Virtual Particles: Creation & Destruction in 10-43 Seconds?

[A. Neumaier]

I suspect here you're referring to the suggestion of doing QED in the Coulomb gauge ? It's my understanding (maybe a QFT expert could confirm ?) that there is no implication from this that there can't be photons in the in and out states, merely that by using the Coulomb you can swap the picture where you describe, say, the Coulomb interaction in terms of virtual photon exchange for one where the virtual photons are not needed.

Even QED in the Coulomb gauge (done, e.g., in the well-known book by Bjorken and Drell)
needs photons.

 

[Dav333]

what about the talk of VP in the documentary of BBCs Atom, the Illusion of Reality?

 

[tom.stoer]

It's my understanding (maybe a QFT expert could confirm ?) ... that ... you can swap the picture where you describe, say, the Coulomb interaction in terms of virtual photon exchange for one where the virtual photons are not needed.

Exactly!

 

[tom.stoer]

Even QED in the Coulomb gauge ... needs photons.

Agreed ...

... but this proves that virtual photons are gauge-dependend objects. Look at QCD a) in Coulomb gauge and b) in axial gauge. In (a) you have ghost (always virtual), whereas (b) is ghost-free. So how could ghosts "exist" if their existence depends on the gauge? As ghosts do exist to cancel certain contributions of virtual partucles how can these virtual particles be "real"?

 

[A. Neumaier]

Agreed ...

... but this proves that virtual photons are gauge-dependend objects. Look at QCD a) in Coulomb gauge and b) in axial gauge. In (a) you have ghost (always virtual), whereas (b) is ghost-free. So how could ghosts "exist" if their existence depends on the gauge? As ghosts do exist to cancel certain contributions of virtual partucles how can these virtual particles be "real"?

Yes. It is even worse. The virtual photons are completely different in the instant form (''old-fashioned perturbation theory''), the covariant form (the modern textbook formalism) and the front form (light cone formalism), and completely disappear from the picture in lattice QED.

But people like kexue have a very liberal view, in which reality looks very different depending on who describes it, and how. That's why it can be determined simply by asking people about their views via email and discarding dissenting answers (such as Weinberg's). Objective arguments don't count in such a view of reality.

This is not the reality physicists are studying, though.

 

[tom.stoer]

But people like kexue have a very liberal view, in which reality looks very different depending on who describes it, and how. That's why it can be determined simply by asking people about their views via email and discarding dissenting answers (such as Weinberg's). Objective arguments don't count in such a view of reality.

Agreed again!

If you like - and if you want to waste your time - you can check other threads where I made the same experience with him :-)

 

[PhanthomJay]

As to the physicality of vacuum fluctuations, I do not think that it has been proven. Vacuum fluctuations can be used to derive a number of phenomenon like the Lamb shift and Casimir force. However, like I stated previously, you can also derive these phenomena without the vacuum theory. So there are strong indicators that the vacuum fluctuations have physical consequences but I have not heard that it has been conclusively proven that they are the actual physical perpetuators.

Thank you for the response and references!

 

[PhanthomJay]

Lifetimes are defined in terms of the imaginary part of the sigenenergy E of an unstable particle, given by a solution to the Schroedinger equation H psi = E psi in rigged Hilbert space. Virtual particles don't have associated wave functions, hence cannot satisfy such an equation, and therefore have no life-time in any meaningful sense.

Numbers quoted at various places are figments of the imagination only, nowhere derived from proper definitions.



The vacuum fluctuations involved in calculations of the Casimir force are in the usual 4 dimensions of space-time.

Thanks for the response. I found this explanation which is a bit simpler to understand. Whether it is correct is something else:

http://www.angelfire.com/ga/dracodraconis/physics.html

But in that article, it talks about virtual electrons and positrons, the real counterparts of which have mass. It also also talks about the virtual photon, the real counterpart of which has no mass. The synopsis, however, is silent on the existence of other virtual particles like virtual gluons, virtual W and Z bosons, and the postulated virtual graviton. I assume that the mathematics of virtuality covers these particles as well?? Does it cover protons? atoms?

