# Active versus passive mass in classical mechanics

1. Nov 18, 2011

### TurtleMeister

I like your explanation, and I agree. However, why does it not work for the case of gravity? To be more specific, I'm talking about the mainstream classical justification for the equivalence principle as it applies to active gravitational mass. Let me give an analogy that applies to the OPs question:

Two men with a rope are standing face to face on a frictionless surface (or ice). Regardless of which man pulls on the rope, one, the other, or both, they will always meet at their center of mass. Just as your post describes, the third law does not discriminate between the action and reaction.

However, it does discriminate for the case of gravity:

http://en.wikipedia.org/wiki/Equivalence_principle#Active.2C_passive.2C_and_inertial_masses

In fact, the equivalence principle depends on the discrimination! In the two body problem, if the gravitational field of M1 disappears, then the third law will be violated (they will not meet at their center of mass). And this is used as the justification for the equivalence of active gravitational mass and passive gravitational mass, even though there is no physical evidence to support it.

Am I missing something?

2. Nov 20, 2011

### D H

Staff Emeritus
Re: Coloumbs law and Newtons third law

You are missing that the cited wikipedia article is yet another reason to avoid wikipedia.

There is no such thing as active versus passive mass in Newtonian mechanics. There is only mass.

3. Nov 20, 2011

### TurtleMeister

Re: Coloumbs law and Newtons third law

Thanks for the response DH. Yes, I realize that wikipedia is not the best source, but it was convenient and the quoted section does agree with other mainstream sources I have encountered, such as:

Concepts Of Mass In Contemporary Physics And Philosophy by Max Jammer:
He then goes on to to give equations that predict a third law violation should there be an inequality between mp and ma.

4. Nov 20, 2011

### D H

Staff Emeritus
Re: Coloumbs law and Newtons third law

Emphasis mine:
Exactly. The topic at hand was Newtonian physics, not contemporary physics.

The equivalence principle posits that passive and active mass are one and the same thing, so even in general relativity there is no distinction between the two. The equivalence principle now stands as one of the most precisely tested axioms of physics.

5. Nov 20, 2011

### Matterwave

I wouldn't call the equivalence principle an axiom of physics. Postulate maybe, but axiom means to me like a mathematical construct which is true by definition. Maybe it's just personal preference.

6. Nov 20, 2011

### atyy

In Newtonian physics, the third law holds for non-test masses, and says that things interact mutually, as they do when they have the form of Coulomb's law. It's the third law that enforces the equivalence of active and passive charge. It does not enforce that charge is proportional to inertial mass.

One form of EP in Newtonian physics is that two test masses will hit the earth at the same time. This formulation requires that the test masses that don't affect the earth's motion. This observation leads to the formulation that charge (of the gravitational type) is proportional to inertial mass. The EP does not hold for non-test masses.

Last edited: Nov 20, 2011
7. Nov 20, 2011

### TurtleMeister

Re: Coloumbs law and Newtons third law

Well, if they were the same thing then there would be no point in having an equivalence principle. The equivalence principle posits that mp is proportionally equivalent to ma.

That's not true for ma. It is very poorly tested. Only one laboratory test in the past 45 years.

8. Nov 20, 2011

### TurtleMeister

I agree. But not what I am questioning in my op.

I think you're talking about the universality of free fall? I agree also, but not what I am questioning in my op.

9. Nov 20, 2011

### atyy

Can you restate your question then? I didn't understand it. I thought you were saying that the EP requires test masses to have only passive gravitational mass, not active gravitational mass, which is true.

10. Nov 20, 2011

### TurtleMeister

My question is: What reason do I have to believe the wiki quote in the op when there is no physical evidence that a third law violation would occur when $M^{pass}_1<>M^{act}_1$? In my analogy of the men with a rope in a tug of war, if one man pulls and the other does not, there is not going to be a third law violation. The same can be said for electric charges or any other example you can think of. So why should I believe the third law will be violated in the case of gravity?

11. Nov 20, 2011

### atyy

The third law would be violated. The third law says if I pull you, you must pull me. That causes active and passive charge to be the same.

