# Are Maxwell's equations causal?

85 views

### FrediFizzx

Jan 8, 2013, 8:04:24 PM1/8/13
to
anyways]

"Larry Harson" <larry...@softhome.net> wrote in message
> On Jan 7, 5:41 am, "FrediFizzx" <fredifi...@hotmail.com> wrote:
>> "Larry Harson" <larryhar...@softhome.net> wrote in message
>> > On Jan 6, 6:07 am, "FrediFizzx" <fredifi...@hotmail.com> wrote:
>> >> "Larry Harson" <larryhar...@softhome.net> wrote in message
>>
>> > [snipped]
>>
>> >> > You can convert Maxwell's equations to infinitesimal difference
>> >> > equations which are functional expressions: values at time t - dt
>> >> > are
>> >> > mapped to values at time t.
>>
>> >> Keyword you use here; "convert". Not Maxwell after conversion. I
>> >> haven't
>> >> even checked if what you are doing in fact works correctly. Have you?
>> >> Show
>> >> us an example using some real values.
>>
>> > All I'm doing is rearranging a Maxwell equation such as Faraday's law
>> > with
>>
>> > dB/dt = (B(t+dt) - B(t))/dt for infinitesimal dt.
>>
>> And what would that have to do with "cause"? The relationship of E and B
>> in
>> Faraday's law will just be evolving in time.
>
> As Jos keeps pointing out, it's important people define what exactly
> they mean by cause and effect.

The definition of *cause* as related to Maxwell's equations is a no brainer.
Don't even have to think about it very much. I'm not playing any silly
"game" for this as someone keeps suggesting.

> Some time ago, me, Benj and Jos agreed upon a physical measurement as
> being *a* cause for another physical measurement, an effect, if it's a
> necessary condition for this effect to take place. In general, other
> causes are also necessary, so phrases like "the cause" are ambiguous.

Sorry, there is nothing ambiguous at all as far as *cause* relates to
is no one stopping you but you are just fooling yourselves.

> So for B to take a certain value at time t+dt requires B and Curl E to
> take certain values at time t. i.e physical quantities at time t are
> causes for physical quantities at time t+dt.

Nope. The relationship between E and B is just evolving in time the way you
are doing it. There is NO *cause* there.

>>Here is the causal expression
>> for Faraday's law in case you might be interested,
>>
>> curl E = -dB/dt = - (mu0/4pi) \$ (curl (1/r)[dJ/dt])dv'
>>
>> \$ is integral over all space, square brackets are retardation symbol, r
>> is the distance between the field point x, y, z and the source point x',
>> y', z'(volume element dv').

Now, the above expression is a definition of *cause* as relates to Faraday's
law that you can sink your teeth into. :-)

Best,

Fred

### p.ki...@ic.ac.uk

Jan 9, 2013, 5:28:17 AM1/9/13
to
FrediFizzx <fredi...@hotmail.com> wrote:
> > As Jos keeps pointing out, it's important people define what exactly
> > they mean by cause and effect.

> The definition of *cause* as related to Maxwell's equations is a
> no brainer. Don't even have to think about it very much.

is so very clear to you. However, in order that I may get to understand
your line of reasoning better, can you explain it to me, starting at the
very beginning?

--
---------------------------------+---------------------------------
Dr. Paul Kinsler
Blackett Laboratory (Photonics) (ph) +44-20-759-47734 (fax) 47714
Imperial College London, Dr.Paul...@physics.org
SW7 2AZ, United Kingdom. http://www.qols.ph.ic.ac.uk/~kinsle/

### Larry Harson

Jan 9, 2013, 7:52:06 AM1/9/13
to
On Jan 9, 1:04Â am, "FrediFizzx" <fredifi...@hotmail.com> wrote:
> anyways]
>
> Fred- Hide quoted text -
>
> - Show quoted text -

You believe Jefimenko has it right when he says that Maxwell's
equations aren't causal, so let's take a look at a fairly recent paper
he published on the subject:

Eur. J. Phys. 25 (2004) 287â€“296
Presenting electromagnetic theory in accordance with the principle of
causality
Oleg D Jefimenko

---start quote---
In general, then, according to the principle of causality, an equation
between two or
more quantities simultaneous in time but separated in space cannot
represent a causal relation between these quantities. In fact, even an
equation between quantities simultaneous in time and not separated in
space cannot represent a causal relation between these quantities
because, according to this principle, the cause must precede its
effect. Therefore the only kind of equations representing causal
relations between physical quantities, other than equations
representing cause and effect by definition, must be equations
involving â€˜retardedâ€™ (previoustime) quantities.
---end quote---

I agree with this. Any equation with d/dt terms involves infinitesimal
'retarded' quantities making the equations infinitesimally causal.
Therefore those Maxwell's equations with d/dt terms are
infinitesimally causal.

because he missed it.

Regards, Larry.

### benj

Jan 9, 2013, 12:43:05 PM1/9/13
to
On Wed, 09 Jan 2013 04:52:06 -0800, Larry Harson wrote:

> I agree with this. Any equation with d/dt terms involves infinitesimal
> 'retarded' quantities making the equations infinitesimally causal.
> Therefore those Maxwell's equations with d/dt terms are infinitesimally
> causal.
>
> he missed it.

Most of us agree with it also. And yes, Jefimenko sort of swept the whole
question of two simultaneous events NOT separated by space under the rug.
And it obviously is a borderline case, but as you note, also of some
interest. Although somewhere I recall that he said without proof that
even not separated by space they still weren't causal. I have no idea
what he had in mind on that one.

So is velocity "caused" by position? Obviously if I give you a single
point in time on some trajectory you cannot give me the velocity. And
that is because as you note, velocity is determined by looking that the
rate of change of position with with time and then approaching a limit
that gets closer and closer to the point in question. Which as you say
COULD make Maxwell's equations "infinitesimally causal". But as I've
pointed out, you can choose whether you take the limit from the past or
from the future. One is causal, and the other is not. Now one can take
the usual E&M "solution" of simply throwing out all the wrong answers
that come up as "non-physical" and ignoring that there might be problems
with your model. But I suggest that what we are doing is looking at the
model.

So does velocity "cause" position? Or does position "cause" velocity.
And does velocity "cause" acceleration? Of is it the other way round?

Jefimenko does talk about "causality by definition". He says: "An
exception to this rule [past determines present action] are equations
constituting causal relations by definition; for example, if force is
defined as the cause of acceleration, then the equation F=ma, where F is
the force and a is the acceleration, is a causal equation by definition."

To me this is where he sweeps the dirt under the rug. It's basically word
games to say we define force as the cause of acceleration. Although F=ma
has quantities simultaneous in time, that really isn't what happens. You
apply a force to some block and we know what happens. The fields of the
atoms compress slightly and then the block starts to accelerate! So it
makes some sense define force as the "cause" of acceleration. But
mathematically it just isn't so.

On the other hand the interrelationship of position, velocity and
acceleration is the derivative of calculus. And I've pointed out that
this can come from the past or the future. So basically it's a borderline
case that is somewhat indeterminate. My premise on this whole "gap" in
Jefimenko's arguments is that position, velocity and acceleration are
really all the SAME thing. By that I mean that they are different aspects
of a body's motion. They don't "cause each other" they simply are
displaying qualities of that body and it's progress. It's sort of like
if you describe the motion of a red block and how it moves and you say
that force causes red! Word games would argue that if you were shoving it
through a paint booth trajectory MIGHT "cause" red, but that is just
games. See what I mean?

### Poutnik

Jan 9, 2013, 2:49:14 PM1/9/13
to

Larry Harson posted Wed, 9 Jan 2013 04:52:06 -0800 (PST)

> ---start quote---
> In general, then, according to the principle of causality, an equation
> between two or
> more quantities simultaneous in time but separated in space cannot
> represent a causal relation between these quantities. In fact, even an
> equation between quantities simultaneous in time and not separated in
> space cannot represent a causal relation between these quantities
> because, according to this principle, the cause must precede its
> effect. Therefore the only kind of equations representing causal
> relations between physical quantities, other than equations
> representing cause and effect by definition, must be equations
> involving ?retarded? (previoustime) quantities.
> ---end quote---

Do I understand it well from the quote that
in the 2nd Newton law a force is not cause of acceleration ? :-)

> I agree with this. Any equation with d/dt terms involves infinitesimal
> 'retarded' quantities making the equations infinitesimally causal.
> Therefore those Maxwell's equations with d/dt terms are
> infinitesimally causal.
>

--
Poutnik

### Larry Harson

Jan 9, 2013, 3:32:41 PM1/9/13
to
Just before that section, he says there are equations, such as
Newton's law, where the quantities are causal by definition and so
there's no need to make the retarded time explicit.

Regards, Larry.

### Poutnik

Jan 9, 2013, 3:59:05 PM1/9/13
to

Larry Harson posted Wed, 9 Jan 2013 12:32:41 -0800 (PST)

> Just before that section, he says there are equations, such as
> Newton's law, where the quantities are causal by definition and so
> there's no need to make the retarded time explicit.
>

And is it true just because he says it ?

Are there no causal relations
until a man comes and defines it ?

Causality is not when then, but if then,
rather quality than quantity given by equation.

--
Poutnik

### FrediFizzx

Jan 9, 2013, 4:33:19 PM1/9/13
to
"Poutnik" <pou...@privacy.invalid> wrote in message
news:MPG.2b57f88...@news.eternal-september.org...
Causality in equations is more about common sense than anything else. As
far as Newton's second law, you have to look at what is causing the force
also.

Best,

Fred

### Poutnik

Jan 9, 2013, 4:39:46 PM1/9/13
to

FrediFizzx posted Wed, 9 Jan 2013 13:33:19 -0800

> > And is it true just because he says it ?
> >
> > Are there no causal relations
> > until a man comes and defines it ?
> >
> > Causality is not when then, but if then,
> > rather quality than quantity given by equation.
>
> Causality in equations is more about common sense than anything else. As
> far as Newton's second law, you have to look at what is causing the force
> also.
>
Sure. But I was not looking for a primary cause.
It is well known there are causal chains.

--
Poutnik

### Larry Harson

Jan 9, 2013, 4:42:40 PM1/9/13
to
On Jan 9, 5:43Â pm, benj <b...@iwaynet.net> wrote:
> On Wed, 09 Jan 2013 04:52:06 -0800, Larry Harson wrote:
> > I agree with this. Any equation with d/dt terms involves infinitesimal
> > 'retarded' quantities making the equations infinitesimally causal.
> > Therefore those Maxwell's equations with d/dt terms are infinitesimally
> > causal.
>
> > he missed it.
>
> Most of us agree with it also. And yes, Jefimenko sort of swept the whole
> question of two simultaneous events NOT separated by space under the rug.

