Quantum Foam and Virtual Particles

[Curious6]

I have read a bit about quantum foam and the creation of virtual particles. I understand the basic concepts, but there is one question that bothers me though: can we think of the virtual particles as just being a 'concentration' of spacetime caused by the uncertainty principle inherent in the quantum foam?

 

[marlon]

I have read a bit about quantum foam and the creation of virtual particles. I understand the basic concepts, but there is one question that bothers me though: can we think of the virtual particles as just being a 'concentration' of spacetime caused by the uncertainty principle inherent in the quantum foam?

i don't really know the connection between foam and virtual particles but generally virtual particles arise in two ways. First they are used as the force mediating particles in matter-particles-interactions. In this case virtual particles are a direct consequence of perturbation theory and they represent the intermediate stages during the actual interaction. Energy conservation is not respected during this perid but momentum comservation IS respected because the virtual particles carry a definite momentum value that is determined by applying mometum conservation at each vertex.

The second option, and this is what you are referring to, is the zero point energy. If you set a physical system into its lowest possible energystate, the energy expectation value is non-zero because of HUP. But during a period of time this energy value can become uncertain also due to the HUP. this means that the vacuum fields will vibrate around some equilibrium state and it are these vibrations that correspond to virtual particles. In your case, i suppose it is the foam that is in its vacuum state.

regards
marlon

 

[Kruger]

@marlon: Does the lowest energy state (h(bar)w/2) of a electromagnetic oscillation contain virtual photons? (I refer to your "second option"). Or is is just the case that a virtual particle let's the oscillation state raising and after a short time lowering so that we have during this period (lifetime) an oscillation energy of h(bar)w/2+energyofvirtualparticle?

 

[marlon]

@marlon: Does the lowest energy state (h(bar)w/2) of a electromagnetic oscillation contain virtual photons?

YES, though the energy is the one you gave, HUP states that this energy does not remain constant over a period of time. It can start to fluctuate and thus fulfulling the delta E part of the HUP. It is these fluctuations of the quantum field that correspond to virtual particles. The vibrations have certain energy that corresponds to a virtual particle of that specific energy. remember that in QFT, particles arise because of field-fluctuations

marlon

 

[Kruger]

I always had trouble with this fields and particles, ufff.

We derive the ground state energy of a h.osc. with the momentum-position-uncertainty and thus get an energy of: h(bar)omega/2=E. Now this energy is fixed for a fixed omega. The lifetime of such a oscillator is infinity. And for a short period of time this energy E can become uncertain according to HUP. This uncertain energy belonges to one virtual photon. But only the uncertain part of the energy of a harmonic oscillation belonges to a virtual photon. The real ground state, vacuum state |0> with fixed energy h(bar)omega/2 doesn't contain virtual photons only oscillations of the em-field cause of the momentum-position-uncertainty.

I need to clear up this thing.

 

[marlon]

I always had trouble with this fields and particles, ufff.

We derive the ground state energy of a h.osc. with the momentum-position-uncertainty and thus get an energy of: h(bar)omega/2=E. Now this energy is fixed for a fixed omega. The lifetime of such a oscillator is infinity. And for a short period of time this energy E can become uncertain according to HUP. This uncertain energy belonges to one virtual photon. But only the uncertain part of the energy of a harmonic oscillation belonges to a virtual photon. The real ground state, vacuum state |0> with fixed energy h(bar)omega/2 doesn't contain virtual photons only oscillations of the em-field cause of the momentum-position-uncertainty.

I need to clear up this thing.

The real ground state indeed has to fluctuate because of HUP. The uncertainty in energy can also given certain energy values to the HO that do NOT obey the Einstein energy relation. They are said to be off mass shell. It are these energies that correspond to virtual particles.

The energy of the groundstate corresponds to the averaged energy during the oscillation of the wave function in its ground state. So globally, you can say it is fixed but this is an averaged value

marlon

 

[Curious6]

OK, thanks for the replies!

 

[straycat]

can we think of the virtual particles as just being a 'concentration' of spacetime caused by the uncertainty principle inherent in the quantum foam?

My short answer: yes, although in the abscence of a quantum theory of gravity, you have entered the realm of speculation.

