Simple question on Dark Matter

[bapowell]

Just one question: What prevent the ups and down quarks from 'imploding' into a micro black hole? (Uncertainty principle?) Or reversed, what creates the strong tension?

In order for an object to become a black hole, its stress-energy must be compressed into a region smaller than a sphere of radius equal to the Schwarzschild Radius:

$$R_S = \frac{2Gm}{c^2}$$

where m is the mass of the object. While elementary particles don't have a well defined 'size', a common way to give them dimension is to talk about their Compton wavelength:

$$\lambda = \frac{h}{mc}$$.

From the uncertainty principle, one sees that this is the minimum uncertainty in the location of the particle.

Therefore, the question of whether an elementary particle will collapse into a black hole depends on whether its Compton wavelength is larger or smaller than its Schwarzschild radius. The particles of the Standard Model have Compton wavelengths many many orders of magnitude larger than their Schwarzschild radii (try it!)

 

[DevilsAvocado]

... Therefore, the question of whether an elementary particle will collapse into a black hole depends on whether its Compton wavelength is larger or smaller than its Schwarzschild radius.

Thanks bapowell, the Schwarzschild solution is very interesting, and I’m going to dig into that.

So one could say that the Uncertainty principle + Compton wavelengths give the quarks a "dimension/size", right?

And this "dimension/size" is what causes the gluon "springs" tension, right?

Could one also summarize and say that - the Uncertainty principle is the base for the "Quantum Chromodynamics Mass" in nucleons?

 

[Chalnoth]

So one could say that the Uncertainty principle + Compton wavelengths give the quarks a "dimension/size", right?

Not really, no. In QCD, quarks are precisely point-like particles. In a quantum-mechanical sense, of course, this is a bit subtle of a definition to grasp, but ultimately it means that the interactions between quarks and gluons are modeled in QCD as occurring at singular points.

And this "dimension/size" is what causes the gluon "springs" tension, right?

Nope. Now, it turns out that the mathematics that goes into modeling the particles as points in QCD (and in electroweak theory) leads to infinities. We get rid of these infinities by sort of artificially cutting off the sums at some high energy (which is equivalent to assuming that there is some size, even if we don't know what it is). The behavior at high energies is then modeled with a series of parameters that must be measured experimentally. So if the particles are actually extended objects, such as strings (as in string theory strings), then these sums have a natural cutoff at some rather high energy, and the theory is finite.

This has nothing to do with the uncertainty principle, mind you.

Could one also summarize and say that - the Uncertainty principle is the base for the "Quantum Chromodynamics Mass" in nucleons?

I don't think that it has anything to do with that at all.

 

[DevilsAvocado]

Thanks Chalnoth. This is real hard for a layman to grasp, especially in translating this into a 'working picture'. I guess these things (only) works best in the mathematical world.

I’ll try to rephrase:

... Anyway, so if you have three quarks, two ups and a down, sort of the minimum-distance configuration they can have is actually so that these gluon "springs" between them actually have quite a lot of tension.

Not really, no. In QCD, quarks are precisely point-like particles. In a quantum-mechanical sense, of course, this is a bit subtle of a definition to grasp, but ultimately it means that the interactions between quarks and gluons are modeled in QCD as occurring at singular points.

The strong nuclear force is the (attractive) force that holds quarks together to form nucleons, right?

What force (or phenomenon) sets "the minimum-distance configuration", which results in that the gluon springs "actually have quite a lot of tension" (outward)?

 

[Chalnoth]

I think it can be understood as just the zero-point energy configuration of the system, in a similar way to the zero-point energy configuration of the Hydrogen atom (S0). Obviously the math is quite a bit more complex, but I don't think the uncertainty principle has a lot to say here.

 

[DevilsAvocado]

Could you think of it like – the quarks always want to be free (maybe silly), they always want to "run away", but the strong force wants to hold them together? And this is what causes the gluon "springs" tension...?

(... maybe this works in kindergarten ...? )

 

[Chalnoth]

Could you think of it like – the quarks always want to be free (maybe silly), they always want to "run away", but the strong force wants to hold them together? And this is what causes the gluon "springs" tension...?

(... maybe this works in kindergarten ...? )

That might be more reasonable.

 

[bapowell]

Could you think of it like – the quarks always want to be free (maybe silly), they always want to "run away", but the strong force wants to hold them together? And this is what causes the gluon "springs" tension...?