Now here's what I understand also...a photon can interact with the quantum field to produce the virtual electron and virtual positron, which annihilate each other in less than 10^-43 seconds. Then it goes on to say, that sometimes a photon does not have to interact with the Field, and virtual particles can be created spontaneously. That seems to make them real.

Am I being fed more lies?

 

[Born2bwire]

Thanks for the response. I found this explanation which is a bit simpler to understand. Whether it is correct is something else:

http://www.angelfire.com/ga/dracodraconis/physics.html

But in that article, it talks about virtual electrons and positrons, the real counterparts of which have mass. It also also talks about the virtual photon, the real counterpart of which has no mass. The synopsis, however, is silent on the existence of other virtual particles like virtual gluons, virtual W and Z bosons, and the postulated virtual graviton. I assume that the mathematics of virtuality covers these particles as well?? Does it cover protons? atoms?

Now here's what I understand also...a photon can interact with the quantum field to produce the virtual electron and virtual positron, which annihilate each other in less than 10^-43 seconds. Then it goes on to say, that sometimes a photon does not have to interact with the Field, and virtual particles can be created spontaneously. That seems to make them real.

Am I being fed more lies?

I have not heard of any lifetimes being associated with virtual particles. You can read about physical analogues that describe the process of a virtual particle. That is, from the Heisenberg Uncertainty Principle, over a very very small amount of time we can observe a large bandwidth of possible energies. If these energies are high enough, you can spontaneously pull out a particle or pair of particles (whatever be appropriate) from the vacuum but since the energy is just a fluctuation these particles must be quickly annihilated. So you can think of these particles popping in and out of the vacuum all the time and thus some may or may not play a role in the interactions. But the big caveat in all this is that these particles are never observed.

So take your vacuum fluctuations of the electromagnetic fields. If we are in the vacuum state, there are no photons but virtual photons pop in and out to create the fluctuations of the electromagnetic field. Still, we will never observe these photons under this theory. A real particle is different. We can detect individual photons, electrons, buckyballs and so forth. But we will not detect a virtual particle.

I don't think it is very useful to think of virtual particles having a lifetime. Because if we were to ascribe a lifetime for them, then we could define a bandwidth of energies to be observed over this lifetime via the Heisenberg Uncertainty Principle. But the theories of vacuum fluctuations ascribe the vacuum to have a zero point energy of infinite bandwidth. Now proof of the zero point energy is even less certain than the vacuum fluctuations themselves because, from the theories that I have read that have dealt with it, we can always renormalize the zero point energy without consequence. It is the change in the zero point energy that is of concern and which produces such effects like the Casimir effect.

You might be able to get away with the vacuum particles being produced only over a finite bandwidth. The vacuum phenonenon that I am familiar with assume that interactions at higher frequencies become negligible and can be ignored (thus we truncate the bandwidth of the problem). But I would think that the restrictions on the energy bandwidth by a given lifetime would cause the lower energies to be more favorable and these vacuum phenomena assume no such weighting to the vacuum energies. For the most part, like I said above, I have not heard of lifetimes being discussed when it comes to virtual particles.

 

[Deric Boyle]

weejee and kexue please don't derail the thread as it had put PhantomJay in trouble.
I think tom.stoer, A.Neumaier are the ones who can guide us; as I've heard from other PF member that they are QFT QCD QED giants.

 

[tom.stoer]

I certainly was a QCD expert; but NEVER a giant.

 

[A. Neumaier]

Thanks for the response. I found this explanation which is a bit simpler to understand. Whether it is correct is something else:

http://www.angelfire.com/ga/dracodraconis/physics.html

It starts off with ''The preceding paragraph was taken from a mock-science journal known as "THE MOCK SCIENCE JOURNAL OF UNTRUE PHYSICS" and as such is totally untrue.''
which should make you already suspicious...

Accounts of virtual particles for the laymen are almost always unreliable when you want to dig deeper. They are meaningful only in a very roundabout fashion, when you don't ask about more precision of what the concepts mean.

