If a neutron were not composed of any smaller charged particles, then there would be nothing particularly improbable about the fact that neutrons are electrically neutral. But according to the Standard Model of Physics, the neutron is composed of three smaller charged particles. The Standard Model says that a neutron is composed of one Up quark and two Down quarks.
According to the Standard Model of Physics, the Up quark has a positive electric charge equal to two thirds of the charge of a proton. The Down quark has a negative electric charge equal to one third the charge of the proton. The amount of positive charge in the neutron therefore exactly balances the amount of negative charge in the neutron, leaving the neutron with a net electric charge of 0.
I can illustrate this balance by the following visual. The scale shows the positive charge of the neutron on the left, and the negative charge of the neutron on the right. The two balance each other precisely (as represented by the balanced scale).
How precise is this balance? In the above visual I only use 9 decimal places to avoid making the numbers too small to read. But the actual balance is to at least twenty decimal places. The exact figure given in this scientific paper is that the neutron charges is less than 1.8 X 10-21 of an electron charge. For this to be true, the positive charge within a neutron must differ from the negative charge within the neutron by less than than 1 part in 100,000,000,000,000,000,000.
It would seem that the chance of this coincidentally happening is incredibly low. To give an analogy, imagine you make a great deal of money as a Wall Street investment banker, and your spouse is always losing money at the casino. At the end of the year, you calculate your net income, and find that even though you've made millions this year, when you subtract your spouse's gambling losses, you find that you net income is exactly 0 dollars and 0 cents, because your spouse's gambling losses coincidentally exactly canceled out your income, to the penny.
But isn't there some way to avoid believing that we have been blessed by a coincidence in this matter, a coincidence with a probability of less than 1 in 100,000,000,000,000,000,000? We might avoid the coincidence if we could say that an Up quark is made up of exactly two Down quarks – except that wouldn't really work, because the charge of the Down quark is negative and the charge of the Up quark is positive. Also, scientists do not actually think that an Up quark is made up of two Down quarks.
We might also avoid the coincidence if we had some good basis in believing in a required quantization of electric charge – a reason why electric charge must necessarily occur in a multiple of one third of the proton charge or one third of the electron charge. But no such reason is known. In fact, the scientific paper I just cited says at its beginning, “The Standard Model with three generations does not have electric charge quantization.”
One may ask whether this coincidence is the same coincidence as the fact that the proton charge exactly equals the electron charge (the only difference being that the proton charge is positive and the electron charge is negative). No, that is a separate coincidence, but one equally improbable, also requiring something with a chance smaller than 1 in 1,000,000,000,000,000,000.
The Standard Model gives us three stable charged particles: the Up quark with a charge of 2/3e, the Down quark with a charge of -1/3e, and the electron with a charge of -1e (where e is the proton charge of 1.60217657 coulomb). Protons are made of 2 Up quarks and one Down quark, and neutrons are made of 2 Down quarks and one Up quark. We have two separate coincidences here: (1) the fact that the charge of the Up quark is precisely twice the charge of the Down quark (not considering the sign), and (2) the fact that 2 Up quarks and a Down quark (the constituents of a proton) have a total charge that adds up to a number exactly equal to the charge of the electron (not considering the sign). Experiments have verified that the proton charge and the electron charge differ by less than 1 part in 1,000,000,000,000,000,000 (not considering the signs).
The second coincidence is perhaps more astonishing, given the fact that the rest mass of the proton is 1836 times larger than the rest mass of the electron, but I won't dwell on this fact given that this post is about the neutron.
Both of these coincidences are necessary for our existence, as are numerous other coincidences discussed here. Is there some simple way to visualize this strange situation, in which a habitable universe depends on an exquisite balance within nature? Perhaps the following visual will do. The spiral galaxy symbolizes our habitable universe. The upside-down pyramid symbolizes the degree of balance required for that habitability.
The exquisite balance