Higgs field and the casimir effect

[srfriggen]

Would/should the mass of a particle measured between the two plates (typical casimir experiment setup) be different than measured outside the plates? If so would this be evidence of the Higgs field/mechanism?

 

[tom.stoer]

What is measured by the Casimir effect is the difference between the effect of unrestricted vacuum fluctuations outside the plates and restricted vacuum fluctuations between the plates resulting in a "force". There are no real particles involved, no need for mass (it works with massless photons) and no need for a Higgs field.

 

[srfriggen]

It was my understanding that the Higgs field was created from vacuum fluctuations of the Higgs boson. Do you see the implicatios now? If the higgs boson exists it's power may be different between the plates.

 

[tom.stoer]

It was my understanding that the Higgs field was created from vacuum fluctuations of the Higgs boson. Do you see the implicatios now? If the higgs boson exists it's power may be different between the plates.

Yes, I see what you mean. In general all quantum fields are subject to vacuum fluctuations and the Casimir force. But afaik the coupling of the Higgs boson (not the vev) is suppressed by the usual Fermi coupling constant G_F~ 1/M_W². That means that the weak Casimir effect is weak compared to the electromagnetic one. I have to check the details.

 

[humanino]

The only way I can imagine a change in the Weinberg angle is if the putative Casimir effect would be different for W and Z. I think this is hopelessly small. For instance the electromagnetic "Casimir effect" can be very well understood in terms of van der Walls forces. Imagine the plate separation you need to undercover weak van der Walls forces.

Now even I can conceive that the measurement of radioactive decay change can be performed quite accurately, and still I doubt that the Weinberg angle could be changed enough.

 

[tom.stoer]

Has the van der Walls force anything to do with the Casimir effect?

 

[humanino]

I think Casimir himself recognized this equivalence, but I do not have a link to a reference from him. The article below quotes Casimir's talk at the "Fourth workshop on QFT under external influence" 98.

The Casimir Effect: Physical Manifestations of Zero Point Energy

Zero-point fluctuations in quantum fields give rise to observable forces between material bodies, the so-called Casimir forces. In these lectures I present the theory of the Casimir effect, primarily formulated in terms of Green's functions. There is an intimate relation between the Casimir effect and van der Waals forces. Applications to conductors and dielectric bodies of various shapes will be given for the cases of scalar, electromagnetic, and fermionic fields. The dimensional dependence of the effect will be described. Finally, we ask the question: Is there a connection between the Casimir effect and the phenomenon of sonoluminescence?

The Casimir Effect and the Quantum Vacuum

In discussions of the cosmological constant, the Casimir effect is often invoked as decisive evidence that the zero point energies of quantum fields are "real''. On the contrary, Casimir effects can be formulated and Casimir forces can be computed without reference to zero point energies. They are relativistic, quantum forces between charges and currents. The Casimir force (per unit area) between parallel plates vanishes as \alpha, the fine structure constant, goes to zero, and the standard result, which appears to be independent of \alpha, corresponds to the \alpha\to\infty limit.

 

[srfriggen]

I'm not a physicist, so a lo of that is foreign to me, but is the conclusion to my original question that in order to see an effect of the Higgs field the plates would need to be much too close togeter to rule out any practical experiment? Can someone please explain this to me in laymen's terms?

Thanks. :)

 

[tom.stoer]

Yes, something like this. The weak force acts on length scales below the size of a proton.

 

[srfriggen]

Ok I understand. So what is the force that acts on the order of micrometers that causes the casimir effect?

 

[tom.stoer]

The electromagnetic force.

Let me explain a little bit more: in physics the "force" (e.g. the gravitational force) is a derived concept; the basic concept is a field or a potential (e.g. the gravitational potential). Based on the field the force can be derived.

In quantumfield theory one introduces the concept of "virtual particles as mediators of the force". Please don't take this too literally and don't confuse simple (but physically inconsistent) pictures with reality!

If one does that one finds that every force (or field) corresponds to a particle:
electromagnetic force <==> photon
strong force <==> gluon (inside protons and neutrons binding quarks togetehr)
weak force force <==> W- and Z-boson (causing nucleons and quarks to decay)
gravitational force <==> graviton (not observed)

These particles are not only matehmatical concepts but can be detected as real paerticles in principle (except for the graviton as its interaction is much too weak). Especially the W- and the Z-boson have been observed as "real" particles.

One knows that electromagnetic + weak force can be unified to the electro-weak force. So the photon and the Z are "cousins".

One can derive mathematically that the range over which a force can act has something to do with the mass of the corresponding particle or - which is equivalent - with the potential.

The massless photon causes a slow decay of the electromagnetic force, whereas the rather heavy W and Z (they get their mass from the Higgs) cause a fast decay of the eak force with a typical range smaller than the size of a nucleon.