Here's a link to the paper:

No, in the quote I gave he says that simultaneous events at the same
position can't be causal.

> And it obviously is a borderline case, but as you note, also of some
> interest.

The interest lies in him not seeming to notice d/dt having a unique
status when talking about causality in equations.

>Although somewhere I recall that he said without proof that
> even not separated by space they still weren't causal. I have no idea
> what he had in mind on that one.

He was saying that a cause can only precede an effect even at the same
location, and therefore can't be simultaneous with one another.

> So is velocity "caused" by position?

Let's start with a quick recap of a definition of cause and effect
that me, you and Jos agreed upon, and I've expanded upon a little:

1. An event is a physical measurement

2. If event1 is a *necessary* condition for event 2 to take place,
then event1 and event2 are said to be causally connected, with event1
called *a* cause and event2 *an* effect.

3. Time is defined to be that physical process which assigns a unique
real number to each cycle of a self repeating sequence of causally
connected events.

4. If t1, t2, t3 are three times where t1<t2<t3, and t2 is the current
value for t
then t1 is called the past, t2 the present and t3 the future.

So back to velocity where v(t) = dx/dt = (x(t+dt) - x(t))/dt

It's then obvious that x(t+dt) is caused by x(t) and v(t), which is
equivalent to saying velocity causes change in position.

Therefore, no, velocity is not caused by position using the above
arguments.

>Obviously if I give you a single
> point in time on some trajectory you cannot give me the velocity.
>And
> that is because as you note, velocity is determined by looking that the
> rate of change of position with with time and then approaching a limit
> that gets closer and closer to the point in question. Which as you say
> COULD make Maxwell's equations "infinitesimally causal".

OK.

>But as I've
> pointed out, you can choose whether you take the limit from the past or
> from the future. One is causal, and the other is not.

In the real world as used by physicists, they both approach the same
limit. Velocity is a continuous function. The future position can be
predicted from the present velocity and present position alone.

>Now one can take
> the usual E&M "solution" of simply throwing out all the wrong answers
> that come up as "non-physical" and ignoring that there might be problems
> with your model. But I suggest that what we are doing is looking at the
> model.
>
> So does velocity "cause" position? Â Or does position "cause" velocity.
> And does velocity "cause" acceleration? Of is it the other way round?

> Jefimenko does talk about "causality by definition". He says: "An
> exception to this rule [past determines present action] are equations
> constituting causal relations by definition; for example, if force is
> defined as the cause of acceleration, then the equation F=ma, where F is
> the force and a is the acceleration, is a causal equation by definition."

I agree with this.

> To me this is where he sweeps the dirt under the rug. It's basically word
> games to say we define force as the cause of acceleration. Although F=ma
> has quantities simultaneous in time, that really isn't what happens. You
> apply a force to some block and we know what happens. The fields of the
> atoms compress slightly and then the block starts to accelerate! So it
> makes some sense define force as the "cause" of acceleration. But
> mathematically it just isn't so.

I think it's just easier not to bother making Newton's laws
unnecessarily complicated by bringing in irrelevant time delays
between the application of a force and the effect of acceleration.

> On the other hand the interrelationship of position, velocity and
> acceleration is the derivative of calculus. And I've pointed out that
> this can come from the past or the future. So basically it's a borderline
> case that is somewhat indeterminate. My premise on this whole "gap" in
> Jefimenko's arguments is that position, velocity and acceleration are
> really all the SAME thing. By that I mean that they are different aspects
> of a body's motion. They don't "cause each other" they simply are
> displaying qualities of that body and it's progress. Â It's sort of like
> if you describe the motion of a red block and how it moves and you say
> that force causes red! Word games would argue that if you were shoving it
> through a paint booth trajectory MIGHT "cause" red, but that is just
> games. See what I mean?

It's essential to define the terms we use, otherwise we end up arm
waving when arguing our point across.

Regards, Larry.

### FrediFizzx

Jan 9, 2013, 7:11:11 PM1/9/13
to
"Larry Harson" <larry...@softhome.net> wrote in message

> You believe Jefimenko has it right when he says that Maxwell's
> equations aren't causal, so let's take a look at a fairly recent paper
> he published on the subject:
>
> Eur. J. Phys. 25 (2004) 287Ă¯Â¿Â½296
> Presenting electromagnetic theory in accordance with the principle of
> causality
> Oleg D Jefimenko
>
> ---start quote---
> In general, then, according to the principle of causality, an equation
> between two or
> more quantities simultaneous in time but separated in space cannot
> represent a causal relation between these quantities. In fact, even an
> equation between quantities simultaneous in time and not separated in
> space cannot represent a causal relation between these quantities
> because, according to this principle, the cause must precede its
> effect. Therefore the only kind of equations representing causal
> relations between physical quantities, other than equations
> representing cause and effect by definition, must be equations
> involving Ă¯Â¿Â½retardedĂ¯Â¿Â½ (previoustime) quantities.
> ---end quote---
>
> I agree with this. Any equation with d/dt terms involves infinitesimal
> 'retarded' quantities making the equations infinitesimally causal.
> Therefore those Maxwell's equations with d/dt terms are
> infinitesimally causal.

I keep telling you that it is not Maxwell any more when you do that.

> because he missed it.

I suppose Jefimenko figured most people interested in this would have the
common sense to realize it is not Maxwell any more. :-)

Let me put it another way; Maxwell's set of equations are about
instantaneous *correlations* between the various quantities involved. It is
impossible for them to be causal.

Best,

Fred

### FrediFizzx

Jan 9, 2013, 7:17:02 PM1/9/13
to
"Poutnik" <pou...@privacy.invalid> wrote in message
news:MPG.2b58020...@news.eternal-september.org...
Think about trying to solve a practical problem. I accelerate a particular
object of mass 1Kg, 1meter/sec^2 by pushing on it. I believe you will
always have to specify the cause of the force and acceleration.

Best,

Fred

### Poutnik

Jan 9, 2013, 7:38:40 PM1/9/13
to

FrediFizzx posted Wed, 9 Jan 2013 16:17:02 -0800
Cause of acceleration is applied force.
Cause of applied force is my pushing.
Cause of pushing is stretching my muscles.
Cause of stretching is action of special protein in muscles,
sliding a muscle layers each other.
Cause of this action is neural impulse.
Cause of this impulse is my decision.
Cause of this decision is to provide Usenet example.
Cause of this example.......
......
......

--
Poutnik

### FrediFizzx

Jan 9, 2013, 8:28:00 PM1/9/13
to
"Poutnik" <pou...@privacy.invalid> wrote in message
news:MPG.2b582bf...@news.eternal-september.org...
Yes, and you know that by common sense so once an immediate cause is
specified, then you will most likely know the rest of the chain.

Best,

Fred

### FrediFizzx

Jan 9, 2013, 10:00:56 PM1/9/13
to
<p.ki...@ic.ac.uk> wrote in message
news:1btvr9-...@ph-kinsle.qols.ph.ic.ac.uk...
> FrediFizzx <fredi...@hotmail.com> wrote:
>> > As Jos keeps pointing out, it's important people define what exactly
>> > they mean by cause and effect.
>
>> The definition of *cause* as related to Maxwell's equations is a
>> no brainer. Don't even have to think about it very much.
>
> I'm pleased your definition of cause (as related to Maxwell's equations)
> is so very clear to you. However, in order that I may get to understand
> your line of reasoning better, can you explain it to me, starting at the
> very beginning?

Sorry Paul, but I have to reject how you use causality as related to
Maxwell's equations in the paper you did about it. It is just wrong. I
prefer Jefimenko's definition of causality to use when relating to Maxwell's
equations. He said about the *principle of causality*,

"According to this principle, all present phenomena are exclusively
determined by past events. Therefore equations depicting causal relations
between physical phenomena must, in general, be equations where a
present-time quantity (the effect) relates to one or more quantities
(causes) that existed at some previous time." But he does allow an
exception to the rule for equations that are defined as causal to start
with. I suspect that exception needs to be used with utmost care and I am
not sure that I even agree with it.

Best,

Fred

### Poutnik

Jan 10, 2013, 1:47:52 AM1/10/13
to

FrediFizzx posted Wed, 9 Jan 2013 17:28:00 -0800

> >> Think about trying to solve a practical problem. I accelerate a
> >> particular
> >> object of mass 1Kg, 1meter/sec^2 by pushing on it. I believe you will
> >> always have to specify the cause of the force and acceleration.
> >>
> > Cause of acceleration is applied force.
> > Cause of applied force is my pushing.
> > Cause of pushing is stretching my muscles.
> > Cause of stretching is action of special protein in muscles,
> > sliding a muscle layers each other.
> > Cause of this action is neural impulse.
> > Cause of this impulse is my decision.
> > Cause of this decision is to provide Usenet example.
> > Cause of this example.......
>
> Yes, and you know that by common sense so once an immediate cause is
> specified, then you will most likely know the rest of the chain.
>
I think not necesserily.
Sometime would make trouble to write even the second line.

--
Poutnik

### Szczepan Bialek

Jan 10, 2013, 3:48:17 AM1/10/13
to

news:MPG.2b58828...@news.eternal-september.org...
Could you write the simmilar line for EM?

You werote: "Are there no causal relations
until a man comes and defines it"

The math is a very primitive language. You must know what you calculate or
describe.

Maxwell described his equations in English and Figures.
Authors of textbooks are using only the Heaviside's math.
S*

### Poutnik

Jan 10, 2013, 4:26:27 AM1/10/13
to

Szczepan Bialek posted Thu, 10 Jan 2013 09:48:17 +0100
>
> >> > Cause of acceleration is applied force.
> >> > Cause of applied force is my pushing.
> >> > Cause of pushing is stretching my muscles.
> >> > Cause of stretching is action of special protein in muscles,
> >> > sliding a muscle layers each other.
> >> > Cause of this action is neural impulse.
> >> > Cause of this impulse is my decision.
> >> > Cause of this decision is to provide Usenet example.
> >> > Cause of this example.......
> >>
> >> Yes, and you know that by common sense so once an immediate cause is
> >> specified, then you will most likely know the rest of the chain.
> >>
> > I think not necesserily.
> > Sometime would make trouble to write even the second line.
>
> Could you write the simmilar line for EM?

