Coupling constants, units and measurements

In summary, the weak force has a coupling constant which is proportional to the electron rest mass, while the strong force has a coupling constant which is proportional to the proton mass.
  • #1
kith
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I was thinking about units and started wondering about coupling constants. In unit-independent form, the fine-structure 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?
 
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  • #2
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.
 
  • #3
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?
 
  • #4
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?
 
  • #5
kith said:
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.
 
  • #6
mfb said:
All forces have a dimensionless parameter
Except for gravity.
 
  • #7
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
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
rbj said:
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."
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.
 
  • #10
Bill_K said:
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.
 
  • #11
mfb said:
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!
 
  • #12
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.
 

1. What are coupling constants?

Coupling constants are numerical values that describe the strength of the interaction between two or more particles or fields in a physical system. They are used in various fields of physics, such as quantum mechanics, nuclear physics, and particle physics, to quantify the strength of fundamental interactions.

2. How are coupling constants measured?

Coupling constants are typically measured through experiments or theoretical calculations. In experiments, they can be derived from analyzing the results of particle collisions or other physical processes. In theoretical calculations, they can be obtained by solving mathematical equations that describe the behavior of the system.

3. What units are coupling constants measured in?

The units of coupling constants depend on the specific physical system they are describing. In particle physics, they are often measured in energy units, such as electron volts (eV) or gigaelectron volts (GeV). In nuclear physics, they may be measured in units of force, such as newtons (N) or pascals (Pa). In quantum mechanics, they can be measured in units of energy, length, or time, such as joules (J), meters (m), or seconds (s).

4. How do coupling constants affect physical systems?

The value of coupling constants can significantly impact the behavior and properties of physical systems. For example, in quantum mechanics, a strong coupling constant can result in a strong interaction between particles, leading to the formation of bound states. In nuclear physics, the strength of coupling constants can determine the stability of atomic nuclei. In general, larger coupling constants indicate a stronger interaction between particles or fields in a system.

5. Can coupling constants change over time?

Yes, coupling constants can change over time in certain physical systems. For example, in particle physics, it is believed that the coupling constants of the fundamental forces (electromagnetic, weak, strong, and gravitational) were different in the early universe compared to their current values. This is due to the effects of cosmic inflation and other phenomena that occurred during the early stages of the universe's evolution.

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