Why is gravity weaker than the other fundamental forces?

[George Jones]

personally, i would like to know in what sense do you mean that gravity is weak?

Often, in this sense.

why are the masses of the fundamental particles so, so small?

In other words, why does Nature sprinkle an electron so liberally with electric charge and so conservatively with gravitational charge.

The answer could be "That's just the way it is." or it could be due to some profound new physics.

Or it could be that the gravitational charge of an electron is not (relatively) small, and that, as nrqed oulines, gravity leaks out into other dimensions while other forces don't.

 

[rbj]

In other words, why does Nature sprinkle an electron so liberally with electric charge and so conservatively with gravitational charge?

we agree that this is the question to ask (and anwer). so does Frank Wilzcek.

The answer could be "That's just the way it is." or it could be due to some profound new physics.

i agree that there is potentially some profound physics in answering this. i think it answers the same question of "why is the size of atoms so much bigger than the natural unit of length?" since

$$a_0 = \frac{m_P}{m_e \alpha} l_P$$

Or it could be that the gravitational charge of an electron is not (relatively) small,

not from a POV of natural units. the mass of even a proton or neutron is exceedingly small (in terms of the natural unit of mass).

and that, as nrqed oulines, gravity leaks out into other dimensions while other forces don't.

i remember seeing that hypothesis from the Brian Greene NOVA special ("The Elegant Universe"). for some reason, this seems speculative while the salience of Planck Units (or something close to them - i think that $4 \pi G$ and $\epsilon_0$ should be normalized for the most natural units) seems to be right there. we know that these dimensionful scaling factors go away if we measure and describe physical quantities in terms of natural units. then we have a basis for saying something is really big or really small.

 

[George Jones]

not from a POV of natural units. the mass of even a proton or neutron is exceedingly small (in terms of the natural unit of mass).

But Planck units change as the number of spacetime dimensions changes.

The gravitational constant in $D$ dimensions is given by

$$G^{\left( D \right)} = G \left( l_{C} \right)^{D-4},$$

where $G$ is the usual gravitational constant and $l_C$ is the "cirumference of compactification" of the extra spatial dimensions.

The Planck mass, for example, is the product of appropriate powers of $G^{\left( D \right)}$, $c$, and $\hbar$. When I work this out for, say, $D = 6$ and an $l_C$ of 10 microns, I get much less discrepancy between the Planck mass and the mass of fundamental particles, and between the Planck mass and the Planck charge (if gravity and not electromagnetism leaks into the extra dimensions).

This why the work at the University of Washington is so important.

Chapter 3 of Zwiebach's book A First Course in String Theory gives a readable presentation of these ideas. Problems 3.9 and 3.10 are quite interesting.

Zwiebach points out that this just trades the mass hierarchy problem for a length hierarchy problem. Why is the Planck length so much smaller than than the compactification scale?

 

[Farsight]

Did anybody say what one of these action-at-a-distance forces actually is?

I'd like to establish what an action-at-a-distance force is before talking about one being weaker than the other. Is there a consensus or official line here? In layman's terms?

I don't like to rely on Wikipedia:

http://en.wikipedia.org/wiki/Action_at_a_distance_(physics )