Coil and resistor induction paradox

[tita...@gmail.com]

In my article Faraday's Law Paradox, I have explained that in a magnetically induced coil the line integral of electric field is paradoxically zero in contraction with Faraday's law. This paradox has aroused a long discussion which also reveals that the air gap between the coil's terminals confused the understanding of the paradox. The closed coil below makes this paradox sharper. I will give my solution to this paradox.


Please read the article at
Coil and resistor induction paradox
http://pengkuanem.blogspot.com/2015/02/coil-and-resistor-induction-paradox.html

or
https://www.academia.edu/11113117/Coil_and_resistor_induction_paradox

[benj]

As usual Peng Kuan is totally confused again!

There is no "Faraday paradox"

A changing current (say linearly rising) produces an electric field
circulating about the conductor in question. The potential between the
ends is is given by the line integral around the loop E dot dl. It is
NOT zero because E is the field created by the induction.

But you say the electrons are not moving so the electric field at their
position must be zero. And indeed it is. That is because the induced
electric field produces a force upon the electrons which "sloshes" them
toward one end of the wire. This concentrated charge due to the
potential there creates an opposite field which at equilibrium cancels
the induced field at every electron. But the potential is rising as you
go around the ring so obviously the electric field at every point is not
zero.

Suppose we look at it a different way. Say I've got this long skinny
neutral rod of + and - charge in space. And then "somehow" I separate
some of the charge with more of the + on one end and - on the other and
somehow "hold" them there. If I now take my test charge and move it
through the rod, this distribution of charge will give me an increasing
potential as I move from one end to the other due to the charge
distribution alone!

You can think of the induced E field as that "something" that is holding
the charges in place.

However you ARE correct that the induced electric field and a static
Electric field are two different things. They have widely differing
properties. But they are the same in that they are both force fields.

For more read: www.hypersphere.us

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[benj]

On 02/28/2015 08:56 AM, tita...@gmail.com wrote:

> Le vendredi 27 février 2015 18:08:40 UTC+1, benj a écrit :
>
>>
>> There is no "Faraday paradox"
>>
>> A changing current (say linearly rising) produces an electric field
>> circulating about the conductor in question. The potential between the
>> ends is is given by the line integral around the loop E dot dl. It is
>> NOT zero because E is the field created by the induction.
>

> If you integrate"E the field created by the induction", you will get a negative voltage because the induced E is in the direction of current while the correct voltage is positive and opposes the current. So, your reasoning is wrong.
>
> But the "very good point" I cited in my article was yours, as you explain here the role of charge distribution.

The induced E field depends on whether the current is rising for falling
not on it's direction. It shows Lenz's Law in that if current is rising
field opposes it and if it is falling it tries to keep the current going.

--
___ ___ ___ ___
/\ \ /\ \ /\__\ /\ \
/::\ \ /::\ \ /::| | \:\ \
/:/\:\ \ /:/\:\ \ /:|:| | ___ /::\__\
/::\~\:\__\ /::\~\:\ \ /:/|:| |__ /\ /:/\/__/
/:/\:\ \:|__| /:/\:\ \:\__\ /:/ |:| /\__\ \:\/:/ /
\:\~\:\/:/ / \:\~\:\ \/__/ \/__|:|/:/ / \::/ /
\:\ \::/ / \:\ \:\__\ |:/:/ / \/__/
\:\/:/ / \:\ \/__/ |::/ /

\_:/__/ \:\__\ /:/ /
\/__/ \/__/

[tita...@gmail.com]

Le samedi 28 février 2015 22:14:27 UTC+1, benj a écrit :

>
> The induced E field depends on whether the current is rising for falling
> not on it's direction. It shows Lenz's Law in that if current is rising
> field opposes it and if it is falling it tries to keep the current going.
>
>

The induced E field opposes always the electrostatic field of the electrons distribution, because the two added up make zero.

IF you line-integrate the electric field for computing the voltage, you are not allowed to take only the induced one but not the electrostatic one. You have to take both.

PK

[benj]

So you are saying transformers don't work? You are saying that if I
compress a spring with a force and the spring pushes back so that the
net force is zero so the spring doesn't accelerate, that therefore there
is no energy stored in the spring and it can do no work because work =
force x distance and force is clearly zero so therefore nothing happens!
It's a paradox!

[tita...@gmail.com]

Le dimanche 1 mars 2015 01:28:17 UTC+1, benj a écrit :

>
> So you are saying transformers don't work? You are saying that if I
> compress a spring with a force and the spring pushes back so that the
> net force is zero so the spring doesn't accelerate, that therefore there
> is no energy stored in the spring and it can do no work because work =
> force x distance and force is clearly zero so therefore nothing happens!
> It's a paradox!
>

The outline of my article:
1) The classical theory uses line integral to compute voltage and obtain zero. So, classical theory is paradoxical.
2) The two forces: induced force and electrostatic force.
3) Real voltage is not zero but equal the negative line-integral of the electrostatic field that equals positive line-integral of induced field.
4) Solution: separate the two forces.

My point is the real voltage is not zero, but the classical theory gives zero, so it is not correct.The two forces are different, while the classical theory puts them in the same class. This is how classical theory makes error.

PK

[larry harson]

Right at the beginning of your article, your statement of Faraday's law is wrong.

Faraday's law states that if you take a *closed* circuit and calculate E*dl *completely* around it so you end up where you started, then this value will equal the rate of change of magnetic flux passing through any surface area closed by this same circuit:

http://en.wikipedia.org/wiki/Faraday%27s_law_of_induction#Quantitative

Regards,

Larry Harson.

[tita...@gmail.com]

Le lundi 2 mars 2015 00:23:06 UTC+1, larry harson a écrit :
> Right at the beginning of your article, your statement of Faraday's law is wrong.
>
> Faraday's law states that if you take a *closed* circuit and calculate E*dl *completely* around it so you end up where you started, then this value will equal the rate of change of magnetic flux passing through any surface area closed by this same circuit:
>
> http://en.wikipedia.org/wiki/Faraday%27s_law_of_induction#Quantitative
>
> Regards,
>
> Larry Harson.

This is why I said the resistor was thin. It can be so thin as the induced part in it is negligible. Or even it can be outside the circle so that the wire is closed. In this case, B=A.

PK

[larry harson]

I've a feeling we've been through this already some time ago.

If you're only integrating the *induced E*, then its contribution along the resistor is negligible. But you've stated that through the wire E is zero, which means you're looking at the *total E*, and this can't be ignored through the resistor as "negligible".

Regards,

Larry.

[Don Kelly]

Your feeling is correct. Peng has great faith in math but does have
problems tying this to reality and tends to ignore factors that are
present and contrary to his assumptions.
His starting premise is, although unstated, that the coil has 0
resistance AND 0 self inductance-neither of which is physically
possible. Some of his other "theoretical" paradoxes are based on such
assumptions.

To his credit, he does experiment but is limited to rather crude
experiments with sufficient errors to mask any conclusions that he
states. From extensive correspondence in the past, I think he is a
likeable, self taught individual with an enquiring mind.

Don Kelly
remove the cross to reply directly

[benj]

Your problem is you haven't taken into account that there are two
different types of electric fields here. There is an electrokinetic E
field (which is the induction) and the electrostatic E field which is
due to charge.

What happens is that the Induced E field produces a force on the free
electrons in the conductor moving them toward one end. If the ring is
open this happens until the internal E field is zero as you say (They
aren't moving) However in the gap (and around the ring) there is another
E field that is electrostatic from the moved charge.

So there are TWO electric fields. The Key is that the electrostatic
field is conservative. That means if you integrate THAT field around the
ring you get zero! While induced electrokinetic field in
non-conservative so an integral around the ring give the potential
difference across the gap.

This is exactly the same way a battery works in a circuit. The battery
is essentially a non-conservative field.

From this one can actually derive Kicrhoff's law which is a circuit
approximation that cleverly sweeps these problems under the
electromagnetic rug.

[Jos Bergervoet]

On 3/3/2015 6:50 PM, benj wrote:
> On 03/01/2015 06:50 PM, tita...@gmail.com wrote:
>> Le lundi 2 mars 2015 00:23:06 UTC+1, larry harson a écrit :

...
..

> So there are TWO electric fields.

Not really, It is better to say that there are two
contributions to E: from the charge density and from
the current density, rho and J.

rho --> E
/
/
J --> B

For the magnetic field there is only the contribution
from J.

If you use the Lorenz gauge, you can even include the
potentials: J determines A, and rho determines V, and
subsequently A determines B, while A and V *together*
determine E.

rho --> V --> E
/
/
J --> A --> B

> The Key is that the electrostatic field is conservative.

I think the key is that many people do not realize that
there is a mixing in the dependencies, such that E is
determined by charge and also by the currents.

> This is exactly the same way a battery works in a circuit. The battery
> is essentially a non-conservative field.

Not at all! The battery is the same as a charged capacitor
The charge is in the chemicals, e.g. electrons in zinc
atoms. The zinc loses electrons (like one capacitor plate
would lose them during discharging) and at the other
electrode electrons come in, which go e.g. to the
manganese atoms (like they would go to the other plate in
the capacitor!)

In a charged capacitor, and in a battery likewise, the
E-field is a nicely conservative field, benj!

--
Jos

[PengKuan Em]

Le lundi 2 mars 2015 22:01:28 UTC+1, larry harson a écrit :
>
> I've a feeling we've been through this already some time ago.

Yes. The last discussion is here
https://groups.google.com/d/msg/sci.physics.electromag/su7Jfa9yNEQ/iJb5V_3Sh4cJ

>
> If you're only integrating the *induced E*, then its contribution along the resistor is negligible. But you've stated that through the wire E is zero, which means you're looking at the *total E*, and this can't be ignored through the resistor as "negligible".
>
> Regards,
>
> Larry.

You are right that the total E in the resistor is non negligible. The paradox is that the line integral A-wire-B gives zero but A-resistor-B gives U. Thus what is the voltage at the point B ?

I have added a energy analysis to show this paradox from another view.

PK

[PengKuan Em]

Le lundi 2 mars 2015 22:01:28 UTC+1, larry harson a écrit :

> I've a feeling we've been through this already some time ago.

> Larry.

This time, I give my solution to the paradox

PK

[Don Kelly]

No- that doesn't work and in fact negates your argument (Eq1 is then
nonsense, etc).

- Faraday's law (as you correctly showed in in Eq1 of your first
"Faraday Paradox" is independent of the loop material or shape. The E at
any point is dependent on the material and shape. Whether the resistor
is thin or thick is immaterial to Faraday's Law . which deals with the
whole loop. You have to consider the sum of the coil part and the
resistor part.- You specifically have dealt with an A-B resistor
section as well as a coil section and treated these separately. In that
treatment the thickness is not a factor,

Eq1 assumes that all the induced voltage is across the resistor and not
in the wire(which apparently is superconductive) Eq2 is OK but not
Faraday's Law. Eq3 makes an assumption that the force on the electrons
in the wire is 0 because there is no acceleration (i.e. di/dt=0) Why?-
the situation is not as in the case of the open coil. Force is not
necessarily related to acceleration. If you are considering the result
of Eq3 to be true- you are ignoring coil resistance. Note that Eq2-Eq3
considers the full loop and satisfies Faraday. If you assume the coil
has resistance r , then you can modify eq1 to -(d(phi)/dt =( r+R)I and
that satisfies Faraday for any combination or r and R

So your "paradox" vanishes as you went from A to B in two directions
and not from A to A. You cannot claim that A=B as you specifically have
something, however thin.

--

[benj]

On 03/03/2015 01:24 PM, Jos Bergervoet wrote:
> On 3/3/2015 6:50 PM, benj wrote:
>> On 03/01/2015 06:50 PM, tita...@gmail.com wrote:
>>> Le lundi 2 mars 2015 00:23:06 UTC+1, larry harson a écrit :
> ...
> ..
>> So there are TWO electric fields.
>
> Not really, It is better to say that there are two
> contributions to E: from the charge density and from
> the current density, rho and J.
>
> rho --> E
> /
> /
> J --> B
>
> For the magnetic field there is only the contribution
> from J.

Really. What current are you talking about? Consider a loop with a gap
rather than PK's "resistor". There are now TWO electric fields. The
induced field described by the Faraday effect and the second field due
to the moved charge in the conductive loop. That field is electrostatic.
The total field in the loop is ZERO! (no charge is moving) So explain
the voltage that appears across the gap? Does not the integral of E dot
dl = 0? It's a paradox Jos, that you have not explained!

> If you use the Lorenz gauge, you can even include the
> potentials: J determines A, and rho determines V, and
> subsequently A determines B, while A and V *together*
> determine E.
>
> rho --> V --> E
> /
> /
> J --> A --> B

No current, no B (except original changing B) The induced E is actually
equal to the negative derivative of A and A is determined by the current
J that is producing the changing Faraday magnetic field. But this is not
relevant to the discussion.

>> The Key is that the electrostatic field is conservative.
>
> I think the key is that many people do not realize that
> there is a mixing in the dependencies, such that E is
> determined by charge and also by the currents.

I think you do not understand the difference between a conservative and
non-conservative E field. You are still laboring under the old "one E
field" idea. Electrostatic E fields are conservative. Electrokinetic
(induced) E fields are non-conservative. Transformers and batteries CAN
supply a steady current (sources in circuit theory) Hence two different
properties (there are many more differences) means the E fields are not
the "same". You are allowed to add them up only because they are both
force fields.

>> This is exactly the same way a battery works in a circuit. The battery
>> is essentially a non-conservative field.
>
> Not at all! The battery is the same as a charged capacitor
> The charge is in the chemicals, e.g. electrons in zinc
> atoms. The zinc loses electrons (like one capacitor plate
> would lose them during discharging) and at the other
> electrode electrons come in, which go e.g. to the
> manganese atoms (like they would go to the other plate in
> the capacitor!)

All. Battery is NOT the same as a capacitor. Not even close. Again you
do not understand the difference between conservative and
non-conservative fields. A capacitor cannot produce a steady current.
The movement of charge eventually builds up a field that stops the
current. Electrostatic fields are not capable of setting up steady currents.

> In a charged capacitor, and in a battery likewise, the
> E-field is a nicely conservative field, benj!

Completely and utterly wrong, Jos. (Well the capacitor part is right but
the battery part is utterly wrong.)

And here I thought you knew it all?

[PengKuan Em]

Le mardi 3 mars 2015 18:50:52 UTC+1, benj a écrit :

> Your problem is you haven't taken into account that there are two
> different types of electric fields here. There is an electrokinetic E
> field (which is the induction) and the electrostatic E field which is
> due to charge.

The "two fields" view is my solution to this paradox.

