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Coupling constants, units and measurements 
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#1
Aug2313, 06:01 AM

P: 744

I was thinking about units and started wondering about coupling constants. In unitindependent form, the finestructure constant is defined as [tex]\alpha = \frac{k_e e^2}{\hbar c}[/tex]
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 [itex]k_e[/itex] for the weak and strong interaction which can be measured? Or do our experiments somehow force us to set them equal to one? 


#2
Aug2313, 06:17 AM

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P: 11,925

k_{e} 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.



#3
Aug2313, 07:08 AM

P: 744

Why can k_{e} 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? 


#4
Aug2313, 08:15 AM

P: 744

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 relabeling 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? 


#5
Aug2313, 08:45 AM

Mentor
P: 11,925

*well, this parameter depends on the energy scale, but let's ignore this here. 


#7
Aug2313, 10:29 AM

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P: 11,925

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). 


#8
Aug2313, 02:54 PM

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 [itex]\alpha[/itex] 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."



#9
Aug2313, 03:21 PM

Sci Advisor
Thanks
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#10
Aug2313, 03:28 PM

P: 2,251

it's not that gravity is weak. (weak w.r.t. what?) it's that the masses of particles are small. 


#11
Aug2413, 05:00 AM

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#12
Aug2613, 02:54 PM

P: 85

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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