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

[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.

 

[lightarrow]

...
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?

I could be wrong, but the case you aree discussing here doesn't seem to me a good metaphor of virtual particles being real/not real: here the Taylor expansion in 0 doesn't exist; in the case of virtual particles, the superposition instead does exist (mathematically, I mean).

 

[A. Neumaier]

I could be wrong, but the case you aree discussing here doesn't seem to me a good metaphor of virtual particles being real/not real: here the Taylor expansion in 0 doesn't exist; in the case of virtual particles, the superposition instead does exist (mathematically, I mean).

Superpositions of virtual particles do not exist in any sense, since virtual particles have no associated states.

On the other hand, the function f(x):={ 0 if x=0; e^{-1/x^2} otherwise} is infinitely often differentiable and has a Taylor series, but the Taylor series does not converge to the function since f(x) is not analytic. -
The point here is that one must distinguish between objects that have an intrinsic meaning (such as f(x) or the S-matrix) and auxiliary quantities used to compute them
(here perturbation series, that need not even be related to the function value).

Thus one should avoid calling something existing that has a mathematical meaning in some calculus for computing something that exists in the usual (non-mathmetical) sense.

 

[tom.stoer]

@A.Neumeier: so it seems you like my example :-)

What I wanted to show is that something that is rather familiar - the Taylor expansion - may fail completely in certain cases. But whereas the Taylor expansion fails the object "f(x)" still does exist!

"f(x)" and its Taylor expansion are simplified examples for "S-matrix" and its perturbation series. I hope it becomes clear that - even if the analogy is not perfect - virtual particles may fail to be a reasonable concept in the same way as the Taylor expansion may fail. But why should a rather limited mathematical tool be as real as physically measurable entities w/o such limitations?

 

[lightarrow]

Superpositions of virtual particles do not exist in any sense, since virtual particles have no associated states.

Thank you.

On the other hand, the function f(x):={ 0 if x=0; e^{-1/x^2} otherwise} is infinitely often differentiable and has a Taylor series, but the Taylor series does not converge to the function since f(x) is not analytic. -
The point here is that one must distinguish between objects that have an intrinsic meaning (such as f(x) or the S-matrix) and auxiliary quantities used to compute them
(here perturbation series, that need not even be related to the function value).

Thus one should avoid calling something existing that has a mathematical meaning in some calculus for computing something that exists in the usual (non-mathmetical) sense.

Probably it's already been asked, but is it possible to compare the non reality of virtual particles with the non reality of the wave represented by a wavefunction?

 

[tom.stoer]

Thank you.Probably it's already been asked, but is it possible to compare the non reality of virtual particles with the non reality of the wave represented by a wavefunction?

No.

Of course you could start a (philosophical) discussion regarding the reality of the wave function, but the mathematical status is different as (I am referring to A. Neumeier now)

Superpositions of virtual particles (in QFT) do not exist in any sense, since virtual particles have no associated states.
whereas
Superpositions of wave functions (in QM) do exist; wave functions are in one-to-one correspondence with states.

 

[A. Neumaier]

@A.Neumeier: so it seems you like my example :-)

Not really - I tried to rescue it. But it introduces an additional complication in what is
already a problematic thing...

"f(x)" and its Taylor expansion are simplified examples for "S-matrix" and its perturbation series. I hope it becomes clear that - even if the analogy is not perfect - virtual particles may fail to be a reasonable concept in the same way as the Taylor expansion may fail. But why should a rather limited mathematical tool be as real as physically measurable entities w/o such limitations?

But experiment shows that in case of QED, the additional problems of exp^{-1/x^2} are absent since the perturbation series indeed approximates the function.

 

[tom.stoer]

QED yes; QCD below Lambda, no!

 

[A. Neumaier]

QED yes; QCD below Lambda, no!

In my understanding, the situation in QCD is different - here the divergent perturbation series is asymptotic to a physically meaningless object since the S-matrix must feature asymptotic bound stats rather than quarks, but the computed S-matrix has quarks as asymptotic states.

But this kind of nonexistence seems to me quite different from the misconvergence in your example, where a meaningful function is approximated by a meaningful (and correct) asymptotic expansion, which just happens to be convergent but to a different function.

