolute" divergence of A. And even if
you could measure the divergence of A what would it give you? The
divergence plays no role in the determination of B which is the
defining property of A. The divergence is arbitrary in that regard.

Finding that kernel allows us to calculate A from J, including the
divergence. The ability to determine that kernel experimentally,
then, makes me think the the divergence of A has easily measurable,
physical consequences instead of being an arbitrary guage choice.

It does seem right to me that what you'd want to do is SOMEHOW find a
physical property that is linked directly to the divergence of A. It's
not B, so it must be something else if it exists. Once you find that
property and measure it in relation to J then your plan is on it's
way.

I personally have no idea what that property would be. I don't think
that taking a second derivate of Induction will do it. You'll have to
find something other than B and induction to set this. From the
arbitrary value of A you can easily see how E&M guys dismiss A as
simply a mathematical calculating trick without any physical
significance.

I think you are thinking on the right track here, and you obviously
are going after this just like a bulldog! I'm hoping you won't
induce me to actually spend the time to go back and understand all
this once again! Good Luck!

Personally I have a problem imagining a "model" for A. The Biot-
Savart relation gives a reasonable model for B where a charged
particle that represents the current is thought to have a spinning
field about it. If one assumes that in a current somehow all the
charged particles line up with their axes in the same direction one
can see how an integration of all particles making up the current
produces the B-S relation for a B field. But what is the model for
A? What kind of thing would a spinning charged particle exude
isotropically in all directions and even more interesting only fall
off as 1/r? What kind of thing would give another field by just
taking it's curl. So here we have a field that is quite weird and
obscure in the sense of modeling it and yet physicists agree is
somehow more "fundamental" that the more easily imagined B field. So
what is going on? Damned if I know!

The electrokinetic impulse is a measurable quantity (in principle) so the
above represents both a definition and a physical interpretation of A.
Please see, Jefimenko' "Causality, Electromagnetic Induction and
Gravitation" Section 2-4. You *have* ordered it, haven't you, Benj?

Bill Miller wrote:

The electrokinetic impulse is a measurable quantity (in principle) so the
above represents both a definition and a physical interpretation of A.
Please see, Jefimenko' "Causality, Electromagnetic Induction and
Gravitation" Section 2-4. You *have* ordered it, haven't you, Benj?

sigh> Benj rubs teeth marks on his butt... I'm getting right on
it!
Wait a minute! I'm looking here at my note to order from Amazon:
it says "Electromagnetic Retardation and Theory of Relativity". I know
he has several books is there one that is the "best" to get or one
that should be the "first" to buy?

Benj

Well... I have 'em all. Each has its own merits, but the best starting point

Its intensity is proportional to the rate of change of current flow and
inversely proportional to r (distance) and to cSQR. It is equal to the
negative time derivative of A, the magnetic vector potential. or,
Ek= -dA/dt.

Hi, Bill

On Sep 26, 5:40 pm, "Bill Miller" <billmillerkt...@worldnet.att.net
wrote:
Its intensity is proportional to the rate of change of current flow and
inversely proportional to r (distance) and to cSQR. It is equal to the
negative time derivative of A, the magnetic vector potential. or,
Ek= -dA/dt.

Yes, that's exactly what I was thinking. But that would mean that
Gauss' law, which fails to distinguish E from Ek, is incorrect in the
presence of varying currents. If that's true, wouldn't it be common
knowledge by now?

Thanks much for the reference,

You're welcome!

Mr. E

Hell "Mr. E"... Please see below...

"Mr. Entropy" <egim2k@yahoo.com> wrote in message
news:1190920163.750141.255400@y42g2000hsy.googlegroups.com...
Hi, Bill

On Sep 26, 5:40 pm, "Bill Miller" <billmillerkt...@worldnet.att.net
wrote:
Its intensity is proportional to the rate of change of current flow and
inversely proportional to r (distance) and to cSQR. It is equal to the
negative time derivative of A, the magnetic vector potential. or,
Ek= -dA/dt.