In the discussion about my previous article, bja...@teranews.com said: "the free negative ones move so as cancel the induced E field. Hence there is a gradient in the electron charge density in the wire from one end to the other". This may be the first time in history that such electrostatic field is mentioned. Before my Faraday's Law Paradox, the voltage across the terminals of an induced coil is equalized to the line-integral of the induced field in all text books, suggesting this field to be the sole field in the wire. It is a major advance to understand that there are two fields in the wire: induced and electrostatic. My solution to this paradox complete the second step: the induced field is not an electric field. Indeed, if it were of electric nature, the total field is still zero in the wire and the voltage would be zero too.

> What happens is that the Induced E field produces a force on the free
> electrons in the conductor moving them toward one end. If the ring is
> open this happens until the internal E field is zero as you say (They
> aren't moving) However in the gap (and around the ring) there is another
> E field that is electrostatic from the moved charge.

This is true in reality. But in classical theory electrostatic field within the wire is mentioned nowhere. Only the one in the gap is known but no one knows how the charge accumulation is built in the two terminals.

>
> So there are TWO electric fields. The Key is that the electrostatic
> field is conservative. That means if you integrate THAT field around the
> ring you get zero! While induced electrokinetic field in
> non-conservative so an integral around the ring give the potential
> difference across the gap.

When you take the two fields in your computation, it seems you treat them in different way. The electrostatic one is integrated from A to B that gives the voltage of B, but not the electrokinetic because it would cancel this voltage.

It is not correct to pick up one field as you wish just because it gives you the wished result. You have to apply the same law to the same fields, e.i. electrostatic and electrokinetic. If you fail to obtain a correct result, the law is incorrect. This is the purpose of my paradox.

PK

[Timo Nieminen]

On Wednesday, March 4, 2015 at 8:50:30 PM UTC+10, benj wrote:
>
> I think you do not understand the difference between a conservative and
> non-conservative E field. You are still laboring under the old "one E
> field" idea.

I think you are over-interpreting the mathematics. Just because you have two terms in an equation giving the (total) E field doesn't mean that there are two, physically different, E fields.

Do you really need to be reminded that maths isn't reality? With your "two E fields" mantra, you are insisting that math is reality.

[PengKuan Em]

Le mercredi 4 mars 2015 03:33:49 UTC+1, Don Kelly a écrit :

> Eq1 assumes that all the induced voltage is across the resistor and not
> in the wire(which apparently is superconductive) Eq2 is OK but not
> Faraday's Law. Eq3 makes an assumption that the force on the electrons
> in the wire is 0 because there is no acceleration (i.e. di/dt=0) Why?-
> the situation is not as in the case of the open coil. Force is not
> necessarily related to acceleration. If you are considering the result
> of Eq3 to be true- you are ignoring coil resistance.

The resistance of the wire is negligible before R.

> Note that Eq2-Eq3
> considers the full loop and satisfies Faraday. If you assume the coil
> has resistance r , then you can modify eq1 to -(d(phi)/dt =( r+R)I and
> that satisfies Faraday for any combination or r and R
>

-(d(phi)/dt =( r+R)I is the line-integral from B to B. More precisely,
B in the wire -> wire -> A in the wire -> A in the resistor -> B in the resistor.

So the line integral from B in the wire to B in the resistor = -(d(phi)/dt. This is illustrated by Figure 2.

This makes the discontinuity of the potential at B. Hence the paradox.

> So your "paradox" vanishes as you went from A to B in two directions
> and not from A to A. You cannot claim that A=B as you specifically have
> something, however thin.
>
> --
> Don Kelly

Why " not from A to A"?

PK

[benj]

We've been through this before, Iimo. So what is your model? (nobody is
saying the model is actual reality)

Do you agree with Slepian that there is only ONE E field? You've seen
the table of properties (Jos refuses to read anything like that so he
hasn't). So how do YOU explain those different properties. How can you
explain that one is conservative and one is not? Do you imagine a model
for E fields that have this little gear shifter on them that shifts from
one type of field to another depending on what is going on? Or do you
imagine that an E field is this huge complexity that includes ALL
properties and certain terms become zero as you move from one kind of
source to another?

None of these models are very satisfying.

We do agree that fantasy math is at least a PARTIAL reflection of some
kind of underlying truth, no? Math is not a proof of reality, however,
nor is reality a proof of math.

[benj]

yes, but the two different fields obey different mathematical laws! For
example the Curl of E = 0 for electrostatic, while Div E = 0 for
electrokinetic. An electrostatic E obeys inverse square. Electrokinetic
does not. Integral around a loop for electrostatic always = 0, in
general for electrokinetic it does not. Hence two different fields. Two
different sets of rules.

[Don Kelly]

On 04/03/2015 2:50 PM, PengKuan Em wrote:
> Le mercredi 4 mars 2015 03:33:49 UTC+1, Don Kelly a écrit :
>
>> Eq1 assumes that all the induced voltage is across the resistor and not
>> in the wire(which apparently is superconductive) Eq2 is OK but not
>> Faraday's Law. Eq3 makes an assumption that the force on the electrons
>> in the wire is 0 because there is no acceleration (i.e. di/dt=0) Why?-
>> the situation is not as in the case of the open coil. Force is not
>> necessarily related to acceleration. If you are considering the result
>> of Eq3 to be true- you are ignoring coil resistance.
> The resistance of the wire is negligible before R.
>
>> Note that Eq2-Eq3
>> considers the full loop and satisfies Faraday. If you assume the coil
>> has resistance r , then you can modify eq1 to -(d(phi)/dt =( r+R)I and
>> that satisfies Faraday for any combination or r and R
>>
> -(d(phi)/dt =( r+R)I is the line-integral from B to B. More precisely,
> B in the wire -> wire -> A in the wire -> A in the resistor -> B in the resistor.
>
> So the line integral from B in the wire to B in the resistor = -(d(phi)/dt. This is illustrated by Figure 2.
>
> This makes the discontinuity of the potential at B. Hence the paradox.

Two points of discontinuity- A and B --- so what.? This doesn't produce
a paradox with regard to Faraday's Law. The cause of this discontinuity
is in the model. The assumption that negligible wire resistance=0
resistance and that the resistor is a point element are approximations
which make life simpler- and give results that are usually quite good-
Circuit theory is an approximation to field theory.

>> So your "paradox" vanishes as you went from A to B in two directions
>> and not from A to A. You cannot claim that A=B as you specifically have
>> something, however thin.
>>
>> --
>> Don Kelly
> Why " not from A to A"?
>
> PK

A to A is OK -in either direction - it is still all around the loop.

[Timo Nieminen]

On Thursday, March 5, 2015 at 9:01:33 AM UTC+10, benj wrote:
> On 03/04/2015 05:33 PM, Timo Nieminen wrote:
> > On Wednesday, March 4, 2015 at 8:50:30 PM UTC+10, benj wrote:
> >>
> >> I think you do not understand the difference between a conservative and
> >> non-conservative E field. You are still laboring under the old "one E
> >> field" idea.
> >
> > I think you are over-interpreting the mathematics. Just because you have two terms in an equation giving the (total) E field doesn't mean that there are two, physically different, E fields.
> >
> > Do you really need to be reminded that maths isn't reality? With your "two E fields" mantra, you are insisting that math is reality.
>
> We've been through this before, Iimo. So what is your model? (nobody is
> saying the model is actual reality)
>
> Do you agree with Slepian that there is only ONE E field?

Why not? The operational definition of the E field suggests that there is only one E field.

Tie a rope to something. Pull on the rope. You exert a force, via that rope, on that something. Wiggle the rope, make waves in the rope, and you exert a force. The way that wave-force works is quite different from the static pull force. Does that mean that there are two ropes? Doesn't matter if you pull/push/wiggle it in two ways, or 30 ways, there's still only one rope.

Why should the E field be different?

> You've seen
> the table of properties (Jos refuses to read anything like that so he
> hasn't). So how do YOU explain those different properties. How can you
> explain that one is conservative and one is not?

Hit Heaviside's book. Read his gravitation paper, where he describes a "relativistic" theory of gravitation.

(It isn't really relativistic. He assumes it works, as written, in the rest frame of the aether. Like Maxwell's EM. But, just like Maxwell, if you assume it works in every inertial frame, you have a relativistic theory in the special relativity sense.)

> Do you imagine a model
> for E fields that have this little gear shifter on them that shifts from
> one type of field to another depending on what is going on? Or do you
> imagine that an E field is this huge complexity that includes ALL
> properties and certain terms become zero as you move from one kind of
> source to another?

What's the difference between the fields of static charges and the fields of moving charges? Why do they behave so very differently? But "static" and "moving" are artifacts of our choice of coordinate system. Why should our choice of what coordinate system to use affects the fields? Answer: it doesn't. It only affects our mathematical description of the fields. If you don't get hung up on the special cases resulting from a charged being at rest or moving at constant velocity as a consequence of our choice of coordinate system, what's the difference between the "different" types of fields?

Do you think that charged particles have little gear shifters that make them spit out different types of E fields when stationary, moving at constant v, and accelerating? Charges don't know about our choice of coordinate system - they don't know when to shift those gears.

> None of these models are very satisfying.
>
> We do agree that fantasy math is at least a PARTIAL reflection of some
> kind of underlying truth, no? Math is not a proof of reality, however,
> nor is reality a proof of math.

Our mathematical model lets us calculate E and B from a bunch of sources, however they might be moving. Then use that E and B to calculate the force exerted on some charge, however it might be moving. Since that model agrees with reality in the classical limit, it does seem to be a partial reflection of reality.

But insisting that just because you can write E = E1 + E2 + E3 there are 3 different E fields is over-interpreting the maths. Consider that I can choose a different writing of E, as E = E4 + E5 + E6 + E7. Does that mean, by the awesome power of mathematics, there are now FOUR different E fields? No, I don't think that mathematics is THAT powerful, that our mathematical choices create reality (that's good old-fashioned magical thinking).

[PengKuan Em]

Le jeudi 5 mars 2015 01:17:26 UTC+1, Don Kelly a écrit :
> Two points of discontinuity- A and B --- so what.? This doesn't produce
> a paradox with regard to Faraday's Law.

> Don Kelly
>
> remove the 'cross' to reply directly

So, you accept that discontinuity in potential, that it reflect physical fact.

PK

[benj]

Well you are correct for all E fields Force is given by qE. But the
similarity ends there. If you are calculating force. Then one E field
theory is fine. But what if you are doing say line integrals? Things are
then changed.

>> You've seen the table of properties (Jos refuses to read anything
>> like that so he hasn't). So how do YOU explain those different
>> properties. How can you explain that one is conservative and one is
>> not?
>
> Hit Heaviside's book. Read his gravitation paper, where he describes
> a "relativistic" theory of gravitation.
>
> (It isn't really relativistic. He assumes it works, as written, in
> the rest frame of the aether. Like Maxwell's EM. But, just like
> Maxwell, if you assume it works in every inertial frame, you have a
> relativistic theory in the special relativity sense.)

Well I think the jury is out on co-gravitation. Nevermind that GE
actually done experiments and owns patents on it! Not to get into the
"who is smarter than Einstein" debate, but relativity has been around
since Galileo and before Einstein it was widely guessed that relativity
applied to electromagnetic phenomena just as it did to mechanical laws.
Einstein just sort of brought all that stuff together.

Jefimenko also took a run at all this (this is getting off topic now)
deriving basic relativity from just the relativity principle and
electromagnetic retardation. WITHOUT any of the assumptions Einstein
made. Interesting.

>> Do you imagine a model for E fields that have this little gear
>> shifter on them that shifts from one type of field to another
>> depending on what is going on? Or do you imagine that an E field is
>> this huge complexity that includes ALL properties and certain terms
>> become zero as you move from one kind of source to another?
>
> What's the difference between the fields of static charges and the
> fields of moving charges? Why do they behave so very differently? But
> "static" and "moving" are artifacts of our choice of coordinate
> system. Why should our choice of what coordinate system to use
> affects the fields? Answer: it doesn't. It only affects our
> mathematical description of the fields. If you don't get hung up on
> the special cases resulting from a charged being at rest or moving at
> constant velocity as a consequence of our choice of coordinate
> system, what's the difference between the "different" types of
> fields?

what you say is true, charge in motion is a source of magnetic fields.
Hence you propose a "one field" theory where all fields either electric
and magnetic are labeled "F" (for field) because they are really all the
same thing? Yeah, you could do that. But it doesn't mean anything
because the "right" description is the one that reflects what is going
on in reality. EM is FILLED with "redundancies". There are MANY ways to
calculate the same thing. Yes electric and magnetic fields do indeed
have quite different properties. But are they the same thing? I can
calculate the force on a capacitor 4 different ways and all give the
same answer. But philosophically the 4 methods are quite different
implying a different structure of reality for each one. So are all EM
fields just ONE field?

Nobody can say because the fundamental underlying structure of such
things is unknown at this time.

> Do you think that charged particles have little gear shifters that
> make them spit out different types of E fields when stationary,
> moving at constant v, and accelerating? Charges don't know about our
> choice of coordinate system - they don't know when to shift those
> gears.

Yes it's an interesting question. How is it that when I move relative to
a charge that magnetic effects appear? What kind of mechanism can cause
that? But the question remains. Are magnetic and electric fields two
things or one thing? That a one field model somehow works is not proof
of a real structure. The two field model also works. What is needed is
an understanding of what exactly is going on in reality and that is
missing. My personal opinion (which you didn't ask for) happens to be
that E and H fields are not the same thing. It will probably be a while
before this is proved, though.

>> None of these models are very satisfying.
>>
>> We do agree that fantasy math is at least a PARTIAL reflection of
>> some kind of underlying truth, no? Math is not a proof of reality,
>> however, nor is reality a proof of math.
>
> Our mathematical model lets us calculate E and B from a bunch of
> sources, however they might be moving. Then use that E and B to
> calculate the force exerted on some charge, however it might be
> moving. Since that model agrees with reality in the classical limit,
> it does seem to be a partial reflection of reality.
>
> But insisting that just because you can write E = E1 + E2 + E3 there
> are 3 different E fields is over-interpreting the maths. Consider
> that I can choose a different writing of E, as E = E4 + E5 + E6 + E7.
> Does that mean, by the awesome power of mathematics, there are now
> FOUR different E fields? No, I don't think that mathematics is THAT
> powerful, that our mathematical choices create reality (that's good
> old-fashioned magical thinking).

What is magical thinking is trying to go backward from maths to reality.
That is the old math is more real than reality thing again.

Point is if I have a charge it creates a certain type of force field.
(electrostatic)

If I have the movement of charge (current) it creates a totally
different type of force field (magnetic)

If I have a movement of charge increasing or decreasing in time (dJ/dt)
it creates a field similar to the first field but with different
properties. (electrokinetic)

So your point is that this is just some single phenomena in different
situations. OK. Valid. My point is that these are different fields
because they have different properties. Also valid. Which is "true"?

Nobody knows. But one thing is clear: If PK sets up a situation with
both an electrostatic E field AND an electrokinetic E field and then
attempts a line integral around his loop, he sure can add the two fields
together and find the force (and in his case get zero) but if he tries
to apply the line integral for the electrostatic case (conservative) to
induction case (non-conservative) he is going to get the wrong answer
(as he did).

