Why don't virtual particles cause decoherence?

[JK423]

The 'Explantations' from Peskin is unacceptable.

Yep! And by the way, i don't say that Feynman had such intentions, but unwillingly caused a lot of trouble (when at the same time made perturbation theory more approachable).

I wouldn't give so much significance to that introductory paragraph, when he writes "multiparticle states" he is simply justifying the necessity of dealing with more than a single particle in relativistic QM. The example is admittedly not very fortunate.
It is true that it might be misleading, but I don't know many textbooks on complex mathematical or physical matters that are not completely misleading at one point or another. Although it shouldn't be used as an excuse let's agree that writing/teaching is hard.

Yeah, multiparticle states do appear! You want to talk about them, teach them and explain them? Begin with the electromagnetic vacuum, put an interaction and
\hat U\left( t \right)\left| {vac} \right\rangle = \sum\limits_n {\left\langle n \right|} \hat U\left( t \right)\left| {vac} \right\rangle \,\,\underbrace {\left| n \right\rangle }_{}
the multiparticle states \left\{ {\left| n \right\rangle } \right\} popped out from the vacuum, at finite time t of the interaction. At large times, none may survive
\left\langle n \right|\hat U\left( {t \to \infty } \right)\left| {vac} \right\rangle = 0\,\,\forall n \ne vac\,,
but still here you can see there is indeed an exchange of energy between the two fields, and real particles popped out from the vacuum and disappeared. Why don't we describe QFT like that? Virtual particles have nothing to do with these real excitations that do take place, so there is no need to talk about them afterall!
(Note: In the equations above i have omitted the states of the other field, e.g. electrons)

 

[maxverywell]

Yep! And by the way, i don't say that Feynman had such intentions, but unwillingly caused a lot of trouble (when at the same time made perturbation theory more approachable).

Yep, but that's why he was saying "shut up and calculate". Feynman's diagrams can be used for calculations, but when you try to interpret them ontologically you get into troubles.

 

[maxverywell]

Saying that virtual particles exist in reality is quite the same as saying that in the quantum double slit experiment a particle goes through one specific slit.

In quantum mechanics, it can't be known - in principle - what's going on "inbetween" (or prior to a measurement).

 

[rkastner]

Saying that virtual particles exist in reality is quite the same as saying that in the quantum double slit experiment a particle goes through one specific slit.

In quantum mechanics we simply don't know what's going on "inbetween" (or before a measurement).

No, we don't know what a photon is doing between the slit plane and the detection plate -- but we know it's THERE.

Similarly, we don't know where a 'virtual particle' is or what it's doing, but we know it's THERE because otherwise the two scattering fermions would not know about each other and there would be no scattering when they encountered each other. Now, by 'virtual particle' I don't mean a little tiny corpuscle moving around (just as there isn't a little tiny corpuscle in the 2-slit experiment). But there is a physical entity described by the vacuum expectation value of the relevant field (i.e. propagator). If you want to say that these entities don't exist then you have to explain what is doing the measurable work when particles scatter.

 

[JK423]

Saying that virtual particles exist in reality is quite the same as saying that in the quantum double slit experiment a particle goes through one specific slit.

In quantum mechanics, it can't be known - in principle - what's going on "inbetween" (or prior to a measurement).

No, it has nothing to do with that! A particle in a superposition of states has nothing to do with the internal lines of Feynman diagrams!

 

[JK423]

No, we don't know what a photon is doing between the slit plane and the detection plate -- but we know it's THERE.

Similarly, we don't know where a 'virtual particle' is or what it's doing, but we know it's THERE because otherwise the two scattering fermions would not know about each other and there would be no scattering when they encountered each other. Now, by 'virtual particle' I don't mean a little tiny corpuscle moving around (just as there isn't a little tiny corpuscle in the 2-slit experiment). But there is a physical entity described by the vacuum expectation value of the relevant field (i.e. propagator). If you want to say that these entities don't exist then you have to explain what is doing the measurable work when particles scatter.

Since when propagators do work?
In order to have a scattering process, you need states and an interaction Hamiltonian. There are your physical entities, states, that interact!
Edit: The fermions interact with the vacuum state of the E/M field, both of them. That's how they "know about each other".

