Dr. Christopher S. Baird

# Why is gravity the strongest force?

Category: Space      Published: May 22, 2013

Gravity is so weak that the hydrogen bonding in a single drop of water, which is one of the weakest forms of the electromagnetic force, can overpower the gravity of an entire planet. Public Domain Image, source: Christopher S. Baird.

Actually, gravity is the weakest of the four fundamental forces. Ordered from strongest to weakest, the forces are 1) the strong nuclear force, 2) the electromagnetic force, 3) the weak nuclear force, and 4) gravity. If you take two protons and hold them very close together, they will exert several forces on each other. Because they both have mass, the two protons exert gravitational attraction on each other. Because they both have a positive electric charge, they both exert electromagnetic repulsion on each other. Also, they both have internal "color" charge and thus exert attraction via the strong nuclear force. Because the strong nuclear force is the strongest at short distances, it dominates over the other forces and the two protons become bound, forming a helium nucleus (typically a neutron is also needed to keep the helium nucleus stable). Gravity is so weak at the atomic scale that scientists can typically ignore it without incurring significant errors in their calculations.

However, on astronomical scales, gravity does dominate over the other forces. There are two reasons for this: 1) gravity has a long range, and 2) there is no such thing as negative mass. Each force dies off as the two objects experiencing the force become more separated. The rate at which the forces die off is different for each force. The strong and weak nuclear forces are very short ranged, meaning that outside of the tiny nuclei of atoms, these forces quickly drop to zero. The tiny size of the nuclei of atoms is a direct result of the extreme short range of the nuclear forces. Two particles that are nanometers apart are far too distant from each other to exert an appreciable nuclear force on each other. If the nuclear forces are so weak for two particles only nanometers apart, it should be obvious that the nuclear forces are even more negligible on astronomical scales. For instance, the earth and sun are far too distant from each other (billions of meters) for their nuclear forces to reach each other. In contrast to the nuclear forces, both the electromagnetic force and gravity have effectively infinite range* and die off in strength as 1/r2.

If both electromagnetism and gravity have effectively infinite range, why is the earth held in orbit around the sun by gravity and not by the electromagnetic force? The reason is that there is no such thing as negative mass, but there is such thing as negative electric charge. If you place a single positive electric charge near a single negative electric charge, and then measure their combined force on another, distant charge, you find that the negative charge tends to cancel out the positive charge somewhat. Such an object is called an electric dipole. The electromagnetic force caused by an electric dipole dies off as 1/r3 and not 1/r2 because of this canceling effect. Similarly, if you take two positive electric charges and two negative charges and place them close together properly, you have created an electric quadrupole. The electromagnetic force due to an electric quadrupole dies off even more rapidly, as 1/r4, because the negative charges do such a good job of canceling the positive charges. As you add more and more positive charges to an equal number of negative charges, the range of the electromagnetic force of the system gets shorter and shorter. The interesting thing is that most objects are made out of atoms, and most atoms have an equal number of positive and negative electric charges. Therefore, despite the fact that the raw electromagnetic force of a single charge has an infinite range, the effective range of the electromagnetic force for typical objects such as stars and planets is much shorter. In fact, neutral atoms have an effective electromagnetic range on the order of nanometers. On astronomical scales, this leaves only gravity. If there were such a thing as negative mass (antimatter has positive mass), and if atoms generally contained equal parts of positive and negative mass, then gravity would suffer the same fate as electromagnetism and there would be no significant force at the astronomical scale. Fortunately, there is no negative mass, and therefore the gravitational force of multiple bodies close together is always additive. In summary, gravity is the weakest of the forces in general, but it is the dominant one at astronomical scales because it has the longest range and because there is no negative mass.

*NOTE: In the above description, I have used the older Newtonian formulation of gravity. Gravity is more accurately described by the formulation of General Relativity, which tells us that gravity is not a real force but is a warping of spacetime. On scales smaller than galaxy groups and away from super-dense masses like black holes, Newtonian gravity is an excellent approximation to General Relativity. However, to properly explain all effects, you have to use General Relativity. According to General Relativity and the many experimental measurements confirming it, gravity does not have infinite range but goes away on the scale larger than galaxy groups. Therefore, gravity only has 1/r2 behavior and "unlimited" range on the scale smaller than galaxy groups. That is why I said gravity has "effectively" infinite range. On the largest scales, our universe is expanding rather than being drawn together by gravitational attraction. This behavior is predicted by General Relativity. On scales smaller than galaxy groups, spacetime acts dominantly like attractive Newtonian gravity, while on larger scales, spacetime acts like something completely different that is expanding.