I understand that most of our mass (3599/3600)comes from neutrons and
protons. I also understand that nucleons are made from up and down
quarks. I even understand that only a small percentage of the mass of
the nucleons come from the quarks, while the rest comes from the force
field that holds them together. But I have several questions:

1. Does this imply that most of our mass (85%) is made of a force
field and not matter?

2. Is it gluons that make up this force field and thus the energy of
the gluons that accounts for the 85% of our mass? Please explain this
strong nuclear force field in detail. How do sea quarks and mesons
(which I think are exchanged by the nucleons to hold them together)
play into this?

3. My final question has more to do with biophysics (and nothing to do
with the above), but I think it is appropriate to ask it here. During
an exothermic chemical reaction, a very tiny amount of rest mass is
converted to energy (supposedly). Where does this rest mass come from
that turns into energy? I mean, the rest mass of the individual
particles has to be the same right? So is it the rest mass of the
atoms or molecules that is decreasing?

Thanks for your help.

(TheScientificTruth) writes:

I understand that most of our mass (3599/3600)comes from neutrons and
protons. I also understand that nucleons are made from up and down
quarks. I even understand that only a small percentage of the mass of
the nucleons come from the quarks, while the rest comes from the force
field that holds them together. But I have several questions:

1. Does this imply that most of our mass (85%) is made of a force
field and not matter?

The fraction is considerably more than 85%, and it mostly consists of
quark kinetic energy, not "force fields." The `u' and `d' quarks have quite
low masses compared to a proton mass; our best estimates are that both of
them probably mass less than 10 MeV, or less than 1% of the nucleon mass!
(Note that our "best" is still not very good in this case --- the `u'
and `d' masses are not know to even a single significant digit!
http://pdg.lbl.gov/2003/q123.ps, http://pdg.lbl.gov/2003/q123.pdf)
If you work out the compton wavelength corresponding to these masses,
you'll find that it is on the order of several tens of fermi, which is
_MUCH_ larger than a proton's radius, which is only on the order of a fermi;
likewise (and essentially equivalently), if you work out the uncertainty
in the momentum of a quark localized inside a proton, you'll find that
it is over an order of magnitude larger than m_q*c. Both these preceding
observations imply that the `u' and `d' quarks are "rattling around" inside
a nucleon at ultra-relativistic velocities --- i.e., their kinetic energies
are more than an order of magnitude larger than their rest masses.


2. Is it gluons that make up this force field and thus the energy of
the gluons that accounts for the 85% of our mass?

No. See my response to your preceding question.


Please explain this strong nuclear force field in detail.

A _detailed_ description would require a textbook-length post covering
the entire theory of QCD --- and frankly I have better things to do
with my time than write Yet Another Textbook On QCD! :-T


How do sea quarks and mesons (which I think are exchanged by the nucleons
to hold them together) play into this?

Nucleons do not "exchange" sea quarks. To leading order, they exchange
a gluon, then do a one-for-one swap of a "valence" quark, and finally
exchange another gluon to balance the energy, momentum, and "color" books;
this process is to leading order equivalent to the exchange of a pion.


3. My final question has more to do with biophysics (and nothing to do
with the above), but I think it is appropriate to ask it here. During
an exothermic chemical reaction, a very tiny amount of rest mass is
converted to energy (supposedly). Where does this rest mass come from
that turns into energy?

From the binding energy of the electrons in the molecules. The electrons
in the reaction products are more tightly bound (i.e., in a state of lower
total energy) than the electrons in the reactants; the difference in binding
energy between the reactants and the product is released as "reaction heat."


I mean, the rest mass of the individual particles has to be the same
right?

Yes --- however, in relativistic physics, rest mass is not "additive,"
i.e., the rest mass of a composite object is =NOT= necessarily the sum
of the rest masses of its constituents!


So is it the rest mass of the atoms or molecules that is decreasing?

Yes. The sum of the rest mass of the reaction products is microscopically less
than the sum of the rest masses of the reactants. (Since typical atoms have
rest masses on the order of `A' GeV, where `A' is the "molecular weight,"
whereas typical chemical energies are on the order of an eV or so, the
change in rest mass during a chemical reaction is typically on the order
of a part per billion or so --- which is very small, but theoretically
measurable.)


-- Gordon D. Pusch

perl -e '$_ = \n"; s/NO\.//; s/SPAM\.//; print;'

Yes. The sum of the rest mass of the reaction products is microscopically less
than the sum of the rest masses of the reactants. (Since typical atoms have
rest masses on the order of `A' GeV, where `A' is the "molecular weight,"
whereas typical chemical energies are on the order of an eV or so, the
change in rest mass during a chemical reaction is typically on the order
of a part per billion or so --- which is very small, but theoretically
measurable.)


-- Gordon D. Pusch

perl -e '$_ = \n"; s/NO\.//; s/SPAM\.//; print;'

So let me make sure I got this straight:

The rest mass of a molecule is:

The sum of the rest mass of the individual electrons.

