Source of Virtual Particles in Space?

[Bill_K]

Rovelli: “…we observe that if the mathematical definition of a particle appears somewhat problematic, its operational definition is clear: particles are the objects revealed by detectors, tracks in bubble chambers, or discharges of a photomultiplier…”

This definition leaves out a lot of particles! Many particles in the Standard Model have lifetimes too short to leave a visible track.

Consider the Z meson. It has a mass of 91 GeV and a lifetime of 3 x 10^-25 sec. Implying, at velocity c it can travel at most a tenth of a fermi before it decays, less than the diameter of a proton. And thanks to its short lifetime the Z meson has a width of 2.5 GeV. GEV! It is never on the mass shell. It always appears as an "internal line" in some Feynman diagram.

So what do you say - is the Z meson a real particle? Or is it merely an "artifact of perturbation theory".

W mesons, top quarks and Higgs bosons have equally short lifetimes. If you consider these particles somehow not real, you're drawing an artificial distinction between particles that are otherwise closely related.

 

[JK423]

This definition leaves out a lot of particles! Many particles in the Standard Model have lifetimes too short to leave a visible track.

Consider the Z meson. It has a mass of 91 GeV and a lifetime of 3 x 10^-25 sec. Implying, at velocity c it can travel at most a tenth of a fermi before it decays, less than the diameter of a proton. And thanks to its short lifetime the Z meson has a width of 2.5 GeV. GEV! It is never on the mass shell. It always appears as an "internal line" in some Feynman diagram.

So what do you say - is the Z meson a real particle? Or is it merely an "artifact of perturbation theory".

W mesons, top quarks and Higgs bosons have equally short lifetimes. If you consider these particles somehow not real, you're drawing an artificial distinction between particles that are otherwise closely related.

Please give an answer to my post #26, thanks!

Roveli talks about leaving tracks in principle! Even when the particle has a lifetime 3 x 10^-25 sec you can in principle interact with it during that time because it acquires a quantum state! In the case of an internal line of a Feynman diagram in perturbation theory, even if it had a lifetime of 1 year you wouldn't be able to interact with it all this time because it has no quantum state and it does not exist!

So, let's put it this way:

Internal lines in Feynman diagrams of perturbation theory, even if they had a A HUGE lifetime, you cannot in principle interact with them because they have no quantum state to interact with! They do not exist.

Real particles, no matter how SMALL a lifetime they have, you can in principle interact with them because they have a quantum state!

If that's not a clear distinction then what is?

 

[tom.stoer]

yes, and Hawking acknowledged that distinction...He called it an 'intuitive' explanation...

I think he says something like that in the non-math part of his famous paper.

 

[Naty1]

Bill_k...

Consider the Z meson.

Now you are just making stuff up! ...just joking,
but I could not even find Z meson on 'the list'...

http://en.wikipedia.org/wiki/List_of_mesons

But the note at the bottom of the table is interesting:

Because this table was initially derived from published results and many of those results were preliminary, as many as 64 of the mesons in the above table may not exist or have the wrong mass or quantum numbers.

Methinks we have way too many particles!jk423...good point you beat me to posting...

Rovelli talks about leaving tracks in principle! Even when the particle has a lifetime 3 x 10-25 sec you can in principle interact with it ...

 

[Bill_K]

Now you are just making stuff up! ...just joking, but I could not even find Z meson on 'the list'...

Sorry, I'm referring to the Z⁰ boson.

 

[JK423]

jk423...good point you beat me to posting...

Well i am waiting for Bill_K to respond to these counter-arguments against his views, but he seems to ignore me.

 

[strangerep]

Well i am waiting for Bill_K to respond to these counter-arguments against his views, but he seems to ignore me.

Didn't you see the tears in his initial post in this thread? There's a reason for that...

Many SAs and Mentors are sick to death of the endless "virtual particle" threads and the endless misunderstandings therein.

Arnold Neumaier went to great lengths a couple of years ago to explain it all, but such threads inevitably recur. For a good (imho) explanation of the distinction between the concepts of "stable, unstable, resonance, virtual, etc" in this context, you'll find it hard to do better than this:

http://arnold-neumaier.at/physfaq/topics/unstable.html

It is more concise and far superior to most of the "virtual particle" garbage spewing endlessly onto this forum.