But you probably know much more about QCD specific things than I, so please explain
in which sense the QCD situation is analogous to your example.

 

[tom.stoer]

Correct, is not possible to construct few-particle states from vacuum, quarks and gluons and to study their scattering below Lambda b/c quarks and gluons are "the wrong d.o.f." in this regime. But of course we should try something like Bogoljubov trf., dressing, integrating out d.of.s, ... in order to derive an effective theory.

The situation in QCD is even worse as in my exp(-1/x²) example as the physically reasonable operators are something like <Delta|J|proton> = <0|Delta* J Proton|0> where now |0> is the Fock vacuum and Delta, J and Proton are operators consisting of infinitly many Fock space operators.

I think we better stop discussing exp(-1/x²).

 

[Bararontok]

I read the replies and many of them say that the virtual particles are in fact no more than mathematical tools used to make calculations in quantum field theory but that they are not necessary to perform the calculations since there are other methods for making the calculations. Perhaps I have confused the virtual particles of mathematical calculations with the concept of field particles. When a gauge boson is within a field, is it appropriate to call it a field particle?

 

[tom.stoer]

In quantum field theory all "particles" ara quanta of the field.

 

[Bararontok]

Okay then, thank you for the clarification. It seems that there are only two distinctions for the boson; when the boson is within the force field, it is referred to as a field particle and when it travels freely in space outside the range of a force field, it is referred to as radiation.

 

[tom.stoer]

Okay then, thank you for the clarification. It seems that there are only two distinctions for the boson; when the boson is within the force field, it is referred to as a field particle and when it travels freely in space outside the range of a force field, it is referred to as radiation.

Unfortunately it seems that there is no such clarification. Your ideas are inspired by classical field theory, not by quantum field theory. The boson "is" somehow the force field. It is never outside the range of a force field; it is the quantum of the force field is is therefore never isolated from that field.

 

[Bararontok]

But what about when Fermions emit radiation? And I know that fields such as the electromagnetic field of a magnet have only a finite range so any particle that escapes the field no longer interacts with it. The same can be said when an object escapes the gravitational field of a planet, the object is no longer subject to the planet's gravity. And what about individual photons that are not part of a stream of radiation?

Of course I am not saying that the bosons are not the quanta of the fields, I am just saying that it is possible for a single boson to travel individually without being surrounded by other bosons.

 

[jtbell]

But what about when Fermions emit radiation?

Then we have real photons, not virtual ones.

 

[Bararontok]

Then what term is used for the bosons that make up a static force field such as is the case with the photons of a permanent magnet or the gravitons of the Earth's gravitational field but are not traveling independently of each other and are clustered into a given volume depending on the range of the field?

 

[Vanadium 50]

Bararontok, there is no "bosons that make up a static force field" or "traveling" or "clustered" in any sense whatever. You're coming at this from the very direction that got this thread started. Rather than repeat what has been said, let me encourage you to reread the messages already posted.

 

[Bararontok]

Alright, based on what you have said, virtual particles are not real but are just calculation tools used in some of the mathematical forumlas of quantum physics. The actual bosons that are physically detectable and cause force interaction are not classified as virtual but are real and not just abstract mathematical tools. The distinction will be summarized below:

1.) Virtual Particle - mathematical tool used in some quantum physics forumlas.

2.) Real Particle - the actual bosons.

Since virtual particles are non-existent and abstract mathematical tools, why not just call them Math Particles?

 

[jamjr1979]

Unfortunately popularizations in particular seem to misunderstand that the reason we distinguish between "real" and "virtual" particles is that virtual particles are not real.

Hawking radiation (black hole radiation) is built on the principle that the virtual partner particles are realized. Unless I am misunderstanding it. This is not yet proven because the amount of radiation is so small we currently can not detect it. Correct me if I am wrong.

 

[tom.stoer]

Hawking radiation (black hole radiation) is built on the principle that the virtual partner particles are realized. Unless I am misunderstanding it. This is not yet proven because the amount of radiation is so small we currently can not detect it. Correct me if I am wrong.

This is the most common explanation.