No, I cannot, I am not particularly good in EM.
My physics lectures in univerity were like 25 years ago.

>
> You werote: "Are there no causal relations
> until a man comes and defines it"

It was in form of a quation, I hope.
>
> The math is a very primitive language. You must know what you calculate or
> describe.

In fact, common language is often even more primitive
in some logical aspects.

>
> Maxwell described his equations in English and Figures.
> Authors of textbooks are using only the Heaviside's math.

which have big avantage to be more compact
and harder to misinterpret.

--
Poutnik

### Szczepan Bialek

Jan 10, 2013, 4:47:41 AM1/10/13
to

news:MPG.2b58a7a...@news.eternal-september.org...
>
> Szczepan Bialek posted Thu, 10 Jan 2013 09:48:17 +0100
>>
>> >> > Cause of acceleration is applied force.
>> >> > Cause of applied force is my pushing.
>> >> > Cause of pushing is stretching my muscles.
>> >> > Cause of stretching is action of special protein in muscles,
>> >> > sliding a muscle layers each other.
>> >> > Cause of this action is neural impulse.
>> >> > Cause of this impulse is my decision.
>> >> > Cause of this decision is to provide Usenet example.
>> >> > Cause of this example.......
>> >>
>> >> Yes, and you know that by common sense so once an immediate cause is
>> >> specified, then you will most likely know the rest of the chain.
>> >>
>> > I think not necesserily.
>> > Sometime would make trouble to write even the second line.
>>
>> Could you write the simmilar lines for EM?
>
> No, I cannot, I am not particularly good in EM.
> My physics lectures in univerity were like 25 years ago.

Heaviside's EM is more than 100 years old.
Nobody is able to write the lines.
>
>>
>> You werote: "Are there no causal relations
>> until a man comes and defines it"
>
> It was in form of aquation, I hope.
>>
>> The math is a very primitive language. You must know what you calculate
>> or
>> describe.
>
> In fact, common language is often even more primitive
> in some logical aspects.

At the descriptions it is absolutelly precise.
>
>>
>> Maxwell described his equations in English and Figures.
>> Authors of textbooks are using only the Heaviside's math.
>
> which have big avantage to be more compact
> and harder to misinterpret.

And why after 100 years nobody know if the Heaviside equations are causual
or not?

Heaviside wrote: "Then I set Maxwell aside and followed my own course. And I
progressed much more quickly... It will be understood that I preach the
gospel according to my interpretation of Maxwell.[4]"

Was Heaviside better than Maxwell?
S*

### Poutnik

Jan 10, 2013, 7:12:30 AM1/10/13
to
Szczepan Bialek posted Thu, 10 Jan 2013 10:47:41 +0100
>
> Heaviside's EM is more than 100 years old. Nobody is able to write the
> lines.

I would not say so.

> > In fact, common language is often even more primitive in some logical
> > aspects.
>
> At the descriptions it is absolutelly precise.

It is not and it is reason why some systems of math formalism
> >
> >>
> >> Maxwell described his equations in English and Figures. Authors of
> >> textbooks are using only the Heaviside's math.
> >
> > which have big avantage to be more compact and harder to
> > misinterpret.
>
> And why after 100 years nobody know if the Heaviside equations are
> causual or not?

How do you know that nobody. Very most of those who knows
do not visiti Usenet sci groups anymore.
Fame of Usenet faded for scientiests years ago.
>
> Heaviside wrote: "Then I set Maxwell aside and followed my own course.
> And I progressed much more quickly... It will be understood that I
> preach the gospel according to my interpretation of Maxwell.[4]"
>
> Was Heaviside better than Maxwell? S*

Was different.

--
Poutnik

### p.ki...@ic.ac.uk

Jan 10, 2013, 9:05:09 AM1/10/13
to
Poutnik <pou...@privacy.invalid> wrote:
> Do I understand it well from the quote that
> in the 2nd Newton law a force is not cause of acceleration ? :-)

It may amuse you to hear that I wouldn't say "force causes acceleration".

Neither F=ma or a=F/m have any time derivatives, so I can't identify any
time-dependent change in a quantity that I might want to label "the effect".
Instead, I'd say (e.g.) "Force causes changes in velocity", using dv/dt=F/m.

### p.ki...@ic.ac.uk

Jan 10, 2013, 9:13:53 AM1/10/13
to
FrediFizzx <fredi...@hotmail.com> wrote:
> Causality in equations is more about common sense than anything else. As
> far as Newton's second law, you have to look at what is causing the force
> also.

I think all these discussions on causality in this group demonstrate
quite admirably that what is seen as "common sense" differs to some
degree or other from person to person.

Consqeuently words like "obvious", "common sense", "no-brainer" etc
generally fail to clarify anyone preferred definition of causality.
What we need are rules or tests we can apply to a given model situation
which tell us whether or not it is X-causal (whether X=kinsler, benj, fizzx,
or whoever).

With those rules and tests clearly explained, we can see how they perform
in typical physical models, and then decide on their utility (or possibly,
in what way they are incorrect or unhelpful).

### Larry Harson

Jan 10, 2013, 9:52:13 AM1/10/13
to
On Jan 10, 2:05Â pm, p.kins...@ic.ac.uk wrote:
> Poutnik <pout...@privacy.invalid> wrote:
> > Do I understand it well from the quote that
> > in the 2nd Newton law a force is not cause of acceleration Â ? :-)

> It may amuse you to hear that I wouldn't say "force causes acceleration".
>
> Neither F=ma or a=F/m have any time derivatives, so I can't identify any
> time-dependent change in a quantity that I might want to label "the effect".
> Instead, I'd say (e.g.) "Force causes changes in velocity", using dv/dt=F/m.

Hmm, it didn't occur to me that the acceleration can be thought of
like this in two ways, making Newton's law causal or not. But yes, I
see you're right.

Larry Harson.

> ---------------------------------+---------------------------------
> Dr. Paul Kinsler
> Blackett Laboratory (Photonics) Â  (ph) +44-20-759-47734 (fax) 47714
> Imperial College London, Â  Â  Â  Â  Â Dr.Paul.Kins...@physics.org

### Poutnik

Jan 10, 2013, 10:12:52 AM1/10/13
to

p.ki...@ic.ac.uk posted Thu, 10 Jan 2013 14:05:09 +0000

>
> Poutnik <pou...@privacy.invalid> wrote:
> > Do I understand it well from the quote that
> > in the 2nd Newton law a force is not cause of acceleration ? :-)
>
> It may amuse you to hear that I wouldn't say "force causes acceleration".
>
> Neither F=ma or a=F/m have any time derivatives, so I can't identify any
> time-dependent change in a quantity that I might want to label "the effect".
> Instead, I'd say (e.g.) "Force causes changes in velocity", using dv/dt=F/m.

Implicit parameters are not less real than explicit ones.

What else is acceleration if not time change in velocity ?

vec a = d(vec v)/dt = d2 (vec p)/dt2 ( p = position vector )

--------------------- Side note ---------

As not EN native, I am not sure if EN has different words
for acceleration vector and norm, as have for velocity ones.

E.g. in czech language we use instead of velocity "vector of speed"

### Jos Bergervoet

Jan 10, 2013, 4:16:12 PM1/10/13
to
On 1/10/2013 3:05 PM, p.ki...@ic.ac.uk wrote:
> Poutnik <pou...@privacy.invalid> wrote:
>> Do I understand it well from the quote that
>> in the 2nd Newton law a force is not cause of acceleration ? :-)
>
> It may amuse you to hear that I wouldn't say "force causes acceleration".
>
> Neither F=ma or a=F/m have any time derivatives, so I can't identify any
> time-dependent change in a quantity that I might want to label "the effect".
> Instead, I'd say (e.g.) "Force causes changes in velocity", using dv/dt=F/m.

In GR, where you are allowed to use an arbitrary,
curvilinear coordinate grid, a completely force-
free situation might still have nonzero d^2x/dt^2.

--
Jos

### Larry Harson

Jan 10, 2013, 4:22:07 PM1/10/13
to
On Jan 10, 12:11Â am, "FrediFizzx" <fredifi...@hotmail.com> wrote:
> "Larry Harson" <larryhar...@softhome.net> wrote in message
>
>
>
>
>
>
> > You believe Jefimenko has it right when he says that Maxwell's
> > equations aren't causal, so let's take a look at a fairly recent paper
> > he published on the subject:
>
> > Eur. J. Phys. 25 (2004) 287â€“296
> > Presenting electromagnetic theory in accordance with the principle of
> > causality
> > Oleg D Jefimenko
>
> > ---start quote---
> > In general, then, according to the principle of causality, an equation
> > between two or
> > more quantities simultaneous in time but separated in space cannot
> > represent a causal relation between these quantities. In fact, even an
> > equation between quantities simultaneous in time and not separated in
> > space cannot represent a causal relation between these quantities
> > because, according to this principle, the cause must precede its
> > effect. Therefore the only kind of equations representing causal
> > relations between physical quantities, other than equations
> > representing cause and effect by definition, must be equations
> > involving â€˜retardedâ€™ (previoustime) quantities.
> > ---end quote---
>
> > I agree with this. Any equation with d/dt terms involves infinitesimal
> > 'retarded' quantities making the equations infinitesimally causal.
> > Therefore those Maxwell's equations with d/dt terms are
> > infinitesimally causal.

> I keep telling you that it is not Maxwell any more when you do that.

You're taking a very black and white view of them being Maxwell or
not.

For dt --> oo, they become less Maxwell, dt -->0 they approach
Maxwell. But no matter how small dt is, we're still talking about
terms at different times t and retarded time
t-dt that comes from a Maxwell d/dt term. So they satisfy Jefimenko's
definition of an equation being causal.

You telling me they're not Maxwell isn't going to change my mind, so
how about showing where my arument above is wrong, rather than telling
me it's wrong? :)

> > because he missed it.
>
> I suppose Jefimenko figured most people interested in this would have the
> common sense to realize it is not Maxwell any more. Â :-)

:) I think it's more a case of him not realizing the d/dt term
introduces infinitesimal causality. It's such an important point to
leave out, far less obvious than the points he makes in the rest of
his paper. His writing style is very clear so that even I can
understand it. :)

> Let me put it another way; Maxwell's set of equations are about
> instantaneous *correlations* between the various quantities involved. Â It is
> impossible for them to be causal.

