The meaning of the relative strength of forces

[Tac-Tics]

It's common to hear people say that gravity is a "weak force" and that it is "32 times weaker than the weak nuclear force." But what does that even mean, if it has any meaning at all. The gravity on a particle is proportional to its mass. The electric force on an object is proportional to its charge. To make a statement about relative strengths, that would mean you're making an implicit statement about the relationship between an object's charge and mass, right?

 

[Nabeshin]

Here's a simple illustration using simplifed forms of the gravitational and electric forces:

$$F_{g}=G\frac{m_{1}m_{2}}{r^{2}}$$

$$F_{e}=k\frac{q_{1}q_{2}}{r^{2}}$$

If we compare the constants of proportionality, k and G, we find that k=10^20 G. It's basically saying that per whatever unit the force uses to measure its strength, one force is much stronger than another.

 

[Tac-Tics]

Here's a simple illustration using simplifed forms of the gravitational and electric forces:

$$F_{g}=G\frac{m_{1}m_{2}}{r^{2}}$$

$$F_{e}=k\frac{q_{1}q_{2}}{r^{2}}$$

If we compare the constants of proportionality, k and G, we find that k=10^20 G. It's basically saying that per whatever unit the force uses to measure its strength, one force is much stronger than another.

Yeah, but that's comparing apples (mass) to oranges (charge). The units are different, so you can't simply divide and find the ratio of the strengths... you're left with a conversion factor of kg/C or something.

 

[Nabeshin]

You are of course right. That example was pretty terrible and I was making light of what is a much more complicated situation. I don't fully understand this myself but after looking around I think it has something to do with the relative coupling constants for the four fundamental forces.

See:http://en.wikipedia.org/wiki/Coupling_constant