(... maybe this works in kindergarten ...? )

There is electrostatic repulsion amongst some of the quarks. That makes them maybe want to run away. At least that's what my 1st grade teacher always said.

 

[Ich]

But it's the uncertainty principle that makes the quarks want to run away. I don't see why one should say that it has nothing to do with it - or with zero point energy, for that matter.

 

[DevilsAvocado]

That might be more reasonable.

There is electrostatic repulsion amongst some of the quarks. That makes them maybe want to run away. At least that's what my 1st grade teacher always said.

Thanks Chalnoth & bapowell. This gives me some hope on 'basic understanding'.

 

[DevilsAvocado]

But it's the uncertainty principle that makes the quarks want to run away. I don't see why one should say that it has nothing to do with it - or with zero point energy, for that matter.

Okay, now I’m confused again... I feel little like that "uncertainty principle" has taken over my whole body...

 

[Chalnoth]

Actually, the electrostatic repulsion is nearly negligible for the interiors of nucleons. The strong nuclear force is just so vastly stronger that it doesn't make much difference (it makes some, of course). I think I'll have to revise my statement and suggest that Ich is largely correct here.

 

[George Jones]

Unlike photons, gluons can be (colour) charged, and the interaction of virtual gluons plays a role here. See pages 68-70 (largely qualitative) from

http://books.google.com/books?id=w9Dz56myXm8C&printsec=frontcover#v=onepage&q&f=false.

 

[Chalnoth]

Unlike photons, gluons can be (colour) charged, and the interaction of virtual gluons plays a role here. See pages 68-70 (largely qualitative) from

http://books.google.com/books?id=w9Dz56myXm8C&printsec=frontcover#v=onepage&q&f=false.

Yup, the fact that the gluons themselves carry strong-force (color) charge means that they couple not only to quarks, but also to themselves. This is what makes it so that the strong force acts sort of like springs between the quarks, as the charged gluons form a sort of tube between nearby quarks.

 

[George Jones]

Yup, the fact that the gluons themselves carry strong-force (color) charge means that they couple not only to quarks, but also to themselves. This is what makes it so that the strong force acts sort of like springs between the quarks, as the charged gluons form a sort of tube between nearby quarks.

And what Griffiths calls "gluon polarization" dominates at short distances and thus drives the strong coupling constant towards zero at short distances (page 70). But, as you say, only detailed calculation (worthy of Nobel prizes ) can verify this.

 

[DevilsAvocado]

Okay guys, if a layman would wrap this up, it’ll be:

"the strong force acts sort of like springs between the quarks"

And the reason the quarks don’t BOOM! gets sucked into a micro black hole, is the uncertainty principle (making it impossible to nail down those little bastards).

This leads to a tension (virtual energy) inside the nucleons, and this energy can be translated to 90% QCD Mass.

Einstein: E = m (big!)

Correct?

(Can I have the Nobel Prize now?? )

P.S. George thanks for the link to http://books.google.com/books?id=w9Dz56myXm8C&printsec=frontcover#v=onepage&q&f=false"!

 

[bapowell]

And the reason the quarks don’t BOOM! gets sucked into a micro black hole, is the uncertainty principle (making it impossible to nail down those little bastards).

Not quite. There's a bit more to the story. It's probably more correct to say that quarks simply aren't energetic enough. If you look back at the expression I posted above, as you increase the mass/energy of the particle, the Schwarzschild radius gets larger while the Compton wavelength gets smaller. Eventually, you reach an energy scale at which they meet. Then you get a black hole. Thinking in terms of the uncertainty principle, one sees that as the energy increases, the minimum uncertainty in the location of the particle decreases (this is the reason for the decrease in the Compton wavelength). Then, when that minumum uncertainty becomes smaller than the Schwarzschild radius, BOOM!, we form a black hole.

 

[DevilsAvocado]

Not quite. There's a bit more to the story. ...

Okay, thanks bapowell.

Correction:
"the strong force acts sort of like springs between the quarks"
And the reason the quarks can resist the strong force (inwards), is the uncertainty principle.
This leads to a tension (virtual energy) inside the nucleons, and this energy can be translated to 90% QCD Mass.

Correct?

 

[Chalnoth]

Potential energy, not virtual energy.

 

[DevilsAvocado]

Thanks Chalnoth! Finally it feels like I have some 'weight' in QCD!