# Electric force much stronger than gravitational force? [duplicate]

It is commonly said that the electric force is much stronger than the gravitational force. Indeed, Coulomb's constant $k_e$ is much larger than the gravitational constant $G$ but they are measured in different units so it is not a reasonable comparison. With other units, it could be reversed.

Consider two electrons in space far from any matter. There will be a tiny gravitational attractive and a much larger electric repulsion.

Consider two protons. The electric repulsion will be the same. The gravitational attraction will be much larger (than for the electrons) but still much smaller than the electric repulsion.

So, those observations support that the electric force is stronger.

However, now consider two neutrons. The gravitational attraction is slightly greater than for the protons. There is no electric repulsion or attraction.

Is there some absolute sense in which the electric force is stronger?

• This might help: en.wikipedia.org/wiki/Gravitational_coupling_constant – Sebastian Jul 31 '18 at 12:55
• @Sebastian Thanks. My question is expressed in a way in that article: "There is an arbitrariness in the choice of which particle's mass to use". It implies an answer to my question that the statement depends on the arbitrary (though defensible) choice of the electron. – badjohn Jul 31 '18 at 12:59
• @badjohn: The ratio of the forces is arbitrary depending on the choice of particle, true. But for any type of subatomic particle for which both forces are non-zero, the electric force is several orders of magnitude larger. – Michael Seifert Jul 31 '18 at 14:29
• @MichaelSeifert Thanks. So, it is as simple as that. If you made that an answer then I could accept it. – badjohn Jul 31 '18 at 14:37

Particle physics, and electrons are elementary particles, is the province of quantum mechanics. There are four fundamental forces and a unified way to compare their strength it with the coupling constants which enter multiplicatievely in the calculations of the probability of interactions.

In particular the electromagnetic is: and the gravitational (of course at the moment there only exists an effective quantization of gravity, but the units hold)

The comparison is not arbitrary, it is in preparation for the unified theory of all four forces, and the constants are dimensionless.

• Thanks. I have seen that page before. My main question here is whether the comparison is fairly arbitrary and Michael's comment seems to have confirmed that. – badjohn Jul 31 '18 at 14:43