Re: [Phys-l] Ampere's original magnetic force law

[John Denker <jsd@av8n.com>]

On 04/14/2010 02:46 AM, Bob Sciamanda wrote:
> I have been asked (by engineers at Penn State) to submit this topic
> to the List for comments:
>
> http://www.df.lth.se/~snorkelf/LongitudinalMSc.pdf
>
> It concerns a controversy regarding Ampere's original formulation of
> the basic magnetic force law between current elements. Apparently he
> was persuaded to this version because it obeys N3 even in the strong
> form (equal and opposite "central" forces). This is contrary to the
> traditional force law, which comes from the Biot Savart relation and
> the Lorentz QVxB force.
>
> Examples of experimental evidence for the Ampere longitudinal force
> component are cited.  Should these results be attributed to an
> other-than-magnetic component of the force between current elements?
>
> Could the original Ampere magnetic force law possibly be reconciled
> with Maxwell's equations and the Lorentz force?
>
> Your comments and analyses, please.

We have a perfectly good well-tested theory of classical 
electromagnetism, namely the Maxwell equation and the Lorentz 
force law.

It involves charges (including moving charges) and fields,
plus the interaction between charges and fields.

The Maxwell/Lorentz theory does not "come from" the Biot-Savart 
law but rather the other way around;  the theory produces the 
Biot-Savart law as a limiting case subject to some simplifying 
approximations.

The theory is not based on "the force between current elements"
although the theory can handle that as a limiting case subject
to some simplifying assumptions.  Foundational questions (such
as the existence or non-existence of "longitudinal" forces)
should not be asked or answered in terms of "the force between
current elements".

The theory is relativistically correct and can be written 
in manifestly invariant form, correct to all orders in v/c.  
The electromagnetic field tensor is the same in all frames.  
In any particular frame, we can identify a component of the 
EM field tensor that we call the "electric" field and another 
component that we call the "magnetic" field.  These components 
are not separately invariant;  the thing we call the electric 
field in one frame is partly magnetic in another frame, and 
vice versa.

In some sense magnetostatics can be seen as the first-order
correction to electrostatics, valid (and obligatory!) to
first order in v/c.

There are plenty of "other-than-magnetic" forces in ordinary
circuits. 
 -- There are the forces of constraint that cause the 
  current to remain inside the wire, to follow the wire 
  around corners, et cetera.  These forces involve
  electrostatics, plus quantum-mechanical solid-state 
  physics (the band structure of metals, the nature of
  insulators, et cetera).
 -- There are higher-than-first-order relativistic terms
  (if you choose to expand things in powers of v/c).
 -- There is energy and momentum in the fields, not just
  in the wires.

It must be emphasized that the conventional equations of 
electromagnetism can be formulated in a way that is correct
to all orders in v/c.  It is only the notion of separate
"magnetic-only" phenomena that is limited to first order 
in v/c.

The higher-order relativistic effects are not large
enough to be significant in the experimental situations
considered by the thesis ... as recognized in section 3.4 
of the thesis.

==============

1) I am not impressed by the experimental data cited in the
thesis.

 All of the experiments involving liquid conductors can be 
 explained in terms of the conventional Maxwell/Lorentz 
 equations (which predict a pinch effect) plus the usual 
 equations of fluid dynamics.

 All of the data involving disks and shattered wires can 
 probably be explained in terms of nonlinear localized 
 heating, plus pinch effects, plus arc/vapor effects.

2) There is a glaring omission from the theoretical
analysis in the thesis.

Things have progressed quite a bit since "Ampère's original
magnetic force law".  In particular, Maxwell emphasized the
idea that current "A" produces a field that acts on current
"B" ... as opposed to an action-at-a-distance theory (such
as Ampère's theory) where current acts on current without 
bothering with a field.

If we think there should be a field, the humongous open
question is:  Can you tell me the value -- or even the
direction -- of the field associated with the "longitudinal
electrodynamic forces" that are the subject of discussion?
The thesis is restricted to the current/current interaction, 
without specifying the field.  I cannot imagine any way of
calculating the field that would be consistent with the 
geometrical symmetries of spacetime.    So unless you want 
to overthrow special relativity (as well as Maxwell/Lorentz 
electromagnetism) there is a fundamental problem here.

=========

As James Randi is fond of saying, extraordinary claims
require extraordinary proof.

If you want me to take seriously the claims of extraordinary
longitudinal forces, I need to see, at a minimum:
 a) Some experimental data that controls for the obvious
  non-extraordinary explanations of the observations; and
 b) A relativistically-correct theoretical description of
  the forces.