 

[tom.stoer]

Arnold Neumaier went to great lengths a couple of years ago to explain it all, but such threads inevitably recur. For a good (imho) explanation of the distinction between the concepts of "stable, unstable, resonance, virtual, etc" in this context, you'll find it hard to do better than this:

http://arnold-neumaier.at/physfaq/topics/unstable.html

It is more concise and far superior to most of the "virtual particle" garbage spewing endlessly onto this forum.

Great summary!

My proposal would be to respond to any question regarding virtual particle stuff simply by posting this link. End-of-Story.

 

[Haelfix]

I actually think that FAQ entry is misleading and making a straw man case (even though a lot of it is correct), nor do I agree with Arnold's discussion about this topic on stack exchange:

http://physics.stackexchange.com/questions/4349/are-w-z-bosons-virtual-or-not

There are several professors with the same opinions as me on that site, including a few famous ones (including Peter Shor, Moshe Rovalli and Jeff Harvey).

I think the problem I have with that entry is that it leads to statements like this written by JK423.

"Real particles, no matter how SMALL a lifetime they have, you can in principle interact with them because they have a quantum state"

This is deeply wrong for a number of reasons. The first is that mathematically this is fantasy. Most Interacting particles in 4d do not have well defined quantum states, especially ones that are not well separated, that haven't undergone clustering and that have arbitrarily small lifetimes. So pathological example.. Low energy quarks do NOT have well defined particle number operators. This is completely independent of perturbation theory and is indeed a nonperturbative statement. If you insist that they do, and give them one anyway, for instance as you ramp up the energies of the collider during deep inelastic scattering experiments then I assure you the distinction between real and virtual really does become a matter of convention (in this case the convention of energetics to contrast to the usual convention of time explained in the other thread).

The second is you have to define what you mean by 'interaction'. You can rewrite all of the contributions of virtual particles in certain specific theories (like QED) as 'dressed' particle interactions. This 'dressing' absolutely, quantitatively makes a separate and very real contribution to physical processes like scattering cross sections, decay times and so forth. So again, you simply can't be consistent and argue that they have nothing to do with interactions at all.

 

[tom.stoer]

Haelfix, I think you misunderstand what I mean (I cannot talk on behalf of others). I do not say that particles in nature are in energy, momentum, ... eigenstates. I do not say that we have states with well-defined particle number. Of course a state |proton> has no well-defined quark number. This is not what I mean.

All I am saying is that for a reasonable formulation of QFT you need a Hilbert space (or some extension to that concept), an algebra of observables and some other operators acting on the states. You do not need perturbation theory or propagators to start with, and in some regimes you must never use it (you do not need Taylor series to define holomorphic functions and Riemann sheets, and for studying cuts you must never them)

In that sense a perturbative treatment of specific phenomena may be useful, for others it's not reasonable.

So the conclusion is that virtual particles are limited regarding validity and applicability, and are therefore subordinated regarding interpretability.

 

[tom.stoer]

If you insist that they do, and give them one anyway, for instance as you ramp up the energies of the collider during deep inelastic scattering experiments then I assure you the distinction between real and virtual really does become a matter of convention .

Mentioning DIS gives me the chance to explain one Common misconception. DIS is often quoted as application of perturbation theory. This is partially wrong, b/c perturbation theory is limited to the QED part and to the Q²-behavior of the structure functions F(x,Q²), whereas the x-dependency is entirely non-perturbative for finite energies and cannot be calculated using perturbation theory. The x-dependency is not calculated, but perturbative treatment of other effects is used to extract it from the data. So within DIS the understanding for the reason of a specific x-behavior is zero.

No we call the small-x contribution "sea-quarks", "virtual particles" or whatever, but this does not explain anything. It is missleading b/c they are NOT virtual particles in the sense of perturbation theory.

Now if you use lattice calculations to extract small-Q² and small-x physics there are no virtual particles in this sense, either. You have quantum fields and a path integral. That means that DIS is - contrary to popular opinion - not a good example for, but on the contrary against the interpretation of virtual particles. What remains is a void name.

