Comparing Gravity to Other Forces in Physics

[waveicle]

I've often heard physicists say that the relative weakness of gravity is 'one of the greatest unsolved problems in physics'. When physicists talk about how puzzling it is that gravity is so much weaker than the other forces, how are they comparing the two? Isn't the unit of charge (Coulomb) and the unit of mass (kilogram), fairly arbitrary?
And if we Compare the two based on the smallest possible unit (charge of electron, mass of a quark or whatever), why should we EXPECT them to be related in the first place?

 

[mgb_phys]

Isn't the unit of charge (Coulomb) and the unit of mass (kilogram), fairly arbitrary?

Yes

And if we Compare the two based on the smallest possible unit (charge of electron, mass of a quark or whatever), why should we EXPECT them to be related in the first place?

You wouldn't necessarily expect them to be similar - but 40 orders of magnitude is difficult to fit into a theory!

 

[Andy Resnick]

When we speak of comparing forces, we mean to compare the (force-mediated) *coupling* between two objects- that is, not 'm' or 'q', but 'G' and 'e_0'.

More precisely, using natural units for the four forces:

http://en.wikipedia.org/wiki/Fundamental_force

allows one to compare them in an 'apples to apples' manner.