But in that article, it talks about virtual electrons and positrons, the real counterparts of which have mass. It also also talks about the virtual photon, the real counterpart of which has no mass. The synopsis, however, is silent on the existence of other virtual particles like virtual gluons, virtual W and Z bosons, and the postulated virtual graviton. I assume that the mathematics of virtuality covers these particles as well??

Yes, since these are the particles corresponding to elementary fields in the standard model and quantum gravity. But they are as unreal as virtual photons, so let us stick to the latter.

Does it cover protons? atoms?

No. These don't occur as internal lines of Feynman diagrams, hence are no virtual particles according to the standard definitions in QFT. (But layman's sources
associate the notion of virtual particles also with other things, such as unstable particles...)

Now here's what I understand also...a photon can interact with the quantum field to produce the virtual electron and virtual positron, which annihilate each other in less than 10^-43 seconds. Then it goes on to say, that sometimes a photon does not have to interact with the Field, and virtual particles can be created spontaneously. That seems to make them real.

Am I being fed more lies?

I wouldn't call it lies but superficial illustrations for lay people.

But the talk about annihilation in10^-43 seconds, or spontaneous creation is meaningless on a more formal level - one cannot translate it into formulas. This would require annihilation and creation operators for virtual particles, which don't exist.

Stuff that is real (according to high standards of reality) always can be modeled on a mathematical level - one can consistently translate all statements in ordinary language into meaningful statements on the level of formulas. This makes electrons, electromagnetic fields, black holes real. For virtual particles, however, you cannot even write down a wave function, let alone calculate a creation probability or a decay time
(things that are related to S-matrix properties, which relate only real particles).

 

[A. Neumaier]

Where and when did I play only with words?

That you only play with words, playing back without real understanding what you read in various sources, can be seen when one tries to give your words more substance. It is impossible, proving the emptiness of your talk.

Try to write down a state vector containing a virtual particle. It is impossible - a physical Hilbert space does not contain such states. But one can easily write down state vectors for the usual, real objects, such as quarks, nuclei, electrons, or photons.

Try to substantiate any of your other statements by backing them up with formulas that match the contents in a verifiable way. This gives you a powerful test for which of your words have substance and which ones are empty.

Virtual particles live only in the thin air created for those who cannot handle a more technical account.

For the experts, the only reality of virtual particles is as internal lines of Feynman diagrams. Here they stand for certain propagators to be integrated over - not for objects that, in real time, pop in and out of existence. That's only the visualization for making the subject sort of intelligible to the non-experts.

 

[tom.stoer]

the only reality of virtual particles is as internal lines of Feynman diagrams. Here they stand for certain propagators to be integrated over - not for objects that, in real time, pop in and out of existence. That's only the visualization for making the subject sort of intelligible to the non-experts.

Agreed! So one could say that the invention of diagrams and lines to draw virtual particles w/o the command to calculate something was the biggest mistake Feynman ever made :-)

 

[kexue]

A.Neumaier, this is still physics, not mathematics. As they like to say in the theoretical physics community, too much rigor soon leads to rigor mortis. Indeed, as Feynman would tell students, if this ain’t rigorous enough for you the math department is just one building over.

On reality in physics, read the Pollitzer quote in the other thread (where I wasted so much of Tom's time).

What a physicist cares about is whether the model matches observation. Quantum field theory, with its virtual particles, matches observation very very well.

Because of this, many, many physicists allow themselves a very little boldness and say that virtual particles are "really out there". "Really out there" in the sense that their contribution certainly affects the amplitudes of particle transitions. "Really out there" in the sense that they represent some real effects, namely a transfer of energy and momentum via fields. "Really out there" in the sense that they are part of a mathematical description of reality, and therefore must correspond to some feature of reality.

But enough of my word play without substance. I'm still waiting on your thoughts why Frank Wilczek would say in http://arxiv.org/PS_cache/hep-th/pdf/9803/9803075v2.pdf" on page 3 that the association of forces with the excange of 'virtual' particles is a general feature of quantum field theory.

Do you really think he is not an expert? That he can not handle a more technical account?