 

[Bill_K]

Arnold Neumaier went to great lengths a couple of years ago to explain it all, but such threads inevitably recur. For a good (imho) explanation of the distinction between the concepts of "stable, unstable, resonance, virtual, etc" in this context, you'll find it hard to do better than this:
http://arnold-neumaier.at/ph.../unstable.html

This is an excellent, well-reasoned exposition of the matter. I agree with about 96 percent of what he says.

Didn't you see the tears in his initial post in this thread? There's a reason for that...

Unfortunately although many a discussion starts with a well-reasoned exposition, the followup often deteriorates into emotional, unprofessional, unreasoning.

Anyway, quoting Neumaier:

A stable particle can be created and annihilated, as there are associated creation and annihilation operators that add or remove particles to the state. According to the QFT formalism, these particles must be on-shell...]multiparticle states are always composed of on-shell particles only...States involving virtual particles cannot be created for lack of corresponding creation operators in the theory.

This is because the creation and annihilation operators were taken to be the Fourier transforms of a free field. This choice is made for its simplicity. One could define things otherwise.

In diagram-free approaches to QFT such as lattice gauge theory, it is impossible to make sense of the notion of a virtual particle.

This may say more about lattice gauge theory than the particles!

Neumaier gives two reasons why he thinks Feynman diagrams, and especially their internal lines, do not represent reality:

Indeed, a single Feynman diagram usually gives an infinite (and hence physically meaningless) contribution to the scattering cross section.

Renormalization is an accepted part of field theory, unpleasant to deal with, but not an argument against virtual particles. Bringing it up in this context is a red herring.

The finite, renormalized values of the cross section are obtained only by summing infinitely many such diagrams. This shows that a Feynman diagram represents just some term in a perturbation calculation, and not a process happening in space-time. Therefore one cannot assign physical meaning to a single diagram but at best to a collection of infinitely many diagrams.

This is IMO the largest error in Neumaier's reasoning, and one I've heard expressed many times. But Feynman diagrams represent amplitudes, and QM tells us that amplitudes must be summed over. Always we sum/integrate over all possible histories. However this does not cause a particle, in going from point A to point B, to somehow lose its reality, and does not justify regarding its intermediate path as an "artificial construct." Yes, even real things must sometimes be summed over.

EDIT: Forgot to mention this one:

Feynman-type diagrams arise in any perturbative treatment of statistical multiparticle properties, even classically, as any textbook of statistical mechanics witnesses. But in the literature, one can find no trace of a suggestion that classical multiparticle physics is sensibly interpreted in terms of virtual particles.

Certainly true, diagram methods are applied in other contexts. And it's also true that this has no relevance to the subject of virtual particles!

 

[JK423]

I think the problem I have with that entry is that it leads to statements like this written by JK423.

"Real particles, no matter how SMALL a lifetime they have, you can in principle interact with them because they have a quantum state"

This is deeply wrong for a number of reasons. The first is that mathematically this is fantasy. Most Interacting particles in 4d do not have well defined quantum states, especially ones that are not well separated, that haven't undergone clustering and that have arbitrarily small lifetimes. So pathological example.. Low energy quarks do NOT have well defined particle number operators. This is completely independent of perturbation theory and is indeed a nonperturbative statement. If you insist that they do, and give them one anyway, for instance as you ramp up the energies of the collider during deep inelastic scattering experiments then I assure you the distinction between real and virtual really does become a matter of convention (in this case the convention of energetics to contrast to the usual convention of time explained in the other thread).

The second is you have to define what you mean by 'interaction'. You can rewrite all of the contributions of virtual particles in certain specific theories (like QED) as 'dressed' particle interactions. This 'dressing' absolutely, quantitatively makes a separate and very real contribution to physical processes like scattering cross sections, decay times and so forth. So again, you simply can't be consistent and argue that they have nothing to do with interactions at all.

