Oh, I think I see what you're getting at. If N is the number of quarks in one body, you're proposing that F = G Nm/r2?
Yeah.
G (the gravitational constant) would have
n (number of particles) instead of
kg (mass) as one of its dimensions.
\(F_{1} = G\frac{n_2 m_1}{r^2} \)
\(F_{2} = G\frac{n_1 m_2}{r^2} \)
likewise:
\(a_{1 \rightarrow 2} = G\frac{n_2}{r^2} \)
\(a_{2 \rightarrow 1} = G\frac{n_1}{r^2} \)
If it's \(G\frac{n_1 m_2}{r^2} \), presumably the force the second body exerts on the first would be \(G\frac{n_2 m_1}{r^2} \), yes?
Yes.
\(n_1 m_2\) would be different from \(n_2 m_1\) whenever the two objects are made of different materials.
Depends, if \(n_1 = n_2 \) and \(m_1 != m_2 \) they'd be different, likewise if \(n_1 != n_2 \) and \(m_1 = m_2 \) they would be different.
There could be cases in which \(n_1 != n_2 \) and \(m_1 != m_2 \) in which \(n_1 m_2 = n_2 m_1 \).
That would mean action would no longer equal reaction. Put a block of carbon next to a block of lead and you'd have a reactionless drive for a spacecraft.
I'm not going to react to that.
and nobody questioned the mass/gravity connection (unless someone did)).
Someone did. People have been doing tests of
inertial and gravitational mass for centuries, most notably
Loránd Eötvös, with a lot more precision than the discrepancy between proton and neutron mass.
As far as I can tell, the
Eötvös experiment simply confirmed that inertial and gravitational mass are the same, which has nothing to do with the number of particles, other than the fact that the
number of particles * the mass of a particle = total mass.
I haven't read of any experiment that tested whether 2 identical masses with different numbers of particles caused different gravitational acceleration. All of the experiments that I've read about have focused upon mass, and the experimenters never mentioned using 100kg of iron vs. 100 kg of lead.
I estimate a particle (nucleon) ratio of around ~1.001067 between the 2- doesn't matter though- I'm not conducting the experiment (yet):
I want to know if an experimental measurement of gravity has been done with mass as a control, and the number of particles as the independent variable.
Objects could be the same size, density, and mass, and just have different numbers of particles. If there is a difference in acceleration towards different objects of the same mass and density it means there is something there. Otherwise, stuff is settled (except for creation of artificial virtual universes that evolve according to slightly different rules....
).
). 
