Re: [Phys-l] violation of N3 ??

[John Denker <jsd@av8n.com>]

On 10/27/2006 05:55 PM, David Bowman wrote:

>                       |
>                       ^
>                       |
>                       |
> ---->-- q --->---     q'
>                       |
>                       |
>                       ^
>                       |
> [There is] .... at the
> location of q a magnetic field generated by q' that is pointing out
> of the screen toward the viewer. ...  q', being in a no-field location,
> has no magnetic force exerted on it by q.  

OK, that's true as stated, and very clear.

> This is a very strong violation of N3.

I'm not convinced;  see below.

> We really can't very well dismiss such magnetic forces as
> being a negligible relativistic effect since it is responsible for
> making nearly all kinds electric motors work (that along with the
> forces of constraint).  

Agreed!

Magnetic fields *are* 2nd-order relativistic effects, but they are
not negligible.
  http://www.av8n.com/physics/magnet-relativity.htm

> Certainly one can easily deal with momentum conservation for
> momentum transfers between particles and force-fields when one also
> considers the field momentum possessed by the fields themselves.

Agreed;  that was what I was saying in my previous note.  Feynman
volume II chapter 27.

> But there seems to be a problem that develops with an *N3* assignment
> saying that a particle exerts a force on a field at some location
> because it requires that the field at that location also transmit
> that force to its various neighboring spatial neighbors at different
> locations in space as the momentum is locally transferred across the
> spatial reaches of the field. 

I don't see what the problem is.  That's why fields were invented.
If a field can exert a force on a particle, surely the particle can
exert a force on the field.  We know how to calculate field energy
and field momentum ... maybe not perfectly, but well enough to deal
with the situations considered here.

I guess it comes down to details of how you formulate N3.  Whenever
anybody says N3 *I* tend to assume they mean conservation of momentum.
This is how *I* understand N3.

If instead you insist on formulating N3 in terms of particle-to-particle
interactions, and action-at-a-distance, treating the field-strength
as only a calculational device ... then sure, you're going to have
violations.  Action-at-a-distance is incompatible with relativity,
and therefore incompatible with electromagnetism.

Let's be clear:  electromagnetism is not inconsistent with conservation
of momentum;  it's just incompatible with action-at-a-distance.

I suggest we formulate N3 in such a way that it does not imply
action-at-a-distance.