Haelfix, your main argument -if i understand correctly- stems from Haag's theorem; all these mathematical difficulties that make QFT ill-defined.
I tell you once more, is this relevant? What you say is "Ok real particles may have a quantum state, but this quantum state is not mathematically well-defined", or something like that.
My immediate response is:
I agree that these mathematical difficulties are present. But the point is that virtual particles just do not have a quantum state in the first place, which means that your reference to the mathematical difficulties on quantum states is irrelevant. If you want to argue about what Haags theorem means for the real particles, let's make another thread! In this thread, let's just agree that virtual particles do not have a quantum state regardless of this issue. (But you have already agreed with that in the other thread, and i don't know why you disagree with the "virtual particles are not real" statement)
Consequently:

An internal line, in Feyman diagrams of perturbation theory, even if it had a lifetime of 10 years you wouldn't be able to interact with it in principle since there is no quantum state to interact with.

This thing would be right there, in front of you, for 10 whole years and you wouldn't be able to "touch" it no matter what you do. You can only "touch" quantum states.

The second is you have to define what you mean by 'interaction'.

It's simple: If a virtual particle had a quantum state \left| {virtual} \right\rangle, then i could sent a probe \left| {probe} \right\rangle to interact with it unitarily, via \hat U\left( t \right), during the time of its existence. The final state of the system will be \hat U\left( t \right)\left( {\left| {virtual} \right\rangle \otimes \left| {probe} \right\rangle } \right). In your example with the photon from the other galaxy (from the other thread) i can write down such an interaction while the photon is on its way to Earth. I can write down such an interaction for every real excitation, in principle. Yes, maybe it's mathematically ill-defined, but as i said let's argue about what that means in another thread.
In the case of virtual particles, such an interaction cannot even be written down. Not even in principle.

I am waiting for your response.

 

[tom.stoer]

Haag's theorem is rather irrelevant, b/c you can avoid it by using compact space, e.g. periodic boundary conditions, and in our context b/c it only says that the free and the interacting theory cannot be constructed on the same Hilbert space; but this is irrelevant b/c the free Hilbert space is relevant only if you want to start with perturbation theory based on free fields.

 

[Naty1]

Can someone help me with this from the Neumaier paper:

Observable particles. ... At energies larger than the real part of the mass, the imaginary part determines its decay rate and lifetime; at smaller energies, the unstable particle cannot form for lack of energy, but the existence of the pole is revealed by a ….resonance in certain cross sections. From its position and width, one can estimate the mass and the lifetime of such a particle before it has ever been observed. Indeed, many particles …are only resonances.

Is the boldface statement an experimentally observed effect or a calculated, theoretical one?

edit: Looks like it IS an observation...
in one of the links I found this:

"THE Z BOSON
Revised March 2009 by M. Gr¨unewald (U. College Dublin and
U. Ghent), and A. Gurtu (Tata Inst.).
Precision measurements at the Z-boson resonance using
electron–positron colliding beams began in 1989 at the SLC and
at LEP...

http://pdg.lbl.gov/2011/reviews/rpp2011-rev-z-boson.pdf

 

[Naty1]

Many SAs and Mentors are sick to death of the endless "virtual particle" threads and the endless misunderstandings therein.

That's understandable, of course, but don't blame the students when the experts don't agree on explanations and relevance of some mathematics! Linking theoretical mathematical results in quantum mechanics to observational results with classical language seems fraught with potential difficulties...Also, it's good to keep in mind many of us do not have a variety of textbooks to compare different interpretations and descriptions. So disagreements among 'experts' is a valuable way to explore interpretations.

regardless, this discussion has helped me better understand some of the subtleties involved.
[But I reserve the right to ask more questions in the future [LOL].]

 

[JK423]

The SAs and Mentors may be sick to death, but not due to the "misunderstandings". They don't even agree with each other. So they may be sick to death to disagreeing.
The behaviour of Bill_K, and in particular his selective responses, are inexplicable and unproffessional. I don't know where he saw the "emotional unreasoning", if one reads any of my posts they are as crystal clear (on the arguments) as possible. Personally, i am just trying to find out what is going on (since i am not god, and i don't know the answer). And from what i have found already, the argument regarding the virtual particles not acquiring a quantum state make the "virtual particle proponents" end the discussion. Am i emotional because i ask this question?

 

[A. Neumaier]

Can someone help me with this from the Neumaier paper:

[namely: ''but the existence of the pole is revealed by a ….resonance in certain cross sections.'']

