Are virtual particles really there?

[kexue]

kexue, personally I think that ontological questions are rather interesting - but unfortunately neither physics nor physicians are good in explaining them; that's why I think we should prevent this thread from a "philosophical turn".

Fair enough.

But is not Feynman saying that questions like: "Are virtual particles "really there" or just a "tool"?" ,"Are they essential or not?" not answerable, or of no interest to an physicist?

(My last philosophical question in this thread, promised.)

 

[tom.stoer]

But is not Feynman saying that questions like: "Are virtual particles "really there" or just a "tool"?" ,"Are they essential or not?" not answerable, or of no interest to an physicist?

They are not answerable by physics and they are not relevant to most physicists, including and especially Feynman :-)

But ...

Look at physics in the 20th century, especially at the birth of quantum mechanics between ~1905 (Einstein) and 1925/26 (Heisenberg, Schrödinger, ...) Most of them discussed philosophical topics of physics - and many of them came to the conclusion that physics is rather closed to positivism (but I bet from Saturday to Sunday they are - secretly - Platonists w/o telling us :-)

So I think in developping new concepts and when establishing new paradigms one MUST ask these questions as they will influence the direction of the whole approach. But the majority of physicists is not involved in these issues; even string theorists and quantum gravity reseachers aren't, except for rare exceptions. Most of us follow Feynman in his "shut up and calculate".

Going beyond that requires some care:
- get the right people to talk to (most physicists arent't the right people)
- understand your set of tools (ontology of virtual particles does not make sense)
- avoid traps and pitfalls (what has been discussed already, what has been rejected and for which reason?)

My impression is that especially today there is a paradigm shift in modern theoretical physics as especially with string theory and quantum gravity we are touching regimes which are neither required by experiment (the SM did not fail in one single case!) nor testable / falsifiable in practice, perhaps not even in principle (Planck scale not reachable, certain concepts are hidden by construction)

Unfortunately many physicists are blind for that new challenge and continue to "shut up and calculate". And there are others which try to make one step further, but unfortunately make some mistakes as mentioned above - resulting in an overall refusal of philosophy in science.

 

[kexue]

Great post, Tom!

PF needs an "I like it" button like on Facebook.

 

[tom.stoer]

Great post, Tom!

PF needs an "I like it" button like on Facebook.

Thanks!



And let me add that I am happy that we went through this long discussion and have some agreement now.

 

[A. Neumaier]

Kaku and especially Maggiore claim in their textbooks that non-pertubative calculations do not work in canonical quantization, since an exponential of an operator is defined by its Taylor expansion.

Only exponentials of bounded operators can be defined by a Taylor expansion.
The general case is nonperturbative, using either Cauchy's integral theorem or the
Hille-Josida theorem.

The rest I wrote was admittely wild speculation. All I know is, that when we got a path integral, either in qm or in qft, we have to integrate over all possible paths. In qm that would be paths that a classical particle never could take, paths that do not obey special relativity, i.e. faster than light, backwards in time, whatever. Similiar wild paths are taken when we integrate over field configurations. I called them freely virtual paths.

My reasoning was (probably naive and wrong) that these "crazy" paths correspond in some sense to the virtual particles in the canonical quantization calculations.

Naive and wrong indeed (with probability 100%)!

This has nothing to do with virtual particles. One integrates over all paths, but only one of them is (approximately) taken, and it is taken by real particles, not by virtual ones.
To see this:

The path integral also applies for a single nonrelativistic particle in an external field.
A particle takes just one of these paths (approximately, as seen in a bubble chamber).
Since the path is observable, nothing about it is virtual, although it does not correspond
to an on-shell condition.

I subscribe to what I arrogantly call the Feynman way of thinking, as described by the Susskind quote or what I was trying to convey more clumsy in post 111 and what I think is an important message to understand, that there is no qualitative difference between virtual and real particles, particles can be more or less "off-shell", but are never actually exactly on-shell.

Basically, this what I like to emphasize. Tom and others do not find that helpful, though I understand they admit it is a legal view.

