View source for Newton's Third Law

'''Newton's third law of motion''' states that if one body exerts a force on a second body, the second exerts on the first a force equal in magnitude and opposite in direction. [[Isaac Newton]] gave it in the ''Principia'' (1687) as ''Actioni contrariam semper et aequalem esse reactionem''.

==The standard account==

The third law is the statement of momentum conservation for a pair of interacting bodies: because the two forces are equal and opposite, the total momentum of the pair does not change. Physicists distinguish a ''weak'' form &mdash; the forces are equal and opposite &mdash; from a ''strong'' form, in which they are additionally directed along the line joining the two bodies, which is what is required for conservation of angular momentum as well. Newtonian gravity and [[Coulomb's Law]] both satisfy the strong form.

The [[Lorentz Force]] does not. It is a standard and entirely uncontroversial result in mainstream electrodynamics that the magnetic forces between two isolated current elements, computed from the Grassmann&ndash;Lorentz expression, are in general neither equal and opposite nor collinear. The textbook resolution is that the electromagnetic field itself carries momentum &mdash; the Poynting momentum density &epsilon;<sub>0</sub>'''E'''&times;'''B''' &mdash; so that momentum is conserved for the system of charges ''plus'' field, even though it is not conserved for the charges alone. In relativistic field theory the third law is therefore not a fundamental axiom but a consequence of translational symmetry (Noether's theorem) applied to the full system. This is a real and well-known subtlety, not a suppressed embarrassment; it is discussed openly in graduate texts.

==On this wiki==

What is disputed here is not the fact but the conclusion drawn from it. Several researchers catalogued on this wiki treat the failure of the Lorentz force to be action&ndash;reaction symmetric as evidence that the force law itself is wrong, rather than as evidence that field momentum must be included.

* [[Thomas E Phipps]] pressed this argument repeatedly; see [[Ampere Tension and Newton's Laws]] (''Apeiron'', 1993), where he analyses whether the longitudinal Ampère force can be detected experimentally, and [[Electrodynamics: Rebirth of an Experimental Science?]].
* [[Panos Pappas]] and Moyssides reported measurements on the "Ampère bridge" intended to show a longitudinal force; the results and their interpretation are examined in [[Ampere's Original Force Law Compared with the Moyssides-Pappas Results]].
* [[Peter Graneau]] and [[Neal Graneau]] argued that exploding wires and railgun recoil demonstrate longitudinal tension in conductors &mdash; [[The Graneau Experiments]], [[Ampere Repulsion and Graneau's Exploding Wires]], [[Ampere-Neumann Electrodynamics of Metals]].
* The attraction of Ampère's original force law and of [[Wilhelm Weber]]'s velocity-dependent law for these authors is precisely that both satisfy the ''strong'' form of the third law between elements, without recourse to field momentum. [[Andre K T Assis]] develops this in [[Webers Electrodynamics]]; [[Charles William Lucas]] pursues it in [[Weber's Force Law for Realistic Finite-Size Elastic Particles]].
* [[James Keele]] and others in [[:Category:Electrodynamics]] argue the opposite case, deriving the observed forces from [[Coulomb's Law]] with propagation delay.

The honest summary is that mainstream physics and these researchers agree on the mathematics and disagree on its meaning: whether a field that carries momentum is a physical thing that can absorb the imbalance, or a bookkeeping device introduced to rescue a defective force law.

==See also==

* [[Electrodynamics]]
* [[Lorentz Force]]
* [[Electric Current]]
* [[Isaac Newton]]
* [[Inertia]]
* [[Mach's Principle]]

[[Category:Electrodynamics]]
[[Category:Theory & Models]]
[[Category:Philosophy]]