Register to reply

Conservation of momentum without newton's third law

by davidbenari
Tags: conservation, momentum, newton
Share this thread:
Aug7-14, 07:36 PM
P: 75
So I've recently read newton's third law violates the principles of relativity. I only know how to prove conservation of momentum if Newton's third law holds. I was hoping someone could explain to me this (proving conservation of momentum when newton's third law is false) without using extremely hefty mathematics, and specifically addressing E&M:

" It turns out that we can ``rescue'' momentum conservation by abandoning action at a distance theories, and instead adopting so-called field theories in which there is a medium, called a field, which transmits the force from one particle to another. In electromagnetism there are, in fact, two fields--the electric field, and the magnetic field." source:

Phys.Org News Partner Physics news on
Three's a charm: NIST detectors reveal entangled photon triplets
How did evolution optimize circadian clocks?
New webcast series brings cutting-edge physics talks to the world
Aug7-14, 08:04 PM
jtbell's Avatar
P: 11,858
In a nutshell, the electromagnetic field carries momentum. We define this in terms of a momentum density (momentum per unit volume), as defined at the top of this page:

The total momentum of a system of particles and electromagnetic fields is the sum of the mechanical momenta of the particles plus the integral of the electromagnetic momentum density over all space. Momentum can be transferred between these two forms by way of the electromagnetic (Lorentz) force ##\vec F = q(\vec E + \vec v \times \vec B)##, but the total is conserved. Unfortunately, to prove that the total is conserved, you need to use a lot of "hefty mathematics" in the form of vector calculus.

Register to reply

Related Discussions
Newton's Third Law and Linear Momentum Conservation General Physics 4
Momentum conservation and Newton's 3rd Introductory Physics Homework 2
Newton's law and conservation of linear momentum Classical Physics 9
Conservation of Angular Momentum from Newton's third law Classical Physics 5
Newton's laws&Conservation of Momentum Introductory Physics Homework 1