There have been various attempts since the advent of relativity to come up with a model of particles -- not just virtual, but regular old particles -- as funky weird pieces of spacetime. I suppose you could call it a "concentration" of spacetime, although it depends on the model.

An early example would be the Einstein-Rosen bridge [1]. Later, John Wheeler tried to develop a model he called "geons" [2] -- I think the description "a concentration of spacetime" might be appropriate here. Others have proposed mini black holes. Recently, Mark Hadley [3] has rediscovered Wheeler's geon model, with a few twists: he uses 4 space instead of 3 space, and he also includes closed timelike curves CTC's (ie, wormholes) as part of his model.

All of these models were intended to model real particles, but there is no reason that they would not also apply to "virtual" particles as well.

I should point out that all of these models are speculative -- none have been proven.

David

[1] Eisntein and Rosen. The particle problem in the general theory of relativity. Phys Rev. July 1, 1935, Vol 48, pp73-77.

[2] Misner and Wheeler. 1957 Ann Phys 2 525-603.

[3] Mark Hadley. Spin half in classical general relativity. Class Quant Grav. 17 no 20 (21 oct 2000) 4187-94. gr-qc/0004029

 

[Kruger]

But the thing isn't that easy with the virtual particles. Think of the cosmological constant problem. If we messure this constant we get a very small value but if we calculate this constant we get a very huge value.

 

[Curious6]

straycat, do you think then once a quantum theory of gravity is found, it will reveal what the true nature of matter really is? I raised this idea about virtual particles perhaps being 'concentrations' of spacetime because I read that Einstein once did and Michio Kaku does believe it. Also, you have referred to papers published 50-70 years ago, and one from 1994, but is there any more recent interest in this as part of string theory perhaps?

 

[marlon]

But the thing isn't that easy with the virtual particles. Think of the cosmological constant problem. If we messure this constant we get a very small value but if we calculate this constant we get a very huge value.

Well, this is indeed a big problem but it is not inherent to the virtual particles. They are correct and a useful instrument of QED and all other valid and experimetally backed up field theories. The problem with the cosmological constant proves that QFT does not explain phenomena that both require very small distance scales and very high masses. The problem is this combination. QFT is THE theory for very small distance scales , as is QM and general relativity takes care of high masses and thus, big gravitational interactions. The combination of these two is the big problem because both theories are so fundamentally different in nature

marlon

 

[straycat]

straycat, do you think then once a quantum theory of gravity is found, it will reveal what the true nature of matter really is?

I think once a quantum theory of gravity (or whatever we decide to call it) is found, it will answer all sorts of questions. But it may raise even more. Keep in mind that quantum mechanics raised all sorts of questions along the lines of "what the hell is 'reality'?" I think the question: "what is reality," at least in the case of QM, depends upon which *interpretation* of QM one ascribes to. IOW, this question is not answered by the theory itself. A TOE or a GUT or whatever may or may not suggest a particular answer. It is possible, for instance, that we may come up with a quantum theory of gravity that, like present-day QM, has more than one interpretation, each of which hinges on a different concept of "reality."

I raised this idea about virtual particles perhaps being 'concentrations' of spacetime because I read that Einstein once did and Michio Kaku does believe it. Also, you have referred to papers published 50-70 years ago, and one from 1994, but is there any more recent interest in this as part of string theory perhaps?

It's hard for me to comment on string theory. My limited understanding of string theory is that it is a bunch of mathematics that are not yet grounded in physical principles, and so not yet amenable to physical "interpretation." It may be that the notion that "a particle is a concentration of spacetime" is buried down deep in string theory, but it's too early to say afaict.

Here's another paper [1] that is related. I'm sure there are others that I don't know about.

Hadley has a bunch of papers besides the one I cited - I can give you refs if anyone is interested. In fact, he is a member of a yahoo group, QM_from_GR, where we talk about this and related notions.

BTW I would recommend Kip Thorne's book _Black Holes and Time Warps_ as an excellent pop-sci book that delves into the quantum foam idea.

David

[1] Holzhey, C. F. E. and Wilczek, F. Black Holes as Elementary Particles, Nuclear Physics B380, 447 (1992). ArXiv:hep-th/9202014. or http://www.elsevier.nl/gej-ng/29/35/27/17/10/13/summary.html