Tube Effect?

[Riogho]

Okay, I am assuming ya'll know what the casimir effect/force is. If you don't look it up on Wiki.

 

My question is simple, what happens to a small hollow tube do to the casimir effect?

[5614]

The only tube small enough to be affected by the Casimir effect would, maybe, be a carbon nanotube (or something smaller, but I can't immediately think of anything that would fit that category).

 

More importantly for such a small construction to be stable it must be quite strong (carbon nanotubes are a great example of this). Given the strong inter-atomic forces, the Casimir effect is so small it would be quite insignificant.

 

In theory you could have a weak, tiny, tube that would collapse in on itself due to the Casimir effect... but I don't think you could construct such a tiny, yet weak, tube to observe this.

[Riogho]

Wouldi t work the same for hollow spheres?

[5614]

Same principle.

 

When your hollow sphere is created, the interatomic forces will make the Casimir effect insignificant.

 

A thought trail lead me to a figure off the Wiki page on Casimir effect which says that: "In fact, at separations of 10 nm — about 100 times the typical size of an atom — the Casimir effect produces the equivalent of 1 atmosphere of pressure (101.3 kPa)". So if you made a sphere of diameter 10nm (100 atoms - which I think we probably could) then you would get 101kPa of force trying to crush that sphere inwards.

 

Sadly even if we really simplified the problem I don't know how to calculate what force it would take to crush a sphere, given that it is just the interatomic forces holding it together.

 

Also remember that if the distance between atoms that enclosed the sphere were big enough then virtual particles could "go through" the wall. So you would need do have the wall of the tube/sphere being sufficiently dense to prevent that.

 

Finally if you were to make a sphere I wonder if the force would be larger than expected, as not only are you limiting the size of the particle (or amplitude of the wave, by confining it), but you're also placing it in the 'particle in a box' configuration, thus limiting the energy levels the particle can take. Although I suppose if the virtual particle existed for a short enough time period it could poses a non-normal-mode energy level, but still, I think it possible that the number of virtual particles is further limited by the fact it is a sphere, and not an (effectively) infinte tube, or between parallel plates, which would make the Casimir effect stronger. Maybe, I'm just guessing at this!

[Riogho]

Does this mean that the Casimir effect makes it impossible for an elementary particle to be hollow?

[5614]

That's an interesting approach to the structure of an elementary particle. I've never considered that if an elementary particle is not point-like then it could be hollow.

 

I suppose, to not-answer the question, it would depend on how strongly the particle wanted to stay together.

 

Assuming that elementary particles are hollow spheres, and given that elementary particles do exist, we must conclude that the Casmir effect is not strong enough to make them collapse on themselves.

 

Personally, along with the mainstream of science, I think that elementary particles are 0-dimensional points, but that doesn't stop your question being theoretically interesting, although I'm not sure we can gain anything from analysing it.

[iNow]

My own somewhat ignorant stance on the issue is that the entire concept of "hollow" is meaningless when taken at the scale of the particle. AFAIK, It's like asking if the space between the earth the sun is hollow.

[Klaynos]

Doesn't the concept of a particle breakdown when you get down to scales of fundemental particles though?

[Riogho]

if it was hollow that would solve our little problem of sping angular momentum and exactly what it is.

[5614]

iNow: I don't see your reasoning. Rather than assuming point-like fundemental particles we have spherical particles, why then could they not be hollow? Mind you, a particle as a sphere is one thing, but a particle as a spherical shell is even worse!

 

Klay: I don't really see your point. Are you saying that even if an electron were hollow then how could a virtual electron fit inside? But then if, and I don't think this is so, but if fundemental particles do have a non-zero size, then could they not be different sizes? Must an electron and a quark have the same radius?

 

Ah, this is all a load of hyper-theoretical stuff anyway! Here's a better thought: a construction as small as we're talking about is so tiny that the number of virtual particles colliding with it must be tiny, thus making the Casimir effect correspondingly tiny (even more so than usual). So for example the "1atm at 10nm" value from my previous post is probably far too high for things on a molecular level.

[Klaynos]

My point was more quantum mechanically they are not spheres etc... they're undefined, it was more a response to inow than the thread in general... our measurement attempts at electron radii have come out as zero...

[swansont]

I think you run into trouble when you try and apply classical concepts (hollow sphere or tube) at this level. Hollow and point-like would seem to be conceptually orthogonal.

 

But how does a hollow particle solve the spin angular momentum "problem"?

[Riogho]

Because that would give the mass a point to spin around

[Klaynos]

Because that would give the mass a point to spin around

 

A solid body can spin around its centre of mass, or infact any other point and have angular momentum.

[5614]

My point was more quantum mechanically they are not spheres etc... they're undefined, it was more a response to inow than the thread in general... our measurement attempts at electron radii have come out as zero...

I agree with you then, but can you explain this:

http://scienceworld.wolfram.com/physics/ElectronRadius.html

it never made any sense to me, and I still don't understand what it's really talking about, especially as I think your quote is totally correct.

[Klaynos]

It's not physically real, but an "effective" radius where some effects become apparent.

 

I believe that all experiments to find the radius of an electron have found it to be smaller than their sensitivity allows.

[5614]

It's not physically real, but an "effective" radius where some effects become apparent.

 

I believe that all experiments to find the radius of an electron have found it to be smaller than their sensitivity allows.

The second part of the quote sounds in-line with what I know, but can you expand on the first bit? What physical effects become apparent?

 

I read on the Wiki page that the value is calculated from the energy required to assemble a charge e of radius r_e, so I can see why it's very much a classical value. I also see it crops up in a Thomson scattering equation, and seems to work nicely there, but do you know of any other examples? Or anywhere it ties in with a theoretical model, as opposed to an equation? If it didn't (seemingly successfully) appear in that Thomson scattering equation I'd be tempted to call it a classical trick that isn't really useful in "everyday" life, would I be justified in saying that?

[Klaynos]

I think it's used for other scattering events as well, I'm pretty sure I remember using it in solid state this year, something to do with scattering in electron transport in magnetised samples...

[swansont]

A solid body can spin around its centre of mass, or infact any other point and have angular momentum.

 

Right. The issue with the electron is that if you require the surface speed to be below c, you end up with an electron that's much bigger than experimental values give.