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.
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.
To clarify: the force remains constant with increasing distance, which means the energy required grows until it reaches the pair production threshold is reached.
> 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.
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."
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.
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.
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.
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 :)
That's a great question getting to the heart of the physics at play, so please don't apologize. A good model for quark-quark interaction is to imagine them in the context of their color charge, which acts like a complex form of the more familiar concept of EM charge. Since they carry this charge they're coupled to the strong force in a manner analogous to the more familiar EM flux tubes. When you add energy to the qq system you're adding energy this flux tube and making the whole system "hotter". Eventually instead of one flux tube defining one qq interaction you get the "snap" and end up with 2 flux tubes and two qq pairs. Assuming that you aren't still dumping energy into the system with some way to confine it, everything is going to fly apart and rapidly cool down. This leads to the really neat part, the reason we see particle showers at colliders and elsewhere: Hadronization. You can think of this as the condensation of Hadrons from the high energy quark-gluon plasma you find in conditions like a particle accelerator of sufficient capability, or the very early universe.
So in the model of two proton beams near c intersecting you essentially have the protons go through a phase change- they almost melt into a quark-gluon plasma that's stupendously hot- followed by a rapid condensation into a showers of kaons, pions, new protons... all of it adds up to the original mass of the protons in the collision. If you surround the area of that collision with EXTREMELY sensitive calorimeters and devices designed to monitor this process you can do some incredible accounting to find out what if anything is missing. That missing bit would be a possible new particle, some new physics, or as is often the case a chance to learn more about possible errors in measurement.
I think a lot of people have an understanding that the force that binds the nucleus together is quite a bit stronger than the electromagnetic force. (Obligatory xkcd: https://xkcd.com/1162/)
What is not always appreciated is that the forces binding the nucleus together are the strong force analog of the van der Waals force in electromagnetism. So it is not really right to compare the way the electron is bound to the nucleus to the way the nucleus itself is bound together. If you want to compare the electromagnetic force to the strong force, the better comparison is between the force binding the nucleus to a hydrogen bond.
The strong force itself is many orders of magnitude stronger than the force binding the nucleus together.
I don't really have the time to learn the math to really understand this stuff myself, and I'm not entirely sure I could learn it even if I had the time.
But I love to read about it and marvel that we as a species even managed to figure out this much about something so tiny and complex
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.
> 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.
To clarify: the force remains constant with increasing distance, which means the energy required grows until it reaches the pair production threshold is reached.
Also, the strong force is extremely repulsive at shorter distances.
The good news is that wikipedia has very good (and simple) figures for the shape of the force: https://en.wikipedia.org/wiki/Nuclear_force
> 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?)
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."
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.
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.
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.
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 :)
Gluons are just the manifestation of the curvature of the color field.
Just like photons arise from the curvature of the electric charge field.
This is extremely complicated, it's called gauge theory.
> Is there a link where I could read more?
Ask your favourite LLM, it will explain much better.
Or 5 hour video on the subject, but with all the math:
https://www.youtube.com/watch?v=GfeeIwmb_hw
That's a great question getting to the heart of the physics at play, so please don't apologize. A good model for quark-quark interaction is to imagine them in the context of their color charge, which acts like a complex form of the more familiar concept of EM charge. Since they carry this charge they're coupled to the strong force in a manner analogous to the more familiar EM flux tubes. When you add energy to the qq system you're adding energy this flux tube and making the whole system "hotter". Eventually instead of one flux tube defining one qq interaction you get the "snap" and end up with 2 flux tubes and two qq pairs. Assuming that you aren't still dumping energy into the system with some way to confine it, everything is going to fly apart and rapidly cool down. This leads to the really neat part, the reason we see particle showers at colliders and elsewhere: Hadronization. You can think of this as the condensation of Hadrons from the high energy quark-gluon plasma you find in conditions like a particle accelerator of sufficient capability, or the very early universe.
So in the model of two proton beams near c intersecting you essentially have the protons go through a phase change- they almost melt into a quark-gluon plasma that's stupendously hot- followed by a rapid condensation into a showers of kaons, pions, new protons... all of it adds up to the original mass of the protons in the collision. If you surround the area of that collision with EXTREMELY sensitive calorimeters and devices designed to monitor this process you can do some incredible accounting to find out what if anything is missing. That missing bit would be a possible new particle, some new physics, or as is often the case a chance to learn more about possible errors in measurement.
https://modern-physics.org/hadronization/
https://profmattstrassler.com/articles-and-posts/particle-ph...
https://www.slac.stanford.edu/econf/C990809/docs/webber.pdf
I think a lot of people have an understanding that the force that binds the nucleus together is quite a bit stronger than the electromagnetic force. (Obligatory xkcd: https://xkcd.com/1162/)
What is not always appreciated is that the forces binding the nucleus together are the strong force analog of the van der Waals force in electromagnetism. So it is not really right to compare the way the electron is bound to the nucleus to the way the nucleus itself is bound together. If you want to compare the electromagnetic force to the strong force, the better comparison is between the force binding the nucleus to a hydrogen bond.
The strong force itself is many orders of magnitude stronger than the force binding the nucleus together.
I don't really have the time to learn the math to really understand this stuff myself, and I'm not entirely sure I could learn it even if I had the time.
But I love to read about it and marvel that we as a species even managed to figure out this much about something so tiny and complex