Important question about violation of Newton's third law

[Johnny5]

I long ago encountered a question which I have never seriously discussed with anyone at length, and I wish to do so now.

 

Suppose that there is a way that some hollow shell object could be constructed so that Newton's third law is untrue to travellers inside of it, if the object is accelerated.

 

For definiteness, let the object accelerate by emitting a massive amount of virtual photons. The idea is to be that the ship emits particles which follow F=ma, in the frame, but there is no reaction force on the ship.

 

If the object starts off in space in a frame where v=0 and W=0, and then accelerates to g in that frame, and then maintains that acceleration, what would be the weight of people inside the shell?

 

Thank you

 

PS: Here are some links related to this topic.

 

IOP Abstract for experimental test of Newton's third law

 

IOP abstract discussing violations of NTL

 

This one seems interesting Engineering Lecture

 

It contains the following:

 

 

A little consideration will then show that, had Newton asserted his 'rule' as a law, then by appealing to the Principle of Conservation of Energy he could have deduced instead the 'rule' that action equals reaction. The point one can now make is that Newton's Third Law need not be sacrosanct and can be broken if one has a situation where energy can be deployed, not at the moment of collision and immediate separation, but by an interaction across space separating the two bodies. This puts us in the realm of electrodynamics, where one encounter's the Neumann Potential and can trace its association to a 19th century proposition known as Fechner's Hypothesis by which one can derive the energy potential of two interacting electric charges in motion as being a function of the square of their relative velocities. Furthermore, electrodynamics involves so-called 'field energy' which is energy seated in whatever it is that we refer to as the 'vacuum', but which used to be called the 'aether'. Can one ever hope to find a way of pushing against that aether and, in so doing, tapping some of its energy?

 

Notice that there was talk of pushing off the vacuum.

 

My interest in this question actually comes from problems in classical electrodynamics. In the solution of certain problems (solenoidal fields if memory serves me) in electrodynamics, there are violations of action/reaction, but I never personally understood how people were concluding that certain electromagnetic effects were demonstrating violations of Newton's third law.

 

The reason I have focused so much on this issue, is because if Newton's third law can be violated under the right set of circumstances, then I know that the weight of the passenger in the shell will not be Mg, where M is their inertial mass, and the shell is essentially the "Einstein elevator" of the General theory of relativity, so the question is interesting on theoretical grounds alone.

 

Mathematically, Newton's laws don't predict conservation of energy, and virtual photons depend upon violation of conservation of energy (over small amounts of time governed by the energy/time uncertainty principle... which is wishy washy). And the article above says that action/reaction can be deduced from conservation of energy, so I am not sure how all this jives with the General theory of relativity and/or the principle of equivalence.

 

Any ideas, comments would be most welcome.

 

Thank you

[Meir Achuz]

NIII follows from conservation of linear momentum, which is more basic than simple action and reaction.

Newton never incorporated magnetism into his mechanics.

The magnetic interaction between two moving charged particles does not satisfy N III.

If the changing momentum of the electromagnetic fields of the two particles is incuded,

then overall momentum is conserved. Energy has nothing to do with NIII.

I do not understand the wording of your original question, and the quote seems to be

archaic.

[Johnny5]

NIII follows from conservation of linear momentum' date='

[/quote']

 

Prove this.

[Meir Achuz]

Look in any UG mechanics book that derives conservation of momentum from NII,

and follow the steps backward. In a grad text (like Goldstein), conservation of momentum is derived from the Lagrangian. Then NIII is shown to follow from that.

[Guest noinipo]

Prove this.

Momentum is always conserved.

[swansont]

Momentum is always conserved.

 

When the net force on the system is zero.

[Johnny5]

Look in any UG mechanics book that derives conservation of momentum from NII' date='

and follow the steps backward. In a grad text (like Goldstein), conservation of momentum is derived from the Lagrangian. Then NIII is shown to follow from that.[/quote']

 

The whole point is I wanted to see a mathematical proof of the fact. Use the Lagrangian, I don't care how you do it. Or better yet, prove it several ways. I am not saying that it's false, nor am I saying that it's true. If you have access to a proof, then let me see it please.

 

Postulate 1: The differential calculus is error free.

 

[math] \vec F \equiv \frac{d\vec P}{dt} [/math]

 

[math] \vec P \equiv M \vec v [/math]

 

[math] \vec F = \frac{d(M \vec v)}{dt} [/math]

 

[math] \frac{d(M \vec v)}{dt} = M \frac{d\vec v}{dt} +\vec v \frac{dM}{dt}[/math]

 

[math] \vec F = M \frac{d\vec v}{dt} +\vec v \frac{dM}{dt}[/math]

 

Consider the case where F=0.

 

[math] \vec 0 = M \frac{d\vec v}{dt} +\vec v \frac{dM}{dt}[/math]

 

It now follows that:

 

[math] \vec 0 - M \frac{d\vec v}{dt} = \vec v \frac{dM}{dt}[/math]

 

Assume the following mathematical step is valid:

[math] - M \frac{d\vec v}{dt} = \vec v \frac{dM}{dt}[/math]

 

Multiply both sides of the statement above by a time differential:

 

[math] - M d\vec v = \vec v dM[/math]

 

Can you finish it up from here?

 

 

PS: I don't mean to imply that the differential calculus is error free, but somehow that gets assumed. Unless you know of a reason why we shouldn't use it, you may use it in your derivation. If you would like to switch to the finite discrete difference calculus, that is also fine by me. It's up to you, I just want to see the proof.