The Particle Physics Millennium Problem: Why does Mass Gap Matter and Where Does it Come From?

The Yang-Mills Mass Gap Problem is the only Millennium Prize problem from particle physics. It states that even a theory of pure forces, such as Yang-Mills theory, can generate matter-like particles. This is surprising because forces like electromagnetism and gravity do not exhibit this behavior. However, when we attempt to generalize electromagnetism to include self-interactions, a mass gap emerges.

Why do we care about mass gaps? They are important because, for a long time, physicists believed that a mass gap is what differentiates forces from matter. The discovery that pure forces can generate a mass gap was unexpected. Yet, the mathematical origin of this phenomenon remains a mystery. The theory itself does not contain any parameters with units, so how is it able to generate mass?

From physics, the answer seems to lie in what we call "dimensional transmutation." This is an odd behavior that seemingly generates units out of thin air. However, it turns out this behavior might be more ubiquitous than we realize. In fact, many parameters we encounter in real life may result from dimensional transmutation.

In this episode, we'll explore the significance of the Yang-Mills Mass Gap Problem and how to understand a potential solution physically, which may help elucidate its mathematics.