It is not a legal view. Susskind is extremely sloppy in his answer. He equates being off-shell with being virtual, which is not the case. Particles are off-shell once they are not free (i.e., always when they cannot be described by the asymptotic state required by scattering theory). So this is the usual situation for real particles.

On the other hand, particles are virtual if they are exchanged by an internal line in a Feynman diagram. It can happen that virtual particles have imaginary mass (the photon exchanged between two interacting electrons in the tree approximation is of this kind),
while this can never happen for real particles, no matter how off-shell they are.

And of course Tom's objections (first and foremost: where are the virtual particles in non-pertubative calculations?!) are well taken, and to be honest I'm not in the position to argue with him. For that I know way to little quantum field theory.

The nonexistence of virtual particles in nonperturbative calculations (whether conformal field theory or lattice gauge theory) is proof that the virtual particle concept is an
artifact of perturbation theory. Something whose existence depends on the method of calculation cannot exist in a strong sense of the word.

For a thorough discussion of many aspects discussed in this thread see
Chapter A7: Virtual particles and vacuum fluctuations
of my theoretical physics FAQ at
http://arnold-neumaier.at/physfaq/physics-faq.html

 

[tom.stoer]

Only exponentials of bounded operators can be defined by a Taylor expansion.
The general case is nonperturbative, using either Cauchy's integral theorem or the
Hille-Josida theorem.

Does this say anything canonical quantization?

The nonexistence of virtual particles in nonperturbative calculations (whether conformal field theory or lattice gauge theory) is proof that the virtual particle concept is an artifact of perturbation theory. Something whose existence depends on the method of calculation cannot exist in a strong sense of the word.

Thanks. This is the only part of this thread that should really become sticky.

 

[kexue]

First of all, thank you A. Neumaier for contributing to this thread! When I was googling for virtual particles, I also stumbled upon older posts of you here at PF and your FAQ where you quite passionately argue against the "reality of virtual particles".

Let me just say this, I for my taste do not like to call something that explains empirical observations very well as "just mathematics" or not "real". Especially, when it involves quantum physics, where the question what is real is a rather thorny one.

 

[A. Neumaier]

First of all, thank you A. Neumaier for contributing to this thread! When I was googling for virtual particles, I also stumbled upon older posts of you here at PF and your FAQ where you quite passionately argue against the "reality of virtual particles".

Let me just say this, I for my taste do not like to call something that explains empirical observations very well as "just mathematics" or not "real". Especially, when it involves quantum physics, where the question what is real is a rather thorny one.

Taste is not what decides in science. Well-grounded arguments do.

You don't understand how superficial the level is at which virtual particles
explain empirical observations. They don't explain anything.

You were lightly dismissing the one-line answer of Weinberg that he sent you.
He is one of very few who understand quantum field theory at the deepest level
currently accessible to people. Instead you took side with Susskind who is a very speculative physicist.

Since virtual particles are unobservable, one can attribute to them
whatever properties one likes, without any real consequence or
testability. This explains the phantastic aura surrounding virtual
particles, and it also explains their name - they are called virtual
since they are not real in any strong sense of the word.

None of the speculative aspects of virtual particles can be verified by experiment,
which places them outside the realm of science and into the realm of fiction.


What can be verified with high accuracy are physical effects derivable
form the scattering theory of the particles, i.e., from the fully
summed and renormalized perturbative calculations involving an
evaluation of the multiple integrals represented by the Feynman
diagrams. Plenty of experiments establish without doubt the correctness
of the scattering theory and the phenomena predicted by it, such as
Coulomb scattering and the Casimir effect.

But (in spite of frequent claims in the popular physics literature
and sources from the internet) none of these experiments verify
anything of the unobservable phantastic scenarios frequently associated
with virtual particles. The claims simply rest on taking the successes
of perturbation theory with its Feynman diagrams as proof of the
validity of the virtual particle picture. But these successes are
based on the multiple integral interpretation of the Feynman diagrams,
not on their virtual particle interpretation. No evidence at all
exists that the latter had any roots in space and time.