Hence the two field model gives you the big hint right away that two
rules must be applied. Your one field model works too, but one must
always remember the complex rules so that in such a case the two
situations are calculated differently.

Arguing as to whether there are two fields or one is a waste of time
since the answer has not yet been proved. But I do argue that the
multi-field model does provide a better thinking tool for what is going
on until such time as the real situation is determined.

[Jos Bergervoet]

On 3/4/2015 11:33 PM, Timo Nieminen wrote:
> On Wednesday, March 4, 2015 at 8:50:30 PM UTC+10, benj wrote:
>>
>> I think you do not understand the difference between a conservative and
>> non-conservative E field. You are still laboring under the old "one E
>> field" idea.
>
> I think you are over-interpreting the mathematics. Just because
> you have two terms in an equation giving the (total) E field
> doesn't mean that there are two, physically different, E fields.

Of course there is the color-electric field of chromo-dynamics
which benj might be referring to? He's now working on the top-
priority millennium problem of the Clay institute of mathematics:
http://www.claymath.org/millennium-problems

> Do you really need to be reminded that maths isn't reality?
> With your "two E fields" mantra, you are insisting that math
> is reality.

Berenger used two E-fields (to make almost perfect boundary
conditions!) And benj is of course far ahead of this all..

--
Jos

[Jos Bergervoet]

Yes, and what if you use tables of multiplication?!
Then there are at least 10 E-fields, benj!

BTW: are you also going to decline the one million
dollar, like Grigory Perelman?

--
Jos

[benj]

On 03/05/2015 02:55 AM, Jos Bergervoet wrote:
> On 3/4/2015 11:33 PM, Timo Nieminen wrote:
>> On Wednesday, March 4, 2015 at 8:50:30 PM UTC+10, benj wrote:
>>>
>>> I think you do not understand the difference between a conservative and
>>> non-conservative E field. You are still laboring under the old "one E
>>> field" idea.
>>
>> I think you are over-interpreting the mathematics. Just because
>> you have two terms in an equation giving the (total) E field
>> doesn't mean that there are two, physically different, E fields.
>
> Of course there is the color-electric field of chromo-dynamics
> which benj might be referring to? He's now working on the top-
> priority millennium problem of the Clay institute of mathematics:
> http://www.claymath.org/millennium-problems

Hey I have a mathematician friend who is all ga-ga over solving the
Riemann Hypothesis. He's all impressed with it. A while back he thought
he had the approach to the answer, but I had to point out the mistake he
was making. He's the smartest guy I know.

>> Do you really need to be reminded that maths isn't reality?
>> With your "two E fields" mantra, you are insisting that math
>> is reality.
>
> Berenger used two E-fields (to make almost perfect boundary
> conditions!) And benj is of course far ahead of this all..

As Timo has amply demonstrated, current thinking is to consider ALL of
EM (electric and magnetic) as just ONE field with complex properties.

I, of course, am going the other way, subdividing properties into
separate groups with different names. Hey, Jos, you are in love with
word games! Join in!

[benj]

Well, Jos, I am no mathematician. I appreciate reality far too much for
that! And I'm not moving to a country with as much winter as Sweden. And
I am also equally disappointed with the Science community and their
childish games trying to turn science into word games, trying to steal
credit from each other and ridiculing each other's work.

So yeah, I'd turn down the Field's medal over that too. But a million
bucks? Hey as a long time consultant I am ALWAYS ready for the
traditional payment of a suitcase full of small bills for "interesting"
problems. No question, I can be bought.

Quite frankly, Jos I've always had trouble with the "tables of
multiplication". In my view mathematics is something most suitable to be
something done by machines. Isn't it a sobering thought, Jos, that
everything you do that you think is so advanced, will one day be
replaced by a PC with AI software?

[larry harson]

You can place two voltmeters in parallel across A-B such that the measurement loop areas are zero. The one adjacent to the wire will measure 0v, the one adjacent to A-B will measure a finite voltage across A-B.

The "paradox" is resolved by noting the circuit is non-conservative and therefore voltmeters in parallel can measure different voltages! I'm pretty sure I posted a link to a Walter Lewin video emphasizing this point, to the shock of some MIT physics/engineering professors so Prof Lewin claims.

Regards,

Larry.

[larry harson]

I think Benj, influenced by the work of Jefimenko, is decomposing the electric field into a static and dynamic component, just as physicists decompose the electromagnetic force into an E and a B part.

Maybe it isn't a bad idea after all that has its uses.

Regards,

Larry.

[benj]

Yes, you did some time ago. And this is exactly PengKuan's problem. He's
thinking conservative fields when some are not.

--

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~~ \/__/ \/__/

[Jos Bergervoet]

On 3/5/2015 6:08 PM, benj wrote:
> On 03/05/2015 02:55 AM, Jos Bergervoet wrote:
>> On 3/4/2015 11:33 PM, Timo Nieminen wrote:
>>> On Wednesday, March 4, 2015 at 8:50:30 PM UTC+10, benj wrote:
>>>>
>>>> I think you do not understand the difference between a conservative and
>>>> non-conservative E field. You are still laboring under the old "one E
>>>> field" idea.
>>>
>>> I think you are over-interpreting the mathematics. Just because
>>> you have two terms in an equation giving the (total) E field
>>> doesn't mean that there are two, physically different, E fields.
>>
>> Of course there is the color-electric field of chromo-dynamics
>> which benj might be referring to? He's now working on the top-
>> priority millennium problem of the Clay institute of mathematics:
>> http://www.claymath.org/millennium-problems
>
> Hey I have a mathematician friend who is all ga-ga over solving the
> Riemann Hypothesis. He's all impressed with it. A while back he thought
> he had the approach to the answer, but I had to point out the mistake he
> was making. He's the smartest guy I know.

He's lucky to have you, saving him from prof. Otelbaev's fate.

>>> Do you really need to be reminded that maths isn't reality?
>>> With your "two E fields" mantra, you are insisting that math
>>> is reality.
>>
>> Berenger used two E-fields (to make almost perfect boundary
>> conditions!) And benj is of course far ahead of this all..
>
> As Timo has amply demonstrated, current thinking is to consider ALL of
> EM (electric and magnetic) as just ONE field with complex properties.
>
> I, of course, am going the other way, subdividing properties into
> separate groups with different names. Hey, Jos, you are in love with
> word games! Join in!

This time I prefer math. To replace the E-field with a
distribution over infinitely many field configurations, each
with its own complex amplitude giving its weight in the
distribution. In short: just the original replacement of a
wave by a wave functional! (It was this concept that started
the whole framework of quantum field theory.)

--
Jos

[benj]

Exactly my thinking. Except of course that you can decompose into three
fields. An Electrostatic E field, an Electrokinetic E field, and a
Lorentz E field. Jefimenko only uses two E fields because he allows the
Lorentz E field to fall out of the Electrokinetic E field when motion in
a B field is introduced.

So the development of a system of decomposed E fields is not exactly
cast in stone.

On the other hand, if it's influenced by Jefimenko and posted to USENET
it obviously must be a bad idea!

[See table p 14]

http://www.hypersphere.us/EM6.pdf

--

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\:\/:/ / \:\ \/__/ |::/ /

\::/__/ \:\__\ /:/ /
~~ \/__/ \/__/

[benj]

Yes sad, isn't it? You are aware of course that probability is the
science of ignorance, right? I mean if you knew what was REALLY going
on you wouldn't have to play all kind of silly games to calculate some
probability of what is going to happen. Arguments that it's impossible
to know what is really going on to the contrary not withstanding.

--

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\:\~\:\/:/ / \:\~\:\ \/__/ \/__|:|/:/ / \::/ /
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\:\/:/ / \:\ \/__/ |::/ /

\::/__/ \:\__\ /:/ /
~~ \/__/ \/__/

[Jos Bergervoet]

What has probability got to do with it?

> I mean if you knew what was REALLY going on

Well, simple: there are infinitely many field configurations
all with their complex amplitudes!

You already believe that there are infinitely many points in
space, all with their own value of Ex, Bx, Ey, etc. This new
concept is essentially of the same type!

> you wouldn't have to play all kind of silly games to calculate
> some probability of what is going to happen.

What?! If you believe there are many points in space, each with
their own E-field, then you *do not* have to calculate a
"probability" which one of these points is "going to happen".

If I say there are many field configurations in Hilbert space,
each one has its own amplitude, then I do not need to calculate
which one is "going to happen". They all happen!

> Arguments that it's impossible to know what is really going
> on to the contrary not withstanding.

You also cannot know exactly what goes on in each point of
the classical universe. Not exactly knowing what goes on in
each point of the Hilbert space is just the same..

--
Jos

[PengKuan Em]

Le jeudi 5 mars 2015 19:35:47 UTC+1, larry harson a écrit :
> You can place two voltmeters in parallel across A-B such that the measurement loop areas are zero. The one adjacent to the wire will measure 0v, the one adjacent to A-B will measure a finite voltage across A-B.
>
> The "paradox" is resolved by noting the circuit is non-conservative and therefore voltmeters in parallel can measure different voltages! I'm pretty sure I posted a link to a Walter Lewin video emphasizing this point, to the shock of some MIT physics/engineering professors so Prof Lewin claims.
>
> Regards,
>
> Larry.

I haven't seen the Walter Lewin video, but I have saved a document of Robert Romer from a discussion :
http://www.uvm.edu/~dahammon/Demonstrations/5ElectricityAndMagnetism/5bElectricFieldsAndPotential/5b10ElectricField/Faraday'sTeaser/Romer/Romer.pdf

My paradox is not about measurement, but that the potential at one point has 2 values. This is not possible. Like if you climb a mountain to the sommet. Through one track the sommet is 1000 m, but through another track the sommet is 200 m. The sommet has one altitude and only one. If you get two values, this means you have done a error somewhere.

PK

[benj]

On 03/05/2015 04:11 PM, Jos Bergervoet wrote:> On 3/5/2015 9:37 PM, benj

"Infinite"? "Points"?

>> you wouldn't have to play all kind of silly games to calculate
>> some probability of what is going to happen.
>
> What?! If you believe there are many points in space, each with
> their own E-field, then you *do not* have to calculate a
> "probability" which one of these points is "going to happen".

And the way you determine a measured configuration from an "infinite"
collection of "points" in some mathematical transformative manifold is?

There is not a lick of reality in anything you are going on about Jos.

The philosophy behind even the idea of "infinite numbers of points in
space" is already fantasy, let alone some transformation field attached
to each point.

> If I say there are many field configurations in Hilbert space,
> each one has its own amplitude, then I do not need to calculate
> which one is "going to happen". They all happen!

You mean in your mind they all happen. Fair enough. My Tinkerbell theory
says fields are all generated by Tinkerbell too. It happens! So much
simpler than an infinite number of points in an infinite dimensional
imaginary space whatever that means.

Your view is to look down upon science as a God from on high, seeing it
all past, present and future in the utmost abstract detail. But in our
reality, causality is a natural law. In your world velocity is a real
(fantasy) thing. But in our world, velocity is the result of a
transformation on information we can't have. So does that mean you know
more than everybody else or do you just have a better imagination?

>> Arguments that it's impossible to know what is really going
>> on to the contrary not withstanding.
>
> You also cannot know exactly what goes on in each point of
> the classical universe. Not exactly knowing what goes on in
> each point of the Hilbert space is just the same..

One cannot know what goes on in any mathematical fantasy because, well,
it's fantasy! "Infinite" is fantasy. "Points" are fantasy. "2" is a
fantasy! Hilbert space is a fantasy. In mathematics fantasy is good
enough because only consistency matters. But in science. Fantasy is
always tested against observation. And in that world observation trumps
all fantasy.

Of course classical physics is fantasy too, but it's tested fantasy.
Classical theory is based upon an continuous differentiable manifold.
This is KNOWN to be false in our reality! No matter, if we are careful
we still get lots of useful answers. But basing philosophy upon an error
is not a good plan. There is something in electromagnetic mathematical
theory called "non-physical solutions". All that stuff goes in the
rubbish bin of science. But that does not mean the math is not valid. It
is. Why people today are digging in the garbage pail trying to locate a
nugget of truth I have no idea.

[Timo Nieminen]

It can certainly have its uses. For example, in a scattering problem, I can write the E field as E_total = E_incident + E_scattered. It's useful. But I wouldn't say that it means that there are two real E fields.

Where the division of a field into static and dynamic components depends on our choice of coordinate system - e.g., if we can choose a coordinate system where one of those is zero - then we shouldn't be claiming that division to be physical. Unless we think that our choice of coordinate system alters reality.

[Don Kelly]

No- I didn't say that.
I said that such discontinuities are often due to the mathematical
model which doesn't fully represent reality.
Effectively you are using a resistor lumped at a point- along with a 0
resistance wire. Neither of which are actually true. This has no effect
on Faraday's Law.
If you mean that Kirchoff's Law (conservative) is violated -you are
right. But this case is not conservative.

For Larry
Unfortunately Prof Lewin has apparently been a naughty boy and his
lectures are no longer available

--

[PengKuan Em]

Le vendredi 6 mars 2015 03:48:41 UTC+1, Don Kelly a écrit :

> No- I didn't say that.
> I said that such discontinuities are often due to the mathematical
> model which doesn't fully represent reality.
> Effectively you are using a resistor lumped at a point- along with a 0
> resistance wire. Neither of which are actually true. This has no effect
> on Faraday's Law.
> If you mean that Kirchoff's Law (conservative) is violated -you are
> right. But this case is not conservative.
>

I did not say that Faraday's law is wrong. I use it as the name of this paradox. The paradox shows inconsistency of EM theory. Line integral is not Faraday's law, but electrostatic.

So, what is your opinion? The potential should be continu or can be discontinu? If the mathematical model is discontinu, then it must be wrong.

PK

[Don Kelly]

Ah but you are dealing with a gravitational field which is conservative.
A magnetic field is also conservative.
In such cases, integrating around a path and returning to the origin
gives a result of 0 . Strictly speaking Kirchoffs voltage law is the
Faraday law that you quote but with the right hand side 0.
It is often possible to simply replace the induced voltage by an ideal
voltage source as long as it is in part of the circuit that you can't
actually take measurements at. In your loop, one could put an ideal
voltage source (-d(phi)/dt)anywhere in the loop as long as you don't try
to measure it . This is often done in circuit models.
Unfortunately Prof Lewin was apparently a very bad boy and his lecture
material has been removed from the MIT website.