Yes, dB/dt occurs at the same time as Curl E, but the dB/dt term
introduces a B(t - dt) term at time t - dt, no matter how small dt is,
as I keep explaining to you. :)

Regards, Larry.

### Jos Bergervoet

Jan 10, 2013, 4:44:02 PM1/10/13
to
On 1/10/2013 4:00 AM, FrediFizzx wrote:
> <p.ki...@ic.ac.uk> wrote in message
> news:1btvr9-...@ph-kinsle.qols.ph.ic.ac.uk...
>> FrediFizzx <fredi...@hotmail.com> wrote:
>>> > As Jos keeps pointing out, it's important people define what exactly
>>> > they mean by cause and effect.
>>
>>> The definition of *cause* as related to Maxwell's equations is a
>>> no brainer. Don't even have to think about it very much.
>>
>> I'm pleased your definition of cause (as related to Maxwell's equations)
>> is so very clear to you. However, in order that I may get to understand
>> your line of reasoning better, can you explain it to me, starting at the
>> very beginning?
>
> Sorry Paul, but I have to reject how you use causality as related to
> Maxwell's equations in the paper you did about it. It is just wrong.

I'm sorry to hear Paul's use of causality is
wrong. However, in order that readers here may
get to understand your line of reasoning better,
can you explain why it is wrong, starting at the
>> very beginning?

> I prefer Jefimenko's definition of causality
..

Yes Fred. I think the readers know that, Fred. It
is, however, no explanation of why Paul is wrong..

--
Jos

### Jos Bergervoet

Jan 10, 2013, 4:44:36 PM1/10/13
to
On 1/10/2013 1:11 AM, FrediFizzx wrote:
> "Larry Harson" <larry...@softhome.net> wrote in message
...
>> .. Any equation with d/dt terms involves infinitesimal
>> 'retarded' quantities making the equations infinitesimally causal.
>> Therefore those Maxwell's equations with d/dt terms are
>> infinitesimally causal.
>
> I keep telling you that it is not Maxwell any more when you do that.

It seems that all you ever do is "telling" things.
Can you do anything else?

--
Jos

### Jos Bergervoet

Jan 10, 2013, 4:48:49 PM1/10/13
to
On 1/9/2013 10:33 PM, FrediFizzx wrote:
..
...
>>> Just before that section, he says there are equations, such as
>>> Newton's law, where the quantities are causal by definition and so
>>> there's no need to make the retarded time explicit.
>>>
>>
>> And is it true just because he says it ?
>>
>> Are there no causal relations
>> until a man comes and defines it ?
>>
>> Causality is not when then, but if then,
>> rather quality than quantity given by equation.
>
> Causality in equations is more about common sense than anything else.
> As far as Newton's second law, you have to look at what is causing the
> force also.

Or you just ask Fred. Things are causal when he says so.
(Or if Jefimenko says so. Both are allowed. It's obvious!)

--
Jos

### FrediFizzx

Jan 10, 2013, 8:16:27 PM1/10/13
to
"Larry Harson" <larry...@softhome.net> wrote in message
> On Jan 10, 12:11 am, "FrediFizzx" <fredifi...@hotmail.com> wrote:
>> "Larry Harson" <larryhar...@softhome.net> wrote in message
>> > You believe Jefimenko has it right when he says that Maxwell's
>> > equations aren't causal, so let's take a look at a fairly recent paper
>> > he published on the subject:
>>
>> > Eur. J. Phys. 25 (2004) 287Ă¯Â¿Â½296
>> > Presenting electromagnetic theory in accordance with the principle of
>> > causality
>> > Oleg D Jefimenko
>>
>> > ---start quote---
>> > In general, then, according to the principle of causality, an equation
>> > between two or
>> > more quantities simultaneous in time but separated in space cannot
>> > represent a causal relation between these quantities. In fact, even an
>> > equation between quantities simultaneous in time and not separated in
>> > space cannot represent a causal relation between these quantities
>> > because, according to this principle, the cause must precede its
>> > effect. Therefore the only kind of equations representing causal
>> > relations between physical quantities, other than equations
>> > representing cause and effect by definition, must be equations
>> > involving Ă¯Â¿Â½retardedĂ¯Â¿Â½ (previoustime) quantities.
>> > ---end quote---
>>
>> > I agree with this. Any equation with d/dt terms involves infinitesimal
>> > 'retarded' quantities making the equations infinitesimally causal.
>> > Therefore those Maxwell's equations with d/dt terms are
>> > infinitesimally causal.
>
>> I keep telling you that it is not Maxwell any more when you do that.
>
> You're taking a very black and white view of them being Maxwell or
> not.
>
> For dt --> oo, they become less Maxwell, dt -->0 they approach
> Maxwell. But no matter how small dt is, we're still talking about
> terms at different times t and retarded time
> t-dt that comes from a Maxwell d/dt term. So they satisfy Jefimenko's
> definition of an equation being causal.

Nope. See below.

> You telling me they're not Maxwell isn't going to change my mind, so
> how about showing where my arument above is wrong, rather than telling
> me it's wrong? :)

I already have more than once.

[snip]
>> Let me put it another way; Maxwell's set of equations are about
>> instantaneous *correlations* between the various quantities involved. It
>> is
>> impossible for them to be causal.
>
> Yes, dB/dt occurs at the same time as Curl E, but the dB/dt term
> introduces a B(t - dt) term at time t - dt, no matter how small dt is,
> as I keep explaining to you. :)

You still have a problem; there is NO cause. What exactly is the cause?
For the last time, here is the cause,

curl E = -dB/dt = - (mu0/4pi) \$ (curl (1/r)[dJ/dt])dv'

\$ is integral over all space, square brackets are retardation symbol, r
is the distance between the field point x, y, z and the source point x',
y', z'(volume element dv').

Now do your t - dt with that then you have something with a cause. Though
it works without even having to do t - dt.

Best,

Fred

### p.ki...@ic.ac.uk

Jan 11, 2013, 6:18:06 AM1/11/13
to
FrediFizzx <fredi...@hotmail.com> wrote:
> You still have a problem; there is NO cause. What exactly is
> the cause? For the last time, here is the cause,

> curl E = -dB/dt = - (mu0/4pi) \$ (curl (1/r)[dJ/dt])dv'

The whole expression is the "F"-cause? Or just one part? Which part?

--
---------------------------------+---------------------------------
Dr. Paul Kinsler
Blackett Laboratory (Photonics) (ph) +44-20-759-47734 (fax) 47714
Imperial College London, Dr.Paul...@physics.org

### Larry Harson

Jan 11, 2013, 12:05:05 PM1/11/13
to
On 11 Jan, 01:16, "FrediFizzx" <fredifi...@hotmail.com> wrote:
> "Larry Harson" <larryhar...@softhome.net> wrote in message
>
>
>
>
>
>
> > On Jan 10, 12:11 am, "FrediFizzx" <fredifi...@hotmail.com> wrote:
> >> "Larry Harson" <larryhar...@softhome.net> wrote in message
> >> > You believe Jefimenko has it right when he says that Maxwell's
> >> > equations aren't causal, so let's take a look at a fairly recent paper
> >> > he published on the subject:
>
> >> > Eur. J. Phys. 25 (2004) 287â€“296
> >> > Presenting electromagnetic theory in accordance with the principle of
> >> > causality
> >> > Oleg D Jefimenko
>
> >> > ---start quote---
> >> > In general, then, according to the principle of causality, an equation
> >> > between two or
> >> > more quantities simultaneous in time but separated in space cannot
> >> > represent a causal relation between these quantities. In fact, even an
> >> > equation between quantities simultaneous in time and not separated in
> >> > space cannot represent a causal relation between these quantities
> >> > because, according to this principle, the cause must precede its
> >> > effect. Therefore the only kind of equations representing causal
> >> > relations between physical quantities, other than equations
> >> > representing cause and effect by definition, must be equations
> >> > involving â€˜retardedâ€™ (previoustime) quantities.
I'll split my argument into a number of parts so that you can point
out where you diagree with me.

1. The question is asking: "Are Maxwell's equtaions causal?"
The answer depends upon how we define causality.

2. To answer the question, I could use a Larry definition and call it
L-causality, but since it's you who asked it and you're familiar with
Jefimenko's view, I'll use Jefemenko's definition given in his most
recent paper on the subject, top of page 288:

"Therefore the only kind of equations representing causal relations
between physical quantities, other than equations representing cause
and effect by definition, must be equations involving
â€˜retardedâ€™ (previoustime) quantities"

Let's call Jefimenko's definition J-causal.

3. The partial derivative wrt t, @f/@t, of a continuous function
f(x.t) is defined to be either:

dt--> 0, Limit (f(x, t) - f(x,t-dt))/dt

dt--> 0, Limit (f(x, t+dt) - f(x,t))/dt

This just says that for a continuous function, the derivatives
approaching the limit from either side are equal.

4. Maxwell's equations have @E/@t, @B/@t terms and are therefore have
infinitesimally retarded in time dt terms, E(x, t-dt), B(x, t-dt)

5. Therefore from Jefimenko's definition of a causal equation,
Maxwell's equations are infinitesimally J-causal.

6. Using simple algebra, they can be rearranged with the t+dt terms on
the lhs, t terms on the right similar to Jefimenko's equations. E.g

B(t+dt) = B(t) - Curl E(t)dt

Regards, Larry.

### Jack...@hotmail.com

Jan 11, 2013, 12:46:07 PM1/11/13
to
On Thu, 10 Jan 2013 22:44:36 +0100, Jos Bergervoet
<jos.ber...@xs4all.nl> wrote:

>ng the equations infinitesimally causal.
>>> Therefore those Maxwell'
This discussion is going nowhere because additional information is
required. Maxwell's equations are incomplete.
And this business of cause and effect should be replaced by
considerations of source and sink because it is energy that is being
transferred.
It helps to keep in mind that any EMF generated is a circular or
solenoidal field as shown below.

Consider a solenoid with voltage applied to its terminals.
Magnetic momentum is being loaded into the magnetic Field which
increases with time.
Input
The engineering "input" equation for this is
V = N dphi/dt or V/N = dphi/dt. (source equation)
This is the "cause" phase: positive voltage, positive flux rate.
Energy is being inserted from the outside.
The flux can be calculated at any time from simple integration:
phi = 1/N*Int V.dt = volt/turn sec

Output
Once the flux is built up and has a magnetic momentum, then if
you disconnect the battery, a very large positive voltage will appear
at the terminals from the negative flux rate, in a very short time.