 

[PhanthomJay]

Stuff that is real (according to high standards of reality) always can be modeled on a mathematical level - one can consistently translate all statements in ordinary language into meaningful statements on the level of formulas. This makes electrons, electromagnetic fields, black holes real. For virtual particles, however, you cannot even write down a wave function, let alone calculate a creation probability or a decay time
(things that are related to S-matrix properties, which relate only real particles).

Thank you very much for the response.

I am becoming more and more convinced that the secret of the Universe may only be unlocked by discovering the secrets of the miniscule quantum dimensions and properties of spacetime. The secret of the Zero, I call it. Speculation, of course, but do you agree?

 

[weejee]

Where and when did I play only with words? Pretty strong claims that you should better back up.

Where and when did you 'not' play with words? Well, maybe I'm being a little bit unfair here, since for something like the 'realness of virtual particles', there is not much to do with quantitative stuff (and therefore it is a dangerous realm where it is hard to distinguish between physics and mere words).

I used strong words because when I didn't, you seemed to interpret what I said too much in your favor. I realize that using strong words doesn't help much either, since it seems to only make you angry.

As far as my "theory of lifetime of virtual particles" is concerned, I got that from a Professor who wrote a leading book on quantum field theory.

Whoever said this, it doesn't make sense. Maybe you are misinterpreting what the professor actually said.

Your question somewhere earlier, where do virtual particles arise in free field theory? Nowhere. A photon that never interacts, that is nowhere emited and absorbed is indeed a 'real' particle.
But every field (and it associated particle) we probe in an experiment is no free field anymore!

Right. However, my point was that according to your claim that virtual particles are allowed by the uncertainty principle, there is no reason for them not to appear in free field theories.

Also, which you won't believe me, 'virtual' particle do appear (implicitly) in non-perturbation theory. I learned that from many replies I received. One explanation, I gave to you in post 37.

Yes they do, as long as we adhere to start from free particles and treat the interaction as a correction to them. Yet this just means that we are pushing the limit of the perturbation theory into the regime where it doesn't really hold, although it isn't necessarily true that such attempt is totally meaningless.
Still, if we somehow exactly solve the problem, that is, without treating the interaction as a correction to free particles, no virtual particle should appear.

My view is that of Frank Wilczek, no more no less, which will qoute again and for the last the time for your convenience.

It comes down to what you mean by "really there". * When we use a concept with great success and precision to describe empirical observations, I'm inclined to include that concept in my inventory of reality. * *By that standard, virtual particles qualify. * *On the other hand, the very meaning of "virtual" is that they (i.e., virtual particles) don't appear *directly* in experimental apparatus. * Of course, they do appear when you allow yourself a very little boldness in interpreting observations. * It comes down to a matter of taste how you express the objective situation in ordinary language, since ordinary language was not designed to deal with the surprising discoveries of modern physics.*

He is just talking about how he would describe certain things in ordinary language, presumably because your original question is formulated in terms of ordinary language.

I think that what he said is acceptable, but I also think it might be misleading.

The thing is, he didn't talk about anything like the lifetime of virtual particles or mix up between 'being virtual' and 'being non-classical'. If you are really saying that what you've been claiming is no more or no less to what Frank Wilczek said, it is very confusing to me.Let me tell you just one more thing. I think that people use the term 'fluctuation' in the quantum field theory to describe two different things.

1. Fluctuation from the classical solution: This corresponds to non-classical paths in the path integral.

2. Virtual particles that "pop out from the vacuum": I would say that in a formal sense, this just means the difference between the interacting vacuum(=free vacuum + various particle states * small coefficients) and the free vacuum.

I highly suspect that you are mixing up these two.

p.s. No more derailing. I quit arguing with kexue.

 

[Dynamic Sauce]

What Does it mean when virtual particles travel "Backwards in time" does it mean literally?

 

[Dynamic Sauce]

I certainly was a QCD expert; but NEVER a giant.

I also see that virtual particles travel faster than c?

 

[A. Neumaier]

Agreed! So one could say that the invention of diagrams and lines to draw virtual particles w/o the command to calculate something was the biggest mistake Feynman ever made :-)

No. The diagrams were actually the device that made his approach intelligible and superior to the approaches by Tomonaga and by Schwinger.