Is the boldface statement an experimentally observed effect or a calculated, theoretical one?

edit: Looks like it IS an observation...

It is the way real experiments are interpreted; see, e.g., the following link to a page from the
manual for the PYTHIA program, ''intended to generate complete events, in as much detail as experimentally observable ones, within the bounds of our current understanding of the underlying physics'' (from the preface):

http://cepa.fnal.gov/psm/simulation/mcgen/lund/pythia_manual/pythia6.3/pythia6301/node192.html

 

[A. Neumaier]

This is because the creation and annihilation operators were taken to be the Fourier transforms of a free field. This choice is made for its simplicity. One could define things otherwise.

How would you create virtual particle states otherwise, with less simplicity?

 

[JK423]

A. Neumaier, would you agree with my understanding of the distinction between real/virtual particles summarized in this small post
https://www.physicsforums.com/showpost.php?p=4286488&postcount=32 ?
Or have i understood something wrong?

 

[A. Neumaier]

A. Neumaier, would you agree with my understanding of the distinction between real/virtual particles summarized in this small post
https://www.physicsforums.com/showpost.php?p=4286488&postcount=32 ?
Or have i understood something wrong?

The formalism of quantum field theory does not provide any way to assign a lifetime to an internal line of a Feynman diagram; all lifetimes attached to them are the result of wishful thinking, not the results of defendable quantum computations.

So a corrected - and then correct - form of your formulation would be:

''Internal lines in Feynman diagrams of perturbation theory: you cannot in principle interact with them because they have no quantum state to interact with! In this sense, they do not exist.

Real particles, no matter how SMALL a lifetime they have: you can in principle interact with them because they have a quantum state!''

 

[JK423]

Agreed, thank you very much!

 

[Naty1]

Bill_K asks, post #31:"This definition { from Rovelli, what's 'observable'} leaves out a lot of particles! Many particles in the Standard Model have lifetimes too short to leave a visible track.

"Consider the Z meson. It has a mass of 91 GeV and a lifetime of 3 x 10-25 sec. Implying, at velocity c it can travel at most a tenth of a fermi before it decays, less than the diameter of a proton. And thanks to its short lifetime the Z meson has a width of 2.5 GeV. GEV! It is never on the mass shell. It always appears as an "internal line" in some Feynman diagram.

So what do you say - is the Z meson a real particle? Or is it merely an "artifact of perturbation theory".

W mesons, top quarks and Higgs bosons have equally short lifetimes. If you consider these particles somehow not real, you're drawing an artificial distinction between particles that are otherwise closely related..."It 'never being on the mass shell', always an an 'internal line' in Feynman diagram, suggests it does not have a quantum state, is not a 'real' particle'...but I do not know if either of those quoted statements is correct.

"It has a mass of 91 GeV and a lifetime of 3 x 10-25 sec." means in principle it does have a quantum state, and is in principle at least 'detectable'. Are these observed or calculated?

However Wikipedia suggests mesons are routinely observed:

However, such particles are regularly created in experiments, in order to understand the nature of the heavier types of quark which compose the heavier mesons...While no meson is stable, those of lower mass are nonetheless more stable than the most massive mesons, and are easier to observe and study in particle accelerators or in cosmic ray experiments.

http://en.wikipedia.org/wiki/Meson

But for me, this is not necessarily conclusive one way or another...I don't know what interpretations are assumed in such statements. For example, that the Casimir effect proves the existence of virtual particles...and that they have observable effects..has always seemed to me to be a bit of a stretch.

 

[JK423]

A. Neumaier, i'd like to ask you one more thing, taking advantage of the fact that you visited the forum :)
You are a researcher and professor in Vienna, and you must have talked to many other experts in the field. If the argument

virtual particles don't have a state ==> they don't exist

is correct, why is there such a confusion among the experts? This argument is so simple(!), that i cannot believe that experts do not understand it! Every QFT textbook, should emphasize this, so that generations of students don't get confused. However, you open Peskin & Schroeder, and from the first page they say virtual states pop out from nowhere, obeying energy-time uncertainty relations etc.