The magnetic field attempts to maintain its momentum and reproduces a
positive voltage impulse whose area is equal to that which created it,
being exactly the same product in volts/turn seconds as it was during
charging.

Now the output equation becomes V/N = -dphi/dt. There is a negative
sign because now the collapsing field, formerly the sink, has now
become the "cause".

This last equation for the collapse of the flux is the exact analog of
the equation curl E. =-dB/dt and is easy to derive.
To analyze this we employ Stokes theorem (I reluctantly proceed with
the crude teletype font permitted us).
Loop integral E.dl = surface integral (curl E).dS=
surface integral (-dB/dt)*dS = -dphi/dt
The first-term E.dl is the voltage for one turn in the loop integral,
but in fact is more intelligently described as volts per turn
regardless of the number of turns. The last two terms equate to the
negative flux rate.
It boils down to
V/N = -dphi/dt (sink equation)
which defines the voltage appearing at the terminals of the coil
resulting from the collapse of flux (same volt second product).
So, what is clear is that Stokes theorem is essential to deal with the
curl and also it becomes clear that the electric field is solenoidal,
denominated in volts per turn.
It is puerile to argue cause-and-effect after you understand what is
going on and where you can see that the magnetic field is at one time
a sink for energy and then can instantly act as a source for energy.

The input equation is a little harder to derive, involving H amp
turns/m, which is the driving force, but it is simply a development of
the equation
curl H = J + dD/dt
Again, using Stokes theorem, it's the amp-turns that is a forcing
function in the term
H.dl (amp turns/m)*meter = amp turns.
This is left as an exercise for the student.

Debating Maxwell's equations as merely the processing of capital
letters is an approach we must leave for the parlor physicists.

John Polasek

### FrediFizzx

Jan 13, 2013, 11:48:01 PM1/13/13
to
"Larry Harson" <larry...@softhome.net> wrote in message
> On 11 Jan, 01:16, "FrediFizzx" <fredifi...@hotmail.com> wrote:

[snip]
>> You still have a problem; there is NO cause. What exactly is the cause?
>> For the last time, here is the cause,
>>
>> curl E = -dB/dt = - (mu0/4pi) \$ (curl (1/r)[dJ/dt])dv'
>>
>> \$ is integral over all space, square brackets are retardation symbol, r
>> is the distance between the field point x, y, z and the source point x',
>> y', z'(volume element dv').
>>
>> Now do your t - dt with that then you have something with a cause.
>> Though
>> it works without even having to do t - dt.
>
> I'll split my argument into a number of parts so that you can point
> out where you diagree with me.
>
> 1. The question is asking: "Are Maxwell's equtaions causal?"
> The answer depends upon how we define causality.

There should be no ambiguity about the definition of causality as related to
Maxwell's equations. Cause then effect is simple enough.

> 2. To answer the question, I could use a Larry definition and call it
> L-causality, but since it's you who asked it and you're familiar with
> Jefimenko's view, I'll use Jefemenko's definition given in his most
> recent paper on the subject, top of page 288:
>
> "Therefore the only kind of equations representing causal relations
> between physical quantities, other than equations representing cause
> and effect by definition, must be equations involving
> â€˜retardedâ€™ (previoustime) quantities"
>
>
> Let's call Jefimenko's definition J-causal.
>
> 3. The partial derivative wrt t, @f/@t, of a continuous function
> f(x.t) is defined to be either:
>
> dt--> 0, Limit (f(x, t) - f(x,t-dt))/dt
>
> dt--> 0, Limit (f(x, t+dt) - f(x,t))/dt
>
> This just says that for a continuous function, the derivatives
> approaching the limit from either side are equal.
>
> 4. Maxwell's equations have @E/@t, @B/@t terms and are therefore have
> infinitesimally retarded in time dt terms, E(x, t-dt), B(x, t-dt)
>
> 5. Therefore from Jefimenko's definition of a causal equation,
> Maxwell's equations are infinitesimally J-causal.
>
> 6. Using simple algebra, they can be rearranged with the t+dt terms on
> the lhs, t terms on the right similar to Jefimenko's equations. E.g
>
> B(t+dt) = B(t) - Curl E(t)dt

You still did not answer my question. What exactly is the cause here? I
showed you what I think the cause is for Faraday's Law. What do you think
the cause is? You are doing the same thing as Paul; mixing up causality
with correlated behavior.

Best,

Fred

### p.ki...@ic.ac.uk

Jan 14, 2013, 5:22:44 AM1/14/13
to
Jos Bergervoet <jos.ber...@xs4all.nl> wrote:
> In GR, where you are allowed to use an arbitrary,
> curvilinear coordinate grid, a completely force-
> free situation might still have nonzero d^2x/dt^2.

I think in that case I would end up interpreting the
situation as "curvature causes a change in velocity".

### p.ki...@ic.ac.uk

Jan 14, 2013, 5:31:03 AM1/14/13
to
FrediFizzx <fredi...@hotmail.com> wrote:
> There should be no ambiguity about the definition of causality
> as related to Maxwell's equations.

Whether there "should" be or not - there is. My choice is not something
I invented, it is an existing definition used both explicitly and
implicitly by many physicists. Your Jefimenko-like choice is also a
reasonable one, and has its own constituency of advocates. Therefore
you need to specify which you mean, otherwise there will be ambiguity.
"Causality", whether you like it or not, means different things to different
people; therefore the work "causality" is ambiguous.

### Jos Bergervoet

Jan 14, 2013, 12:14:00 PM1/14/13
to
On 1/14/2013 11:22 AM, p.ki...@ic.ac.uk wrote:
> Jos Bergervoet <jos.ber...@xs4all.nl> wrote:
>> In GR, where you are allowed to use an arbitrary,
>> curvilinear coordinate grid, a completely force-
>> free situation might still have nonzero d^2x/dt^2.
>
> I think in that case I would end up interpreting the
> situation as "curvature causes a change in velocity".

Situations like that of course were known before GR.
A rotating coordinate system, for instance. People
used centripetal force and Coriolis force to explain
the dv/dt that is observed for a freely moving object
in that case.

But those forces are often termed "fictitious" forces
or "pseudo forces". So even if you see them as a cause,
you might consider "fictitious cause" or "pseudo cause".

--
Jos

### FrediFizzx

Jan 14, 2013, 9:49:46 PM1/14/13
to
<p.ki...@ic.ac.uk> wrote in message
news:7c3ds9-...@ph-kinsle.qols.ph.ic.ac.uk...
> FrediFizzx <fredi...@hotmail.com> wrote:
>> There should be no ambiguity about the definition of causality
>> as related to Maxwell's equations.
>
> Whether there "should" be or not - there is. My choice is not something
> I invented, it is an existing definition used both explicitly and
> implicitly by many physicists. Your Jefimenko-like choice is also a
> reasonable one, and has its own constituency of advocates. Therefore
> you need to specify which you mean, otherwise there will be ambiguity.
> "Causality", whether you like it or not, means different things to
> different
> people; therefore the work "causality" is ambiguous.

As applied to Maxwell's equations it is not. I said what I think causality
is in this case and you snipped it out. "Cause then effect." That is the
pretty standard definition of causality and is really simple.

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

"The assumption that A causes B simply because A correlates with B is a
logical fallacy Ă¯Â¿Â½ it is not a legitimate form of argument."

Best,

Fred

### Poutnik

Jan 15, 2013, 2:15:20 AM1/15/13
to

FrediFizzx posted Mon, 14 Jan 2013 18:49:46 -0800

> "The assumption that A causes B simply because A correlates with B is a
> logical fallacy ? it is not a legitimate form of argument."
>
Unless it is not just simply.

A and B can have a single common cause C,
while B my or may not have even other cause D...

Or B occurs IF AND ONLY IF A occurs,
and no common cause C is known.

--
Poutnik

### Poutnik

Jan 15, 2013, 2:18:48 AM1/15/13
to

Poutnik posted Tue, 15 Jan 2013 08:15:20 +0100
Also, let take classical case of Newton action and reaction law.
Both occurs simultaneously.

According to some opinions in this groups,
action cannot be the cause of reaction.

--
Poutnik

### p.ki...@ic.ac.uk

Jan 15, 2013, 4:55:56 AM1/15/13
to
Jos Bergervoet <jos.ber...@xs4all.nl> wrote:
> > I think in that case I would end up interpreting the
> > situation as "curvature causes a change in velocity".

> Situations like that of course were known before GR.
> A rotating coordinate system, for instance. People
> used centripetal force and Coriolis force to explain
> the dv/dt that is observed for a freely moving object
> in that case.

> But those forces are often termed "fictitious" forces
> or "pseudo forces". So even if you see them as a cause,
> you might consider "fictitious cause" or "pseudo cause".

That seems entirely reasonable to me.

### Larry Harson

Jan 18, 2013, 12:48:04 PM1/18/13
to
On Jan 14, 4:48Â am, "FrediFizzx" <fredifi...@hotmail.com> wrote:
> "Larry Harson" <larryhar...@softhome.net> wrote in message
>
>
> > On 11 Jan, 01:16, "FrediFizzx" <fredifi...@hotmail.com> wrote:
>
> [snip]
>
>
>
>
>
> >> You still have a problem; there is NO cause. Â What exactly is the cause?
> >> For the last time, here is the cause,
>
> >> curl E = -dB/dt = - (mu0/4pi) \$ (curl (1/r)[dJ/dt])dv'
>
> >> \$ is integral over all space, square brackets are retardation symbol, r
> >> is the distance between the field point x, y, z and the source point x',
> >> y', z'(volume element dv').
>
> >> Now do your t - dt with that then you have something with a cause.
> >> Though
> >> it works without even having to do t - dt.

I left this thread for a few days while you were discussing Paul's
paper with him.

> > I'll split my argument into a number of parts so that you can point
> > out where you diagree with me.
>
> > 1. The question is asking: "Are Maxwell's equtaions causal?"
> > The answer depends upon how we define causality.
>
> There should be no ambiguity about the definition of causality as related to
> Maxwell's equations. Â Cause then effect is simple enough.

So you say, but I've shown to you something at time t_dt then effect
at time t. Yet you don't see this as cause and then effect, so it
isn't that simple.
Slight typo, the above should be:

B(t) = B(t-dt) - Curl E(t-dt)dt

The J-causes are the terms at time t-dt: B(t-dt) and Curl E(t-dt).
Cause then effect B(t)

You are doing the same thing as Paul; mixing up causality
> with correlated behavior.

