The relative strength of the fundamental forces determines how matter holds together, how stars shine and which elements can exist. Changing that balance opens up a wide range of possible simulations that explore entirely different kinds of atoms, stars and universes.

The relative strength of a fundamental force F at a distance r is thought to be weak if Fr² is much smaller than ℏc, and strong if Fr² is close to the value of ℏc. (Matt Strassler, The Strengths of the Known Forces, 2013)

Changing the value of the gravitational constant and the elementary charge would affect the relative strengths of the fundamental forces. This can be observed by looking at the coupling constants of the electromagnetic and the gravitational forces.

Coulomb’s law for two electrons or two protons states

where r is the distance between the charges, k is the Coulomb constant and qₑ is the elementary charge. With the electromagnetic force, Fr² equals k(qₑ)². The dimensionless coupling constant for the electromagnetic force can then be acquired from the relation

and it has a value of

The value of the coupling constant tells that the force is weak in relative terms. It is proportional to the square of the elementary charge. Increasing the value of the elementary charge would strengthen the relative strength of the electromagnetic force.

The same approach works for the gravitational force. The relative strength of gravity can be observed by looking at the force between two masses

For two protons, the relative strength of the gravitational force expressed as the gravitational coupling constant is

and it has a value of

The gravitational coupling constant is directly proportional to the gravitational constant G. Increasing its value would increase the relative strength of the gravitational force.

For gravity and the electromagnetic force to have the same relative strength their coupling constants should have the same value. From the above we get

Getting to this situation by only changing the gravitational constant means that it would have to have a value of

Its current value is approximately 6.674×10⁻¹¹.

On the other hand we could change the elementary charge. It would have to have a value of

Its current value is approximately 1.6×10⁻¹⁹.

For an 80 kilogram person to be able to walk on the ceiling with some sort of pointlike gravity boots that work on electricity, the gravitational force pulling the person down and the electromagnetic force keeping them attached to the ceiling would have to have the same value. We would have a situation of

where m is the person’s mass, q₁ and q₂ are the charges of the ceiling and the boot(s) and r is the distance between those charges. If we assume that the charges on the boots and the ceiling had the same magnitude and a different sign we get (g is the gravitational acceleration)

If the charge of the pointlike gravity boots was at a distance of one centimetre from the pointlike charge on the ceiling, so r would be 0.01 metres, we get for the value of the charges