How can you explain this phenomenon?

 

[Naty1]

oh, I just saw post #51:

''Internal lines in Feynman diagrams of perturbation theory: you cannot in principle interact with them because they have no quantum state to interact with! In this sense, they do not exist.

Real particles, no matter how SMALL a lifetime they have: you can in principle interact with them because they have a quantum state!''

Nice!...now let's wait to see who tries to refute that...Sounds like a 'go to' statement!

 

[Naty1]

However, you open Peskin & Schroeder, and from the first page they say virtual states pop out from nowhere, obeying energy-time uncertainty relations etc.

yes, and that such activity violates conservation of energy! Even the quote I posted from Lisa Randall [Harvard] says that...and I have repeatedly read such things...and repeatedly not understood whether such can be 'correct'...

 

[A. Neumaier]

Consider the Z meson. It has a mass of 91 GeV and a lifetime of 3 x 10-25 sec. Implying, at velocity c it can travel at most a tenth of a fermi before it decays, less than the diameter of a proton. And thanks to its short lifetime the Z meson has a width of 2.5 GeV. GEV! It is never on the mass shell. It always appears as an "internal line" in some Feynman diagram.

So what do you say - is the Z meson a real particle? Or is it merely an "artifact of perturbation theory".

All this says that the Z-meson is a real, unstable particle (hence has a complex mass shell - it is not off-shell in the same sense as this term is used for virtual particles) and _not_ a virtual particle.
Thus of course it is not an artifact of perturbation theory.

 

[A. Neumaier]

A. Neumaier, i'd like to ask you one more thing, taking advantage of the fact that you visited the forum :)
You are a researcher and professor in Vienna, and you must have talked to many other experts in the field. If the argument

virtual particles don't have a state ==> they don't exist

is correct, why is there such a confusion among the experts? This argument is so simple(!), that i cannot believe that experts do not understand it! Every QFT textbook, should emphasize this, so that generations of students don't get confused. However, you open Peskin & Schroeder, and from the first page they say virtual states pop out from nowhere, obeying energy-time uncertainty relations etc.

How can you explain this phenomenon?

I tried to explain this towards the end of
http://arnold-neumaier.at/physfaq/topics/unstable.html
Most people try to give some intuition to the abstract matter, which virtual particles do very well, and accept as its cost the resulting confusion. It is a trade-off, where many opt for the nice visualization. Many people also use quite different words for journal publications and for essays addressed to laypeople. Those who care about clear concepts are more careful with their language. For example, Weinberg's QFT book avoids the whole concept of virtual particles and still covers everything of importance in QFT.

Also, if I remember correctly, Peskin and Schroeder in their book never claim that virtual states pop out from nowhere, obeying energy-time uncertainty relations etc.. If you want to uphold your claim above, you'd cite page and line numbers.

 

[Jim Kata]

Maybe a better question is what is a particle? I guess just the inputs and outputs of a scattering process. What is a virtual particle? I just think of them as the internal lines in a Feynman diagram and real particles are the external lines of a Feynman diagram, and don't put too much more thought into it than that.

 

[JK423]

I tried to explain this towards the end of
http://arnold-neumaier.at/physfaq/topics/unstable.html
Most people try to give some intuition to the abstract matter, which virtual particles do very well, and accept as its cost the resulting confusion. Those who care about clear concepts are more careful with their language. For example, Weinberg's QFT book avoids the whole concept of virtual particles and still covers everything of importance in QFT.

Also, if I remember correctly, Peskin and Schroeder in their book never claim that virtual states pop out from nowhere, obeying energy-time uncertainty relations etc.. If you want to uphold your claim above, you'd cite page and line numbers.

They are trying to put some intuition, and as a result a huge percent of graduate students (and even researchers!) have misunderstood this concept..
Ofcourse, have a look at Peskin & Schroeder, page 13, 3rd paragraph,

Even when there is not enough energy for pair creation, multiparticle states appear, for example, as intermediate states in second-order perturbation theory. We can think of such states as existing only for a very short time, according to the uncertainty principle ΔΕΔt=h. As we go to higher orders in perturbation theory, arbitrarily many such "virtual" particles can be created.