# Location of new mass when added to grav system

• Steve Harris

#### Steve Harris

Hi, Folks

I'm embroiled in a discussion on the TALK page for the Wikipedia article "E=mc2".

In this wikipedia article (Wiki), somebody has claimed that when a mass (OBJECT) of mass M is raised in a g field by a height h, adding energy M*g*h from outside the system, that the energy shows up as extra mass in the OBJECT. We all agree the mass-energy has to show up in the system. But this guy claims it all goes physically to the OBJECT raised, which alone gains mass, and he has some French physics article cite to "prove" it. I personally think it's baloney, but I'm not a physicist nor an authority. I personally think that extra mass-energy added is hard to locate physically in such situations, and could as easily be in the Earth or the gravitational field. Does modern physics speak authoritatively on this point, and (more importantly) can somebody give me a reference?

I'm not even sure that the case for a g-field is not different from that for an electrical field. If two attracting charges are separated, the work involved goes into electric field, and the mass increase to the system can be tracked as some kind of integral over the total field strength, yes? Since electric fields have definable energy/volume (unlike g fields). And yet particles (or collections of particles) are partly given their mass by their fields (as in an atomic nucleus, which masses less than the sum of the free masses of the particles composing it). We don't need to take this to mean that all those nucleons each has a slightly lesser mass, just because the collection of them does. Do we?

Steve Harris

In GR the gravitational potential energy used in raising a body is NOT added to the 'rest' mass of the body. In that sense GR does not locally conserve energy.

However, various theories do make this assumption, but they are non-standard alternative gravitational theories such as is described http://en.wikipedia.org/wiki/Self_creation_cosmology [Broken].

As far as charged particles such as an electron and proton are concerned the bound state, a hydrogen HI atom, has less 'rest' mass than the free state.

Mass of electron = 9.1 x 10-28gm.
Mass of proton = 1.67266 x 10-24gm.

Free state: mass of proton + mass of electron = 1.67357 x 10-24gm
Bound state: mass of HI atom = 1.67352 x 10-24gm

Garth

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If one has a static system, one probably could say that the Komar mass of the ball changes with its height (as the redshift factor changes) - see for instance http://en.wikipedia.org/wiki/Komar_mass

This is specific to the concept of Komar mass, though, and wouldn't apply to other important sorts of mass in GR, such as the ADM mass. In general, you are right in saying that one can't assign a particular location to energy in GR (which implies that one can't assign a particular location to mass, either).

see for instance the wiki article "mass in general relativity"
Unfortunately, energy conservation in general relativity turns out to be much less straightforward than it is in other theories of physics. In other classical theories, such as Newtonian gravity, electromagnetism, and hydrodynamics, it is possible to assign a definite value of energy density to fields. For instance, the energy density of an electric field E can be considered to be 1/2 ε0 E2.

This is not the case in general relativity. It turns out to be impossible in general to assign a definite location to "gravitational energy". (Misner et al, 1973 chapter 20 section 4).

also

http://www.physics.ucla.edu/~cwp/articles/noether.asg/noether.html

makes much the same point.

So I would say that it is wrong to assign the mass to the ball in such an unqualified manner, this assignment does not work in general, only in the special case of a static system.

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In GR the gravitational potential energy used in raising a body is NOT added to the 'rest' mass of the body. In that sense GR does not locally conserve energy.

However, various theories do make this assumption, but they are non-standard alternative gravitational theories such as is described http://en.wikipedia.org/wiki/Self_creation_cosmology [Broken].

As far as charged particles such as an electron and proton are concerned the bound state, a hydrogen HI atom, has less 'rest' mass than the free state.

Mass of electron = 9.1 x 10-28gm.
Mass of proton = 1.67266 x 10-24gm.

Free state: mass of proton + mass of electron = 1.67357 x 10-24gm
Bound state: mass of HI atom = 1.67352 x 10-24gm

Garth
Thanks, Garth. I understand an H atom has less mass than the proton or the electron. But this person essentially asserts that all the lost mass is to be attributed to loss of mass of the electron, in effect. I'm asserting that it's a system loss. In an EM system (like an atom), the loss is localized to the EM field between the particles. In a grav system, you can't even do that well, for reasons well laid out by Pervect. Steve

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If one has a static system, one probably could say that the Komar mass of the ball changes with its height (as the redshift factor changes) - see for instance http://en.wikipedia.org/wiki/Komar_mass

This is specific to the concept of Komar mass, though, and wouldn't apply to other important sorts of mass in GR, such as the ADM mass. In general, you are right in saying that one can't assign a particular location to energy in GR (which implies that one can't assign a particular location to mass, either).

see for instance the wiki article "mass in general relativity"

also

http://www.physics.ucla.edu/~cwp/articles/noether.asg/noether.html

makes much the same point.

So I would say that it is wrong to assign the mass to the ball in such an unqualified manner, this assignment does not work in general, only in the special case of a static system.
Thanks. I read the article and quoted it in the TALK page, but it had no effect. This person claims to have their own private Ph.D. telling them they are right that ONE raised mass in a system gains all the mass when energy is added to a grav potential, and they simply shrug off my attempts to explain that it's not so, as being anti-authority. As though their own misquoted authorities and anonymous authorities trump mine. Wikipedia really has credibility and citation problems, as you may know from JIMBO's talk page. Anyway, you might put in a visit to the E=mc2 TALK page to help, but I doubt anybody signing in as PERVECT, no matter how much GR math they may know, is going to make much difference. Thanks again for your input again, however. Steve

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Thanks. I read the article and quoted it in the TALK page, but it had no effect. This person claims to have their own private Ph.D. telling them they are right that ONE raised mass in a system gains all the mass when energy is added to a grav potential, and they simply shrug off my attempts to explain that it's not so, as being anti-authority.

I would hope that not many Wikipedians would buy into the "private PHD" argument as a credible source. If they do, you might gently point them at WP:Verifiability.

As though their own misquoted authorities and anonymous authorities trump mine. Wikipedia really has credibility and citation problems, as you may know from JIMBO's talk page. Anyway, you might put in a visit to the E=mc2 TALK page to help, but I doubt anybody signing in as PERVECT, no matter how much GR math they may know, is going to make much difference. Thanks again for your input again, however. Steve

So, would it be better if I changed my handle to Aahz? :-)

I just looked up Paul Marmet. If

http://www.Newtonphysics.on.ca/BIGBANG/Bigbang.html [Broken]

is a sample of his work, I am *not* impressed.

I'm not terribly active on Wikipedia anymore, so I'd suggest you talk to some of the physics regulars (if they are still around, I haven't been around much recently), like Pjacobi, Ed Schaeffer, and Mpatel as far as how to handle this particular individual.

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