Then there's the whole problem that if you take two moving point charges
(q1 and q2) with non-parallel velocities (v1 and v2), Newton's 3rd Law
doesn't work for the Lorentz forces they exert on each other if you
calculate the B-field using the Biot-Savart Law. The force on q2 will
have a component in the v1 direction and the force on q1 will have a
component in the v2 direction....impossible to be opposite in the
general case.
Is there a way to make N3L work in this classical situation?
Bill Nettles
John Denker <jsd@av8n.com> 12/9/2008 12:51 pm >>>
Hi Folks --
I'm conflicted about the following:
1) As I see it, Newton's third law implies conservation of
momentum ... and vice versa. They're equivalent. So far
so good.
{snip}
Here's another way of looking at the whole issue. This
may explain why it is hard to think clearly about this
topic.
We need to carefully distinguish
-- natural, physical reality
-- our intuition
-- our formal models and equations
Just because something is true physics-wise doesn't mean
it is logically derivable formalism-wise. Gödel had
something to say about this.
A) In this case, we formalize force as a vector. Formally,
vectors have direction and magnitude, period.
B) Meanwhile, I suspect that many of us, and many students,
have an intuitive force-like notion that involves direction,
magnitude, and *point of attachment*.
There is a huuuge difference between (A) and (B), as we
can see from the following diagrams:
<----------
action (A)
---------->
reaction (A)
=================================================
<---------- ---------->
action (B) reaction (B)
You can see that diagram (A) conserves momentum and
upholds the usual vector-based version of Newton's
third law, but violates conservation of angular momentum.
Meanwhile, diagram (B) upholds conservation of angular
momentum as well as conservation of plain old linear
momentum.
The point is that in terms of vectors, strictly speaking,
there is no difference between diagram (A) and diagram (B).
Vectors have magnitude and direction, period.
If you want to talk about something having magnitude,
direction, and point of attachment, you need a bivector:
torque = force /\ lever_arm
So ... as far as I can see, so long as the third law is
formalized in terms of forces i.e. vectors, the formal
law does not capture the full physical reality.