I would try to explain it slightly different: Hawking radiation is due to the fact that in curved spacetime (or in spacetime with horizons) there is no unique choice for a vacuum state. Hawking radiation are "vacuum fluctuations" w.r.t. one vacuum state that "become real" w.r.t. a different vacuum state. So a transformation between vacuum states "creates" "real" particles out of vacuum fluctuations (I don't think that this is a better decription - it's just a different one).

A related effect is the Unruh effect where there is no physical curvature but a horizon due to accelerated motion. The Unruh effect shows that it's not essential to have a physical entity like a black hole; an observer-dependend horizon is sufficient to "create" the radiation.

 

[Boy@n]

Note to moderator(s): I've revised my post so it doesn't include link to “crackpot article” and my own speculation. Please do understand that by being a layman I cannot be the judge to which articles are accepted by current science and which aren’t, that’s why I asked about it. By asking here I certainly don’t mislead any layman readers, on the contrary, they too might find those articles by themselves and THEN be misled, as I was re Tesla/ether, so, asking here can only be beneficial for many readers, since once asked mentors and experts here can set the record straight. (I am now afraid to post that link due to warning I got, but I think it should be posted and labeled as crackpot, so others don't get mislead as well.)


Before posting this I've read most of the posts in various threads and articles regarding virtual particles, and as a layman I'd say that from all the reading I understand that virtual-particles are not real per-se (being just a mathematical tool), but that they do represent something (e.g. a field) which is there for real – do I have a proper understanding of this? For example, https://www.physicsforums.com/showpost.php?p=3018700&postcount=63": "Peskin is simply saying that the momentum of a field is real, and therefore any change in momentum is also real, and if quantised can be considered as a particle."

Regarding existence of virtual particles I find it to be a similar question to ask how many discrete steps are there in a continuous space-time. If space-time is truly continuous it's pointless to ask how many steps are there, since there would be infinite amount of them, and thus, moving my hand from point A to point B would be impossible… Well, I am not sure I got this (understanding/analogy) right either, that’s why I mentioned it... can someone please correct me if wrong?

I would try to explain it slightly different: Hawking radiation is due to the fact that in curved spacetime (or in spacetime with horizons) there is no unique choice for a vacuum state. Hawking radiation are "vacuum fluctuations" w.r.t. one vacuum state that "become real" w.r.t. a different vacuum state. So a transformation between vacuum states "creates" "real" particles out of vacuum fluctuations (I don't think that this is a better decription - it's just a different one).

A related effect is the Unruh effect where there is no physical curvature but a horizon due to accelerated motion. The Unruh effect shows that it's not essential to have a physical entity like a black hole; an observer-dependend horizon is sufficient to "create" the radiation.

So, there is SOMETHING within vacuum itself which enables "creation" (of particles/energy), via transformation between vacuum states due to curved space-time due to gravity? If vacuum were “pure void”, so to say, then I don’t see how anything could be possibly created by transformation between vacuum states?

Isn’t creating something out of void/nothingness a logical and physical impossibility? So, how do physicists here take "creation" into account, if there is only true void and not some kind of field (which we might imagine as virtual particles becoming real particles), since real particles are surely not ever-lasting, not even protons, right?

I'd say "Something must exist since ever, or there would be no existence." And since we do exist, where "I exist", or "I am", is certainly the strongest "evidence of existence" for each of us, then what is that something which exists since ever? As said, it cannot be known fundamental particles of our Universe, right? Is it quantum or say vacuum fluctuations, which are mostly in balance, until they aren’t and Big Bang happens (meaning, out of virtual real happens)?

 

[tiny-tim]

Isn’t creating something out of void/nothingness a logical and physical impossibility? So, how do physicists here take "creation" into account, if there is only true void and not some kind of field (which we might imagine as virtual particles becoming real particles), since real particles are surely not ever-lasting, not even protons, right?

Boy@n, you're missing tom stoer's point …

he put ' "create" ' in quote marks to emphasise that nothing is created …

(the radiation is simply vacuum fluctuations with a different name)

there are two different ways of looking at the same thing, related by a very simple transformation …

if something is in one but not in the other, then the transformation has "created" it …

but transformations can't actually create anything, they only provide a different way of looking at the same things …

if they weren't there the first time, they're not there the second time, even if they appear to be

if reversing the transformation appears to destroy something, then was it ever there?​

 

[Boy@n]

Boy@n, you're missing tom stoer's point …

he put ' "create" ' in quote marks to emphasise that nothing is created …

Makes sense - nothing really “new” is created, just something changed in form, so to say. Well, nice to know that, since something cannot be created out of nothing(ness).

