Active versus passive mass in classical mechanics

[TurtleMeister]

As for which test is stronger, which gave the smaller upper bound on Ma/ma-Mb/mb?

My point is that the current level of technology for torsion balance experiments meets or exceeds the level of precision of the Bartlett and Van Buren thought experiment, but these types of experiments are not being done because of what you posted:

What assumption? That third law violations would result were active, passive, and inertial mass not one and the same thing are a direct consequence of Newton's second law and his universal law of gravitation. That isn't an assumption, it is a consequence. Looking for some consequence of a hypothesis is a standard way of testing said hypothesis. Bartlett and Van Buren's experiment was not assumption-free. They assumed that forces are still subject to the superposition principle and as a consequence, that the observed torsion can still serve as a surrogate for the gravitational attraction.

I notice that you were previously criticized my use of the Wikipedia equations and now you are defending them. But that's good because you're now seeing what I am having a problem with.

That third law violations would result were active, passive, and inertial mass not one and the same thing are a direct consequence of Newton's second law and his universal law of gravitation.

That's true for active and passive gravitational mass but not for inertial mass. A difference between gravitational and inertial mass would be compatible with Newton's third law but not with the Galilean equivalence principle.

I agree that M_a <> M_i would not violate the third law, but I do not know how it would violate the Galilean equivalence principle.

Thanks for the comments atyy. Even though I'm reluctant to discuss GR because of my lack of knowledge in that area, I did notice a possible contradiction between the statements quoted from Rindler and Roche.

Newtonian active gravitational mass (the creator of the field) goes over to GR as the creator of the curvature. Newtonian passive gravitational mass (that which is pulled by the field) goes into banishment along with the ether, ect.

Hermann Bondi developed this classification further in 1957, by adding the term ‘active gravitational mass’ and re-describing Einstein’s ‘gravitational mass’ as ‘passive gravitational mass’

The Rindler quote seems to imply that passive gravitational mass does not exist in GR, while the Roche quote seems to imply that passive gravitational mass is what was once referred to as simply gravitational mass in GR.

Thanks to everyone who has provided comments on this. I will return later to try and explain why I am having a problem understanding the use of the wiki equations as a justification for the M_a equality.

 

[atyy]

Thanks for the comments atyy. Even though I'm reluctant to discuss GR because of my lack of knowledge in that area, I did notice a possible contradiction between the statements quoted from Rindler and Roche.

The Rindler quote seems to imply that passive gravitational mass does not exist in GR, while the Roche quote seems to imply that passive gravitational mass is what was once referred to as simply gravitational mass in GR.

Einstein used ideas of "gravitational mass" in two contexts. One in the equivalence principle during the development of GR, here the gravitational mass is the Newtonian passive gravitational mass. Secondly as the thing that causes spacetime curvature in full GR, this is the analogue of Newtonian active gravitational mass.

So for asking about the analogue of passive gravitational mass in GR, one would ask how the equivalence principle is implemented. The EP is implemented by saying that the spacetime has the same signature as in special relativity, and that matter fields are minimally coupled to spacetime. Anyway the main point is that the geodesic equation (which is essentially universality of free fall to make the connection to the WEP) is no longer an independent principle, but rather derived as an approximate equation from the full field equations containing active gravitational mass.

 

[DrStupid]

I agree that M_a <> M_i would not violate the third law, but I do not know how it would violate the Galilean equivalence principle.

Two bodies with the same inertial mass, initial position and velocity but different gravitational mass would have different trajectories. The Galilean equivalence principle at least requires the same correlation between gravitational and inertial mass for all bodies.

 

[TurtleMeister]

Yes, you are correct DrStupid. M_a <> M_i would indeed violate the Galilean equivalence principle. But it would be extremely difficult, if not impossible, to detect in Earth free fall. We could however use a torsion balance to detect the difference in their active gravitational mass.

Before going on, I would like to do a thought experiment to make sure we are all on the same page and that I do not have any misconceptions. This thought experiment is not possible in reality. I use it here only to demonstrate my understanding of the concepts involved in this discussion. Please let me know if you think I have anything wrong here.

Thought experiment 1:
The scenario is the two body problem where there are no other outside forces acting on the bodies. Bodies A and B are separated by distance r. Initially the bodies are stationary and not allowed to move. The mass of both A and B are equal in all respects, except for the active gravitational mass of B. B generates no gravitational field of it's own. If we now allow the bodies to move, B will accelerate toward A, but A will not move. The point of impact will be at body A, a distance of r/2 from the common center of inertial mass of the two bodies. The third law will be vioated. If we now give B a gravitational field, but only one half that of A, then both A and B will move. The acceleration of B will be double the acceleration of A. The point of impact will be r/4 from the common center of inertial mass of the two bodies. The third law will be violated.

 

[TurtleMeister]

Sorry about the delay. I've been very busy this week. Since there have been no responses to my previous post I will assume that my thought experiment 1 is correct and agrees with the Wikipedia equations and the mainstream concepts. I will try to get to the point of what I'm having trouble with. But first I must do another thought experiment.

Thought experiment 2:
The scenario is the same as before, except the two bodies are composed of ferromagnetic material. Body A is a permanent magnet, so it is the creator of a magnetic field. Body B is not a magnet, so it does not have a magnetic field of it's own. When A and B are allowed to move, they will accelerate toward each other and meet at their common center of inertial mass. The third law is not violated. If I now make body B a permanent magnet but give it only half the pull force of body A, then the acceleration of both bodies will increase by the same amount and they will still meet at their common center of inertial mass. The third law is not violated.

Now let's go back to what started this thread:

The two forces have equal status. You cannot consider one of them to be "cause" and the other to be "effect." You should not take the words "action" and "reaction" in the context of the Third Law as indicating "cause" and "effect". They are simply a commonly-used terminology.

[added] When I teach Newton's Third Law in an introductory course, I avoid using the words "action" and "reaction" except to address confusions such as this.

I agree with jtbell's post, and it is very much true for thought experiment 2. A exerts a force on B (action), and B exerts an equal but opposite force on A (reaction). And when B was given a magnetic field, it exerted a force on A (action), and A exerted a force on B (reaction). The third law holds true regardless of which body is the creator of the force, it could be A, B, or both. I think this is pretty much the standard definition of the third law.

However, in thought experiment 1, there are no reaction forces at all, only action forces. Since there are no reaction forces, then obviously both bodies must have equal but opposite action forces (gravitational fields) to prevent a violation of the conservation of momentum. So how can this be a legitimate use of the third law of motion?

 

[TurtleMeister]

I am bumping this thread up only because this has been an unresolved problem for me for a long time. If there are no replies to this post then I will let it die. Even if you don't have an answer, it would be a great help to me if you just let me know that you understand what I'm talking about. Right now I do not know if I have a misconception or I just did not explain myself very well. Regardless, I would like to thank those who have responded so far. Your input has been helpful.

Also, if for whatever reason you do not feel comfortable replying in the thread, then a PM would be great.

Turtle