[benj]

On 03/05/2015 07:28 PM, Timo Nieminen wrote:
> On Friday, March 6, 2015 at 5:03:34 AM UTC+10, larry harson wrote:
>> On Wednesday, March 4, 2015 at 10:33:57 PM UTC, Timo Nieminen
>> wrote:
>>>
>>> I think you are over-interpreting the mathematics. Just because
>>> you have two terms in an equation giving the (total) E field
>>> doesn't mean that there are two, physically different, E fields.
>>>
>>> Do you really need to be reminded that maths isn't reality? With
>>> your "two E fields" mantra, you are insisting that math is
>>> reality.
>>
>> I think Benj, influenced by the work of Jefimenko, is decomposing
>> the electric field into a static and dynamic component, just as
>> physicists decompose the electromagnetic force into an E and a B
>> part.
>>
>> Maybe it isn't a bad idea after all that has its uses.
>
> It can certainly have its uses. For example, in a scattering problem,
> I can write the E field as E_total = E_incident + E_scattered. It's
> useful. But I wouldn't say that it means that there are two real E
> fields.

Yes, but there is a difference. E incident and E scattered are the same
kind of fields with the same rules applying. What you really should be
saying is you can write at total EM fields (we'll call it F for field)
Where F total = E + H, because indeed H is apparently produced by a mere
coordinate choice with respect to charge. (oddly E is not)

What I'm saying is similar to calculating with E and H as if they were
separate fields because their properties are quite different. You aren't
suggesting that the basics of E and H fields should be dumped because
they are really the same field are you?

> Where the division of a field into static and dynamic components
> depends on our choice of coordinate system - e.g., if we can choose a
> coordinate system where one of those is zero - then we shouldn't be
> claiming that division to be physical. Unless we think that our
> choice of coordinate system alters reality.

So you ARE suggesting that E and H fields should no longer be used
because I can choose a coordinate system (say moving with the charge)
where H disappears? How can the choice of coordinate system alter
reality? Which is an interesting question because we can turn it around
and ask "what kind of system would produce forces and laws that change
with the coordinate system?" Oddly this also seems to fly in the face of
the principle of relativity which says that all laws are the same in
every frame.

It seems to me that the crux here is that something seemingly complex is
going on with this large variety of apparent fields of seemingly
different kinds and yet somehow linked. It's a lot like the old theory
of epicycles. Complex and mysterious, yet gives the right answers (still
used for example to build planetariums), but by simply changing one's
point of view (heliocentric) a sudden simplification occurs. The missing
information here is what is that new point of view?

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[Timo Nieminen]

On Friday, March 6, 2015 at 1:52:48 PM UTC+10, benj wrote:
> On 03/05/2015 07:28 PM, Timo Nieminen wrote:
> > On Friday, March 6, 2015 at 5:03:34 AM UTC+10, larry harson wrote:
> >> On Wednesday, March 4, 2015 at 10:33:57 PM UTC, Timo Nieminen
> >> wrote:
> >>>
> >>> I think you are over-interpreting the mathematics. Just because
> >>> you have two terms in an equation giving the (total) E field
> >>> doesn't mean that there are two, physically different, E fields.
> >>>
> >>> Do you really need to be reminded that maths isn't reality? With
> >>> your "two E fields" mantra, you are insisting that math is
> >>> reality.
> >>
> >> I think Benj, influenced by the work of Jefimenko, is decomposing
> >> the electric field into a static and dynamic component, just as
> >> physicists decompose the electromagnetic force into an E and a B
> >> part.
> >>
> >> Maybe it isn't a bad idea after all that has its uses.
> >
> > It can certainly have its uses. For example, in a scattering problem,
> > I can write the E field as E_total = E_incident + E_scattered. It's
> > useful. But I wouldn't say that it means that there are two real E
> > fields.
>
> Yes, but there is a difference. E incident and E scattered are the same
> kind of fields with the same rules applying.

They behave differently. The incident field is regular, and the scattered field is outward-propagating. The energy flux of the incident field, through a surface surrounding the scatterer, is zero, and the energy flux of the scattered field is non-zero. They're different.

> What you really should be
> saying is you can write at total EM fields (we'll call it F for field)
> Where F total = E + H, because indeed H is apparently produced by a mere
> coordinate choice with respect to charge. (oddly E is not)

Consider the field of a permanent magnet. Stationary, E=0. Moving, E is non-zero.

> What I'm saying is similar to calculating with E and H as if they were
> separate fields because their properties are quite different. You aren't
> suggesting that the basics of E and H fields should be dumped because
> they are really the same field are you?

Is that all you were saying? That dividing the E field into 2 or 3 terms is a mathematical (or calculational) convenience? Weren't you claiming that there were 3 different "real" E fields?

But note that dividing the components of the 4x4 field tensor into separate 3-vector E and H fields is not like E = E1 + E2. It's more like E = Ex*x_hat + Ey*y_hat + Ez*z_hat.

> > Where the division of a field into static and dynamic components
> > depends on our choice of coordinate system - e.g., if we can choose a
> > coordinate system where one of those is zero - then we shouldn't be
> > claiming that division to be physical. Unless we think that our
> > choice of coordinate system alters reality.
>
> So you ARE suggesting that E and H fields should no longer be used
> because I can choose a coordinate system (say moving with the charge)
> where H disappears?

Not at all. It's convenient to use E and H fields. Likewise, I'm happy to use the height of a projectile in some projectile problem, even if that's only a single component of the position vector of the projectile.

> How can the choice of coordinate system alter
> reality? Which is an interesting question because we can turn it around
> and ask "what kind of system would produce forces and laws that change
> with the coordinate system?"

Why would we ask that? Do you really think that our arbitrary choice of coordinate system changes reality? Reality does what reality does, and our coordinate systems etc describe it. The answer to "How can the choice of coordinate system alter reality?" is obvious: it can't (unless you really believe that mathematics is more real than reality, and can be used to control reality). Which makes turning the question around pointless.

> Oddly this also seems to fly in the face of
> the principle of relativity which says that all laws are the same in
> every frame.

Why "oddly"? It's pretty obvious why. Your question assumes mathematics magically alters reality.

> It seems to me that the crux here is that something seemingly complex is
> going on with this large variety of apparent fields of seemingly
> different kinds and yet somehow linked. It's a lot like the old theory
> of epicycles. Complex and mysterious, yet gives the right answers (still
> used for example to build planetariums), but by simply changing one's
> point of view (heliocentric) a sudden simplification occurs. The missing
> information here is what is that new point of view?

Psst! Copernicus still used epicycles. The simplification doesn't come with heliocentricity, but with elliptical orbits.

That a geocentric model and a heliocentric model, both with circular orbits and epicycles, predict motion equally well shouldn't be a surprise. Why should our choice of where to put our origin in the model make such a difference? Take an introductory physics projectile problem about throwing a rock off a cliff. Do you choose y=0 to be the bottom of the cliff or the top of the cliff? Is it really such a mystery that both choices work?

[Jos Bergervoet]

On 3/5/2015 11:36 PM, benj wrote:
> On 03/05/2015 04:11 PM, Jos Bergervoet wrote:
>> On 3/5/2015 9:37 PM, benj wrote:

...
..

>>> you wouldn't have to play all kind of silly games to calculate
>>> some probability of what is going to happen.
>>
>> What?! If you believe there are many points in space, each with
>> their own E-field, then you *do not* have to calculate a
>> "probability" which one of these points is "going to happen".
>
> And the way you determine a measured configuration from an "infinite"
> collection of "points" in some mathematical transformative manifold is?

Definitely not by a silly fairy tale that only one
point is "going to happen".

> There is not a lick of reality in anything you are going on about Jos.

You are just jealous that you have only 2 E-fields,
and the wave functional has a whole continuum of them!

>> If I say there are many field configurations in Hilbert space,
>> each one has its own amplitude, then I do not need to calculate
>> which one is "going to happen". They all happen!
>
> You mean in your mind they all happen.

No, in the theory. And if the theory is true than in
reality they all happen. Whether I exist is irrelevant.

> Fair enough. My Tinkerbell theory
> says fields are all generated by Tinkerbell too.

And if your theory is true that that is the way it
happens. (Simply making the claim does not make
your theory true, of course.)

> So much simpler

Of course, we would not expect anything else from
you, benj!

...

> One cannot know what goes on in any mathematical fantasy

Now you mix it up: you cannot know with absolute accuracy
what goes on in physical reality. But you can know exactly
what goes on in a mathematical theory.

> Of course classical physics is fantasy too, but it's tested fantasy.

Quantum field theory is a tested theory as well.

> Classical theory is based upon an continuous differentiable manifold.
> This is KNOWN to be false in our reality!

Discreteness of space has been proposed, but I do not
believe it is proven.

> There is something in electromagnetic mathematical
> theory called "non-physical solutions".

Could you please name one? I do not believe you.
Those are all results of errors in calculations.

> All that stuff goes in the rubbish bin of science.
> But that does not mean the math is not valid.

Now back up your claim: Name us one non-physical
solution of the classical Maxwell equations! (And
preferably without putting in unphysical boundary
conditions like delta functions to begin with, that
would be cheating! But even then they would smooth
out AFAIK.)

> Why people today are digging in the garbage pail trying to locate a
> nugget of truth I have no idea.

PengKuan Em might be able to tell you. He knows
all the unphysical results of electrodynamics.

--
Jos

[PengKuan Em]

Le vendredi 6 mars 2015 04:27:37 UTC+1, Don Kelly a écrit :
> Ah but you are dealing with a gravitational field which is conservative.
> A magnetic field is also conservative.

Your are right, gravitation is conservative. But this is only an analogy, not a proof. I'm explaining that the potential at Point B has a definite value,
Ub=Ua-d(phi)/dt. It cannot be zero at the same time, conservative or not.

> In your loop, one could put an ideal
> voltage source (-d(phi)/dt)anywhere in the loop as long as you don't try
> to measure it.

> --
> Don Kelly
>

You mean that at the place where you put an ideal voltage source (-d(phi)/dt), potential has two values at once. So, in the coil, nowhere has a definite potential with respect to a fixed point, say, A. This proves that the classical theory is unable to find the correct value of the potential in the coil. THis is what I'm saying through the paradox: this model is wrong.

PK

[benj]

Obviously I was not specific enough. I was referring to static E fields
not the dynamic ones you used to prove me "wrong".

>> What I'm saying is similar to calculating with E and H as if they
>> were separate fields because their properties are quite different.
>> You aren't suggesting that the basics of E and H fields should be
>> dumped because they are really the same field are you?
>
> Is that all you were saying? That dividing the E field into 2 or 3
> terms is a mathematical (or calculational) convenience? Weren't you
> claiming that there were 3 different "real" E fields?

Not all. I was suggesting that when things have different properties
that suggests that they may have different sources. In other words the
"real" things that create them are different things. I have already said
that I don't believe in your "one field" EM theory in spite of the
existence of coordinate transforms because the properties of E and H are
so different that suggests they are produced from separate and differing
mechanisms. That you can manipulate mathematics to have them the "same"
is suggestive but not proof of a single unique source. But in the
meantime, the convenience of thinking about things with differing
properties as different things is useful.

> But note that dividing the components of the 4x4 field tensor into
> separate 3-vector E and H fields is not like E = E1 + E2. It's more
> like E = Ex*x_hat + Ey*y_hat + Ez*z_hat.

Well, yeah. But just think of "+" as representing the proper operator
rather than simple addition.

>>> Where the division of a field into static and dynamic components
>>> depends on our choice of coordinate system - e.g., if we can
>>> choose a coordinate system where one of those is zero - then we
>>> shouldn't be claiming that division to be physical. Unless we
>>> think that our choice of coordinate system alters reality.
>>
>> So you ARE suggesting that E and H fields should no longer be used
>> because I can choose a coordinate system (say moving with the
>> charge) where H disappears?
>
> Not at all. It's convenient to use E and H fields. Likewise, I'm
> happy to use the height of a projectile in some projectile problem,
> even if that's only a single component of the position vector of the
> projectile.

Heh! Not only does velocity not exist but the height of a projectile
doesn't exist either! (Because it's a single point and points are fantasy!)

>> How can the choice of coordinate system alter reality? Which is an
>> interesting question because we can turn it around and ask "what
>> kind of system would produce forces and laws that change with the
>> coordinate system?"
>
> Why would we ask that? Do you really think that our arbitrary choice
> of coordinate system changes reality? Reality does what reality does,
> and our coordinate systems etc describe it. The answer to "How can
> the choice of coordinate system alter reality?" is obvious: it can't
> (unless you really believe that mathematics is more real than
> reality, and can be used to control reality). Which makes turning the
> question around pointless.

Timo you are funny! You are such a great debater that you have totally
turned this around until you are lecturing me on math not being more
real than reality, and I'm backed into a corner supposedly having to
argue that it is! It's simply amazing the amount of confusion you can
create with your arguments! The Question isn't pointless. Questions like
"how is it that motion changes EM Field measurements" or "why is the
speed of light always the same regardless of the velocity of the
observer frame", are directed upon the "reality" which is the mechanisms
generating these Lorentz's force fields and measurements. Examination of
sources and first principles isn't pointless.

>> Oddly this also seems to fly in the face of the principle of
>> relativity which says that all laws are the same in every frame.
>
> Why "oddly"? It's pretty obvious why. Your question assumes
> mathematics magically alters reality.

Absolutely not true. Nice debate twist Timo!

>> It seems to me that the crux here is that something seemingly
>> complex is going on with this large variety of apparent fields of
>> seemingly different kinds and yet somehow linked. It's a lot like
>> the old theory of epicycles. Complex and mysterious, yet gives the
>> right answers (still used for example to build planetariums), but
>> by simply changing one's point of view (heliocentric) a sudden
>> simplification occurs. The missing information here is what is that
>> new point of view?
>
> Psst! Copernicus still used epicycles. The simplification doesn't
> come with heliocentricity, but with elliptical orbits.

As usual you miss the whole point and introduce obfuscation. Elliptical
orbits give greater accuracy. Heliocentricity is the philosophy that
simplifies the odd erratic apparent motion of the planets in the
firmament.

> That a geocentric model and a heliocentric model, both with circular
> orbits and epicycles, predict motion equally well shouldn't be a
> surprise. Why should our choice of where to put our origin in the
> model make such a difference?

So to ask the age-old question: Does the sun go around the earth or the
earth around the sun? :)

> Take an introductory physics projectile
> problem about throwing a rock off a cliff. Do you choose y=0 to be
> the bottom of the cliff or the top of the cliff? Is it really such a
> mystery that both choices work?

Yes, it is Timo! I am master of my Universe and in my mind the universe
changes according to what I think and what I choose! My mathematics
clearly is more real than reality! My equations determine what is going
on when action happens in the world! It makes a GREAT difference if y=0
is at the top or bottom of the cliff! It's really as simple as that,
Timo, and one day you'll realize it too!

Timo you are a Hoot! You should run for public office! Missing Tax
dollars? No! It's just a matter of a slight change in the counting
coordinates! Nothing is missing!