By the way, rkastner, both tom.stoer and I have asked you for clarifications in previous posts. So, if you want a conversation to actually continue you have to respond and not just "throw something in the air" and leave afterwards.

 

[rkastner]

JK423, you've misunderstood my point. I'm just noting that it's legitimate to regard 'virtual photons,' or propagators, as representing something physically real. Of course I'm not saying that a 'virtual photon' is 'like' a photon in a 2-slit experiment. I believe someone else on this discussion board made that comparison initially.

Also, I've been checking in from time to time, and have certainly been replying to specific questions or challenges, but apparently I missed some. If you have a specific question, please feel free to ask it at my website, rekastner.wordpress.com; that's the quickest way to get hold of me. You can also email me, rekastner@hotmail.com

I'll be glad to try to address a specific question about my proposal. But I regret I have limited time to spend on physicsforums -- so if I miss a comment or question please don't take it personally. I also think you'll have an easier time understanding my proposed ontology if you just read my papers and/or my book. Before you summarily dismiss what I've said here about 'virtual particles,' note that I have a paper on the interpretation of propagators in the TI picture in FooP (see my website and the arxiv for preprint version). (That paper also discusses the classical limit of the EM field in terms of coherent states, with reference to the work of Breitenbach, which you may find interesting.) If you don't want to buy the book, you can get it via WorldCat through interlibrary loan. The UMCP library is in the process of acquiring it.

Tom, you say "In order to have a scattering process, you need states and an interaction Hamiltonian." Yes. All I'm saying is that the physical interaction described by interaction Hamiltonians, in which field propagation plays a crucial part, is a real physical process. Judging by some of the reactions here, you'd think what I'm saying is heretical or bizarre. It's perfectly natural. Perhaps some of you are reading a lot into the phrase 'virtual particle' that isn't necessarily intended. Of course the entity corresponding to the VEV of a quantum field is not the same thing as the entity described by a quantum state -- yes, it does violate conservations laws, etc. That doesn't mean that the former does not physically exist. Of course it's not a classical object, it's very strange, and it's hard to conceptualize as a non-classical object, but it exists.

Here's what Berestetskii, Lifgarbagez and Pitaevskii (QED, vol 4 2nd ed) have to say about propagators: "The propagation functions or propagators defined in [sections 73,73] are of fundamental importance in the formalism of [QED]. The photon propagator [Dmn] is a basic characteristic of the interaction of two electrons..." (p.295 in 2004 paperback edition)

So all I'm saying is: whatever you want to call the entity described by a quantity that is of 'fundamental importance' in accounting for the interaction of two electrons, it EXISTS -- otherwise there would BE NO INTERACTION! OK, suppose you want to argue that you could use a different theory than QED to account for the interaction between 2 electrons described by quantum states. Well, whatever formal object in your theory does the job done by the propagator, the entity described by that formal object exists!

I think the only reason this is coming across as controversial is because some might want to ascribe particular kinds of pictures to it, none of which I'm buying into. I don't think ANY quantum entity is a little corpuscle traveling along a trajectory. I make this very clear in my book.

Best wishes,
RK

 

[maxverywell]

No, it has nothing to do with that! A particle in a superposition of states has nothing to do with the internal lines of Feynman diagrams!

Of course it has nothing to do with that, It's simply an analogy.

Similarly, we don't know where a 'virtual particle' is or what it's doing, but we know it's THERE because otherwise the two scattering fermions would not know about each other and there would be no scattering when they encountered each other.

We simply know that there is an interaction taking place in that process, not that the virtual particles are there and that they are "real". It's your wrong interpretation of the situation, like saying that in the double slit experiment a particle went through one specific slit.

 

[JK423]

Of course it has nothing to do with that, It's simply an analogy.

It's a very bad analogy! In the double slit experiment you have particle in a quantum state. In the case of virtual particles, the latter are NOT described by a quantum state. So, the way you interpret the quantum state in the double slit experiment (i.e "the actual particle" goes through one slit or both) is irrelevant. We are not talking about interpreting the quantum state. We are talking about virtual particles that are not described by quantum states in the first place, so you don't have anything to interpret

 

[rkastner]

We simply know that there is an interaction taking place in that process, not that the virtual particles are there and that they are "real". It's your wrong interpretation of the situation, like saying that in the double slit experiment a particle went through one specific slit.

