# Active versus passive mass in classical mechanics

## Main Question or Discussion Point

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 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?

## Answers and Replies

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D H
Staff Emeritus

Am I missing something?
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.

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.
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:
Just as a violation of the mi = mp equality would be fatal to Einstein's general relativity, a violation of the mp = ma equality would be fatal to Newtonian physics, for it would invalidate Newton's third law of motion.
He then goes on to to give equations that predict a third law violation should there be an inequality between mp and ma.

D H
Staff Emeritus

Emphasis mine:
Concepts Of Mass In Contemporary Physics And Philosophy by Max Jammer:
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.

Matterwave
Gold Member
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.

atyy
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.
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.

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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.
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.

The equivalence principle now stands as one of the most precisely tested axioms of physics.
That's not true for ma. It is very poorly tested. Only one laboratory test in the past 45 years.

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

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

atyy
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.
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.

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.
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?

atyy
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?
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.

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.
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.

atyy
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.
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.

D H
Staff Emeritus
I like your explanation, and I agree. However, why does it not work for the case of gravity?
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.

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

The equivalence principle posits that mp is proportionally equivalent to ma.
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.

D H
Staff Emeritus

The equivalence principle posits that gravitational mass is proportionally equivalent to inertial mass.
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).

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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.

D H said:
DrStupid said:
The equivalence principle posits that gravitational mass is proportionally equivalent to inertial mass.
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).
Before Bondi, what did gravitational mass refer to, active, passive, both, or something else?

D H said:
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.
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?

D H said:
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).
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.

D H
Staff Emeritus
Before Bondi, what did gravitational mass refer to, active, passive, both, or something else?
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.

D H said:
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.
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?
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.")

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 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.

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.
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.

D H said:
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.
I understand and agree. In Newton's time there was no distinction.
D H said:
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.
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.
D H said:
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.
I understand and agree.
D H said:
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.
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.

D H said:
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.")
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.

D H said:
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 observed during the 1922 eclipse that convinced physicists that general relativity was correct, not some puny human-scale laboratory experiment.
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.

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

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D H
Staff Emeritus
But here you have omitted what my question was about. What two concepts of mass did Einstein see an opening for?
Inertial mass and gravitational mass. By focusing on passive versus active gravitational mass you are missing big chunks of what the equivalence principle is about. Einstein had already established another equivalence in his 1905 papers: That between inertial mass and energy. The equivalence principle adds gravitational mass to the mix. Einstein had no need to distinguish between passive and active gravitational mass. He had a much better name for "active gravitational mass": Energy. It is energy, not mass, that gravitates in general relativity.

You appear to be getting a lot of your information from that wikipedia article on the equivalence principle. Take a close look at that article. Take an even closer look at the largish section entitled "Active, passive, and inertial masses." That section is very out of place. Moreover, it is missing something that is supposedly very crucial to wikipedia articles: Where are the references?

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.

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D H said:
Inertial mass and gravitational mass. By focusing on passive versus active gravitational mass you are missing big chunks of what the equivalence principle is about. Einstein had already established another equivalence in his 1905 papers: That between inertial mass and energy. The equivalence principle adds gravitational mass to the mix. Einstein had no need to distinguish between passive and active gravitational mass. He had a much better name for "active gravitational mass": Energy. It is energy, not mass, that gravitates in general relativity.
Thanks for the info. Unfortunately, I am reluctant to comment on this as I have not studied Einstein and GR enough to be comfortable with discussing it in any great detail.
You appear to be getting a lot of your information from that Wikipedia article on the equivalence principle. Take a close look at that article. Take an even closer look at the largish section entitled "Active, passive, and inertial masses." That section is very out of place. Moreover, it is missing something that is supposedly very crucial to Wikipedia articles: Where are the references?
Actually no, I am not getting most of my information from that article. As I've stated before, I simply cited that section because it was convenient. It agrees with everything else I have read on the subject. I would not have posted it otherwise. Please notice that I only posted a small section of that article. If you need other sources then try chapter 4 page 102 of the Max Jammer book I mentioned previously. I can also find others if needed.
"D H" said:
TurtleMeister said:
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.
Well, if this is really considered to be a fringy concept by most physicists, then I can understand why they would publicly disagree. All I'm asking is for anyone who is remotely interested in this discussion to just study the experiments and articles and draw your own conclusion.

Update:
I just read the introduction to the Rubincam article you cited. It is based on the same assumptions (Wikipedia equations) as the Bartlett and Van Buren article. It even states in the introduction that the experiment is similar to the Bartlett and Van Buren experiment which uses the lack of observed self-acceleration of an astronomical body to justify it's conclusion that the equivalence principle holds for Ma = Mi / Mp.

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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.
There is a sign in definition I:

"The quantity of matter is the measure of the same, arising from its density and bulk conjointly.

THUS AIR of a double density, in a double space, is quadruple in quantity; in a triple space, sextuple in quantity. The same thing is to be understood of snow, and fine dust or powders, that are condensed by compression or liquefaction, and of all bodies that are by any causes whatever differently condensed. I have no regard in this place to a medium, if any such there is, that freely pervades the interstices between the parts of bodies. It is this quantity that I mean hereafter everywhere under the name of body or mass. And the same is known by the weight of each body, for it is proportional to the weight, as I have found by experiments on pendulums, very accurately made, which shall be shown hereafter."

In the last sentence he distinguishes between mass and weight. But in the same breath he declares that he will take them as identical in the following text because the proportionality has been proven experimentally. This is the weak equivalence principle.

Good catch DrStrupid. It appears that Newton did make a distinction between inertial mass (mass) and passive gravitational mass (weight). It is evidenced by his pendulum experiments, where he used a bob made of different materials and compared their periods. 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.

Edit: I noticed an error in my post #22. The reference to page 102 in Max Jammer's book should be page 132.

Also, I just wanted to mention that there is a short paper by John Roche "What Is Mass?" that covers the history of the three concepts of mass that we have been discussing in this thread.