today at 8:55 AM
For those looking for a more satisfying answer implied by the simple title here goes. The “αs” number quoted is a dimensionless unit so let’s pick a distance of 1 femtometer so that we can use newtons. The strong force between two gluons is about 150,000N at this distance, compared to 230N for electromagnetism. Electromagnetism weakens with the square of the distance and the strong force does a similar thing up to a point and then it becomes constant. At about 1.1 - 1.5 fm it “snaps”. The energy in the tension is enough to create another pair of gluons. To put it in perspective, the width of a proton is 0.85 fm. It’s all waves down there so my layman view is probably oversimplified.
today at 10:20 PM
> the strong force does a similar thing
No, in the heuristic approximation you are using here, the strong interaction does not weaken with distance; it strengthens with distance, so it takes more and more energy to try to pull two quarks apart, for example, as they get further apart (whereas the energy it takes to pull, say, an electron and a proton apart gets less and less as they get further apart).
So, for example, if you try to pull apart the quark and antiquark inside a pion, at a distance scale of roughly a femtometer, the energy required to pull the two quarks apart is large enough to create another quark-antiquark pair, and so you end up with two pions. You never get free quarks.
Similar remarks would apply to trying to pull a gluon out of, say, a glueball; you just end up making more gluons and making the glueball larger; you never get free gluons.
today at 8:13 PM
> At about 1.1 - 1.5 fm it “snaps”. The energy in the tension is enough to create another pair of gluons. To put it in perspective, the width of a proton is 0.85 fm. It’s all waves down there so my layman view is probably oversimplified.
That sort of makes intuitive sense, right? If the force were weaker so that it "snapped" at 10 femtometers, you'd expect protons themselves to be somewhere in that size range as well.
(Or am I totally wrong?)
today at 9:42 PM
The actual size is not defined by this "snapping" point, but by the equilibrium between the kinetic energy from the Heisenberg uncertainty of the quarks pushing outwards and the strong force pulling inwards. It's actually the same concept as for the size of an atom, where the kinetic energy of the electron and the electromagnetic force define what you would call "size."
today at 8:32 PM
Do you have the weak force number as well? I'm curious.
I _think_ I expect it to be quite high. My understanding is it's "weak" because it falls off quickly, past a certain distance, due to the force carrier having mass.
today at 9:08 PM
The weak force is weak in two ways. One is as you mention the massive-ness of the W/Z resulting in exponential decrease of force over distance, but there's also the fact that at our usual energy scales, creating a (virtual/off-shell) W/Z is close to impossible - so it's not only weak over distance, but also very rare.
today at 8:13 PM
It’s pretty intuitive in the context of confinement theory. Intuitively we imagine something like a rubber band, as you add energy in the form of tension the material passes a threshold and as you say snaps. For confinement however as you add energy to the system it doesn’t snap, you simply reach the moment when you’ve added enough energy to the system to create a new particle pair that are also confined.
This is the explanation for why when we collide beams of protons at near c they don’t produce a new higher energy particle, but a massive shower of secondary and tertiary particles like pions and kaons as a result of the decay chain from initial pair production.
today at 10:09 PM
Forgive me for being a layman, but where do these new gluons "go"? It seems to me that pretty much all the energy in the bond between to particles is between those two particles.
But then when the energy becomes great enough and it snaps into a new pair of gluons, do those new gluons go anywhere or do they stay in between the original pair of particles. Do the original particles shoot off into the distance because the force holding them together got converted into some new particles?
Is there a link where I could read more? At these super small scales all my intuitions break down so I'd like something more mathematical to get a grasp on things :)