--

___ ___ ___ ___
/\ \ /\ \ /\__\ /\ \
/::\ \ /::\ \ /::| | \:\ \
/:/\:\ \ /:/\:\ \ /:|:| | ___ /::\__\
/::\~\:\__\ /::\~\:\ \ /:/|:| |__ /\ /:/\/__/
/:/\:\ \:|__| /:/\:\ \:\__\ /:/ |:| /\__\ \:\/:/ /
\:\~\:\/:/ / \:\~\:\ \/__/ \/__|:|/:/ / \::/ /
\:\ \::/ / \:\ \:\__\ |:/:/ / \/__/
\:\/:/ / \:\ \/__/ |::/ /

\::/__/ \:\__\ /:/ /
~~ \/__/ \/__/

[benj]

I am beaten, Jos! From now on I will only discuss electromagnetics with
PengKuan. Just like mental spoon-bending, when there are skeptics in the
room the phenomena doesn't work!

[Jos Bergervoet]

On 3/6/2015 6:02 PM, benj wrote:
> On 03/05/2015 11:49 PM, Timo Nieminen wrote:

...

>> But note that dividing the components of the 4x4 field tensor into
>> separate 3-vector E and H fields is not like E = E1 + E2. It's more
>> like E = Ex*x_hat + Ey*y_hat + Ez*z_hat.
>
> Well, yeah. But just think of "+" as representing the proper operator
> rather than simple addition.

That doesn't help you, you need the opposite: you need
to split the field! Show us how we can see your 2 parts
of E (if you are right that there really are 2). If I
have an E-field what do I do to see the "E1" and "E2" part?

If you have a prescription to split it into two distinct
parts then no-one can deny it any more. (Splitting it in
three cartesian components is similar, in that sense.)

..

>> Not at all. It's convenient to use E and H fields. Likewise, I'm
>> happy to use the height of a projectile in some projectile problem,
>> even if that's only a single component of the position vector of the
>> projectile.
>
> Heh! Not only does velocity not exist but the height of a projectile
> doesn't exist either!

Well, of course it's an operator in Hilbert space. I'm
glad you have come to that insight at last!

...

>> Psst! Copernicus still used epicycles. The simplification doesn't
>> come with heliocentricity, but with elliptical orbits.
>
> As usual you miss the whole point

This time it actually is an excellent point from Timo. It's
not the shift of origin but the inclusion of eccentricity..

The solar system is described by epi-ellipses!!

> Heliocentricity is the philosophy that simplifies the
> odd erratic apparent motion of the planets in the firmament.

On the contrary, the apparent motion remains exactly the same.

--
Jos

[benj]

On 03/06/2015 01:33 PM, Jos Bergervoet wrote:
> On 3/6/2015 6:02 PM, benj wrote:
>> On 03/05/2015 11:49 PM, Timo Nieminen wrote:
> ...
>>> But note that dividing the components of the 4x4 field tensor into
>>> separate 3-vector E and H fields is not like E = E1 + E2. It's more
>>> like E = Ex*x_hat + Ey*y_hat + Ez*z_hat.
>>
>> Well, yeah. But just think of "+" as representing the proper operator
>> rather than simple addition.
>
> That doesn't help you, you need the opposite: you need
> to split the field! Show us how we can see your 2 parts
> of E (if you are right that there really are 2). If I
> have an E-field what do I do to see the "E1" and "E2" part?
>
> If you have a prescription to split it into two distinct
> parts then no-one can deny it any more. (Splitting it in
> three cartesian components is similar, in that sense.)

Lessee. One field has the amount of charge as a source. The other field
is produced by the time rate of change of current. One field is
irrotational, and conservative. The other field is solenoidal and
non-conservative. One field obeys an inverse square law, the other does
not. Each is derived from a different potential function. I could go on.
They sure sound like the same field to me! Why not just add them up as
being the same thing? Obviously there is no prescription to split them
apart. There is no way in hell that two things this identical cannot
fundamentally be the same thing!

Same thing holds for electric and magnetic fields. Clearly since they
both produce forces on a charge they are identical. It's just the choice
of coordinate systems that makes them appear to be different things. I'm
sure with the right choice of frames a solenoidal field can be "unwound"
into an irrotational electric field. Seems obvious.

> ..
>>> Not at all. It's convenient to use E and H fields. Likewise, I'm
>>> happy to use the height of a projectile in some projectile problem,
>>> even if that's only a single component of the position vector of the
>>> projectile.
>>
>> Heh! Not only does velocity not exist but the height of a projectile
>> doesn't exist either!
>
> Well, of course it's an operator in Hilbert space. I'm
> glad you have come to that insight at last!
>
> ...
>>> Psst! Copernicus still used epicycles. The simplification doesn't
>>> come with heliocentricity, but with elliptical orbits.
>>
>> As usual you miss the whole point
>
> This time it actually is an excellent point from Timo. It's
> not the shift of origin but the inclusion of eccentricity..
>
> The solar system is described by epi-ellipses!!
>
>> Heliocentricity is the philosophy that simplifies the
>> odd erratic apparent motion of the planets in the firmament.
>
> On the contrary, the apparent motion remains exactly the same.

But the thinking about it doesn't. One is a complex mess only able to be
followed by you, and the other is simplicity able to be understood by
anyone (even me).

[Timo Nieminen]

On Saturday, March 7, 2015 at 3:02:04 AM UTC+10, benj wrote:
> On 03/05/2015 11:49 PM, Timo Nieminen wrote:
> > On Friday, March 6, 2015 at 1:52:48 PM UTC+10, benj wrote:
>
> >> How can the choice of coordinate system alter reality? Which is an
> >> interesting question because we can turn it around and ask "what
> >> kind of system would produce forces and laws that change with the
> >> coordinate system?"
> >
> > Why would we ask that? Do you really think that our arbitrary choice
> > of coordinate system changes reality? Reality does what reality does,
> > and our coordinate systems etc describe it. The answer to "How can
> > the choice of coordinate system alter reality?" is obvious: it can't
> > (unless you really believe that mathematics is more real than
> > reality, and can be used to control reality). Which makes turning the
> > question around pointless.
>
> Timo you are funny! You are such a great debater that you have totally
> turned this around until you are lecturing me on math not being more
> real than reality, and I'm backed into a corner supposedly having to
> argue that it is!

Your argument that there are _really_ in _reality_ 2 (or more) _really_ different E fields is based on a mathematical expression for E having more than 1 term. Sounds like "maths is more real than reality" to me.

> It's simply amazing the amount of confusion you can
> create with your arguments! The Question isn't pointless. Questions like
> "how is it that motion changes EM Field measurements" or "why is the
> speed of light always the same regardless of the velocity of the
> observer frame", are directed upon the "reality" which is the mechanisms
> generating these Lorentz's force fields and measurements. Examination of
> sources and first principles isn't pointless.

Your question, "what kind of system would produce forces and laws that change with the coordinate system?" _is_ pointless. The forces and laws don't change. The magnitude and direction of the 4-force are the same in all inertial frames. The laws are the same. They don't change, dependent on our choice of coordinate system. When the vector components of a force change from (3,4,0) to (0,5,0) from one coordinate system to another, the force doesn't change - don't confuse the real thing (the force) with our mathematical description of it (e.g., a set of vector components).

> >> It seems to me that the crux here is that something seemingly
> >> complex is going on with this large variety of apparent fields of
> >> seemingly different kinds and yet somehow linked. It's a lot like
> >> the old theory of epicycles. Complex and mysterious, yet gives the
> >> right answers (still used for example to build planetariums), but
> >> by simply changing one's point of view (heliocentric) a sudden
> >> simplification occurs. The missing information here is what is that
> >> new point of view?
> >
> > Psst! Copernicus still used epicycles. The simplification doesn't
> > come with heliocentricity, but with elliptical orbits.
>
> As usual you miss the whole point and introduce obfuscation. Elliptical
> orbits give greater accuracy. Heliocentricity is the philosophy that
> simplifies the odd erratic apparent motion of the planets in the
> firmament.

You made the false claim that heliocentricity eliminated epicycles. I was just correcting that error. You don't care about factual correctness in arguments? You're happy to support your argument with errors? What about lies and fabrications?

In any case, you're the one arguing on the side of the complex "geocentric" model. We _know_ what the simple system is:
4-laplacian(4-potential) = 4-current,
which says that we have one law, the same in all inertial coordinate frames, and there is one field, the same in all inertial coordinate frames. Your "two E fields" insistence is like claiming that, rather than epicycles being a useful mathematical tool, that the planets are really attached to circular wheels.

> > That a geocentric model and a heliocentric model, both with circular
> > orbits and epicycles, predict motion equally well shouldn't be a
> > surprise. Why should our choice of where to put our origin in the
> > model make such a difference?
>
> So to ask the age-old question: Does the sun go around the earth or the
> earth around the sun? :)

Neither. Both go around the centre of mass of the solar system (which isn't even inside the sun).

[Jos Bergervoet]

On 3/6/2015 10:07 PM, Timo Nieminen wrote:
> On Saturday, March 7, 2015 at 3:02:04 AM UTC+10, benj wrote:

..
..

>> So to ask the age-old question: Does the sun go around the earth or the
>> earth around the sun? :)
>
> Neither. Both go around the centre of mass of the solar system (which isn't even inside the sun).

No no! Both go around the centre of our galaxy (which isn't
even inside the black hole in Sgr A*).

--
Jos

[Jos Bergervoet]

On 3/6/2015 8:57 PM, benj wrote:
> On 03/06/2015 01:33 PM, Jos Bergervoet wrote:
>> On 3/6/2015 6:02 PM, benj wrote:
>>> On 03/05/2015 11:49 PM, Timo Nieminen wrote:
> ...

>> If you have a prescription to split it into two distinct
>> parts then no-one can deny it any more. (Splitting it in
>> three cartesian components is similar, in that sense.)
>
> Lessee. One field has the amount of charge as a source.

OK, but is it some type of retarded field of that charge
or simply the instantaneous Coulomb field (like the potential
in the Coulomb gauge?)

> The other field
> is produced by the time rate of change of current. One field is
> irrotational, and conservative. The other field is solenoidal and
> non-conservative.

Perfect! Doesn't that uniquely split any arbitrary vector
field?

> Obviously there is no prescription to split them apart.

I think there is, but there may be several possibilities.
If you somehow fix the gauge you can say that the 2 parts
are the terms coming from grad V and d/dt A, respectively.

And to fix the gauge you could take the potentials obtained
with the Green function exp(ikr)/r acting on the charge and
current. Then it's unique.

--
Jos

[Don Kelly]

Faradays Law (or the Maxwell version that you cited in your first blog
is fine. It is an electrodynamic situation.
In the electrostatic case the line integral is 0. Conservative situation.
In the electrodynamic situation the line integral os not 0
-non-conservative.

Yes, your model is wrong in terms of continuity of potential. However it
still satisfies Faradays Law and conservation if energy.as well it
provides a good approximation (Ri =-d(phi)/dt )because it is known that
the total loop resistance is R (approximately) and the total voltage
induced is -d(phi)/dt

which doesn't specify the distribution of the induced voltage. I think
that you are trying to apply electrostatic principles to an
electrodynamic situation.
Note that not only Faradays Law but also conservation of energy are
valid- as is the fact that the current is the same in both sections of
the loop. I would like comments from others re this continuity problem
(one source implies that it doesn't apply where induced voltages are
present)

. *-- Don Kelly
remove the 'cross' to reply directly*

[benj]

Not even that. To know "what goes around what" one would have to know
where the exact center of the universe is. It COULD be located right in
the center of the earth in which case EVERYTHING goes around man! Or
perhaps in the sun which reverses things. Or according to modern physics
the center is "everywhere" which makes both correct. Or you could go
with my BBB theory which places the center of the universe (a
hyperdimensional sphere) outside our 3D space altogether.

--
___ ___ ___ ___
/\ \ /\ \ /\__\ /\ \
/::\ \ /::\ \ /::| | \:\ \
/:/\:\ \ /:/\:\ \ /:|:| | ___ /::\__\
/::\~\:\__\ /::\~\:\ \ /:/|:| |__ /\ /:/\/__/
/:/\:\ \:|__| /:/\:\ \:\__\ /:/ |:| /\__\ \:\/:/ /
\:\~\:\/:/ / \:\~\:\ \/__/ \/__|:|/:/ / \::/ /
\:\ \::/ / \:\ \:\__\ |:/:/ / \/__/
\:\/:/ / \:\ \/__/ |::/ /

\_:/__/ \:\__\ /:/ /
\/__/ \/__/

[benj]

On 03/06/2015 05:19 PM, Jos Bergervoet wrote:
> On 3/6/2015 8:57 PM, benj wrote:
>> On 03/06/2015 01:33 PM, Jos Bergervoet wrote:
>>> On 3/6/2015 6:02 PM, benj wrote:
>>>> On 03/05/2015 11:49 PM, Timo Nieminen wrote:
>> ...
>>> If you have a prescription to split it into two distinct
>>> parts then no-one can deny it any more. (Splitting it in
>>> three cartesian components is similar, in that sense.)
>>
>> Lessee. One field has the amount of charge as a source.
>
> OK, but is it some type of retarded field of that charge
> or simply the instantaneous Coulomb field (like the potential
> in the Coulomb gauge?)

This is really the problem, isn't it? Are fields instantaneous? Is the
potential in a Coulomb gauge instantaneous? You'll argue that it is,
because that's what the math says. But (dare I say it again?) in actual
fact, causality is still a natural law in the Earth. (whew!) It seems
the instantaneous potential somehow cancels in real life and fields and
even potentials are still propagating at the speed of light as their
usual retarded selves. Choice of gauge allows descriptive models to
change but actual fields are not allowed to change from reality. So what
does "instantaneous Coulomb potential" really mean? It only means that
in my mathematical fantasy I have created something that is an
instantaneous field but still allows reality to remain as it was. No
matter what the gauge, the fields must remain retarded and unchanged.

>> The other field
>> is produced by the time rate of change of current. One field is
>> irrotational, and conservative. The other field is solenoidal and
>> non-conservative.
>
> Perfect! Doesn't that uniquely split any arbitrary vector
> field?
>
>> Obviously there is no prescription to split them apart.
>
> I think there is, but there may be several possibilities.
> If you somehow fix the gauge you can say that the 2 parts
> are the terms coming from grad V and d/dt A, respectively.

Perhaps the gauge can be somehow "fixed" but to try to use grad V and
dA/dt as sources is a problem. Because (influenced by Jefimenko) those
potential functions are also retarded and thus not the "cause" of the
fields. The true "cause" remains charge and moving charge. From that
source E, H, A etc. all propagate into space at the speed of light and
for that reason E and A and even worse d/dt A arrive simultaneously
meaning one can't cause the other. It's just another variation on the E
and H can't cause each other thing. So either A is just a mathematical
thing (like instantaneous coulomb potential) and not real at all, or
there is a problem. Jefimenko suggests (as does Feynman) that A is
indeed a real field that can be measured like E and B. J even suggests
an "A meter". Current thinking seems to be going this way as opposed to
the old idea that A was simply a mathematical trick.

So can one somehow do a gauge transformation on A such that all this is
somehow "fixed"? Perhaps, but it's not for me to do.