PLUS

The sum of the rest mass of the individual nuclei

PLUS

The kinetic energy of the electrons

So whenever an exothermic chemical reaction occurs, the total energy
of the electrons in the reactants is more than in the products. Thus,
since the rest mass of the individual particles remain the same, the
rest mass of the products is less than the reactants.

(TheScientificTruth) writes:

Yes. The sum of the rest mass of the reaction products is microscopically less
than the sum of the rest masses of the reactants. (Since typical atoms have
rest masses on the order of `A' GeV, where `A' is the "molecular weight,"
whereas typical chemical energies are on the order of an eV or so, the
change in rest mass during a chemical reaction is typically on the order
of a part per billion or so --- which is very small, but theoretically
measurable.)

So let me make sure I got this straight:

The rest mass of a molecule is:

The sum of the rest mass of the individual electrons.

PLUS

The sum of the rest mass of the individual nuclei

PLUS

The kinetic energy of the electrons

PLUS

The sum of the potential energies of all the electrostatic interactions
between the various electrons and nuclei.

Note that since this last term is what provides the "binding energy" that
holds that atoms and molecules together, its sign is actually negative,
not positive --- i.e., unlike the previous three terms, it _decreases_
the effective mass of the molecule, rather than increasing it.

Note also that the above is merely a leading-order approximation to a far
more complex relativistic expression.


So whenever an exothermic chemical reaction occurs, the total energy
of the electrons in the reactants is more than in the products. Thus,
since the rest mass of the individual particles remain the same, the
rest mass of the products is less than the reactants.

That is roughly correct, yes.


-- Gordon D. Pusch

perl -e '$_ = \n"; s/NO\.//; s/SPAM\.//; print;'

Note that since this last term is what provides the "binding energy" that
holds that atoms and molecules together, its sign is actually negative,
not positive --- i.e., unlike the previous three terms, it _decreases_
the effective mass of the molecule, rather than increasing it.

Ok, so I think I understand the molecular rest mass (restmass of
particles+kinetic energy of particles-potential energy of
electromagnetic interaction). I also think you answered something else
that has been bothering me about
particle/nuclear/atomic/molecular(yes, I like them all) physics, which
is:

Why is the rest mass of a nucleon greater than the sum of the rest
mass of its constituents, but the rest mass of a nucleus is less than
the sum of the rest mass of its constituents.

Based on your answers to my previous posts, I take it that the reason
the above is so is that the combined kinetic energies of quarks are
far greater than the potential energy holding them together, but the
potential energy holding a nucleus together is greater than the
kinetic energy of its constituents.

(TheScientificTruth) writes:

Note that since this last term is what provides the "binding energy"
that holds that atoms and molecules together, its sign is actually
negative, not positive --- i.e., unlike the previous three terms, it
_decreases_ the effective mass of the molecule, rather than increasing it.

Ok, so I think I understand the molecular rest mass (restmass of
particles+kinetic energy of particles-potential energy of electromagnetic
interaction). I also think you answered something else that has been
bothering me about particle/nuclear/atomic/molecular(yes, I like them
all) physics, which is:

Why is the rest mass of a nucleon greater than the sum of the rest
mass of its constituents, but the rest mass of a nucleus is less than
the sum of the rest mass of its constituents.

Based on your answers to my previous posts, I take it that the reason
the above is so is that the combined kinetic energies of quarks are
far greater than the potential energy holding them together, but the
potential energy holding a nucleus together is greater than the
kinetic energy of its constituents.

That is correct. However, please not that the two cases are not directly
comparable, because the "nuclear force" is a _short-ranged_ effective
force, whereas the "color force" between quarks is thought to be a
nonlinear, long-ranged force that has an unusually property called
"confinement," which means that the potential energy of a pair of particles
carrying different "colors" increases without bound as they are separated,
so that, theoretically, an "isolated" free quark would have an _infinite_
color potential energy! Also, the "color" potential energy of a group of
particles is _NOT_ just a simple "linear superposition" sum of pairwise
interactions, like the electromagnetic force, but a nonlinear interaction
that depends on _all_ the particles in a "cluster." (In that respect,
the "color force" is vaguely like General Relativistic gravitation, which,
while not "confining," also becomes nonlinear in the "strong field" limit,
and fails to satisfy either "superposition" or "cluster decomposability.")

Thus, unlike a nucleus, which will "blow apart" if one adds enough kinetic
energy to it, if one adds lots of energy to the quarks in a nucleon, it is
energetically cheaper to instead convert some of that kinetic and potential
energy into one or more quark/antiquark pairs, which will ultimately result
in some number of "colorless" hadrons instead of "free quarks."


-- Gordon D. Pusch

perl -e '$_ = \n"; s/NO\.//; s/SPAM\.//; print;'