Yes, that's exactly what I was thinking. But that would mean that
Gauss' law, which fails to distinguish E from Ek, is incorrect in the
presence of varying currents. If that's true, wouldn't it be common
knowledge by now?

Up 'til now it has been masked by at least three issues. The first is the
idea that an E field can *cause* an H field. The second is that an H field
can *cause* an E field. The third is Lentz's law.

The first has been proven empirically false since no one has ever been
able to measure the Magnetic field "caused" by Displacement Current.

The second has been masked by the assumption that induction is a magnetic
effect when it is an interaction between the movement of charges as
manifested by Ek.

The third has been *ignored*. This is Lentz's law, an interactive property
that has remained unexplained/unexplainable since it was determined
empirically way back when. The equations that define Ek show how and why
Lentz's law "works" the way it does.

I hope this helps. There's lots more, and that's why I was "ragging" on
Benj. Much of the "stuff" that he (and I) are interested in is covered by
Jefimenko's work.

Thanks much for the reference,

You're welcome!

Bill

Mr. E

Its intensity is proportional to the rate of change of current flow and
inversely proportional to r (distance) and to cSQR. It is equal to the
negative time derivative of A, the magnetic vector potential. or,
Ek= -dA/dt.

Yes, that's exactly what I was thinking. But that would mean that
Gauss' law, which fails to distinguish E from Ek, is incorrect in the
presence of varying currents. If that's true, wouldn't it be common
knowledge by now?

The third has been *ignored*. This is Lentz's law, an interactive property
that has remained unexplained/unexplainable since it was determined
empirically way back when. The equations that define Ek show how and why
Lentz's law "works" the way it does.

I was reading up about the magnetic vector potential (A) on Wikipedia
(http://en.wikipedia.org/wiki/Magnetic_vector_potential) , and got
myself confused about something that I'm hoping y'all can help me
with.

That article says that there is a big guage choice in defining the
vector potential because the divergence doesn't affect the magnetic
field, and could therefore be anything at all. It seems to me,
however, that:

- The E field is directly measurable, and has a -dA/dt term
- A at every point is a linear function of nearby currents
- We can create an oscillating current element (not a loop) and
correlate dE/dt at nearby points to ddJ/dtdt in that current element.
- this would tell us exactly how the vector potential is generated by
currents, including its divergence.

So how can the divergence be a guage choice?

Thanks for any help,

Mr. E

Hell "Mr. E"... Please see below...

"Mr. Entropy" <egi...@yahoo.com> wrote in message

news:1190920163.750141.255400@y42g2000hsy.googlegroups.com...

Hi, Bill

On Sep 26, 5:40 pm, "Bill Miller" <billmillerkt...@worldnet.att.net
wrote:
Its intensity is proportional to the rate of change of current flow and
inversely proportional to r (distance) and to cSQR. It is equal to the
negative time derivative of A, the magnetic vector potential. or,
Ek= -dA/dt.

Yes, that's exactly what I was thinking. But that would mean that
Gauss' law, which fails to distinguish E from Ek, is incorrect in the
presence of varying currents. If that's true, wouldn't it be common
knowledge by now?

Up 'til now it has been masked by at least three issues. The first is the
idea that an E field can *cause* an H field. The second is that an H field
can *cause* an E field. The third is Lentz's law.

The first has been proven empirically false since no one has ever been able
to measure the Magnetic field "caused" by Displacement Current.

The second has been masked by the assumption that induction is a magnetic
effect when it is an interaction between the movement of charges as
manifested by Ek.

The third has been *ignored*. This is Lentz's law, an interactive property
that has remained unexplained/unexplainable since it was determined
empirically way back when. The equations that define Ek show how and why
Lentz's law "works" the way it does.

I hope this helps. There's lots more, and that's why I was "ragging" on
Benj. Much of the "stuff" that he (and I) are interested in is covered by
Jefimenko's work.

Thanks much for the reference,

You're welcome!

Bill



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