> And to fix the gauge you could take the potentials obtained
> with the Green function exp(ikr)/r acting on the charge and
> current. Then it's unique.

Of course exp(ikr)/r is the exact retardation delaying function found in
the Jefimenko electrokinetic Field equation as well as in standard
approaches using E = -iwA say when looking at fields from an aperture
current source (diffraction) so that is an excellent choice for a place
to start looking!

--
___ ___ ___ ___
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/::\~\:\__\ /::\~\:\ \ /:/|:| |__ /\ /:/\/__/
/:/\:\ \:|__| /:/\:\ \:\__\ /:/ |:| /\__\ \:\/:/ /
\:\~\:\/:/ / \:\~\:\ \/__/ \/__|:|/:/ / \::/ /
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\:\/:/ / \:\ \/__/ |::/ /

\_:/__/ \:\__\ /:/ /
\/__/ \/__/

[benj]

On 03/06/2015 11:42 PM, Don Kelly wrote:

> which doesn't specify the distribution of the induced voltage. I think
> that you are trying to apply electrostatic principles to an
> electrodynamic situation.

> Note that not only Faradays Law but also conservation of energy are
> valid- as is the fact that the current is the same in both sections of
> the loop. I would like comments from others re this continuity problem
> (one source implies that it doesn't apply where induced voltages are
> present)

Indeed the problem is trying to apply electrostatic rules to an
electrodynamic situation.

Electrostatic field: Integral around any closed path is zero and does
not depend on path.
Field is distorted by other charges.

Electrodynamic field: Integral around a closed path is path dependent
and usually not zero.
Field is NOT distorted by other charges.

So consider a loop with a fine slit in it. If a dynamic E field is
induced in the region it penetrates the conductor inducing free
electrons to move until the electrostatic field from themselves stops
them. This builds up positive and negative charges on both sides of the
gap. And that charge distribution creates an ELECTROSTATIC field in the
region. So there are TWO fields at work here an electrostatic one and a
dynamic one.

Now let us integrate around the loop. Let's divide the fields into the
two types and that means two integrals. The electrostatic field is easy.
We know that ANY closed path will integrate to zero. Hence the value
from one side of the gap back to that same point is zero.

Now take the dynamic field. Assume the gap is narrow so the integral
across it can be taken as zero as dl is small. Then the integral around
the loop is what? Well, by the DYNAMIC field rule, it is E dot dl where
we are going around the loop and it's equal to the Faraday value. It is
NOT zero. Indeed that field is not distorted by the charges present.
Therefore a voltage exists across the gap according to the induced field
even though the integral of E(dynamic) across that gap is zero.

If we compare to the battery situation I mentioned before, One can
derive Kirchoff's second law. Because the non-conservative potential
created by the induction in the loop is exactly equal to the potential
drop across a resistor inserted in the gap. The total then is that all
voltages add to zero which for an electrostatic E field must be true for
any path. This is why batteries are modelled as non-conservative fields
in circuit theory so that the sign is reversed.

[Jos Bergervoet]

On 3/7/2015 8:08 AM, benj wrote:
> On 03/06/2015 05:19 PM, Jos Bergervoet wrote:
>> On 3/6/2015 8:57 PM, benj wrote:
>>> On 03/06/2015 01:33 PM, Jos Bergervoet wrote:
>>>> On 3/6/2015 6:02 PM, benj wrote:
>>>>> On 03/05/2015 11:49 PM, Timo Nieminen wrote:
>>> ...

>> And to fix the gauge you could take the potentials obtained
>> with the Green function exp(ikr)/r acting on the charge and
>> current. Then it's unique.
>
> Of course exp(ikr)/r is the exact retardation delaying function found in
> the Jefimenko electrokinetic Field equation as well as in standard
> approaches using E = -iwA say when looking at fields from an aperture
> current source (diffraction) so that is an excellent choice for a place
> to start looking!

We already saw three options now:
1) E1 = retarded Coulomb field, E2 = E-E1
2) E1 = instantaneaous Coulomb field, E2 = E-E1
3) Just use requirement: rot E1 = 0, div E2 =0

But with choices 1) and 2) it is not clear whether
you really get div E2=0 (And you seem to expect that
rot E1=0, div E2=0 will be properties of E1 and E2.)

With choice 3) these properties are by definition,
but is there always a solution? And is it unique?
(Like: can you write every positive N as N1*N2, with
N1 = product of odd primes, N2 = product of even primes.)

These are nice homework problems for you, benj!
Maybe you should start with the N1*N2 uniqueness
problem, it will stimulate your fantasy.

--
Jos

[larry harson]

On Thursday, March 5, 2015 at 9:51:52 PM UTC, PengKuan Em wrote:
> Le jeudi 5 mars 2015 19:35:47 UTC+1, larry harson a écrit :
> > You can place two voltmeters in parallel across A-B such that the measurement loop areas are zero. The one adjacent to the wire will measure 0v, the one adjacent to A-B will measure a finite voltage across A-B.
> >
> > The "paradox" is resolved by noting the circuit is non-conservative and therefore voltmeters in parallel can measure different voltages! I'm pretty sure I posted a link to a Walter Lewin video emphasizing this point, to the shock of some MIT physics/engineering professors so Prof Lewin claims.
> >
> > Regards,
> >
> > Larry.
>
> I haven't seen the Walter Lewin video, but I have saved a document of Robert Romer from a discussion :
> http://www.uvm.edu/~dahammon/Demonstrations/5ElectricityAndMagnetism/5bElectricFieldsAndPotential/5b10ElectricField/Faraday'sTeaser/Romer/Romer.pdf

> My paradox is not about measurement, but that the potential at one point has 2 values. This is not possible.

You can define the potential to have a number of different values at a point depending upon the path you take to get there. In practice, this isn't very useful compared to the potential being path independent. You believing it's not possible and it being possible are two different things.

>Like if you climb a mountain to the sommet. Through one track the sommet is 1000 m, but through another track the sommet is 200 m. The sommet has one altitude and only one. If you get two values, this means you have done a error somewhere.

Yes, because the gravitational field is conservative as for a static electric field. Yet you want to cling on to forming this comparison with a non-conservative electric field, concluding that classical electromagnetism is wrong!

In a betatron, electrons circulate once around a loop in a vacuum ending up with a different energy they started with:

http://en.wikipedia.org/wiki/Betatron

On the next loop they double their energy and so one. There is no paradox here, and neither is there one in a loop of wire, unless you're fixated with this idea that the potential at a point can only be one value.

Regards,

Larry.

[larry harson]

With hindsight, I've formed a bad comparison since the the two E fields can't be distinguished from one another from the definition of an E field as the force on a stationary charge. Whereas E and B are defined differently from one another via the Lorentz force law.

Regards,

Larry

[benj]

:-)

Yeah, just what I need: Stimulated Fantasy!

[Timo Nieminen]

Consider the Lorentz force law written in 4-tensor/vector form:
(4-force) = (4x4 field tensor).(4-current)

We can distinguish, say, the x-component of E, Ex, from Ey and Ez. We can make devices to measure these vector components. But we don't usually say that we have three physically different fields, Ex, Ey, and Ez. Just three components of a vector-valued field.

Since the representation of the 4x4 field tensor in components (i.e., E and B fields) depends on our choice of coordinate systems, there's a strong argument that E and B are no more physically distinct that Ex and Ey. (The 4x4 field tensor, OTOH, is invariant, i.e., the same in all (inertial) coordinate systems.) This is the punchline of Einstein's 1905 SR paper - restoration of the symmetry for a relatively moving conductor and magnet.

Practically, we still use E and B (it would be a PITA to try to do everything with the 4x4 field tensor). But, practically, we also use Ex alone if we can choose a coordinate system such that Ey=Ez=0, or at least such that Ey and Ez don't affect our calculation/measurement.

The change in perspective going from E and B being completely different things (after all, we have different operational definition) to E and B being components of one field is the big contribution of Einstein 1905 + Minkowski 1907.

[PengKuan Em]

Le samedi 7 mars 2015 05:42:31 UTC+1, Don Kelly a écrit :
>
> Faradays Law (or the Maxwell version that you cited in your first blog
> is fine. It is an electrodynamic situation.
> In the electrostatic case the line integral is 0. Conservative situation.
> In the electrodynamic situation the line integral os not 0
> -non-conservative.

So, you say that in induced coil the situation is non-conservative. In this case, there is not a definite voltage. Right? Or we cannot know the voltage. But we know it.

>
> Yes, your model is wrong in terms of continuity of potential.

Please, it is not my model, but Faraday's law and electrostatic. Can you point out where I did wrong in applying them? Can you compute the voltage with a non-conservative field?

> However it still satisfies Faradays Law and conservation if energy.as well

Faradays Law and conservation of energy are correct. I never said they are wrong. I have just pointed out the inconsistency of the classical theory. Where the error is is still to be discussed.

> it provides a good approximation (Ri =-d(phi)/dt )because it is known that
> the total loop resistance is R (approximately) and the total voltage
> induced is -d(phi)/dt

If it is an approximation, the theory is not exact. Your first time to admit this. So it can be improved by correcting its inconsistency.

>
> which doesn't specify the distribution of the induced voltage. I think
> that you are trying to apply electrostatic principles to an
> electrodynamic situation.

> . *-- Don Kelly

If you distinct electrostatic and electrodynamic here, you are admitting that in induced coil, classical EM theory does not apply. Electrostatic gives discontinuity, electrodynamic does not give voltage. But there is a voltage measured. So the classical theory is not complete.

PK

[PengKuan Em]

Le samedi 7 mars 2015 17:38:41 UTC+1, larry harson a écrit :

> You can define the potential to have a number of different values at a point depending upon the path you take to get there. In practice, this isn't very useful compared to the potential being path independent. You believing it's not possible and it being possible are two different things.

>

> On the next loop they double their energy and so one. There is no paradox here, and neither is there one in a loop of wire, unless you're fixated with this idea that the potential at a point can only be one value.
>
> Regards,
>
> Larry.

Correction

So, You admit that at one point there can be 2 voltages at the same time and the potential at the point B has two values is physically possible. Interesting.

But, why the current in the resistor R is not 0 but I? It shows only one voltage, doesn't it?

PK

[Jos Bergervoet]

On 3/7/2015 11:12 PM, Timo Nieminen wrote:
> On Sunday, March 8, 2015 at 2:44:26 AM UTC+10, larry harson wrote:

...
..

>> With hindsight, I've formed a bad comparison since the the two

> E fields can't be distinguished from one another from the definition
> of an E field as the force on a stationary charge. Whereas E and B
> are defined differently from one another via the Lorentz force law.
>
> Consider the Lorentz force law written in 4-tensor/vector form:
> (4-force) = (4x4 field tensor).(4-current)
>
> We can distinguish, say, the x-component of E, Ex, from Ey and Ez.
> We can make devices to measure these vector components. But we don't
> usually say that we have three physically different fields, Ex, Ey,
> and Ez. Just three components of a vector-valued field.
>
> Since the representation of the 4x4 field tensor in components (i.e.,
> E and B fields) depends on our choice of coordinate systems, there's
> a strong argument that E and B are no more physically distinct that
> Ex and Ey.

That is too simple. The E and B components differ in the same
way as the time and space components of the position vector.
In relativity, the difference between time-like and space-like
quantities is much more fundamental than the difference between
x- and y-direction.

For our fields, the Lorentz invariant E^2-B^2 will tell us
whether a field is electric-like or magnetic-like. (If E
dominates, then it is impossible by any Lorentz transform
to make B the dominant field.)

--
Jos

[larry harson]

On Saturday, March 7, 2015 at 10:55:30 PM UTC, PengKuan Em wrote:
> Le samedi 7 mars 2015 17:38:41 UTC+1, larry harson a écrit :
>
> > You can define the potential to have a number of different values at a point depending upon the path you take to get there. In practice, this isn't very useful compared to the potential being path independent. You believing it's not possible and it being possible are two different things.
>
> >
> > On the next loop they double their energy and so one. There is no paradox here, and neither is there one in a loop of wire, unless you're fixated with this idea that the potential at a point can only be one value.
> >
> > Regards,
> >
> > Larry.
>
> Correction
>
> So, You admit that at one point there can be 2 voltages at the same time and the potential at the point B has two values is physically possible. Interesting.

Yes, you define what potential difference is mathematically, and calculate it physically via a thought experiment. Whether it can be done in practice is another matter.

> But, why the current in the resistor R is not 0 but I? It shows only one voltage, doesn't it?

The resistance represents one path the total E is integrated over.

You have two different resistances in parallel carrying the same current, and having different values of E.dl integrated through each, giving different voltages across each. This isn't a problem mathematically, nor working out a thought experiment that enables us to calculate this.


Regards,

Larry

[PengKuan Em]

Le dimanche 8 mars 2015 19:57:55 UTC+1, larry harson a écrit :
> > So, You admit that at one point there can be 2 voltages at the same time and the potential at the point B has two values is physically possible. Interesting.
>
> Yes, you define what potential difference is mathematically, and calculate it physically via a thought experiment. Whether it can be done in practice is another matter.
>
> > But, why the current in the resistor R is not 0 but I? It shows only one voltage, doesn't it?
>
> The resistance represents one path the total E is integrated over.
>
> You have two different resistances in parallel carrying the same current, and having different values of E.dl integrated through each, giving different voltages across each. This isn't a problem mathematically, nor working out a thought experiment that enables us to calculate this.
>
>
> Regards,
>
> Larry

If you think that one point in space can have multiple potentials, all is OK.

PK

[Don Kelly]

On 07/03/2015 2:24 PM, PengKuan Em wrote:

> Le samedi 7 mars 2015 17:38:41 UTC+1, larry harson a écrit :
>> You can define the potential to have a number of different values at a point depending upon the path you take to get there.
>>

>> On the next loop they double their energy and so one. There is no paradox here, and neither is there one in a loop of wire, unless you're fixated with this idea that the potential at a point can only be one value.
>>

>> Larry.
> So, You admit that at one point there can be voltage at the same time and the potential at the point B has two values is not physically possible. Interesting.
>
> But, why the current in the resistor R is not 0 but I? It must show the two values at once?
>
> PK
>
Potential is measured at a point with respect to another point.

However the crux of your problem is that you have assumed that the wire
resistance is negligible so E in the wire is negligible ( your extension
of wire resistance to 0 implies E= 0 but does not imply I=0 in the wire.)
As per your first equation, you are assuming the total loop integral of
E is concentrated across the resistor-that is between A and B across the
resistor.. That is, you are effectively assuming that both the induced
voltageand the Ri drop are between A and B.
When you integrate from B to A along the wire, you get a different value
than the RI drop in the resistor. but have ignored the induced voltage
in the resistor
Your conclusion arose from comparing the Ri drop in the wire B to A to
the Ri drop B to A in the resistor but ignoring the induced voltage in
the resistor.