I understand the difference between the two. Just because Jefimenko's
equations can be expressed in terms of the retarded quantities charge
and current density doesn't make them causes. They could be
simultaneous with hidden causes. But we're discussing Jefimenko
causality here.

Regards, Larry.

### Salmon Egg

Jan 18, 2013, 5:19:50 PM1/18/13
to
In article
Larry Harson <larry...@softhome.net> wrote:

> I understand the difference between the two. Just because Jefimenko's
> equations can be expressed in terms of the retarded quantities charge
> and current density doesn't make them causes. They could be
> simultaneous with hidden causes. But we're discussing Jefimenko
> causality here.

Using retarded potential does not help. You get the same result using

--

Sam

Conservatives are against Darwinism but for natural selection.
Liberals are for Darwinism but totally against any selection.

### FrediFizzx

Jan 19, 2013, 2:48:50 PM1/19/13
to
"Larry Harson" <larry...@softhome.net> wrote in message
> On Jan 14, 4:48 am, "FrediFizzx" <fredifi...@hotmail.com> wrote:
>> "Larry Harson" <larryhar...@softhome.net> wrote in message
>> > On 11 Jan, 01:16, "FrediFizzx" <fredifi...@hotmail.com> wrote:
>>
>> >> You still have a problem; there is NO cause. What exactly is the
>> >> cause?
>> >> For the last time, here is the cause,
>>
>> >> curl E = -dB/dt = - (mu0/4pi) \$ (curl (1/r)[dJ/dt])dv'
>>
>> >> \$ is integral over all space, square brackets are retardation symbol,
>> >> r
>> >> is the distance between the field point x, y, z and the source point
>> >> x',
>> >> y', z'(volume element dv').
>>
>> >> Now do your t - dt with that then you have something with a cause.
>> >> Though
>> >> it works without even having to do t - dt.
>
> I left this thread for a few days while you were discussing Paul's
> paper with him.

Ok.

>> > I'll split my argument into a number of parts so that you can point
>> > out where you diagree with me.
>>
>> > 1. The question is asking: "Are Maxwell's equtaions causal?"
>> > The answer depends upon how we define causality.
>>
>> There should be no ambiguity about the definition of causality as related
>> to
>> Maxwell's equations. Cause then effect is simple enough.
>
> So you say, but I've shown to you something at time t_dt then effect
> at time t. Yet you don't see this as cause and then effect, so it
> isn't that simple.

"something"???? But OK, you say you have a "cause" at time t_dt and
"effect" at time t. But you are not telling me what the *physical* cause
is. More below.

>> > 2. To answer the question, I could use a Larry definition and call it
>> > L-causality, but since it's you who asked it and you're familiar with
>> > Jefimenko's view, I'll use Jefemenko's definition given in his most
>> > recent paper on the subject, top of page 288:
>>
>> > "Therefore the only kind of equations representing causal relations
>> > between physical quantities, other than equations representing cause
>> > and effect by definition, must be equations involving
>> > Ă¯Â¿Â½retardedĂ¯Â¿Â½ (previoustime) quantities"
>>
>>
>> > Let's call Jefimenko's definition J-causal.
>>
>> > 3. The partial derivative wrt t, @f/@t, of a continuous function
>> > f(x.t) is defined to be either:
>>
>> > dt--> 0, Limit (f(x, t) - f(x,t-dt))/dt
>>
>> > dt--> 0, Limit (f(x, t+dt) - f(x,t))/dt
>>
>> > This just says that for a continuous function, the derivatives
>> > approaching the limit from either side are equal.
>>
>> > 4. Maxwell's equations have @E/@t, @B/@t terms and are therefore have
>> > infinitesimally retarded in time dt terms, E(x, t-dt), B(x, t-dt)
>>
>> > 5. Therefore from Jefimenko's definition of a causal equation,
>> > Maxwell's equations are infinitesimally J-causal.
>>
>> > 6. Using simple algebra, they can be rearranged with the t+dt terms on
>> > the lhs, t terms on the right similar to Jefimenko's equations. E.g
>>
>> > B(t+dt) = B(t) - Curl E(t)dt
>>
>> You still did not answer my question. What exactly is the cause here? I
>> showed you what I think the cause is for Faraday's Law. What do you
>> think
>> the cause is?
>
> Slight typo, the above should be:
>
> B(t) = B(t-dt) - Curl E(t-dt)dt
>
> The J-causes are the terms at time t-dt: B(t-dt) and Curl E(t-dt).
> Cause then effect B(t)

LOL! You are saying that a B field in the past is the cause of a B field in
the present. Larry, you are just showing fields evolving in time. There is
no real *physical* cause and effect in what you are doing. It has nothing
to do with Maxwell and certainly nothing to do with what Faraday's law is
telling us. Again..., you have no real *physical* cause in what you are
doing.

>> You are doing the same thing as Paul; mixing up causality
>> with correlated behavior.
>
> I understand the difference between the two. Just because Jefimenko's
> equations can be expressed in terms of the retarded quantities charge
> and current density doesn't make them causes. They could be
> simultaneous with hidden causes. But we're discussing Jefimenko
> causality here.

If you can express the fields E(r, t) and B(r, t) in terms of retarded
sources it does make those sources causes. That is just plain common sense.
What you don't seem to understand is that in Nature, E and B fields are
correlated with each other when Faraday's law applies and can never affect
each others behavior directly in any situation. Now, remember that in
Jefimenko's equations the two equations are linked by the same changing
current density. Thus we can end up with,

curl E = -dB/dt = - (mu0/4pi) \$ (curl (1/r)[dJ/dt])dv'

For Faraday's law that shows the source (the real physical cause). Now,
what this doesn't show is that EM radiation can become "detached" from the
source so to speak. IOW, since the source was far enough in the past, we
can take as a very good approximation that the EM radiation is source-less.
However, the E and B fields of the radiation are just purely correlated in
is concerned.

Best,

Fred

### Jos Bergervoet

Jan 20, 2013, 6:28:02 AM1/20/13
to
On 1/19/2013 8:48 PM, FrediFizzx wrote:
..
> LOL! You are saying that a B field in the past is the cause of a B
> field in the present. Larry, you are just showing fields evolving in
> time.

So why would that rule out cause and effect? Your
own definition is "cause then effect" (that's all
you ever say about it!), so evolution in time means
automatically that there is cause and effect, by

> There is no real *physical* cause and effect
> in what you are doing.

You only contradict yourself now. At this point
you are not even funny anymore.

--
Jos

### Poutnik

Jan 20, 2013, 6:32:21 AM1/20/13
to

Jos Bergervoet posted Sun, 20 Jan 2013 12:28:02 +0100

>
> So why would that rule out cause and effect? Your
> own definition is "cause then effect" (that's all
> you ever say about it!),

How does the Newton's 3rd law of Action and Reaction
fit this "Cause than effect" approach ?

--
Poutnik

### FrediFizzx

Jan 20, 2013, 4:21:34 PM1/20/13
to
"Jos Bergervoet" <jos.ber...@xs4all.nl> wrote in message
news:50fbd4c2\$0\$6981\$e4fe...@news2.news.xs4all.nl...
> On 1/19/2013 8:48 PM, FrediFizzx wrote:
> ..
>> LOL! You are saying that a B field in the past is the cause of a B
>> field in the present. Larry, you are just showing fields evolving in
>> time.
>
> So why would that rule out cause and effect? Your
> own definition is "cause then effect" (that's all
> you ever say about it!), so evolution in time means
> automatically that there is cause and effect, by
> your own (vehemently repeated) argument!

Sorry, I have to reject that as a form of "cause then effect". It is really
lame to call that some kind of causality but you are welcome to your
opinion. It is definitely not in the spirit of what Jefimenko had in mind
and definitely not what Larry wants to call "J-causal". This is "J-causal",

curl E = -dB/dt = - (mu0/4pi) \$ (curl (1/r)[dJ/dt])dv'

Best,

Fred

### FrediFizzx

Jan 20, 2013, 6:25:03 PM1/20/13
to
"FrediFizzx" <fredi...@hotmail.com> wrote in message
news:am35gf...@mid.individual.net...
To add to this, I would call what Larry is describing as simply an *effect*
that is evolving in time.

Best,

Fred

### Larry Harson

Jan 21, 2013, 2:23:59 PM1/21/13
to
I have many times using the Maxwell Faraday equation: Curl E and B at
time t-dt

> >> > 2. To answer the question, I could use a Larry definition and call it
> >> > L-causality, but since it's you who asked it and you're familiar with
> >> > Jefimenko's view, I'll use Jefemenko's definition given in his most
> >> > recent paper on the subject, top of page 288:
>
> >> > "Therefore the only kind of equations representing causal relations
> >> > between physical quantities, other than equations representing cause
> >> > and effect by definition, must be equations involving
> >> > â€˜retardedâ€™ (previoustime) quantities"
Don't forget also Curl E at time t-dt, and don't forget I'm saying
they're J-causal. It's Jefimenko who's saying this, and my view is
similar to his, but personally I think it's dubious to say that
something is *the* cause of something in general.

>Larry, you are just showing fields evolving in time. Â There is
> no real *physical* cause and effect in what you are doing. Â It has nothing
> to do with Maxwell and certainly nothing to do with what Faraday's law is
> telling us. Â Again..., you have no real *physical* cause in what you are
> doing.

If they're not physical, then why are physicists able to assign a
number to B that can be verified in different laboratories around the
world?

> >> You are doing the same thing as Paul; mixing up causality
> >> with correlated behavior.
>
> > I understand the difference between the two. Just because Jefimenko's
> > equations can be expressed in terms of the retarded quantities charge
> > and current density doesn't make them causes. They could be
> > simultaneous with hidden causes. But we're discussing Jefimenko
> > causality here.
>
> If you can express the fields E(r, t) and B(r, t) in terms of retarded
> sources it does make those sources causes. Â That is just plain common sense.

OK.

> What you don't seem to understand is that in Nature, E and B fields are
> correlated with each other when Faraday's law applies and can never affect
> each others behavior directly in any situation.

I'm just using Jefimenko's definition of causality from his causality
paper that I linked to before:

"Therefore equations depicting causal relations between physical
phenomena must, in general, be equations where a present-time quantity
(the effect) relates to one or more quantities (causes) that existed
at some previous time."

"Therefore the only kind of equations representing causal relations
between physical quantities, other than equations representing cause
and effect by definition, must be equations involving
â€˜retardedâ€™ (previoustime) quantities."