Yes, there is a real interaction. Right? You don't like the term 'virtual particle' -- OK, don't use it! There is a physically real interaction, described by the VEV of the quantum field. The VEV describes a physically real entity -- otherwise there is no interaction! So we agree.

 

[rkastner]

We are talking about virtual particles that are not described by quantum states in the first place, so you don't have anything to interpret

This statement presupposes that no part of a theory that is not a quantum state is reasonably subject to physical interpretation. One can assume this restriction on one's thinking if one wishes, but it's unnecessary. Remember that Ernst Mach railed against the idea of atoms because they were supposedly an artificial, abstract, unobservable theoretical construct.

Also, consider an excerpt from Freeman Dyson's essay about how seemingly abstract mathematics has an uncanny way of reflecting the real world: " [Mathematicians] always thought of complex numbers as an artificial construction, invented by human mathematicians as a useful and elegant abstraction from real life. It never entered their heads that this artificial number system that they had invented was in fact the ground on which atoms move. They never imagined that nature had got there first.

-- Birds and Frogs Freeman Dyson, Notices of the American Mathematical Society, February 2009

 

[maxverywell]

Saying that there are mediated particles in the scattering process is an attempt to interpret scattering classically, but it's wrong because we don't know what's going on during it. It's totally a quantum process and we simply can compute the amplitudes of the transition from the initial state to the final state. That's it.

Similarly in the double slit experiment, we don't know through which slit a particle went. Saying that a particle went through one specific slit is wrong because it didn't. We can only compute amplitudes for the process of interaction of particle with slit.

 

[tom.stoer]

Ruth, I think you completely missed my post #89

https://www.physicsforums.com/showpost.php?p=4283422&postcount=89

 

[rkastner]

Saying that there are mediated particles in the scattering process is an attempt to interpret scattering classically, but it's wrong because we don't know what's going on during it. It's totally a quantum process and we simply can compute the amplitudes of the transition from the initial state to the final state. That's it.

Similarly in the double slit experiment, we don't know through which slit a particle went. Saying that a particle went through one specific slit is wrong because it didn't. We can only compute amplitudes for the process of interaction of particle with slit.

No. This is not a 'classical' ontology; it's a realist ontology. They are not the same thing. A realist ontology need not be classical. Consider this from Ernan McMullin:

“maginability must not be made the test for ontology. The realist claim is that the scientist is discovering the structures of the world; it is not required in addition that these structures be imaginable in the categories of the macroworld.” (1984, ref on request)

So we are discovering the real structures of the world. Nothing I've said requires that these be classical (i.e., expressible in 'categories of the macroworld'). In fact quite the opposite.

 

[rkastner]

Tom, regarding the gauge issue, PTI is based on a direct action theory so see Davies (1971, 1972) for the precise formalism, which uses the Coulomb gauge for QED. If Nature really uses direct action, this fixes the gauge and there is no ambiguity. So the bottom line: it is an empirical matter what the correct gauge is. The feature of theoretical gauge dependence does not necessarily mean that something is 'unphysical'.

The basis of the perturbative expansion approach is the idea of mediated interactions between field currents, with increasingly accurate approximation to reality with the addition of each order. I think of this as a fractal process; keep in mind that fractals are ubiquitous in nature already.[http://www.wired.com/wiredscience/wp-content/gallery/fractal/fractal_10.jpg
If you don't want to use perturbation theory, then use a different theory of interacting fields. You will still have to deal with field propagation in some way. My model is realist about field propagation, that's all. I didn't say this is a classical thing and I didn't say that fields chug along classical trajectories, which they don't.

I did already address your criterion for calling something 'real'. Basically you are equating 'real' with 'empirical,' when you say things like: "therefore it does not represent reality (in the sense we can define it when we want to have agreement with observations)". This is where the McMullin quote is relevant.

 

[tom.stoer]

I think you miss my point.