12. Nov 20, 2011

### TurtleMeister

Okay, that makes sense. But it was my impression that active gravitational mass refered to the strength of a bodies gravitational field (or charge). If that is true then what does passive gravitational mass refer to? Does a body have two gravitational fields? That doesn't make much sense.

13. Nov 20, 2011

### atyy

Let's say it is possible for the sun to pull the earth, but the earth does not pull the sun. This is approximately true since the sun is much more massive. Then the force of the earth on the sun is 0, so the earth has no active gravitational mass. The earth is affected by the sun, so it has passive gravitational mass.

Newton's third law says that this description is not exactly true, and in fact the earth does pull the sun.

14. Nov 20, 2011

### D H

Staff Emeritus
The exact same concept, active mass versus passive mass, applies to charge as well. Both concepts are viewed as "exotic" (aka fringe) physics. In the minds of most physicists, they are not worthy of investigation once a small handful of experiments have been performed (and they have been) to dismiss such concepts.

15. Nov 20, 2011

### TurtleMeister

Thanks for your time DH and atyy. This is something that has bugged me for a long time. I'm still not clear on it, but I have to go now. It may be a day or two before I can get back. If you or anyone else have any other thoughts about this I would greatly appreciate hearing from you.

Turtle

16. Nov 21, 2011

### DrStupid

Re: Coloumbs law and Newtons third law

The equivalence principle posits that gravitational mass is proportionally equivalent to inertial mass. As D H already mentioned Newtonian mechanics does not distinguish between active and passive gravitational mass.

17. Nov 21, 2011

### D H

Staff Emeritus
Re: Coloumbs law and Newtons third law

That's exactly right. The equivalence principle does not distinguish between active and passive gravitational mass. It was Bondi who first introduced the concept of three kinds of mass (inertial mass, active gravitational mass, and passive gravitational mass) in Rev. Mod. Phys. 29, 423 (1957).

Just because something is published in a peer reviewed journal doesn't it is accepted. Getting something published is the starting point of a new scientific idea, not the culmination. In this case, the concept of active versus passive gravitational mass is viewed as an exotic, or fringe, idea.

Nonetheless, this idea has been tested, and more than just once. Just to name a few,

L.B.Kreuzer, "Experimental Measurement of Active and Passive Gravitational Mass," Phys. Rev. 169, 1007–1012 (1968);
D.F.Bartlett, D.van Buren, "Equivalence of active and passive gravitational mass using the moon," Phys. Rev. Lett. 57, 21–24 (1986);
D.P.Rubincam, "Mars seasonal polar caps as a test of the equivalence principle," Phys. Rev. D 84, 042001 (2011).

The exact same concept applies to charge as well as mass. It too has been tested; e.g.,

C.Lämmerzahl, A.Macias, H.Müller, "Limits to differences in active and passive charges," Phys. Rev. A 75, 052104 (2007).

Last edited: Nov 21, 2011
18. Nov 23, 2011

### TurtleMeister

Thanks for the info DH. I'm already familiar with the L.B.Kreuzer and D.F.Bartlett, D.van Buren experiments, but I have not read the other two.

Before Bondi, what did gravitational mass refer to, active, passive, both, or something else?

That's interesting. I did not realize these concepts were considered exotic or fringe. I noticed that you preceded your statement with "in this case". Could you explain what you mean by this? Are there cases where these terms have different meanings?

The L.B.Kreuzer experiment is the one I was referring to in my post #7 where I stated "That's not true for Ma. It is very poorly tested. Only one laboratory test in the past 45 years." The D.F.Bartlett, D.van Buren experiment is not a laboratory experiment. It is better described as a thought experiment based on the Wikipedia equations I posted in the OP of this thread. It assumes that the third law would be violated if Mp <> Ma. The Kreuzer laboratory experiment does not make this assumption.

I really appreciate your comments on this DH. It's hard to find others who have an interest in, or are willing to discuss, this topic. I will read the last two articles you sited if/when I can find a free copy.

