# Why don't protons collapse to a point?

If the quarks that make up the proton are point particles, and the forces binding them together is the strong force which is $137$ times stronger than the electromagnetic force (which makes the quarks repel), why don't the protons collapse to a point because the quarks don't have a finite radius?

• The strong force is repulsive over small domains of separation
– user172864
Commented Nov 25, 2017 at 23:09
• Thanks. You should put that as an answer though.
– user172320
Commented Nov 25, 2017 at 23:12
• Also, angular momentum is a thing. For example, in a gravitational system of two point masses, they only collapse to a point if angular momentum is zero. Commented Nov 25, 2017 at 23:13
• There's also the Heisenberg uncertainty relation, which means that any particle confined to a tiny region must have an enormous amount of kinetic energy. Commented Nov 25, 2017 at 23:15
• Downvoters care to comment?
– user172320
Commented Nov 25, 2017 at 23:55

Ultimately, for the same reason that electrons don't crash into the nuclei they “orbit”: because all massive particles obey the Heisenberg Uncertainty Principle, of the form $$\Delta x\,\Delta p\gtrsim\frac12\hbar,$$ so that if the quarks' motion collapsed to a point, having $\Delta x$ zero (or very small) would require having infinite (or extremely large) $\Delta p$, and since, as a rough approximation, $$\Delta p^2 = ⟨p^2⟩-⟨p⟩^2 = ⟨p^2⟩=T,$$ the kinetic energy, having large $\Delta p$ requires a lot of energy.