Why do we say there are four fundamental forces in the Standard Model (if gravity is included)?

In my physics textbook (and in popular science culture) it is stated that there are four fundamental forces: electromagnetism, strong, weak, and gravity.

But Wikipedia tells me that there is a unified description of electromagnetism and the weak force (electroweak interaction), and that this model is generally accepted in a way that eludes e.g. Grand Unified Theories which would unify the three non-gravity forces.

So why don't we say that there are three fundamental forces instead?

Answer

This is one of my favorite subjects, so I'll add some clarification about what we really mean when we way that the EM and weak forces are "unified".

In the Standard Model of particle physics, which is part of the foundation for our present understanding of nature, there are three distinct force fields (physicists call them gauge fields).

• One corresponds to the strong force that binds quarks into protons and neutrons. In the technical literature, this one is sometimes denoted $SU(3)$.


• The other two gauge fields are the ones relevant to your question. In the technical literature, these two gauge fields are described by the cryptic symbols $SU(2)_L$ and $U(1)_Y$, respectively, and I won't try to invent better names for them here. The important point is that the familiar EM force is a special mixture of $SU(2)_L$ and $U(1)_Y$, and the remainder (a different mixture) is what we call the weak force.

In the Standard Model, each of these three force fields — namely $SU(3)$, $SU(2)_L$, and $U(1)_Y$, couples to matter with a different strength than the others. That's why they are considered to be three distinct fields, not really unified in the strictest sense. However, as indicated in Aaron Stevens' more-concise answer, at a low enough temperatures (what we would call "normal" temperatures today) the famous Higgs field causes the $SU(2)_L$ and $U(1)_Y$ gauge fields to mix with each other, resulting in two different mixtures that we experience as the long-range electromagnetic force and the very-short-range weak force.

The point of this long monologue is to clarify what "unified" really means in this context. The EM and weak forces are two different mixtures of the more-fundamental $SU(2)_L$ and $U(1)_Y$ fields. So there are still four fundamental force fields in our current understanding of modern physics: the strong force $SU(3)$, the one called $SU(2)_L$, the one called $U(1)_Y$, and gravity. (The Standard Model of particle physics does not include gravity.)

On the other hand, we do have indirect theoretical reasons to suspect that $SU(3)$, $SU(2)_L$, and $U(1)_Y$ really are unified in the strict sense of being different parts of a single field with a single coupling strength to matter. We do not yet know exactly how to implement this strict form of unification theoretically. Even if the idea is correct, this higher symmetry would only be evident at even higher temperatures than the ones we would need to "un-mix" $SU(2)_L$ and $U(1)_Y$.