19. Nov 23, 2011

### D H

Staff Emeritus
Taking it in stages,
• In Newtonian mechanics, the mass in F=ma and the masses in F=GMm/r2 are one and the same. Reading through Newton's papers, I don't see any sign that he saw any distinction at all between the inertial mass in his second law of motion and the gravitational mass in his universal law of gravitation.
• Einstein saw that those equations left an opening for a distinction between the two concepts of mass. His equivalence principle says that inertial and gravitational mass are one and the same thing.
• Bondi saw yet another possible bifurcation in Newton's law of universal gravitation. This is where the concept of active versus passive gravitational mass first arose.
What Einstein did and what Bondi did are very different things. While both Einstein and Bondi pointed out implicit assumptions in Newton's theories, that is where the similarity ends. Einstein's equivalence principle make Newton's implicit assumption explicit. He did not ask "what if those concepts of mass are different?" Instead he asked "what does inertial mass and gravitational mass being one and the same mean?" This line of questioning was the key to general relativity.

Contrast that to Bondi's concept of active and passive gravitational mass. Before Bondi, the distinction between the two just didn't exist. His distinction adds nothing new to physics if they are one and the same thing. If they are not necessarily the same, all of the conservation laws go out the window.

Let me rephrase that paragraph of mine:
Just because something is published in a peer reviewed journal doesn't it is accepted. Getting something published is the starting point of a new scientific idea, not the culmination. Just because Bondi got his idea of active versus passive gravitational mass published does not mean that it is accepted science. To the contrary: Most physicists view it as an exotic, or fringe, idea.​

As noted above, the conservation laws would have to be tossed were Bondi correct about passive gravitational mass being distinct from active gravitational mass. Emily Noether had already shown how truly deep those conservation laws are. Throwing the conservation laws out because of what most physicists viewed as an artifice would require a lot of evidence. ("Extraordinary claims require extraordinary evidence.")

It most certainly is a laboratory experiment. The universe is the grand laboratory by which most gravitational theories are tested. It was Kepler's laboratory, and Newton's, and Einstein's. You are not going to see distinctions between general relativity and Newtonian gravity on the scale of what you call a laboratory experiment. Large masses and large velocities are needed to make such distinctions observable. It was the precession of Mercury and the bending of light by the sun as observed during the 1922 eclipse that convinced physicists that general relativity was correct, not some puny human-scale laboratory experiment.

That's because most people don't want to waste time on fringy notions. And this is fringy. Not crackpot, mind you, fringy. There's a huge difference between crackpot and fringe notions.

20. Nov 23, 2011

### TurtleMeister

I understand and agree. In Newton's time there was no distinction.
But here you have omitted what my question was about. What two concepts of mass did Einstein see an opening for? Inertial and active gravitational mass, inertial and passive gravitational mass, or something else? I think I know what it is, but I'll wait and see what your thoughts are.
I understand and agree.
I agree. Except I think it is passive gravitational mass and inertial mass that are usually considered to be one and the same thing. And it is the equality of these two concepts of mass that have been tested to very high precision.

I agree. Except I would replace "active gravitational mass" with "inertial mass" in the above quote. In fact, the title of this thread is not what I would have chosen. My choice would have been "Gravitational (active) mass vs inertial (passive) mass". To give an example, look at the abstract to D.P.Rubincam's article that you cited in post #17.

You missed the point. The point I was trying to make is that the Kreuzer experiment did not assume that the third law of motion would be violated if Ma <> Mi / Mp, while the Bartlett / Buren experiment DID make this assumption (the Wikipedia equations). They did their thought experiment and then concluded "hey look, the third law is not being violated (the moon is not self accelerating), so Ma must be equivalent to Mi / Mp". Compare that to the many, many high precision torsion balance experiments that have been conducted to test the equivalence of Mp and Mi which did not make such an assumption. So why should we give credence to the one (or maybe two) thought experiments to test the equivalence of Ma and Mi / Mp which did make this assumption?

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. And the experiment only achieved a precision of 5x10-5. It's a wide open field for experimentation. But it is being ignored because of those Wikipedia equations.

Well, thank you for taking the time to discuss my fringy interest with me. :)

Last edited: Nov 24, 2011