Why does Newton's 3rd law holds macroscopically?

[ELB27]

Hi all,

I recently learned about the breakdown of Newton's 3rd law in electrodynamics and this got me thinking. The forces we consider in classical mechanics like friction and normal forces are microscopically electromagnetic interactions (repulsions?) of the atoms of two surfaces. If Newton's 3rd law doesn't hold for those interactions (which are certainly not static), how come it holds macroscopically? Perhaps it holds just as a good approximation, "on average"?

Thanks in advance for any comments!

 

[Orodruin]

I recently learned about the breakdown of Newton's 3rd law in electrodynamics

It actually does not break down. You simply have to consider the momentum carried by the electromagnetic field as well.

 

[Vatsal Sanjay]

You simply have to consider the momentum carried by the electromagnetic field as well.

Can you suggest me a few sources to read about this in detail? Please prefer research papers if possible. I had been fascinated by this problem and a little sceptic about this very explanation but could never find reliable relevant sources.
I hope this isn't out of on going discussion domain.

 

[Dale]

If Newton's 3rd law doesn't hold for those interactions (which are certainly not static), how come it holds macroscopically? Perhaps it holds just as a good approximation, "on average"?

As Orodruin mentioned, the key is to recognize that while the 3rd law may not hold, it generalizes to the conservation of momentum, which does hold provided that you include the momentum of the fields as well. Then the reason that the 3rd law holds macroscopically follows from the fact that there are no "macroscopic" fields carrying away momentum.

 

[Dale]

Can you suggest me a few sources to read about this in detail?

Here is my favorite source on the topic.
http://farside.ph.utexas.edu/teaching/em/lectures/node91.html

 

[Orodruin]

while the 3rd law may not hold

It does hold if you consider the force to have a corresponding (local) force acting on the electromagnetic field, i.e., imparting momentum on it. The SR version is simply the conservation of the total energy momentum tensor, i.e., if you have two components of energy and momentum, $\partial_\mu (T_1^{\mu\nu} + T_2^{\mu\nu}) = 0$. Each term can be considered to be a 4-force density.

 

[Dale]

It does hold if you consider the force to have a corresponding (local) force acting on the electromagnetic field

Agreed completely. That is why I used the word "may". I tend to favor exactly the interpretation you mentioned where the matter exerts a "force" on the field which gains momentum, but I haven't seen that as an "official" interpretation so I didn't want to push it.

Even if you take the contrary view and consider the "force" on a field to not be a valid force (so that Newton's 3rd is violated in some cases) you still have conservation of momentum and, if no macroscopic fields carry momentum, then Newton's 3rd is recovered.

 

[ELB27]

Thank you for the replies! I need to think about it a bit more from this point of view of momentum conservation.

By the way, Orodruin, is your name a reference to Mount Doom?

 

[Orodruin]

By the way, Orodruin, is your name a reference to Mount Doom?

Yes, but that is off-topic.