I've shown to you how Maxwell's Faraday equation contains
infinitesimal J-causality, and can be rearranged to show explicitly
what are the J-causes, and what is the J-effect.

>Now, remember that in
> Jefimenko's equations the two equations are linked by the same changing
> current density. Â Thus we can end up with,
>
> curl E = -dB/dt = - (mu0/4pi) \$ (curl (1/r)[dJ/dt])dv'
>
> For Faraday's law that shows the source (the real physical cause). Â Now,
> what this doesn't show is that EM radiation can become "detached" from the
> source so to speak. Â IOW, since the source was far enough in the past, we
> can take as a very good approximation that the EM radiation is source-less.
> However, the E and B fields of the radiation are just purely correlated in
> is concerned.

I'm OK with this as satisfying J-causality.

Regards, Larry.

### Larry Harson

Jan 21, 2013, 2:33:51 PM1/21/13
to
On 20 Jan, 21:21, "FrediFizzx" <fredifi...@hotmail.com> wrote:
> "Jos Bergervoet" <jos.bergerv...@xs4all.nl> wrote in message
>
> news:50fbd4c2\$0\$6981\$e4fe...@news2.news.xs4all.nl...
>
> > On 1/19/2013 8:48 PM, FrediFizzx wrote:
> > Â  ..
> >> LOL! Â You are saying that a B field in the past is the cause of a B
> >> field in the present. Â Larry, you are just showing fields evolving in
> >> time.
>
> > So why would that rule out cause and effect? Your
> > own definition is "cause then effect" (that's all
> > you ever say about it!), so evolution in time means
> > automatically that there is cause and effect, by
> > your own (vehemently repeated) argument!
>
> Sorry, I have to reject that as a form of "cause then effect". Â It is really
> lame to call that some kind of causality but you are welcome to your
> opinion.

"lame". I've never come across that as a scientific term in common
use ;)

It is definitely not in the spirit of what Jefimenko had in mind
> and definitely not what Larry wants to call "J-causal". Â This is "J-causal",
>
> curl E = -dB/dt = - (mu0/4pi) \$ (curl (1/r)[dJ/dt])dv'

It's clear what Jefimenko had in mind from the quote I've give to you
from his paper, and therefore likely that he didn't realize
infinitesimal J-causality existed in Maxwell's equations.

Regards, Larry.

### FrediFizzx

Jan 21, 2013, 8:42:52 PM1/21/13
to
"Larry Harson" <larry...@softhome.net> wrote in message
> On 19 Jan, 19:48, "FrediFizzx" <fredifi...@hotmail.com> wrote:
>> "Larry Harson" <larryhar...@softhome.net> wrote in message
>>
>> > On Jan 14, 4:48 am, "FrediFizzx" <fredifi...@hotmail.com> wrote:
>> >> "Larry Harson" <larryhar...@softhome.net> wrote in message
[snip]
>>
>> > I left this thread for a few days while you were discussing Paul's
>> > paper with him.
>>
>> Ok.
>>
>> >> > I'll split my argument into a number of parts so that you can point
>> >> > out where you diagree with me.
>>
>> >> > 1. The question is asking: "Are Maxwell's equtaions causal?"
>> >> > The answer depends upon how we define causality.
>>
>> >> There should be no ambiguity about the definition of causality as
>> >> related
>> >> to
>> >> Maxwell's equations. Cause then effect is simple enough.
>>
>> > So you say, but I've shown to you something at time t_dt then effect
>> > at time t. Yet you don't see this as cause and then effect, so it
>> > isn't that simple.
>
>> "something"???? But OK, you say you have a "cause" at time t_dt and
>> "effect" at time t. But you are not telling me what the *physical* cause
>> is. More below.
>
> I have many times using the Maxwell Faraday equation: Curl E and B at
> time t-dt

No. See more below.

[snip]
>> >> You still did not answer my question. What exactly is the cause here?
>> >> I
>> >> showed you what I think the cause is for Faraday's Law. What do you
>> >> think
>> >> the cause is?
>>
>> > Slight typo, the above should be:
>>
>> > B(t) = B(t-dt) - Curl E(t-dt)dt
>>
>> > The J-causes are the terms at time t-dt: B(t-dt) and Curl E(t-dt).
>> > Cause then effect B(t)
>
>> LOL! You are saying that a B field in the past is the cause of a B field
>> in
>> the present.
>
> Don't forget also Curl E at time t-dt, and don't forget I'm saying
> they're J-causal. It's Jefimenko who's saying this, and my view is
> similar to his, but personally I think it's dubious to say that
> something is *the* cause of something in general.

Your curl E(t -dt)dt is going to zero in what you have expressed above so
one can just toss it out. It is not going to be a cause of anything
anywise. And for sure it can't be a cause of B(t). :-) So all you are
left with is B(t) = B(t-dt). Doesn't really make much sense.

>>Larry, you are just showing fields evolving in time. There is
>> no real *physical* cause and effect in what you are doing. It has
>> nothing
>> to do with Maxwell and certainly nothing to do with what Faraday's law is
>> telling us. Again..., you have no real *physical* cause in what you are
>> doing.
>
> If they're not physical, then why are physicists able to assign a
> number to B that can be verified in different laboratories around the
> world?

They are physical *effects*. They are NOT physical *causes*. A physicist
would have no trouble assigning a number to B with it being an effect.

>> >> You are doing the same thing as Paul; mixing up causality
>> >> with correlated behavior.
>>
>> > I understand the difference between the two. Just because Jefimenko's
>> > equations can be expressed in terms of the retarded quantities charge
>> > and current density doesn't make them causes. They could be
>> > simultaneous with hidden causes. But we're discussing Jefimenko
>> > causality here.
>>
>> If you can express the fields E(r, t) and B(r, t) in terms of retarded
>> sources it does make those sources causes. That is just plain common
>> sense.
>
> OK.

Good, at least something we agree on.

>> What you don't seem to understand is that in Nature, E and B fields are
>> correlated with each other when Faraday's law applies and can never
>> affect
>> each others behavior directly in any situation.
>
> I'm just using Jefimenko's definition of causality from his causality
> paper that I linked to before:

Sorry, but you are slaughtering Jefimenko's intentions, IMHO. :-) If you
have his "Causality..." book, look at pages 10 and 11 where he presents,

H = (1/4pi) \$ {(@D/@t x r_u)/r^2}dv',

where \$ is integral and @ is partial derivative symbol. He says after that,
"In this equation, too, H and @D/@t are evaluated for the same instant of
time. Hence, by the causality principle, @D/@t cannot be a cause of H, and,
consequently, Maxwell's Eq. (1-1.4), just like EQ. (1.1.3), is not a causal
equation." So he is pretty explicit about that.

> "Therefore equations depicting causal relations between physical
> phenomena must, in general, be equations where a present-time quantity
> (the effect) relates to one or more quantities (causes) that existed
> at some previous time."
>
> "Therefore the only kind of equations representing causal relations
> between physical quantities, other than equations representing cause
> and effect by definition, must be equations involving
> â€˜retardedâ€™ (previoustime) quantities."

He says the same exact thing in his book. The problem is that in your
interpretation, you are mixing up effects with causes. When you go on
reading in his book, it is very clear what quantities he considers to be
causes and which quantities he considers effects depending on the exact
situations. It very common sense as to which quantity is a cause and which
quantity is an effect. I am somewhat mystified that you don't see it.

effect one moment in time and then still be an effect the next moment? Same
with causes; a cause can last for more than just an instant of time.

> I've shown to you how Maxwell's Faraday equation contains
> infinitesimal J-causality, and can be rearranged to show explicitly
> what are the J-causes, and what is the J-effect.

Nope. What you have shown is *effects* evolving in time. You are not even
close to what Jefimenko had in mind with *causes*.

>> Now, remember that in
>> Jefimenko's equations the two equations are linked by the same changing
>> current density. Thus we can end up with,
>>
>> curl E = -dB/dt = - (mu0/4pi) \$ (curl (1/r)[dJ/dt])dv'
>>
>> For Faraday's law that shows the source (the real physical cause). Now,
>> what this doesn't show is that EM radiation can become "detached" from
>> the
>> source so to speak. IOW, since the source was far enough in the past, we
>> can take as a very good approximation that the EM radiation is
>> source-less.
>> However, the E and B fields of the radiation are just purely correlated
>> in
>> their behavior. That is what Faraday's law leads to as far as EM
>> is concerned.
>
> I'm OK with this as satisfying J-causality.

Hey... if you want to go around calling "effects" "causes" nobody is
stopping you. But you will come to the false conclusion like Paul that
Maxwell's equations are causal. I think you two and Jos need to figure out
what a cause is and what an effect is because you all are mixing them up.

Best,

Fred

### FrediFizzx

Jan 21, 2013, 9:03:43 PM1/21/13
to
"Larry Harson" <larry...@softhome.net> wrote in message
> On 20 Jan, 21:21, "FrediFizzx" <fredifi...@hotmail.com> wrote:
>> "Jos Bergervoet" <jos.bergerv...@xs4all.nl> wrote in message
>>
>> news:50fbd4c2\$0\$6981\$e4fe...@news2.news.xs4all.nl...
>>
>> > On 1/19/2013 8:48 PM, FrediFizzx wrote:
>> > ..
>> >> LOL! You are saying that a B field in the past is the cause of a B
>> >> field in the present. Larry, you are just showing fields evolving in
>> >> time.
>>
>> > So why would that rule out cause and effect? Your
>> > own definition is "cause then effect" (that's all
>> > you ever say about it!), so evolution in time means
>> > automatically that there is cause and effect, by
>> > your own (vehemently repeated) argument!
>>
>> Sorry, I have to reject that as a form of "cause then effect". It is
>> really
>> lame to call that some kind of causality but you are welcome to your
>> opinion.
>
> "lame". I've never come across that as a scientific term in common
> use ;)

You are right. It is not lame since it is worse than lame. :-) It's not
even causality at all!

> It is definitely not in the spirit of what Jefimenko had in mind
>> and definitely not what Larry wants to call "J-causal". This is
>> "J-causal",
>>
>> curl E = -dB/dt = - (mu0/4pi) \$ (curl (1/r)[dJ/dt])dv'
>
> It's clear what Jefimenko had in mind from the quote I've give to you
> from his paper, and therefore likely that he didn't realize
> infinitesimal J-causality existed in Maxwell's equations.

Sorry, but you are mixing up what Jefimenko meant by causes and what he
meant by effects. See other post.