Though, this alone still doesn’t help me to understand basics of our physical existence…. We can have transformations going on for eternity, but they for themselves are like non-existent, if they have nothing to transform… Fundamental physical particles, as we know them, are not eternal, right?

So, what’s that which is being transformed (changed in form) since ever? Are quarks eternal? Would string theorist say “strings”?

(the radiation is simply vacuum fluctuations with a different name)

If true it makes me even more puzzled/confused… I imagined radiation to be in domain of observable/measured physical reality, and vacuum fluctuations in domain of unknown/immeasurable virtual reality (e.g. virtual particles pairs popping in existence and almost instantaneously annihilating themselves). Wrong?

there are two different ways of looking at the same thing, related by a very simple transformation …

if something is in one but not in the other, then the transformation has "created" it …

but transformations can't actually create anything, they only provide a different way of looking at the same things …

if they weren't there the first time, they're not there the second time, even if they appear to be

if reversing the transformation appears to destroy something, then was it ever there?​

Is this a riddle? ;) J/K, makes perfect sense, but then again, what’s that “something” which transformation keeps transforming?

P.S. Tiny-tim, I really like your posts, I think they are clear in communicating difficult topics, or let's say, in putting them into quite understandable terms for lay people.

 

[tom.stoer]

The first problem is that "vacuum" and "nothing" are not the same "thing", they are not on the same "ontological level"; "vacuum" means something physically, i.e. something in the context of quantum field theory, whereas "nothing" means something in the context of philosophy.

Second Hawking's (and Unruh's) results show that "physical vacuum" is not "nothing" - which we know since decades - and that there is no unique definition of "nothing" in physics.

 

[Boy@n]

The first problem is that "vacuum" and "nothing" are not the same "thing", they are not on the same "ontological level"; "vacuum" means something physically, i.e. something in the context of quantum field theory, whereas "nothing" means something in the context of philosophy.

Second Hawking's (and Unruh's) results show that "physical vacuum" is not "nothing" - which we know since decades - and that there is no unique definition of "nothing" in physics.

Nice clarification regarding vacuum and nothing(ness), thank you Tom! I hope my next questions will not sound too ignorant or too speculative, I'd just like to make a clearer picture of our existence via the "eyes" of currently prevailing science theories. I hope that you, and others too, can help me out...

Would it be proper to say, that (physical) vacuum, which is and always was filled with fluctuations, "created” our physical reality as we know it (by some kind of powerful vacuum collapse)?

But then, what fluctuates? I guess not quarks, and not Higgs bosons (if proved to exist), right? Is it simply energy, being eternal? Would string theorists call it “strings vibrating”?

Is radiation also present within vacuum or is it just an emergent property once matter is "created"? Similarly, only when matter is present gravity and electromagnetism appear as well, true?

(I’ve put “created” in parenthesis because it seems that “converted” and “transformed” are better words to describe it more properly, since “nothing new” gets really created, just something already existing changes...)

So, in a sense it could be said that "virtual existence (particles)" created the “real existence (particles)”? Well, this would be probably true if we consider “virtual” that which “potentially exists” but it’s simply something which we cannot directly observe and measure… (Thus, “virtual existence” would be “existing” in realm where “everything” in it is smaller than Plank constants.)

Even if vacuum fluctuations do all that, it looks though like that "creation" doesn't happen in our "normal" space-time (if we don't count “creation” of real particles out of virtual particles near the Black Hole horizon, because it's practically impossible to measure that for real, since even background radiation is stronger).

So, true “creation” only happened once, which we call the Big Bang… it surely looks as if something really "unusual" happened at that moment. What could be the possible scenario? What if just before the Big Bang there was the Big Crunch? There being another Universe before ours, which collapsed into itself, which was then immediately followed by birth of our Universe? Simply put, existence of Universe cycling. What are other potential (realistic enough) scenarios in today science? (BTW, I don't think that the Multiverse theory answers "births".)