# coupling constants, units and measurements

by kith
Tags: constants, coupling, measurements, units
 P: 620 I was thinking about units and started wondering about coupling constants. In unit-independent form, the fine-structure constant is defined as $$\alpha = \frac{k_e e^2}{\hbar c}$$ I don't have a deep knowledge of particle physics but I know that there are weak and strong charges which enter the Lagrangian. Also the corresponding alphas can be measured. But are there quantities analogous to Coulomb's constant $k_e$ for the weak and strong interaction which can be measured? Or do our experiments somehow force us to set them equal to one?
 Mentor P: 9,655 ke is something you can measure in the macroscopic effects of the electromagnetic force. There are no macroscopic effects of the strong and weak force, so it is convenient to ignore that.
 P: 620 Why can ke be only measured macroscopically? Isn't it present in the quantisized version of Maxwell's equations and thus part of QED? If yes, how do I know which quantities can be measured only macroscopically?
P: 620

## coupling constants, units and measurements

Now this doesn't seem specific to particle physics.

Maxwell's equations have 3 independent parameters. The SI system sets one of them equal to one, the system of natural units sets all of them equal to one. This doesn't mean that we can't measure them. It is more a re-labeling of the pointer of our measurement apparatus to yield '1' if we measure the corresponding quantity.

So I would say the difference between EM and the weak and strong interaction is that there is no SI labeling for the latter two. Any labeling would be arbitrary and the best arbitrary choice is to set the constants equal to 1.

Is there more to it than that?
Mentor
P: 9,655
 Quote by kith Why can ke be only measured macroscopically?
I did not say that. I just mentioned the (non-exclusive) possibility to measure it with macroscopic setups - as this is different from the weak and strong force, where you cannot do that.

 So I would say the difference between EM and the weak and strong interaction is that there is no SI labeling for the latter two. Any labeling would be arbitrary and the best arbitrary choice is to set the constants equal to 1.
All forces have a dimensionless parameter*, and dimensionless parameters are independent of the unit system. Everything else just depends on the units you choose.

*well, this parameter depends on the energy scale, but let's ignore this here.
P: 3,459
 Quote by mfb All forces have a dimensionless parameter
Except for gravity.
 Mentor P: 9,655 Gravity is different at least, right. You can set G to 1, but then all particles have all sorts of strange numbers for their "gravitational charge" (mass relative to the Planck mass).
 P: 2,251 or you can have all the particles with masses relative to, say, the electron rest mass. and then you get a graviational counterpart to $\alpha$ called the "Gravitational coupling constant" which is dimensionless and is the square of the electron rest mass to the Planck mass. in my opinion, that is the fundamental reason to say that "Gravity is an exceedingly weak force."
P: 3,459
 Quote by rbj or you can have all the particles with masses relative to, say, the electron rest mass. and then you get a graviational counterpart to $\alpha$ called the "Gravitational coupling constant" which is dimensionless and is the square of the electron rest mass to the Planck mass. in my opinion, that is the fundamental reason to say that "Gravity is an exceedingly weak force."
I'd say this observation has more to say about the electron than it does about gravity. It tells us that on the natural scale of things (the Planck scale) that the electron, along with all the other known elementary particles, has an exceedingly small mass.
P: 2,251
 Quote by Bill_K I'd say this observation has more to say about the electron than it does about gravity. It tells us that on the natural scale of things (the Planck scale) that the electron, along with all the other known elementary particles, has an exceedingly small mass.
i fully agree.

it's not that gravity is weak. (weak w.r.t. what?) it's that the masses of particles are small.
P: 620
 Quote by mfb I did not say that. I just mentioned the (non-exclusive) possibility to measure it with macroscopic setups - as this is different from the weak and strong force, where you cannot do that.
Yes, initially, I misunderstood your first post. Thanks!
 P: 51 There are simple relations between the weak coupling and em coupling. These are intimately related through electroweak symmetry breaking. Though, the these couplings receive different types of quantum corrections making them behave quite differently at different energy scales.

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