Is the fine structure constant the biggest myth ever?

[Tio Barnabe]

The fine structure constant $\alpha$ is commonly cited as a very important quantity, because it gives the strengh coupling of the electromagnetic force. But it seems that the fine structure constant is not actually constant. It rather changes with the momentum of the (mediating?) particle and has the well-known result of $1/137$ only when the energy is relatively low.

My apologies if this is wrong. I would need to dig far deeper into QFT to actually respond to myself this question, that's why I'm discussing it here on PF. Of course, PF members are not able to help questioners without the minimum of back ground on the subject. What I'm asking here, I consider, doesn't require a lot of QFT, though.

 

[dextercioby]

Well, you might read here as well: https://en.wikipedia.org/wiki/Landau_pole.

 

[PeterDonis]

it seems that the fine structure constant is not actually constant. It rather changes with the momentum of the (mediating?) particle and has the well-known result of $1/137$ only when the energy is relatively low.

This is basically correct. The only clarification I would make is that the "constant" varies with the momentum involved in the interaction as a whole, i.e., with what is directly measured in experiments.

The same thing is true for the other coupling "constants" in the Standard Model (roughly speaking, the analogues to the fine structure constant for the weak and strong interactions). The general explanation for why this happens has to do with renormalization group flow, which is a complicated subject, but is treated in most QFT texts.

 

[haael]

This is basically correct. The only clarification I would make is that the "constant" varies with the momentum involved in the interaction as a whole, i.e., with what is directly measured in experiments.

The same thing is true for the other coupling "constants" in the Standard Model (roughly speaking, the analogues to the fine structure constant for the weak and strong interactions). The general explanation for why this happens has to do with renormalization group flow, which is a complicated subject, but is treated in most QFT texts.

There is a very useful analogy why this is happening.

Firstly, instead of saying that charge is constant and coupling varies, we may equivalently say that coupling is constant (or better equal to 1) and the charge varies.

The effective charge of interacting particles is different depending on the momentum they have while interacting.

Now how the charge may vary?

Let's look at the analogy with gravity.

First, imagine two point masses. They will attract as we expect them to.
Now imagine two solid balls. When they are far enough, they will attract as they were points and all their mass was in the center.
Now image two hollow spheres. When they are far enough, they will attract too as two points masses.

Now imagine a hollow sphere and a point. The point is interacting with the sphere only via gravity. It can also pass through the sphere surface (you may think it has holes). When the point is outside the sphere it would be attracted as if the sphere was a point too, with the mass at its center. However, when the point finds itself inside the sphere, the net force will cancel and will be effectively zero.

Now imagine a solid ball and a point. (Maybe a liquid ball would be a better example.) The point may pass through the ball, but it's interacting via gravitation. You may think of the ball as a series of infinitely many concentric spheres. When the point is inside the ball it will only feel the attraction of the core. The outer shell will extert zero net force.

You may say that the mass of the ball is varying. The effective mass of the ball will be only the mass of the core, depending how deep the point is submerging.

When the probe point is passing the ball from far away, it fells all the ball's mass. When it is so close that it is submerging, it feels the different effective mass.

Let's go back to quantum mechanics. "How close" two particles may approach each other during a collision is dependent on their momentum. According to Feynmann, particles are not point objects but rather clouds of virtual particles. When they come close enough, their outer shells merge and cancel, providing zero effective interaction, with only the cores contributing to the effective charge.

The only difference to the analogy with gravity is that with particles the charge of the outer shell may be negative. That means, when the outer shell is exposed, the effective charge of the core may be greater than when covered by the shell. The outer shells may be actually screening the big effective charge inside, rather than amplifying it.

When I first learned about that analogy, the world became much more simple.

 

[PeterDonis]

The only difference to the analogy with gravity is that with particles the charge of the outer shell may be negative.

Phrasing it this way might be confusing. The way the coupling constant varies with momentum does not change if the charge of the particles changes sign (for example, in electromagnetism, the fine structure constant varies the same way with momentum for positively and negatively charged particles). The "charge" you are referring to here is a term in the analogy, not in the actual physics.

 

[PeterDonis]

The outer shells may be actually screening the big effective charge inside, rather than amplifying it.

It might also be worth explicitly stating which option (screening vs. anti-screening) applies to each of the three Standard Model interactions. As I understand it, the eletromagnetic interaction exhibits screening: the coupling constant increases with the total momentum of the interaction. The weak and strong interactions exhibit anti-screening: the coupling constants decrease with the total momentum of the interaction. (In the case of the strong interaction, the coupling constant goes to zero as the interaction momentum increases without bound--this is called "asymptotic freedom".)

 

[Vanadium 50]

But it seems that the fine structure constant is not actually constant. It rather changes with the momentum of the (mediating?) particle and has the well-known result of 1/137 only when the energy is relatively low.

My apologies if this is wrong.

It is wrong. And it's unnecessary to use such obnoxious language as "the biggest myth ever".

The electromagnetic coupling constant varies with momentum transfer, sure. But the fine structure constant is defined as the electromagnetic coupling constant at zero momentum transfer. So it is constant.

 

[vanhees71]

One should however say that the many constants in the Standard Model (i.e., in physical terms the coupling constants, mixing parameters, and masses) as well as the "particle content" is purely empirical. There's no known deeper reason for its values or why the leptons, quarks, gauge bosons, and Higgs boson(s) are as they are. E.g., why are there 3 families of quark and leptons and not 2 or 4?

In this sense you can say that all these constants are manifestations of our ignorance, and many physicists hope to find a better model which predicts (or rather postdics) all these parameters' values from some beautiful "underlying principle" (most nice would be again some profound symmetry principle), but of course as long as there is no such theory, it's not even clear whether such a thing indeed does exist or not.