# Can Newton's Third Law Of Motion Be Violated?

1. Oct 10, 2011

### alexanderleg

I have read in several books and also in this site that the Newton's Third Law does not hold true for "Action at a distance". Specifically, in the case of Electrodynamics.

Can someone explain to me, what actually happens in the case of electromagnetism? I've read that the action-reaction forces are not collinear that is 'weak form of third law'. What exactly does this mean?

Early this year, due to lapse of my brain functioning, I committed a serious mistake of neglecting the third law for my Google Science Fair project. Take a look: https://sites.google.com/site/levitationp2wreduction/
You'll understand how flawed the idea is (and maybe have some pity on my foolishness?)

Though, deep inside, I still hope that the third law gets violated so that my idea works.

2. Oct 10, 2011

### atyy

Newton's third law does hold true for action at a distance in Newtonian mechanics, as in the Newtonian gravitational field. If the sun exerts a force on you now, you exert the same force on it now (not 8 minutes later). In Newtonian mechanics, conservation of momentum is derived from the third law.

However, in special relativity, we expect there to be an upper speed limit to the interactions between particles. Thus the force between two charges at a distance is described as being mediated by an electromagnetic field, with changes propagating at the speed of light. We'd like there still to be "Newton's third law" locally, like "the charge exerts a force in the field", and "the field exerts a force on the charge". However, it is difficult to say what "the charge exerts a force in the field" means. Instead, it is easier to assign momentum to the field, and to say that momentum is conserved. Thus in special relativity, one takes conservation of momentum as primary, not derived, preserving the spirit, but not the letter of the third law.

Last edited: Oct 10, 2011
3. Oct 10, 2011

### Andrew Mason

You appear to be trying to accelerate the passengers and their seats without applying a force to them. You can reduce friction by levitating the entire vehicle and then applying a thrust (eg. magnetic or jet propulsion). This works for magnetically levitated trains. In your case, however, you are not trying to reduce friction - you are trying to reduce the mass that the engine has to accelerate. So what causes the passengers to move along with the car?

AM

4. Oct 11, 2011

### MrNerd

I was fairly sure that Newton's Third Law always held true, never hearing of it not holding true. In electromagnetic things, it's fairly simple. Think of it this way:

Particle A has a charge of +1C. Particle B has a charge of +2C. The force is given by $$F = \frac{kQ_{1}Q_{2}}{r^{2}}$$ This force acts identically upon both particles, hence Newton's Third Law holds.

5. Oct 11, 2011

### D H

Staff Emeritus
That is the electrostatic force, static being the key word here. It implicitly assumes an action at a distance (i.e., infinitely fast) kind of force and it is not a complete description of the electromagnetic interactions when the particles are in motion.

Newton's Third Law can fail in a number of cases:
• There is a time delay in the equations of motion, such as is the case for electrodynamics (as opposed to electrostatics). What is happening here is that the field that mediates the interaction is itself storing momentum. There is no room for such in Newton's 3rd. As mentioned before, this can be reconciled by observing that momentum is still conserved. Newton's 3rd law is conservation of momentum in the special case that forces are instantaneous and central in nature.

• The force is not central in nature, which once again is the case for electrodynamics. In the strong form of Newton's third law, third law force pairs must be equal but opposite in nature and the force must be directed along or against the line connecting the pair of particle. This form of Newton's third law conserves both translational and angular momentum. Translational and angular momentum can still be conserved in the case of non-central forces if the mediating field stores these momenta, but Newton's third does not apply in such cases.

• The underlying interaction inherently involves three or more particles. Newton's third demands that forces be resolvable down to pairs of particles. There are some multi-body interactions in quantum mechanics where the interactions only appears when three or more particles are present. These interactions cannot be isolated down to pairs, and once again Newton's third law fails.

In more advanced physics, it is the conservation laws that reign supreme. Newton's third law derives from the conservation laws with the assumption that forces act in pairs, act instantaneously, and act along the line connecting particle pairs. Drop those assumptions and you have to drop Newton's third law. You do not have to drop the conservation laws, however. In even higher level physics, the conservation laws themselves can be derived from the very nature of space and time.

Last edited: Oct 11, 2011
6. Oct 11, 2011

### olivermsun

And what of the magnetic fields if the particles are moving?