We know that perturbation theory is ill-defined; we know that especially in QCD there is no phenomenon which allows for purely perturbative formulation; we know that the gauge artifacts are much more severe in non-abelian gauge theories, so a results for QED don't tell us how to treat them.

Eq. (2) using the free propagator D(x-y) is wrong in QCD! So for everything which follows after eq. (2) extrapolating QED results is simply not applicable.

 

[rkastner]

Tom --to clarify, my basic ontology does not depend on their being a purely perturbative formulation. In fact in PTI there is *not* a continuum of spacetime points, so lattice gauge theory would be more natural for my ontology and that is already used in QCD. I do hope you will read my book and consider these ideas and not reject them out of hand. Thanks again for your questions and interest!

 

[tom.stoer]

Could you provide some hints what PTI has to say about QFT? I agree that it's interesting as an interpretation of QM, but afaik there is no equivalent line of discussion for QFT (do you know Esfeld's book on "philosophy of physics"? it seems to me that there are no reasonable interpretations of QFT on the market)

In addition: you start reasoning based on your paper, based on propagators and perturbative formalism; once confronted with technical arguments regarding an ill-defined starting point and regarding missing key issues your response is to read a book. Does this book contain a nonperturbative analysis of non-abelian quantum gauge theory? If no, then why should I read that book? I still think that you don't address the key issues. But w/o a detailed analysis of these issues and w/o the construction of a well-defined formalism it does no makes sense to interpret a formalism.

 

[JK423]

@RKastner
You are not talking clearly. I bet not even you have exactly understood what you mean by what you're saying,

"it's that, but not exactly that, and it's like this but not exactly like this..."

This is how you talk all this time, i haven't seen a single real argument about the reality of propagators. You say that if propagators didn't exist then interactions wouldn't exist. Now, what kind of argument is that? Do you know how it sounds like?
If e^x represents a real quantity, then every term in the perturbative expansions {e^x} = \sum\limits_n {\frac{{{x^n}}}{{n!}}} MUST BE REAL because if they didn't exist (i.e. weren't present in the expansion) then e^x wouldn't be what it is!
If we start interpreting mathematics like that, in whatever branch of science, we are screwed. Virtual $dollars$ will start popping in finance.

 

[rkastner]

Could you provide some hints what PTI has to say about QFT? I agree that it's interesting as an interpretation of QM, but afaik there is no equivalent line of discussion for QFT (do you know Esfeld's book on "philosophy of physics"? it seems to me that there are no reasonable interpretations of QFT on the market)

In addition: you start reasoning based on your paper, based on propagators and perturbative formalism; once confronted with technical arguments regarding an ill-defined starting point and regarding missing key issues your response is to read a book. Does this book contain a nonperturbative analysis of non-abelian quantum gauge theory? If no, then why should I read that book? I still think that you don't address the key issues. But w/o a detailed analysis of these issues and w/o the construction of a well-defined formalism it does no makes sense to interpret a formalism.

The claim in your last sentence regarding the restriction of interpretation to a 'well-defined formalism' is simply not borne out by careful study. I address this in my book as well, with reference to MacKinnon (ref on request) -- who finds that trying to restrict interpretive efforts to a 'rational reconstruction' of a given (messy or imperfect) theory leads to no better insight than simply working to interpret an existing functioning theory, which is what QM is -- however messy and mathematically 'ill-defined'. QM itself, at both the non-relativistic and relativistic levels, has always had an 'ill-defined starting point'. I'm not creating a new theory, I'm interpreting an existing theory: i.e., proposing physical referents for objects in the theory that do computational work leading to good empirical corroboration. See Chapter 2 of my book for details.

