magnitude of the strong force

[gre]

Is it possible to calculate the magnitude of the strong force in newtons?

[ajb]

Do you mean the force between nucleons or between quarks?

 

The force between nucleons is in the low momentum part of and is generally not very well understood. Methods from exact renormalisation group flow, lattice field theory and effective field theory can be applied. This is a subject that is currently under much investigation.

[gre]

Between quarks.

[ajb]

It depends on the energy/momentum scale, the coupling decreases as the energy increases.

[gre]

How about a ground state hydrogen atom's quarks

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I'm just thinking there should be a way to calculate the strong force between quarks (in proton) with it's relativistic energy. Wouldn't a quark's bond strength be equal to its hadrons mass-energy?

Edited January 12, 2009 by gre
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[ajb]

I don't know. At low energies/momentum QCD is strongly coupled and so perturbative methods fail, including the idea that a proton is simply made of quarks.

[gre]

Why couldn't something like this work:

 

F(binding_proton) = (p * E)/hbar

 

E=(protonmass*cc^2)

p=(protonmass*cc)

 

 

Using this equation, the total binding energy between all quarks (in a proton), would be:

 

F(binding_proton) = 714795.07 N

 

 

Then you could get the proton mass-energy by multiplying:

 

F(binding_electron) * 1.3214095e-15 m / (2*pi) = 1.503e-10 J (or torque)

 

 

I did the same for the electron, and got F(binding_electron) = .212013 N ..

multiply by the Compton wavelength of the electron, you get .511 MeV.

 

I thought this was a strange coincidence: F(binding_electron) * (alpha^4/4) meters = 1.503e-10 J

Edited January 13, 2009 by gre

[ajb]

If you consider the bag model of a proton, it takes something like 1 GeV per fermi to "pull out" a quark. (I think this is phenomenologically determined)

 

I think that is about [math]1.6 \times 10^{5}[/math] Newtons. Please check that I have converted that right.

[gre]

Can you give me an example?

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F = (p * E)/hbar

 

F = (protonmass^2 * c^3)/hbar = 714795.07 Newtons

 

This looks a lot like a Planck constant. Can Planck constants represent a maximum as well?

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I was just informed the strong force between quarks (in newtons) is to the order 100,000 newtons. Which agrees with my calculation.

 

Any comments?

Edited January 14, 2009 by gre
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[ajb]

Great, that agrees with what I also have been told.

[Baby Astronaut]

Magnitude of the other forces.

 

Electromagnetic Force: 1,000 newtons

 

Weak Force: .01 newtons

 

Gravitational Force: [math].10^{-33}[/math] newtons

 

Those are my guesses on each force's approximate strength within a distance of 1 femtometer.

[gre]

I just read you can also multiply the energy density by the area to get a rough estimate.

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ajb, did you come up with an exact number for the strong force (newtons) within a proton?

 

Thanks.

 

 

Greg

[ajb]

No, I did not come up with it, it has been taken from a reference. I believe it comes from a bag or potential model that is then fixed phenomenologically. I don't know if you can easily get such a figure directly from QCD.

[gre]

Here is another way to write it. I doubt this is valid either.

 

F = (m * (c^2 / r)) (centripetal force)

 

or

 

F = E/r

 

E = relativistic energy

r = Compton wavelength / (2*pi)

[bschaeffer]

Magnitude of the other forces.

 

 

Electromagnetic Force: 1,000 newtons

 

 

Weak Force: .01 newtons

 

 

Gravitational Force: [math].10^{-33}[/math] newtons

 

 

Those are my guesses on each force's approximate strength within a distance of 1 femtometer.

 

Perhaps not everything is electromagnetic but, at least the strong force is as shown here

[swansont]

Perhaps not everything is electromagnetic but, at least the strong force is as shown here

 

!

Moderator Note

Interesting definition of "shown;" we're going for explanations that are more widely accepted and supported