Active versus passive mass in classical mechanics

  • #26
D H
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This makes me wonder if the trichotomy of mass that we're familiar with today was actually known about, or at least contemplated, as far back as Newton's time, but was just not referred to by any name.
You mentioned John Roche's paper in very next post. From that paper,
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’​


Going back a few more posts, my answer to this was a bit short.
You missed the point. ... That's the reason I maintain that the Kreuzer experiment is the only legitimate experiment in the past 45 years to test the equivalence of Ma and Mi / Mp.
Most physicists disagree with your contention.
You have a misunderstanding of how experimental science works. Indirect observation is often the only option to scientists available because many things in science are not directly observable. There's no such thing as a gravity detector, but a device that measures acceleration with respect to a local free-falling frame (aka an accelerometer) can serve as a stand-in. There's no way to directly see neutrinos, but they can be seen indirectly thanks to the (occasional) weak interactions between neutrinos and baryonic matter; the subsequent decay of the products created by those interactions is observable.

Even when direct observations can be made, indirect observations oftentimes provide a stronger test. In the problem at hand, violations of Newton's third law necessarily result if active and passive gravitational mass are not equivalent. Looking for such violations most certainly is a valid test of this concept. This indirect observation provides a much stronger test of the proposition than do Cavendish balance type tests.
 
  • #27
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D H said:
TurtleMeister said:
This makes me wonder if the trichotomy of mass that we're familiar with today was actually known about, or at least contemplated, as far back as Newton's time, but was just not referred to by any name.
You mentioned John Roche's paper in very next post. From that paper,

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’
Yes, I noticed that in Roche's paper. It does nothing to disprove my conjecture. It could be that Bondi simply gave names to what had already been contemplated as far back as the time of Newton. It does however answer a question that I asked in a previous post:
TurtleMeister said:
What two concepts of mass did Einstein see an opening for? Inertial and active gravitational mass, inertial and passive gravitational mass, or something else?

D H said:
Even when direct observations can be made, indirect observations oftentimes provide a stronger test. In the problem at hand, violations of Newton's third law necessarily result if active and passive gravitational mass are not equivalent. Looking for such violations most certainly is a valid test of this concept. This indirect observation provides a much stronger test of the proposition than do Cavendish balance type tests.
Good comeback DH. I can tell you're giving this more serious consideration now. You're addressing the point of my thread.

How can the Bartlett and Van Buren type of experiment be considered a stronger test than a torsion balance type experiment when the former relies on an assumption that the latter does not? Why should we base our experimental conclusion on an assumption when we don't have to?
 
  • #28
D H
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How can the Bartlett and Van Buren type of experiment be considered a stronger test than a torsion balance type experiment when the former relies on an assumption that the latter does not? Why should we base our experimental conclusion on an assumption when we don't have to?
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.

As for which test is stronger, which gave the smaller upper bound on Ma/ma-Mb/mb?
 
  • #29
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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.
 
  • #30
atyy
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Just a quick comment that might be useful. Rindler (p21) states that Newtonian active gravitational mass goes over into GR as the creator of the gravitational field, while Newtonian passive gravitational mass goes into banishment along with the ether, and inertial mass survives only in non-gravitational contexts.

I think the experimental evidence is sufficient that we no longer test Newtonian gravity per se (it is already falsified), we only test it as an excellent approximation to GR in some regimes.
 
  • #31
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D H said:
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:
"D H" said:
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.
DrStupid said:
D H said:
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 Ma <> Mi 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 Ma equality.
 
  • #32
atyy
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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.
 
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  • #33
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I agree that Ma <> Mi 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.
 
  • #34
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Yes, you are correct DrStupid. Ma <> Mi 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.
 
  • #35
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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:
jtbell said:
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?
 
  • #36
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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
 

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