Regarding the previous post expressing dissatisfaction with what I've said here, and as for 'missing key issues in my response' -- as I noted earlier, I have very limited time to spend on this forum. I saw an interesting question --the beginning of the thread -- asking about virtual photons, to which I thought I might contribute, since I have published work on this topic and I think the model I'm working with is an interesting and fruitful one. No, the model has not been extended in detail to QCD. But neither, to my knowledge, have the following competing interpretations of QM: (1) many world theories (2) ad-hoc spontaneous collapse theories (3) The Bohmian theory (4) decoherence-based approaches (which, as I've noted, utterly fail to really solve the measurement problem despite their claims), or any other 'mainstream' interpretation of QM of which I'm aware. So why use that as a criticism of PTI? If you yourselves began to explore the PTI model, you might break some new ground and find that it indeed does shed light on some of the issues that you've demanded that I explain here in detail, such as non-Abelian gauge theories. There is a seed here that could be planted and yield fruit, so let's not reject it out of hand.

Regarding the impatience expressed by someone here with my asking that you read my papers and my book before making demands for detailed explanations on PF: again, my time to spend here is limited. I saw a question about virtual particles in the context of decoherence, and provided a suggestion that the PTI model has something useful to say about it -- especially since decoherence arguments are so inadequate to understanding collapse and determinate results in QM. I've already put quite a bit of time and effort into these publications, and I don't quite see how it's a reasonable request for me to rewrite them all here. It's already out there for you to read. If you read it and you still have questions, I'm happy to engage those. But again, I don't think you'll find detailed interpretive treatments of non-Abelian gauge theories in competing interpretive models of QM. Everettian theories are still struggling to explain the Born Rule in their model. So go ahead and explore the PTI model wrt QCD -- I look forward to reading your own work on this.

As for the question about the propagator, as I've said repeatedly, quantities such as VEV values of fields -- more generally, Wightmann correlation functions -- have a well-defined interpretation in PTI as possible offer waves -- that is, entities that have a less-than-unity amplitude for becoming offer waves |X> -- i.e. what you take as well-defined 'quantum systems'. The specific amplitude is given by the relevant coupling constant. I have not 'shifted' my position on this as someone implied above, I've taken note where someone is reading meaning into 'virtual particle' that I did intend. No, of course a 'virtual particle' is not a corpuscle on a worldline so if someone defines a virtual particle that way, that's not, and has never been, what I'm talking about.

Re what PTI has to say about QFT, a detailed QFT discussion applying to the PTI model, although he doesn't himself apply it to the transactional picture, is in Davies' papers:

Davies, P. C. W. (1970). “A quantum theory of Wheeler-Feynman Electrodynamics,” Proc. Cam. Phil. Soc. 68, 751.

___________(1971).”Extension of Wheeler-Feynman Quantum Theory to the Relativistic Domain I. Scattering Processes,” J. Phys. A: Gen. Phys. 6, 836.

____________(1972).”Extension of Wheeler-Feynman Quantum Theory to the Relativistic Domain II. Emission Processes,” J. Phys. A: Gen. Phys. 5, 1025-1036.

And I address this in some detail in my http://arxiv.org/abs/1204.5227 (FoP)

If you read my book, you'll see that PTI does not involve a spacetime continuum, so that's why there is a natural end to the perturbation expansion (if that computational approach is used) and why lattice gauge theory is probably a more accurate underlying framework. In either case, propagators are an essential component of the process and they have a clear ontological meaning in PTI as nascent offer waves (or if you will, 'failed' or 'aborted' offer waves), with the coupling amplitudes quantitatively characterizing their 'nascence' or degree of presence. Yes, these may be unfamiliar concepts, but that doesn't mean they are ill-defined. Remember we are dealing with quantum entities, not the classical world, and remember Ernan McMullin's comment.

So again, I very much appreciate your interest, and I hope you will continue to explore the TI/PTI picture. Remember that everything about PTI with which you have expressed dissatisfaction or reservations (i.e., certain details not fully explained on this forum, no obvious resolution to the challenge of QCD, etc, -- applies even more so to competing QM interpretations. At least TI/PTI can readily explain the Born Rule and the nature of collapse! So put the model to work yourselves, and see what you might do with it, rather than assuming a priori that it will fail.

I am available for discussion by way of my website:

transactionalinterpretation.org

With warm regards,
RK

 

[tom.stoer]

Ruth,

I definately do NEITHER critizise TI/PTI NOR your book which I haven't studied. What I am critizising is that you comment here on a discussion regarding 'existence of virtual particles' w/o addressing the key issues we identified.