The mistake was to sell the internal lines to the public as ''virtual particles''. This interpretation is not needed for the working of QFT and had done more damage than good.

 

[A. Neumaier]

I'm still waiting on your thoughts why Frank Wilczek would say in http://arxiv.org/PS_cache/hep-th/pdf/9803/9803075v2.pdf" on page 3 that the association of forces with the excange of 'virtual' particles is a general feature of quantum field theory.

I comment on his lecture in my theoretical Physics FAQ; see
http://arnold-neumaier.at/physfaq/physics-faq.html#virtual2
In the FAQ, you can also find a lot more information.

 

[tom.stoer]

This interpretation is not needed for the working of QFT and had done more damage than good.

Please make this large and bold!

 

[A. Neumaier]

What Does it mean when virtual particles travel "Backwards in time" does it mean literally?

No. It just means that one can draw Feynman diagrams where internal lines go backward in time. It has no meaning beyond that. In particular, interpreting a Feynman diagram as a process that happens in time is illegitimate.

I also see that virtual particles travel faster than c?

Since they don't travel but are drawn, virtual particles neither travel backwards nor faster than light. Such statements are only figures of speech, in an attempt to give life to lifeless drawings.

 

[A. Neumaier]

Please make this large and bold!

How?

 

[tom.stoer]

The diagrams were actually the device that made his approach intelligible and superior to the approaches by Tomonaga and by Schwinger.

The mistake was to sell the internal lines to the public as ''virtual particles''. This interpretation is not needed for the working of QFT and had done more damage than good.

 

[tiny-tim]

How!

 

[A. Neumaier]

A.Neumaier, this is still physics, not mathematics. As they like to say in the theoretical physics community, too much rigor soon leads to rigor mortis.

Even physics must be backed up with formulas; there is no substance in modern physics without lots of mathematics behind.

One cannot understand quantum mechanics without having understood the underlying mathematical machinery, at least on a level where one can translate claims into the formal language. (Though this is still far from mathematical rigor, which would be needed for an even deeper understanding.)

 

[tiny-tim]

Hi Dynamic Sauce!

What Does it mean when virtual particles travel "Backwards in time" does it mean literally?

I also see that virtual particles travel faster than c?

I've just replied in your https://www.physicsforums.com/showthread.php?t=452491".

 

[danlew]

They don't.

Virtual particles are not real.

Simple, no?

Are you saying they are not real to a humans eye?

 

[kexue]

I comment on his lecture in my theoretical Physics FAQ; see
http://arnold-neumaier.at/physfaq/physics-faq.html#virtual2
In the FAQ, you can also find a lot more information.

Well, I can not understand how anybody would say after reading this lecture that 'virtual' particles are a damage to understanding and describing nature, but whatever.

But I was referring to the survey article which is directed at physicists and what he says there on page 3. A.Neumaier, Tom, Tiny Tim, any thoughts?

It goes like this
With the correspondence of fields and particles, as it arises in quantum field theory, Maxwell’s discovery corresponds to the existence of photons, and the generation of forces by intermediary fields corresponds to the exchange of virtual photons. The association of forces (or, more generally, interactions) with exchange of particles is a general feature of quantum field theory.

 

[tom.stoer]

I think we discussed this example already, but I would like to come back to it. Look at the function

$$f(x) = \frac{1}{1-x} = \sum_{n=0}^\infty f_n x^n$$

Of course we all know that for |x| < 1 the coefficients are all equal to 1 and that for |x| > 1 this Taylor expansion at 0 is undefined.

Now let's talk about the question how "real" the function f(x) itself is and how real the coefficients are - especially if we do NOT specify for which value of x we want to calculate f(x).

I would say that the coefficients are an artifact of the Taylor expansion only, that for a different Taylor expansions we get different coefficients but we still have the same function f(x), so the function f(x) is the "real object" I am interested in. Of course we can find some funny names for the coefficients, we can use them in our calculations, we can speculate how "real" they are - but the object that really counts is f(x).

