Re: [Phys-L] treating force as a vector ... consistently

[John Denker <jsd@av8n.com>]

On 08/27/2016 03:08 PM, Moses Fayngold wrote:
> I want to add to my previous message another example illustrating
> limitations of the "action-reaction" concept. Consider a charged
> point-particle like an electron tracing out a circle in a static
> homogeneous magnetic field, e.g. within a solenoid with constant
> current.

Executive summary:  FIELD MOMENTUM

This situation is very well understood.  The statement of the question,
including a diagram of the apparatus, is presented in
  Feynman volume II chapter 17 "The Laws of Induction"
  section 17-4 "a paradox"
  http://www.feynmanlectures.caltech.edu/II_17.html#Ch17-S4

The answer is spelled out at
  Feynman volume II chapter 27 "Field Energy and Field Momentum"
  section 27–6 "Field momentum"
  http://www.feynmanlectures.caltech.edu/II_27.html#Ch27-S6


=========
Remarks:

This is why it is a mistake to write a physics book where the title
and the central conceit of the book revolve around the alleged
distinction between "matter" and "interactions".

Is the electromagnetic field "matter"?  The book says no.  Yet
the particle interacts with the field.  Is the particle interacting
with an interaction?  It's a silly question.  It's a silly way to
think about physics.

The modern (post-1924) way of thinking about things is to consider
that particles are real, fields are real, and the difference between
particles and fields is not particularly significant.

Rather than talking about the electromagnetic interaction "between"
two charged particles, the smart modern approach is to say that
the particle over here interacts /locally/ with the electromagnetic
field.  The field then propagates to the other particle over there,
and then interacts /locally/ with that particle.

When I say locally I mean at a single point in spacetime ... as
opposed to any version of "action at a distance".

This is relevant to the third law as follows:

  -- As I have mentioned once or twice, it helps to reformulate
   the third law as a statement of conservation of momentum.  For
   the particle interacting with a field, it is utterly straightforward
   to account for the momentum transfered from the particle to the
   field and vice versa, upholding the third law.

  -- If you insist on formulating the third law in terms of equal
   and opposite forces, that is allowed, of course.  However students
   may find it counterintuitive to imagine the particle exerting a
   force "on the field".  That is however necessary, if you insist
   on thinking in terms of forces.

Bottom line:  There is momentum in the /field/.  Momentum can be
transferred to and from the field.  You can describe this process
using whatever words you like, but the physics is the same no matter
what.