In case you have a solution, please elaborate (here).

 

[rkastner]

Tom --not sure I understand your concern. Please specify exactly what problem you see as not solved.

 

[tom.stoer]

Ruth, no single problem regarding non-abelian gauge theories and 'virtual particles' has been addressed.

#16, #32, especially #35, your statements

If one wants to argue that virtual particles (i.e. propagators) don't exist, then one is essentially saying that quantum fields don't exist.

and

[the] presupposing that quantum fields do not exist (and therefore don't propagate -- since you deny that propagators have physical content). So the burden is on you to explain how there can be excitations of something that doesn't exist (quantum states being excitations of quantum fields).

where you ignore that QFT can be formulated w/o propagators but not w/o quantum fields (states), #89, #106, #116 which questions that your paper can be used to understand non-abelian gauge theories, #118.

But we go around in circles. Asked what I miss (e.g. a single statement on non-abelian gauge theories) you respond either with papers on QED or with your book.

 

[JK423]

Ruth, no single problem regarding non-abelian gauge theories and 'virtual particles' has been addressed.

#16, #32, especially #35, your statements and
where you ignore that QFT can be formulated w/o propagators but not w/o quantum fields (states), #89, #106, #116 which questions that your paper can be used to understand non-abelian gauge theories, #118.

But we go around in circles. Asked what I miss (e.g. a single statement on non-abelian gauge theories) you respond either with papers on QED or with your book.

It's not proper to speak from Ruth's behalf, but the answer you are probably going to get is that, she is not implying that quantum states are unnecessary. She just proposes that propagators have a reality that goes beyond the reality of states.

 

[rkastner]

Tom,

If you'd like me to address a specific formulation of QFT not involving propagators, please provide a reference. I've already noted that there is no specific prima facie reason why PTI can't be extended to non-Abelian gauge theories, and invited you to work on that front; and that competing QM interpretations certainly don't provide any detailed account of non-Abelian gauge theories either (because they are too busy trying to explain what is already easily explained in TI/PTI). So let's have a level playing field.

Thanks again for your interest,
RK

 

[tom.stoer]

Ruth,

I'll check TI/PTI in more detail as soon as I have time.

But let's come back to the original question, why virtual particles do not cause decoherence (I do not want to go through all the discussion regarding virtual particles, I simply refer to a perfect summary written by Arnold Neumaier) http://arnold-neumaier.at/physfaq/topics/unstable.html

My first answer why virtual particles are irrelevant for decoherence was

Decohence is due to factorizing the full Hilbert space H in H_system, H_pointer and H_environment and then "tracing out" the environment degrees of freedom. The remaining "subsystem" can be described by an "effective density matrix" which is nearly diagonal in the pointer basis, so it seems as if it collapsed to the a pointer state with some classical probability.

Virtual particles are artifacts of perturbation theory, i.e they are not present in the full theory w/o using this approximation. Using virtual particles does not introduce the above mentioned factorization of H. And last but not least virtual particles are not states in any Hilbert space H_system, H_pointer or H_environment , but they are "integrals over propagators".

I think that the discussion over the last days hasn't changed anything. Do you agree?

 

[mattt]

(I do not want to go through all the discussion regarding virtual particles, I simply refer to a perfect summary written by Arnold Neumaier) http://arnold-neumaier.at/physfaq/topics/unstable.html

Totally agree with everything A. Neumaier wrote there (and like Tom, in the future I will simply refer to that link).

 

[JK423]

Totally agree with everything A. Neumaier wrote there (and like Tom, in the future I will simply refer to that link).

It's not that simple; as you can see in another thread "Source of virtual particles in space?" not everyone agrees with what Neumaier says. So...

 

[tom.stoer]

Anyway, it's irrelevant for decoherence

 

[Mukilab]

I guess we should come back to the question



My first answer was



The discussion over the last couple of days did not change anything; the first answer is still correct.

Let me summarize some additional ideas



But all this is not directly relevant for the original question b/c virtual particles are completely irrelevant in the context of decoherence: they are not present in the full theory; they do neither introduce the above mentioned factorization of H nor the partial trace; and they are not states in any Hilbert space H_system, H_pointer or H_environment .