Best,

Fred

### p.ki...@ic.ac.uk

Jan 22, 2013, 5:13:46 AM1/22/13
to
FrediFizzx <fredi...@hotmail.com> wrote:
> Sorry, but you are mixing up what Jefimenko meant by causes
> and what he meant by effects. See other post.

What other post? The one where you explain how you categorize
causes and effects in a straightforward, self-contained way?
I seem to have missed it. Can you cut and paste it into a reply

### p.ki...@ic.ac.uk

Jan 22, 2013, 7:51:47 AM1/22/13
to
FrediFizzx <fredi...@hotmail.com> wrote:
> [Jefimenko] says the same exact thing in his book. The problem is that in your
> interpretation, you are mixing up effects with causes. When you go on
> reading in his book, it is very clear what quantities he considers to be
> causes and which quantities he considers effects depending on the exact
> situations. It very common sense as to which quantity is a cause and which
> quantity is an effect. I am somewhat mystified that you don't see it.

Brilliant! I don't have a copy of Jefimenko's book here. Can you summarize
what J-causes are by typing out or summarizing the relevant section?

> Hey... if you want to go around calling "effects" "causes" nobody is
> stopping you. But you will come to the false conclusion like Paul that
> Maxwell's equations are causal.

My conclusions are not false - they are valid consequences of my
starting point, which is based on a well established and widely
used approach.

You are (as I have repeatedly said) allowed not to like my preferred
starting point, and are free to specify your own. Only somehow you
never seem to specify it very completely. This is a shame, because
I'm very keen to learn different ways to treat things, and would find
it useful to have another sort of causality hat to wear.

> I think you two and Jos need to figure out what a cause is and
> what an effect is because you all are mixing them up.

I have tried to figure out what you mean by cause and effect,
and posted my guesses, but you pretty much threw it all out;
and failed to replace them with anything (useful) (to me).

Maybe you should just summarize that bit of Jefimenko's book, for
example.

### p.ki...@ic.ac.uk

Jan 22, 2013, 8:30:09 AM1/22/13
to
Larry Harson <larry...@softhome.net> wrote:
> 2. To answer the question, I could use a Larry definition and call it
> L-causality, but since it's you who asked it and you're familiar with
> Jefimenko's view, I'll use Jefemenko's definition given in his most
> recent paper on the subject, top of page 288:

> "Therefore the only kind of equations representing causal relations
> between physical quantities, other than equations representing cause
> and effect by definition, must be equations involving
> ?retarded? (previoustime) quantities"

> Let's call Jefimenko's definition J-causal.

> 3. The partial derivative wrt t, @f/@t, of a continuous function
> f(x.t) is defined to be either:

> dt--> 0, Limit (f(x, t) - f(x,t-dt))/dt

> dt--> 0, Limit (f(x, t+dt) - f(x,t))/dt

> This just says that for a continuous function, the derivatives
> approaching the limit from either side are equal.

> 4. Maxwell's equations have @E/@t, @B/@t terms and are therefore have
> infinitesimally retarded in time dt terms, E(x, t-dt), B(x, t-dt)

> 5. Therefore from Jefimenko's definition of a causal equation,
> Maxwell's equations are infinitesimally J-causal.

> 6. Using simple algebra, they can be rearranged with the t+dt terms on
> the lhs, t terms on the right similar to Jefimenko's equations. E.g

> B(t+dt) = B(t) - Curl E(t)dt

There's a subtlety here, because Jefimenko 2004 explicitly states that
a cause may not be simultaneous with its effect. This means that
the differential Maxwell's equations are not J-causal (and neither,
for example, is the Dirac equation). Indeed, no differential equation
whose "effect term" has only a single extra time derivative as compared
to the "cause terms" would then be causal.

To have a differential equation which is J-causal, you need two extra
time derivatives on the "effect term" as compared to the cause -
most simply

(a) dR/dt = Q <---- K-causal, but not J-causal!
(b) d^2R/dt^2 = S <---- K-causal & J-causal

Essentially, the extra derivative means the response R to a delta-function
cause Q=delta(t-t_0) is a ramp not a step; therefore no effect is seen at
the time t_0 of the cause. Initially, this might seem fine, after all
many wave equations can be written in a second order form.

But: one might imagine tweaking the first order equation to add in a small
delay, and then taking the limit as the delay tends to zero:

(c) lim_{s->0+} dR(t)/dt = Q(t-s)

This would be compatible with J-causality, in that simultaneous cause and
effect are now excluded (since s approaches, but is never exactly 0)

However, barring exotic mathematical situations, I am not sure what
measureable physical difference would exist between solutions of (a) and (c),
despite the fact that (a) is not J-causal, but (c) could be.

Therefore I think it sensible to allow effect simultaneous with cause,
because disallowing it leads to an apparently spurious distinction
between a limiting case (c) and its limit (a). Further, it means that
many physical models in wide use (Maxwell, Dirac, etc) are not categorized
as non-causal on the grounds of this apparently spurious distinction.

Calling the Maxwell and Dirac (etc) equations "non-causal" is a lot of baby
to be throwing out with the bathwater. I'll be wanting a pretty solid
reason to be doing that - and I haven't yet been given one.

Regarding the discrete case (essentially (c) with finite delay s),
one can examine it as if doing a numerical simulation - as I do in the
recently (Oct '12) added appendix on my arxiv:1106.1792

--
---------------------------------+---------------------------------
Dr. Paul Kinsler

### FrediFizzx

Jan 22, 2013, 1:38:14 PM1/22/13
to
<p.ki...@ic.ac.uk> wrote in message
news:qb52t9-...@ph-kinsle.qols.ph.ic.ac.uk...
> FrediFizzx <fredi...@hotmail.com> wrote:
>> Sorry, but you are mixing up what Jefimenko meant by causes
>> and what he meant by effects. See other post.
>
> What other post? The one where you explain how you categorize
> causes and effects in a straightforward, self-contained way?
> I seem to have missed it. Can you cut and paste it into a reply

Well Paul, if you don't know or can't tell the difference between a cause
and an effect, I probably won't be able to help you anywise. As I told you
before concerning Faraday's law, you want to take two effects and make one
the cause of the other. I don't know what more I can tell you beyond that.
That should be a pretty big clue there. :-)

Best,

Fred

### FrediFizzx

Jan 22, 2013, 2:42:22 PM1/22/13
to
<p.ki...@ic.ac.uk> wrote in message
news:3ke2t9-...@ph-kinsle.qols.ph.ic.ac.uk...
> FrediFizzx <fredi...@hotmail.com> wrote:
>> [Jefimenko] says the same exact thing in his book. The problem is that
>> in your
>> interpretation, you are mixing up effects with causes. When you go on
>> reading in his book, it is very clear what quantities he considers to be
>> causes and which quantities he considers effects depending on the exact
>> situations. It very common sense as to which quantity is a cause and
>> which
>> quantity is an effect. I am somewhat mystified that you don't see it.
>
> Brilliant! I don't have a copy of Jefimenko's book here. Can you summarize
> what J-causes are by typing out or summarizing the relevant section?

No. But if you tell me the exact situation, I will tell you what I think
the cause is and what the effect is. Some I have told you already. You
should get a copy of Jefimenko's book. I don't think it is all that
expensive. There is some wild stuff about gravity in it also. Not sure I
agree with all of it but interesting approach just the same.

Best,

Fred

### p.ki...@ic.ac.uk

Jan 22, 2013, 4:39:54 PM1/22/13
to
FrediFizzx <fredi...@hotmail.com> wrote:
> > Can you summarize what J-causes are [...]
> No. [...]

--
---------------------------------+---------------------------------
Dr. Paul Kinsler

### benj

Jan 22, 2013, 6:06:15 PM1/22/13
to
On Tue, 22 Jan 2013 11:42:22 -0800, FrediFizzx wrote:

> No. But if you tell me the exact situation, I will tell you what I
> think the cause is and what the effect is. Some I have told you
> already. You should get a copy of Jefimenko's book. I don't think it
> is all that expensive. There is some wild stuff about gravity in it
> also. Not sure I agree with all of it but interesting approach just the
> same.
>
> Best,
>
> Fred

Heh. Wait until the conversation turns to things like Heaviside
"cogravitation" fields and it will really hit the fan around here! :-)

and for some real fun, point them to his non-Einstein clocks that don't

### benj

Jan 22, 2013, 6:14:04 PM1/22/13
to
On Mon, 21 Jan 2013 11:23:59 -0800, Larry Harson wrote:

> I'm just using Jefimenko's definition of causality from his causality
> paper that I linked to before:
>
> "Therefore equations depicting causal relations between physical
> phenomena must, in general, be equations where a present-time quantity
> (the effect) relates to one or more quantities (causes) that existed at
> some previous time."
>
> "Therefore the only kind of equations representing causal relations
> between physical quantities, other than equations representing cause and
> effect by definition, must be equations involving â€˜retardedâ€™
> (previoustime) quantities."
>
> I've shown to you how Maxwell's Faraday equation contains infinitesimal
> J-causality, and can be rearranged to show explicitly what are the
> J-causes, and what is the J-effect.

Except you have not shown that at all. You've used incorrect mathematics
and tried to pass that off as reality. Sorry. When you take a derivative,
the mathematical process is to approach the point in question. But the
limit is actually TAKEN. Which means that the derivative exists ONLY at
the point in question. Which means that Jefimenko's "previous time"
statement above is not met. And in any case things like "limits" don't
really exist in reality so they establish no physics in this regard.

As I've pointed out several times before, a function and it's derivative
is really just two different descriptions of ONE thing. They do not, can
not, "cause each other". I know but that the term "derivative" makes it
seem as if the function is the "cause" and the "derivative" is the
effect. But it's not so.

### FrediFizzx

Jan 22, 2013, 8:54:58 PM1/22/13
to
<p.ki...@ic.ac.uk> wrote in message
news:aid3t9-...@ph-kinsle.qols.ph.ic.ac.uk...
> FrediFizzx <fredi...@hotmail.com> wrote:
>> > Can you summarize what J-causes are [...]
>> No. [...]
>
> Well, I think that adequately summarizes your position on these matters.

Hmm... another false conclusion by Paul. :-) Give me a physical situation
involving Maxwell's equations or solutions to the equations and I will tell
you which values I consider to be causes and which values are effects. More
common sense; you have to know the situation before you can label which
values are causes and which are effects. Your previous attempt at your
"bullet list" was way too general and mostly wrong right out of the gate.

Best,

Fred