It is a convenient lie to use a conservative model (integral of E around
loop =0) by replacing the induced V by an ideal voltage source (
fictitious ) somewhere in the loop-generally where measurements cannot
or will not be taken. In your case the ideal source can be placed in the
wire so that what you end up with is a lumped source or battery
connected through a wire of negligible resistance. as below

O------------wire-------------OB
| + | +
V R Ri
| | -
O-------------------------------oA
<---- I

However, it is also possible to put V and Ri between A and B to get this
B O---------------------------O
| + |
V |
| |
R | N.B. Ri drop (in the
direction of I ) is of opposite sign to V
| | so sum of voltages =0
A O--------------------------- O
<---- I
You have made the second model but have ignored V which is equal and
opposite to RI
Don't fret-
Lewin had a lot of people at MIT scratching their heads when he
presented the same so-called 'paradox' before you came up with it.

He had a 4 node path ABCD with no resistors in AB and CD but a battery
and a resistor in DA and a resistor in BC and voltmeters across AD and
BC. He found the current and the meter voltages (which summed to 0
He repeated this without the battery but with an equivalent induced loop
voltage to get the same current. The sum of the measured voltages did
not add up.

[PengKuan Em]

Le dimanche 8 mars 2015 23:51:17 UTC+1, Don Kelly a écrit :

> >> Larry.
> > So, You admit that at one point there can be voltage at the same time and the potential at the point B has two values is not physically possible. Interesting.
> >
> > But, why the current in the resistor R is not 0 but I? It must show the two values at once?
> >
> > PK
> >
> Potential is measured at a point with respect to another point.
>
> However the crux of your problem is that you have assumed that the wire
> resistance is negligible so E in the wire is negligible ( your extension
> of wire resistance to 0 implies E= 0 but does not imply I=0 in the wire.)
> As per your first equation, you are assuming the total loop integral of
> E is concentrated across the resistor-that is between A and B across the
> resistor.. That is, you are effectively assuming that both the induced
> voltageand the Ri drop are between A and B.

I did not have this assumption. I have found RI in the resistor, but the induced voltage is missing, which is the discontinuity.

> Don Kelly

What you are suggesting here is to fill the potential gap between B-wire and
B-resistor (see figure 2 in my article) with an ideal battery that provides the jump of voltage. You do not solve the discontinuity problem this way because the distance between B-wire and B-resistor is zero.

PK

[larry harson]

Yes, it boils down to defining a measurement as a value all observers can agree upon, and then defining how the measurement should be carried out to guarantee this.

But I still can't help feeling a little uneasy about this: Two identical observers can calculate different values for the magnitude of the same electric field using different unit lengths. Their different measurements can still be reproduced using their particular units: does it make their measurements an invalid description of reality just because they give different results to one another?

I would say no, since their units can be exchanged to verify they get the same result.

On the other hand, the overwhelming evidence is in favour of us living in a world using a Minkowski rather than a Euclidean metric, assuming gravity can be ignored. Therefore modeling in this 4-dimensional world using 4-vectors will lead to an elegant simplification of classical electrodynamics and that's what motivates physicists.

Regards,

Larry Harson

[Don Kelly]

On 08/03/2015 5:04 PM, PengKuan Em wrote:
> Le dimanche 8 mars 2015 23:51:17 UTC+1, Don Kelly a écrit :
>
>>>> Larry.
>>> So, You admit that at one point there can be voltage at the same time and the potential at the point B has two values is not physically possible. Interesting.
>>>
>>> But, why the current in the resistor R is not 0 but I? It must show the two values at once?
>>>
>>> PK
>>>
>> Potential is measured at a point with respect to another point.
>>
>> However the crux of your problem is that you have assumed that the wire
>> resistance is negligible so E in the wire is negligible ( your extension
>> of wire resistance to 0 implies E= 0 but does not imply I=0 in the wire.)
>> As per your first equation, you are assuming the total loop integral of
>> E is concentrated across the resistor-that is between A and B across the
>> resistor.. That is, you are effectively assuming that both the induced
>> voltageand the Ri drop are between A and B.
> I did not have this assumption. I have found RI in the resistor, but the induced voltage is missing, which is the discontinuity.

Exactly -That is what I have said. You have a loop for which you have a
net IR that is not 0 and with no driving force In that case the only
solution is that the current is 0- which is not the case..
Simply look at the Faraday equation . A voltage is induced in the loop
as a whole. It's not that the induced voltage is missing but that you
ignored it. That is apparent in your Fig 2. Note that you equated the
RI voltage with the induced voltage as if the induced voltage was
completely between A and B in the resistor.

You are trying to make this electrostatic when it isn't. and continuity
of potential is actually invalid..

Actually it does bercause these models replace the non-conservative
model by a conservative circuit model
The continuity of potential, as far as I can see is related to the
conservative case where d(phi)/dt is 0. and can be violated when non-zero.

[PengKuan Em]

Le mardi 10 mars 2015 04:48:39 UTC+1, Don Kelly a écrit :
> Exactly -That is what I have said. You have a loop for which you have a
> net IR that is not 0 and with no driving force In that case the only
> solution is that the current is 0- which is not the case..
> Simply look at the Faraday equation . A voltage is induced in the loop
> as a whole. It's not that the induced voltage is missing but that you
> ignored it. That is apparent in your Fig 2. Note that you equated the
> RI voltage with the induced voltage as if the induced voltage was
> completely between A and B in the resistor.
>
> You are trying to make this electrostatic when it isn't. and continuity
> of potential is actually invalid..

> Actually it does bercause these models replace the non-conservative
> model by a conservative circuit model
> The continuity of potential, as far as I can see is related to the
> conservative case where d(phi)/dt is 0. and can be violated when non-zero.
>
> --
> Don Kelly

"A voltage is induced in the loop as a whole. It's not that the induced voltage is missing but that you ignored it. "

So, you think the energy state of electrons in the wire cannot be known, like in a black hole where no physical laws are invalid. At least you do not know and think useless to try to know. And you explain below why it is impossible to know:

"You are trying to make this electrostatic when it isn't. and continuity
of potential is actually invalid.."

"The continuity of potential, as far as I can see is related to the conservative case where d(phi)/dt is 0. and can be violated when non-zero. "

What you are saying here is in fact in induction case all electrostatic laws fail. Thus, the voltage in the resistor is not potential, but something else. That is, electromagnetic theory is incorrect.

PK

[Don Kelly]

NO NO NO; electromagnetic theory is fine- The electrostatic case is a
specific subset of the general electromagnetic theory. where "there is
no motion of charge" (Artley "Fields ancd Configurations").
I am saying that the electrostatic case is conservative and the case
with induced voltage is non-conservative
but that it is possible to get a circuit model that satisfies
In particular we get
Electrostatic
Nabla cross E=0
integral of E around closed loop=0
no current
and E=_nabla(V)

Electrodynamic
Nabla cross E=-di(B)/(di)t (using di for partial derivative symbol
integral of E dl around closed loop =-d(phi)/dt
Current exists and is continuous (integral over surface of J.nds=0

If the magnetic field is only within the loop then a voltmeter which is
outside the loop will only measure the RI drop across its terminals as
there would be no induced voltage in the measurement loop. I believe
that a reference you gave showed this in a rather lengthy and roundabout
way.

[PengKuan Em]

Your are saying that when there is E, we have to choose artificially which law to use. Electrostatic; use potential; Electrodynamic, not use potential, even if static E exists, we have to exclude it in the computation. For an electron in the wire, it has much work to do in choosing which law is the good one.

This is not a fine theory, but a craft with arbitrary choose.

PK

[Don Kelly]

On 10/03/2015 8:31 PM, PengKuan Em wrote:
> Your are saying that when there is E, we have to choose artificially which law to use. Electrostatic; use potential; Electrodynamic, not use potential, even if static E exists, we have to exclude it in the computation. For an electron in the wire, it has much work to do in choosing which law is the good one.
>
> This is not a fine theory, but a craft with arbitrary choose.
>
> PK
>
>

There is no arbitrary choice.
If you stick to the full EM theory, then you cover both the "static" and
"dynamic " situations.
In the static situation there are terms that are 0 in the static case so
this is simply a subset of the general or dynamic case.
In the case of the open circuit coil enclosing a varying field, there is
no steady state current but there is a shift of the charges to the ends
of the wire- leading to an electrostatic field opposing the induced
field which is dynamic, even though DC, as it is due to a changing flux
in the loop.
Now close the gap with a resistor. There can be no buildup of static
charge at the ends of the coil because there is a conducttve path
between them- a current flows so charge is moving in both the resistor
and coil.


Your "paradox" is discussed in many places on line- look up "non
conservative circuits". There are several university references and
discussions (even some nonsense from the "overunity" site kooks).

--

[PengKuan Em]

Here you insist on separating static and dynamic case so that you conclude that in induced coil where the two fields exist at the same time, the Em theory is not valid.

"Now close the gap with a resistor. There can be no buildup of static
charge at the ends of the coil because there is a conducttve path
between them- a current flows so charge is moving in both the resistor
and coil. "

This means that the measured voltage does not come from potential. So, this is a case that EM is unable to describe and it is an incomplete theory. A good theory must be able to represent all cases.

PK

[Don Kelly]

On 11/03/2015 5:46 PM, PengKuan Em wrote:
> Here you insist on separating static and dynamic case so that you conclude that in induced coil where the two fields exist at the same time, the Em theory is not valid.
>
> "Now close the gap with a resistor. There can be no buildup of static
> charge at the ends of the coil because there is a conducttve path
> between them- a current flows so charge is moving in both the resistor
> and coil. "
>
> This means that the measured voltage does not come from potential. So, this is a case that EM is unable to describe and it is an incomplete theory. A good theory must be able to represent all cases.
>
> PK

The general case includes, among all cases, including the particular
"static" case but the "static" case doesn't extend to the general case.
Essentially the class called "fruit" includes the class called "apples"
but the reverse isn't true
The continuity of potential is not valid in the general case.
If one sets (d(phi)/dt to zero then what you get is the integral of
E.dl =0 around the loop. Essentially this is KVL or "if you go around
the block and end up where you started- you haven't gone anywhere"
In addition, in the static case, current is 0 so RI =0. Your starting
premise includes both a changing magnetic field and current- hence the
static subset is not applicable (your Faraday equation is dynamic).

EM can describe this case- The electrostatic subset cannot.

Le mercredi 11 mars 2015 23:47:25 UTC+1, Don Kelly a écrit :
>> There is no arbitrary choice.
>> If you stick to the full EM theory, then you cover both the "static" and
>> "dynamic " situations.
>> In the static situation there are terms that are 0 in the static case so
>> this is simply a subset of the general or dynamic case.
>> In the case of the open circuit coil enclosing a varying field, there is
>> no steady state current but there is a shift of the charges to the ends
>> of the wire- leading to an electrostatic field opposing the induced
>> field which is dynamic, even though DC, as it is due to a changing flux
>> in the loop.
>> Now close the gap with a resistor. There can be no buildup of static
>> charge at the ends of the coil because there is a conducttve path
>> between them- a current flows so charge is moving in both the resistor
>> and coil.
>>
>>
>> Your "paradox" is discussed in many places on line- look up "non
>> conservative circuits". There are several university references and
>> discussions (even some nonsense from the "overunity" site kooks).
>>
>> --
>> Don Kelly

[PengKuan Em]

"The continuity of potential is not valid in the general case."

This is the second time you assert this. I think you have never gone through discontinuous potential before and it is a thing you have just invented on purpose for this paradox.

If fact discontinuity of potential implies that E field is infinity at this point.

dV = E*dl, dl=0, E = dV/0 = infinity

If you had carefully thought about discontinuity, you would not assert this. You may argue that it is not a real discontinuity but a sharp increase of potential. Then we are back to continuous potential.

PK

Le vendredi 13 mars 2015 04:22:36 UTC+1, Don Kelly a écrit :
> The general case includes, among all cases, including the particular
> "static" case but the "static" case doesn't extend to the general case.
> Essentially the class called "fruit" includes the class called "apples"
> but the reverse isn't true
> The continuity of potential is not valid in the general case.
> If one sets (d(phi)/dt to zero then what you get is the integral of
> E.dl =0 around the loop. Essentially this is KVL or "if you go around
> the block and end up where you started- you haven't gone anywhere"
> In addition, in the static case, current is 0 so RI =0. Your starting
> premise includes both a changing magnetic field and current- hence the
> static subset is not applicable (your Faraday equation is dynamic).
>
> EM can describe this case- The electrostatic subset cannot.
>

[Don Kelly]

On 13/03/2015 8:24 AM, PengKuan Em wrote:
> "The continuity of potential is not valid in the general case."
>
> This is the second time you assert this. I think you have never gone through discontinuous potential before and it is a thing you have just invented on purpose for this paradox.
>
> If fact discontinuity of potential implies that E field is infinity at this point.
>
> dV = E*dl, dl=0, E = dV/0 = infinity
>
> If you had carefully thought about discontinuity, you would not assert this. You may argue that it is not a real discontinuity but a sharp increase of potential. Then we are back to continuous potential.

It gets a bit more complex than that as the vector potential is also
involved. Then you get a correct continuity equation.
However typically the only continuity equation that is of use in this
circuit is the one for current.
You could say then that integral of E.dl =sum or Ri drops in the loop =0
(Kirchoff)
However that is not true as d(phi)dt is not 0
You can solve for the current, losses, etc in the circuit quite nicely
without calling on continuity.

By the way note that you have a dV1=E1*dl1 and dV2= E2*dl2 at the
junction between materials. you will have 2 different E values and as
dl1 and dl2 approach 0 dV1 and Dv2 also approach 0 so you have an
indeterminate condition.but the E1 and E2 are different.

So, the continuity of scalar potential is not necessary at all to
solving this and other such problems but continuity of current is essential



--

[Timo Nieminen]

On Saturday, March 14, 2015 at 1:24:09 AM UTC+10, PengKuan Em wrote:
> "The continuity of potential is not valid in the general case."
>
> This is the second time you assert this. I think you have never gone through discontinuous potential before and it is a thing you have just invented on purpose for this paradox.

No, "continuity of potential is not valid in the general case" is entirely correct. Perhaps it will help if I re-state it as "potential is not valid in the general case". It isn't continuity that's in question, but whether "potential" is meaningful that's in question.

If the force field isn't conservative, then a scalar potential doesn't give you the force field. Which means that the energy of something moving in that force field isn't given by a potential.

For a non-conservative EM field, (a) the E-field isn't conservative, and (b) force isn't given by E alone (since the magnetic field is non-zero), you can't use:
> dV = E*dl
meaningfully.

[Jos Bergervoet]

On 3/14/2015 3:30 AM, Timo Nieminen wrote:
> On Saturday, March 14, 2015 at 1:24:09 AM UTC+10, PengKuan Em wrote:
>> "The continuity of potential is not valid in the general case."
>>
>> This is the second time you assert this. I think you have never gone through discontinuous potential before and it is a thing you have just invented on purpose for this paradox.
>
> No, "continuity of potential is not valid in the general case" is
> entirely correct. Perhaps it will help if I re-state it as "potential
> is not valid in the general case".