In the same sense the "physical object" object we are really interested in is (e.g.) an S-matrix-element. Of course we may calculate the S-matrix using perturbation theory,but this is an artifact of the calculation. If we would be clever enough to calculate it directly nobody would care about the expansion and nobody would try to find interesting names for the coefficients.

Of course the coefficients have a name (Taylor coefficients) and there are applications of Taylor expansions where Taylor expansion is really all we need. But there are other functions (with cuts, Riemann sheets, torus compactification, modular forms, ...) where Taylor expansion is closed to nonsense; it does not make sense, it does not solve your problem, it's the wrong tool, it hides reality and all relevant mathematical properties, ...

Another intersting function you may want to study is

$$g(x) = e^{-1/x^2}$$

How does its Taylor expansion at x = 0 look like?

 

[A. Neumaier]

the generation of forces by intermediary fields corresponds to the exchange of virtual photons. The association of forces (or, more generally, interactions) with exchange of particles is a general feature of quantum field theory.

What Wilczek says here is correct, but what you want it to imply doesn't follow.
This doesn't make virtual particles real. To say that a virtual particle is exchanged is just saying that there is a diagram in which this particle carries an internal line. But as the name says, the exchange is not real but virtual (on paper, in the mind of those telling or reading the story). It is figurative speech only. The correspondence referred to by Wilczek is one in the formulas, not one of processes that happen in space and time.
The latter cannot even be translated into a meaningful formal statement that could be checked for mathematical consistence.

There are infinitely many diagrams with all the possible exchanges and exchanges between exchanged particles, etc. They are all part of a perturbation calculation, not of something really happening. You cannot have at the same time one particle exchanged and 2 particles exchanged and 3 particles exchanged etc for any number of particles, although this is what is needed to compose the Coulomb force perturbatively from virtual particles.

Unlike superpositions of 1,2,3, etc. real particles, which one has in observable coherent states, there is no way to interpret the presence of the infinitely many exchanges as a superposition of 1,2,3 virtual photons. For in order to say this meaningfully, one needs virtual particle states that could be superposed, and these don't exist, not even virtually.

 

[kexue]

A.Neumaier, yes 'virtual' particles are no 'real' particles, we all knew that 300 posts before.

My last words are again the words of Frank Wilczek. (Why not put these up in the PF FAQ?)

It comes down to what you mean by "really there". When we use a concept with great success and precision to describe empirical observations, I'm inclined to include that concept in my inventory of reality. By that standard, virtual particles qualify. On the other hand, the very meaning of "virtual" is that they (i.e., virtual particles) don't appear *directly* in experimental apparatus. Of course, they do appear when you allow yourself a very little boldness in interpreting observations. It comes down to a matter of taste how you express the objective situation in ordinary language, since ordinary language was not designed to deal with the surprising discoveries of modern physics.

It is a matter of taste. Allow you a very little of boldness or don't. Or don't bother at all. That's all there is, really.

I leave the discussion on that. Good night

 

[PhanthomJay]

(..snip..)It comes down to what you mean by "really there" (..snip..).

One thing is certain, I'll be re-reading Hawking's full chapter on "What is Reality" (in his book, "The Grand Design") tonight...

 

[A. Neumaier]

It comes down to what you mean by "really there".

It is a matter of taste. Allow you a very little of boldness or don't.

Except that this boldness (or writing things in bold) doesn't help the slightest in understanding.

If one clearly distinguishes between reality and virtual reality, one finds that the physics of the former is much more rational than that of the latter, where everything goes, and
where (as the Wikipedia article on virtual particles shows) inconsistent statements stand undisputed side by side.

On the other hand, those accustomed to the view that virtual particles are ''really there'' have later a difficult time unlearning it when they want to get real understanding and
want to work with the concepts. Below the surface talk, nothing but internal lines in diagrams is associated with the concept. No states, no positions, no motion (forward or backward in time), no times, no creation or annihilation - nothing.

But of course, everyone has a choice about what to regard as real. Let the esoterically minded choose the fantastic view, unconstrained by the requirements of formal consistency.