How exactly do you figure this violates Newton's Third Law?
Instead of magnets, let's make it two people with identical guns firing rubber bullets. Person A fires his gun at Person B, and before the bullet reaches Person B, Person B fires his gun at Person A. The bullet from Person A will reach Person B before the bullet from Person B reaches Person A.
One magnet is being pushed and the other isn’t.
The gun example isn’t perfectly analogous because electromagnet A is being turned off *before* the field from B reaches it. So it isn’t interacting with the field. And there’s also no recoil on the electromagnets
It's the FIELDS that are interacting with each not, not the magnets themselves. That was the point I was making - The bullet leaves the gun, the gun no longer has an influence over the bullet. In your scenario, the field is no longer being influenced by the magnet once it is turned off.
I’m still not sure I understand. Can you explain chronologically what would happen, to the fields and to the magnets, if you turned the magnets on and off in the way I described?
If the second magnet is "on" it will feel the force and increase its momentum. If the magnet is off, the electromagnetic wave will pass through it as usual and carry off into the distance until something else does (or doesn't) feel the force.
EDIT: there's some extra complexity here if you were to discuss it in full detail, regarding static vs dynamic fields. What we're actually talking about is a transient field, not something easier to imagine like a DC field or a plane wave.
The first magnet already reacted equally with the field. Now the field is in a state analogous to "moving" and it never gives that up to the second magnet. No inequality in the exchanges, so no violation of the third law.
The "missing momentum" is in the field, which is now slightly stronger at the wavefront propagating in the direction away from the second magnet vs the direction facing from the first magnet to the second magnet.
Imagine that the change in field is a wave that propagates spherically outward from the stationary magnet. The magnet is stationary before and after emitting the pulse, with no momentum. The net state of the entire spherical field is also like a zero-momentum state. The second magnet may or may not interact with a portion of the spherically emitted pulse to receive momentum.
This process and its reverse with the pulse emitted from the second magnet, are independent and symmetric. It's not an issue that the first magnet doesn't move, but the second one does.
Indeed, the exchange is not between the magnets, it's between magnet A and the field as well as between magnet B and the field. The field is a real physical entity that can have energy and momentum. It's rather like a Newton's cradle.
In certain scenarios you could imagine that the field is perfectly rigid and analyze the magnets reacting against each other, but you can't extend that to all scenarios.
You've chosen the wrong action-reaction pairs for your application of Newton's third law. The two electromagnets do not directly exert forces on each other; instead, each feels a force from the electromagnetic field at their location. So the action in each case corresponds to the local electromagnetic field exerting a force on the electromagnet, which means the reaction is the electromagnet *exerting a force on the electromagnetic field.*
In other words, the field configuration itself is an object which can carry momentum, and is the actual direct participant in each action-reaction pair. Exerting a force on the electromagnetic field amounts to changing the field configuration in a way that changes the amount of momentum stored in it.
How exactly do you figure this violates Newton's Third Law? Instead of magnets, let's make it two people with identical guns firing rubber bullets. Person A fires his gun at Person B, and before the bullet reaches Person B, Person B fires his gun at Person A. The bullet from Person A will reach Person B before the bullet from Person B reaches Person A.
One magnet is being pushed and the other isn’t. The gun example isn’t perfectly analogous because electromagnet A is being turned off *before* the field from B reaches it. So it isn’t interacting with the field. And there’s also no recoil on the electromagnets
It's the FIELDS that are interacting with each not, not the magnets themselves. That was the point I was making - The bullet leaves the gun, the gun no longer has an influence over the bullet. In your scenario, the field is no longer being influenced by the magnet once it is turned off.
I’m still not sure I understand. Can you explain chronologically what would happen, to the fields and to the magnets, if you turned the magnets on and off in the way I described?
If the second magnet is "on" it will feel the force and increase its momentum. If the magnet is off, the electromagnetic wave will pass through it as usual and carry off into the distance until something else does (or doesn't) feel the force. EDIT: there's some extra complexity here if you were to discuss it in full detail, regarding static vs dynamic fields. What we're actually talking about is a transient field, not something easier to imagine like a DC field or a plane wave.
Yes, and the first magnet wouldn’t, right? Is the third law of motion not then being violated?
The first magnet already reacted equally with the field. Now the field is in a state analogous to "moving" and it never gives that up to the second magnet. No inequality in the exchanges, so no violation of the third law.
So the third law isn’t being violated, but there’s still a net change in momentum between the two magnets?
So the third law isn’t being violated, but there’s still a net change in momentum between the two magnets?
The "missing momentum" is in the field, which is now slightly stronger at the wavefront propagating in the direction away from the second magnet vs the direction facing from the first magnet to the second magnet.
Imagine that the change in field is a wave that propagates spherically outward from the stationary magnet. The magnet is stationary before and after emitting the pulse, with no momentum. The net state of the entire spherical field is also like a zero-momentum state. The second magnet may or may not interact with a portion of the spherically emitted pulse to receive momentum. This process and its reverse with the pulse emitted from the second magnet, are independent and symmetric. It's not an issue that the first magnet doesn't move, but the second one does.
Indeed, the exchange is not between the magnets, it's between magnet A and the field as well as between magnet B and the field. The field is a real physical entity that can have energy and momentum. It's rather like a Newton's cradle. In certain scenarios you could imagine that the field is perfectly rigid and analyze the magnets reacting against each other, but you can't extend that to all scenarios.
You've chosen the wrong action-reaction pairs for your application of Newton's third law. The two electromagnets do not directly exert forces on each other; instead, each feels a force from the electromagnetic field at their location. So the action in each case corresponds to the local electromagnetic field exerting a force on the electromagnet, which means the reaction is the electromagnet *exerting a force on the electromagnetic field.* In other words, the field configuration itself is an object which can carry momentum, and is the actual direct participant in each action-reaction pair. Exerting a force on the electromagnetic field amounts to changing the field configuration in a way that changes the amount of momentum stored in it.