No that is not re-stating it, the two claims are not equivalent
at all!

> It isn't continuity that's in question, but whether "potential" is
> meaningful that's in question.

Both questions are interesting (and they are different). I do not
see why we should confuse the readers by mixing them up. Answers:

1) Potentials need *not* be continuous. If they are not, you can
always find a gauge transform to make them continuous, and if they
are, you can always make them discontinuous.

2) Potentials are meaningfull only up to a gauge transformation.

> If the force field isn't conservative, then a scalar potential
> doesn't give you the force field.

That's a 3rd question: is a *scalar* potential alone sufficient
(as opposed to a full 4-potential). Answer, as you already wrote:

3) A scalar potential alone (or a 4-potential where the 3-vector
components are 0) is only sufficient if rot(E) = 0 and B = 0 (you
have to specify both these requirements).

These three answers completely settle the dispute, so I really
think it is time for PK to come with the next paradox! (Lest his
audience may become impatient..)

--
Jos

[PengKuan Em]

Le samedi 14 mars 2015 03:26:17 UTC+1, Don Kelly a écrit :
> It gets a bit more complex than that as the vector potential is also
> involved. Then you get a correct continuity equation.
> However typically the only continuity equation that is of use in this
> circuit is the one for current.
> You could say then that integral of E.dl =sum or Ri drops in the loop =0
> (Kirchoff)
> However that is not true as d(phi)dt is not 0
> You can solve for the current, losses, etc in the circuit quite nicely
> without calling on continuity.
>
> By the way note that you have a dV1=E1*dl1 and dV2= E2*dl2 at the
> junction between materials. you will have 2 different E values and as
> dl1 and dl2 approach 0 dV1 and Dv2 also approach 0 so you have an
> indeterminate condition.but the E1 and E2 are different.
>
> So, the continuity of scalar potential is not necessary at all to
> solving this and other such problems but continuity of current is essential
> --
> Don Kelly

You speak about things with no relation with the potential's discontinuity. You are unable to argue because the EM theory does not provide any element. Potential's real name is potential energy, it cannot be discarded as nonsensical as you do.

In order to make things clearer, I have also written in terms of energy in my article. The path taken by an electron to complete a cycle in the coil is:
1) Departure from point B-resistor with energy UB
2) Arrival at the end of the resistor point A with 0 energy
3) Travel inside the wire with no force on it, thus no energy is collected
4) Arrival at the entrance of the resistor at point B-wire with 0 energy
5) Problem: how can it jump into the resistor? In other word, it must get the quantity of energy UB within 0 distance to enter the resistor. But how? What is the force that pushes it?

To get the energy UB within 0 distance is the physical sense of infinity E field. You may argue as before: "You ignore the induction". Please describe the way inductance pushes the electron with infinite electric force. You will not be able to do so because this is impossible.

Maybe this will help you. In fact, inside the resistor electrons do not feel any force either:
Force = Electrostatic force - frictional force = 0

So, how do electrons lose energy?

PK

[PengKuan Em]

Potential is in fact potential energy and it must have a sense. Please read my answer to Don Kelly
https://groups.google.com/d/msg/sci.physics.electromag/LYcI-7Ine0c/h-KF1GcD5z4J

[Don Kelly]

Your answer is nonsense. I'll take Jos and Timo' statements as well as
the known EM theory as a basis- the reasons and explanations are
there-stop and think beyond your conservative model which is the cause
of your so called paradox (actually a misunderstanding of the problem).

As Jos says, time to move on.

[larry harson]

I say it's possible to define potential however we want, and then to decide if it's "meaningful" or "useful".

It looks to me that PeunKuan has defined potential difference as the work done between two points, which is different to the conventional view that potential is a scalar function that can be differentiated to get a vector funtion of postion. He then ends up confused over his definition in a non-conservative field having multiple values depending upon the path taken, and believing a paradox exists because potential difference should depend only on the end points.

Regards,

Larry Harson

[PengKuan Em]

Le dimanche 15 mars 2015 20:04:46 UTC+1, larry harson a écrit :
> I say it's possible to define potential however we want, and then to decide if it's "meaningful" or "useful".
>
> It looks to me that PeunKuan has defined potential difference as the work done between two points, which is different to the conventional view that potential is a scalar function that can be differentiated to get a vector funtion of postion. He then ends up confused over his definition in a non-conservative field having multiple values depending upon the path taken, and believing a paradox exists because potential difference should depend only on the end points.
>
> Regards,
>
> Larry Harson

It is a problem of how EM explains energy transfer in induction. How do you explain the unbalance of energy in the coil?

PK

[larry harson]

What is there to explain?

This is how nature is: the energy gained/lost by a charge taken between A and B depends upon the path taken generally.

Maybe you're concerned about energy conservation of the whole system?

Regards,

LH

[PengKuan Em]

When moving in the wire from A to B, the force on the electrons is zero. So they do not get energy.

PK

[larry harson]

Yes, that's correct. Also moving from A to B through the resistor the energy gained/lost will be some value different to zero. So?

LH

[Timo Nieminen]

On Monday, March 16, 2015 at 5:04:46 AM UTC+10, larry harson wrote:
> On Saturday, March 14, 2015 at 2:30:38 AM UTC, Timo Nieminen wrote:
> > On Saturday, March 14, 2015 at 1:24:09 AM UTC+10, PengKuan Em wrote:
> > > "The continuity of potential is not valid in the general case."
> > >
> > > This is the second time you assert this. I think you have never gone through discontinuous potential before and it is a thing you have just invented on purpose for this paradox.
> >
> > No, "continuity of potential is not valid in the general case" is entirely correct. Perhaps it will help if I re-state it as "potential is not valid in the general case". It isn't continuity that's in question, but whether "potential" is meaningful that's in question.
> >
> > If the force field isn't conservative, then a scalar potential doesn't give you the force field. Which means that the energy of something moving in that force field isn't given by a potential.
> >
> > For a non-conservative EM field, (a) the E-field isn't conservative, and (b) force isn't given by E alone (since the magnetic field is non-zero), you can't use:
> > > dV = E*dl
> > meaningfully.
>
> I say it's possible to define potential however we want, and then to decide if it's "meaningful" or "useful".

Given that we already have accepted definitions, I don't think we have that much freedom.

We have two possible definitions we can use:

(a) The general scalar potential as used in electrodynamics. This isn't the potential energy per unit charge. Doesn't tell us anything useful unless we also know the vector potential.

(b) The electrostatic potential, which is the potential energy per unit charge in an electrostatic field.

If we make up new meanings, then we won't be speaking the same language as those who have written about these things before.

> It looks to me that PeunKuan has defined potential difference as the work done between two points,

Which is all well and good, if we're talking about the work done on a unit charge, when that work done is independent of the path taken. This is the same as the difference between electrostatic potential (b) between the two points.

> which is different to the conventional view that potential is a scalar function that can be differentiated to get a vector funtion of postion.

When it works, it's the same. But as you say, he uses this when it doesn't work:

> He then ends up confused over his definition in a non-conservative field having multiple values depending upon the path taken, and believing a paradox exists because potential difference should depend only on the end points.

Yes. But can you communicate this to him?

[PengKuan Em]

I have given the example of zero force in the resistor just to show that mixing forces of two different type into one is the reason that puts EM theory in trouble.

When you consider electron pushed through the resistor by electrostatic force, electric energy is lost. When you consider electron dragged by frictional force heat is created. In this process, the lost electric energy equals the created heat energy. This is how electric energy is transformed into heat energy.

In the induction process, induced force pushes electrons through the wire against an electrostatic field and lost magnetic energy. In the same time, electrons are dragged by electrostatic force and gain in electrostatic energy. The quantity of lost magnetic energy equals the electrostatic one. This is how magnetic energy is transformed into electrostatic energy.

Why is there electrostatic energy? Because electrons accumulate near B and their distribution creates the electrostatic field and the potential field. By going from A to B through the wire against E field electrons gain in potential. Then, they enter the resistor with the same energy or potential. Seen in this way, there is no discontinuity of potential nor unbalance of energy.

The paradox was originated by the view that magnetic induction is electric force. This way, there is only one force on electrons and there cannot be energy transformation. Energy transforms from one form into another because there are two types of force in equilibrium, like E force and friction force in the resistor.

I have conceived this paradox in order to show the absurdity of the one-force-view and to change this view.

PK

[Don Kelly]

From past experience- it is , unfotunately, not likely.


--

[larry harson]

On page (2) in your paper you state:

"Hence the paradox: two different laws give two different values to the same voltage"

Do you agree now that this paradox doesn't exist for you anymore, after the discussion here?

If yes, maybe you could now modify your paper so we can make further progress?

Regards,

LH

[PengKuan Em]

Physically this paradox never existed for me because I know how this thing goes. However, this paradox still exists in the classical EM theory.

What is a paradox? It is the contradiction of two "correct" conclusions. For example the twin paradox in relativity:
1) The twin A stays on earth and expects the traveling twin B returns back younger.
2) The twin B sees A travels and expects him to be younger.
The two statements are correct in relativity. But who will be younger when they rejoin? Statement 1 contradicts statement 2. This paradox is within the theory but not in reality because necessarily only one twin will be younger.

Why my paradox exists? Because EM writes:
curl E = - dB / d t, or U = - d phi/ d t

This means that the induced E is electric and in the wire there is only one force. So no transformation of energy is defined in the EM theory. As long as these equations are part of the EM theory, it will contradict potential energy and maintains this paradox alive.

How can we go forward in our discussion? We should discuss what will be the new form of the Faraday's law that fits E potential and energy conservation.


PK

[larry harson]

On Monday, March 16, 2015 at 2:06:40 AM UTC, PengKuan Em wrote:
> Le lundi 16 mars 2015 02:19:53 UTC+1, larry harson a écrit :
> > On Monday, March 16, 2015 at 12:31:40 AM UTC, PengKuan Em wrote:
> >
> > On page (2) in your paper you state:
> >
> > "Hence the paradox: two different laws give two different values to the same voltage"
> >
> > Do you agree now that this paradox doesn't exist for you anymore, after the discussion here?
> >
> > If yes, maybe you could now modify your paper so we can make further progress?
> >
> > Regards,
> >
> > LH
>
> Physically this paradox never existed for me because I know how this thing goes. However, this paradox still exists in the classical EM theory.

This paradox doesn't exist for anyone here either, because everyone knows that the potential difference between two points as defined by you, is path dependent in classical EM in your example. It's an example of a non-conservative circuit:

http://en.wikipedia.org/wiki/Conservative_vector_field#Path_independence

> What is a paradox? It is the contradiction of two "correct" conclusions. For example the twin paradox in relativity:
> 1) The twin A stays on earth and expects the traveling twin B returns back younger.
> 2) The twin B sees A travels and expects him to be younger.
> The two statements are correct in relativity. But who will be younger when they rejoin? Statement 1 contradicts statement 2. This paradox is within the theory but not in reality because necessarily only one twin will be younger.
>
> Why my paradox exists? Because EM writes:
> curl E = - dB / d t, or U = - d phi/ d t
>
> This means that the induced E is electric and in the wire there is only one force. So no transformation of energy is defined in the EM theory. As long as these equations are part of the EM theory, it will contradict potential energy and maintains this paradox alive.

You stated in your paper that the paradox is that two different laws give two different values for the *same* voltage. So you're the one who believes the voltage should be the same along two different paths in your example when classical EM doesn't.

{snipped}

LH

[PengKuan Em]

Le mardi 17 mars 2015 20:09:39 UTC+1, larry harson a écrit :
> On Monday, March 16, 2015 at 2:06:40 AM UTC, PengKuan Em wrote:
> >
> > Physically this paradox never existed for me because I know how this thing goes. However, this paradox still exists in the classical EM theory.
>
> This paradox doesn't exist for anyone here either, because everyone knows that the potential difference between two points as defined by you, is path dependent in classical EM in your example. It's an example of a non-conservative circuit:
>
> http://en.wikipedia.org/wiki/Conservative_vector_field#Path_independence
>

It does not exist for you and me, but not for the same reason. You think potential depends on path, not me. Your wiki link is a conservative potential that supports me. Please give me an reference that proves your view. Not vector potential because it is not electric energy.

>
> You stated in your paper that the paradox is that two different laws give two different values for the *same* voltage. So you're the one who believes the voltage should be the same along two different paths in your example when classical EM doesn't.
>
> {snipped}
>
> LH

Give me a reference in classical theory, link or book that states: voltage depends on path.

PK

[Don Kelly]

would wiki do ?
http://en.wikipedia.org/wiki/Electric_potential

"When time-varying magnetic fields are present (which is true whenever
there are time-varying electric fields and vice versa), it is not
possible to describe the electric field simply in terms of a scalar
potential /V/ because the electric field is no longer conservative
<http://en.wikipedia.org/wiki/Conservative_force>:"

(equations follow)

"This can be expressed in a conservative form by E=-nablaV - di (A)
/di(t) [di is the partial derivative operator]

"The electrostatic potential is simply the special case of this
definition where *A* is time-invariant. On the other hand, for
time-varying fields,"

integral from a to b of -E.dl is not Vb-Va

"unlike electrostatics."

This is information found in texts on EM theory.

Your problem arises near the beginning of your "coil and resistor paradox"
for the equations (1) you have not defined previous assumptions.
you have an induced source voltage in the loop Your equations (1 ) lead
to the right current but when you integrate around the loop - you
include only the RI drop in the resistor (sink) and ignore the induced
voltage source. If you wish, you can lump the induced voltage at some
point in the circuit and then you simply have a source connected to a
resistor through zero resistance wires.

In fact this is exactly what you have done in your circuit example in
your "induced connected net problem" which is the only correct part of
that blog. (a bit clumsy - it can be reduced to a single equation using
current sources).

The paradox is one of your own making.
The physics as observed leads to the mathematical model
You are trying to fit the physics to your model and in trying to do so
are running into your so- called "Paradoxes"

--

[PengKuan Em]

Le mercredi 18 mars 2015 06:14:46 UTC+1, Don Kelly a écrit :
> On 17/03/2015 1:16 PM, PengKuan Em wrote:
> would wiki do ?
> http://en.wikipedia.org/wiki/Electric_potential

> --
> Don Kelly
>

Wikipedia is not a reliable reference, but it represents what you think to be correct.

You said potential was not continuous for non conservative field. So, for you, there is a potential field. But this text do not propose a potential field. What it says is:" it is not possible to describe the electric field simply in terms of a scalar potential ", i.e.

integral from a to b of -E.dl is not Vb-Va

In your link, V is only the electrostatic potential. And the E is not the gradient of a potential. So, Your definition of a non continuous potential is wrong.

IF integral from a to b of -E.dl is not Vb-Va
How do you find the voltage?
integral from a to b of -E.dl =d phi/dt?

pk