 

[srfriggen]

"In quantumfield theory one introduces the concept of "virtual particles as mediators of the force". Please don't take this too literally and don't confuse simple (but physically inconsistent) pictures with reality!"

What exactly do you mean by that? So those "virtual particles" don't actually exist? So what is the reality of it all then?

 

[tom.stoer]

In many popular books a virtual photon is described as a particle that is emitted by e.g. an electron and absorbed by a positron. There are a couple of questions:
- how can the exchange of a particle be attractive or repulsive?
- what happens if there is no second particle which can absorb the virtual photon?
- how many paticles are exchanged?
- etc.

All these questions arise simply because one takes the concept of one single particle too literally.

First of all the Feynman diagrams with internal lines representing these virtual particles are just book keeping. A virtual particle ina Feynman diagram is simply a rule how to sum over infinitly many exchanges of a mathematical object describig the propagation of particles. It is math!

In addition the identity of virtual particles is by no means unique. In gauge theories the concept of a physical particle is rather clear, whereas the internal particle can be redefined such that the above mentioned rules change drastically. There are formalism where a static electric field is replaced by a bunch of virtual particles. There are formalisms where a rather strange kind of virtual particles appear, the so-called ghosts. In other formalisms there is no need for these ghosts.

And last but not least there are physical problems that cannot be described via virtual particles at all.

That means that virtual particles are nothing else but a rather useful mathematical artefact.

 

[srfriggen]

"- what happens if there is no second particle which can absorb the virtual photon?"

Isn't that precisely how Hawking Radiation works?

How do you conceptualize all of these things without being able to have some visualization of what's going on! lol

I'm a starting math major with an extreme interest in Physics, so I'm hoping one day I'll be able to "see" what's going on in the math.

 

[tom.stoer]

Isn't that precisely how Hawking Radiation works?

No, not precisely. The source of Hawking radiation is a pair of virtual particles created from vacuum (no particle).

How do you conceptualize all of these things without being able to have some visualization of what's going on!

I agree that using (visual) models is sometimes helpful, but one has to be aware of the fact that they are models.

 

[srfriggen]

No, not precisely. The source of Hawking radiation is a pair of virtual particles created from vacuum (no particle).


I agree that using (visual) models is sometimes helpful, but one has to be aware of the fact that they are models.

So Hawking radiation is from real, actual, particles called virtual particles created from vacuum and messenger particles are also "virtual particles" but just mathematical artifacts?

 

[tom.stoer]

Sorry for the confusion.

Graphically in a Feynman diagram a virtual particle is a particle that does not escape to infinity; so its line has two ends (two vertices) where it meets with another line or lines. Now draw a circle and two vertices on the circle. This is a vacuum fluctuation where at one vertex a pair of virtual particles is created out of nothing (vacuum); the two particles propagate to the second vertex where they annihilate into nothing (vacuum). Usually this is a mathematical artefact and is "subtracted" from the theory.

Near the event horizon something strange happens. One of the two virtual particles tunnels through the horizon whereas the other virtual particle is eventually sucked into the black hole. The particle outside the event horizon does not annihilate with the other particle, so it escapes to infinite and is therefore not a virtual particle. The confusion is due to the fact that we compare a process in flat space (with two virtual particles in a vacuum fluctuation) with another, different process in curved spacetime (with one real particle). That's why its strictly speaking not a virtual particle that becomes a real particle, but a particle that is created by tunneling (similar to the alpha particle that tunnels from a nucleus causing alpha decay).

The mathematical reason is difficult: in order to set up quantum field theory one must define a vacuum state. In curved spacetime this is no longer possible uniquely. So what we call virtual particle when its located inside the event horizon is a real particle when it is located outside the horizon. One can evaluate this vacuum ambiguity mathematically. In doing so one finds that one has to redefine the vacuum state outside the event horizon in such a way that is contains real particles with thermal spectrum.

A similar effect is the so-called Unruh effect. It simply says that if an observer at rest observes vacuum w/o particles then a constantly accelerated observer observes thermal radiation! So the same volume of space contains no particles at all or thermal radiation - depending on the observer. Again the very notion of vacuum is no longer unique. The two effects are closely related as in the Unruh case there is again a "kinematical horizon" which means there is a region of spacetime from which no signal can reach the accelerated observer. This is not due tothe eometry of spacetime but due to the acceleration only, but nevertheless it is a horizon.

 

[srfriggen]

Very informative, thank you. :)

 

[sheaf]

Post #17 is the most succinct description of semiclassical gravity that I've ever seen !

 

[tom.stoer]

Thank you very much!

But of course these are not my own results, but these insights are based on studying papers and books of much more talented people. So my work here is more editorial than intellectual.