Last but not least: nobody would assume that any approximation like a Taylor series (or green dwarfs) do introduce additional effects which are not already present in the full theory w/o the approximation (w/o green dwarfs). So if the theory w/o virtual partices green dwarfs) already contains decoherence (gravity) it would be silly to say that decoherence (gravity) is due to virtual particles (green dwarfs). This changes if the theory cannot be formulated w/o virtual particles (w/o green dwarfs), or if the formulation is conceptally simpler (in the sense of Ockham's razor) using virtual particles (green dwarfs).

I am not an expert regarding green dwarfs, but I know that perturbation theory is incomplete and misses relevant non-perturbative effects. So I can't see any reason to rely on the interpretation of partially unphysical artifacts due to an incomplete approximation instead of using the full theory.

Thanks, but if virtual particles don't 'exist' or they are not necessary in many quantum theories, why do they exist?

Please understand that I do not understand the large majority of scientific jargon on this thread, would it be possible for you to try to explain this as if to someone that is slightly above a layman (I have knowledge of most concepts, just not the mathematics behind them, which I do not understand). Thank you.

 

[tom.stoer]

Virtual particles in the sense I define them - as internal lines in Feynman diagrams - are a mathematical tool used for an approximation - so-called perturbation theory. Unfortunately most quantum field theories like QED, QCD etc. are very complicated and we do not have the mathematical tools to solve them exactly. But fortunately we have several approximations. Perturbation theory is used for weak coupling, where it makes sense to start with free, non-interacting particles and to add small corrections for interactions. Interestingly this works very well in many cases, especially for scattering experiments (but there are other problems like QCD bound states, e.g. protons, neutrons, ... where this approximation is useless).

If you would have mathematical tools to solve quantum field theories exactly, there would be no reason to introduce perturbation theory, there would be no name for the mathematical artifacts, and we would not have these discussions. Before studying QCD I was working on two-dimensional models, fields living on a line = one space dimension + one time dimension. These models a rather simple, a good starting point for beginners. There are exactly solvable models with bound states, there are other approximations, and thefore no reason to use perturbation theory. In QCD there are tools to study non-perturbative aspects, tools like chiral effective theories, lattice gauge theories, ... All these tools do not require Feynman diagrams and therefore - using these tools - there is nothing which we call 'virtual particle'.

In addition there are mathematical reasons against perturbation theory. We know that strictly speaking it is ill-defined, it is something which does not exist mathematically, but nevertheless it seems to work in a very restricted sense. And there are applications where this ill-defined math does produce correct results which agree with experiments (strange, isn't it? we can prove that it does not work, but using it seems to work ...). Now what I am saying is that we can START with a formulation w/o any approximation and w/o virtual particles. Then we have to introduce approximations, but doing this we CREATE several problems, or we apply approximations outside their scope of applicability, so the approximation BREAKS DOWN. Doing this we have mathematical artifacts - virtual particles - but due to the problems we introduce there seems to be no good reason to believe in virtual particles to be more than just limited tools.

Does this help?

 

[rkastner]

I would not be quick to dismiss something as only a 'mathematical artifact' just because it is part of an approximation. This is an interesting methodological question that deserves careful study. Remember that the number 'e' is a limiting value for many types of series expressions. It's possible that these 'approximating' series do have specific meaning in themselves; the fact that they have a well-defined limit at a specific irrational number does not negate that the series terms might have physical content if the argument of the exponential has physical content. Remember that the perturbative expansion of QFT has as an argument for the exponential the action of the field, which certainly has physical content. It's a leap to say categorically that terms in the expansion of a quantity with physical content do not themselves have physical content. Now of course we have to be careful about what the physical quantities are. In the earlier example of the radioactive atom, the exponential argument is not a field, it's just a number (decay rate). So that comparison was not a good one to the QFT case.

I appreciate the interesting discussion here but I should let you know that I am currently swamped with various obligations and may not be able to check in for a while. Thanks again everyone for your interest. I hope you will visit my website which presents preview material from my book and explores some of the ideas we've discussed here.

http://transactionalinterpretation.org

Best wishes
RK