There is plenty of evidence that sums of Feynman diagrams, interpreted
as renormalized multidimensional integrals, correctly predict many
phenomena. But to interpret this as evidence for the existence of
virtual particles manifesting themselves in space and time is
stretching the interpretation too far -- something perhaps acceptable
at the at the layman's level to provide some sort of intuition for
otherwise too abstract things (which is what one can find in
popularizing accounts by some well-known physicists), but unacceptable
on a more scientific level.

It seems impossible to place the superficial virtual particle
picture on a sound scientific footing. It is a picture valid only
if restricted to the superficial level where no detailed inquiries
are made. It is like ordinary people using the word ghost to describe
a fleeting but fear-provoking experience. It makes sense only as long
as you don't ask about their precise properties. But once you start
asking how fast a ghost is traveling, things no longer make sense,
since the concept of a ghost is not intended to be applied literally.

 

[A. Neumaier]

Does this say anything canonical quantization?

Well, canonical quantization of a 1-dimensional Lagrangian leads to ordinary quantum mechanics, where things are much clearer than in quantum field theory (QFT).
The Hamiltonians arising there are self-adjoint operators densely defined on a Hilbert space, and their exponentials exp(itH/hbar) are defined using the Hille-Yosida theorem
(see e.g. Volume 3 of the Math. Physics treatise of Thirring).

The same happens (at a much higher level of complexity and difficulty) in 2D quantum
field theory; see, e.g., the quantum physics book by Glimm and Jaffe.

In 4-dimensional QFT, especially in QED, nobody knows how to define the relevant exponentials in a logically stringent way. But it is clear that the operators are unbounded, so a power series definition is impossible. Thus I expect that when, one day, a proper definition is found, it will also be nonperturbative.

 

[kexue]

Well, I took the Frank Wilczek view.

But since only you and Steven Weinberg know how quantum field theory works deep down, let me ask you this, is the electric field of a charge really there?

Since I'm very fond of quoting people, PF mentor ZapperZ wrote some nice post back in this https://www.physicsforums.com/showthread.php?t=124512" (of course, I do not want to drag him into this discussion)

I'm usually amazed when people try to either dismiss, or justify dismissing, quantum fields has being nothing more than mathematical artifact, without realizing that the VERY same argument can be made of the beloved classical fields. If anything, I have more of a justification to dismiss classical fields due to their shorcoming in making all of the predictions that we have verified so far in QED. For some odd reason, this point has been overlooked.

In condensed matter physics, we deal with many of these "quanta" fields that mediate many kinds of interactions. While there may be just 3 (or 4 depending if you buy gravitons), in condensed matter, we have phonons, spinons, magnons, polarons, axions, chargons, holons, etc.. etc. All of them, in one way or another, mediateds many different kinds of interactions. Are these "real"? How do you judge such a thing, and what makes you can tell? You just can't base this on simply a "matter of tastes" or "personal preference", which frankly, is what most of these types of discussion has been based upon. But how about using the criteria that THEY WORK! One may not realize it, but claiming "It Works!" is a freaking big deal in physics. You get a lot of recognition and funding when you can show that a theory or description actually matches very well with experiments. It's what most of us physicists life for!

So when questions like this are asked, I would like to ask something back: When you "accept" something to be "real" or "valid", especially in physics, what criteria do you use? Do you pay attention to experimental verifications that agree with a certain description, or do you only accept things that sit well with your "world view", which is what I call as a matter of tastes? Or have you even though about such a process on how you actually make your decision? I ask this because I'm almost sure that if one applies the same logic to object against "virtual particles", one could easily use that to object against classical fields also. So now what?

 

[tom.stoer]

In 4-dimensional QFT, especially in QED, nobody knows how to define the relevant exponentials in a logically stringent way. But it is clear that the operators are unbounded, so a power series definition is impossible. Thus I expect that when, one day, a proper definition is found, it will also be nonperturbative.

I know QED and QCD both in the canonical and in the PI approach. Both approaches are nearly equivalent, and both are mathematicaly ill-defined :-) Nevertheless I think that the formal definition of H together with some kind of regularization seems to be closer to mathematical rigor then Z[J]. But - as I said in another post - canonical qantization does not (always) require to invent something exp(-iHt). It depends on the questions you are asking. For the spectrum the exponential is not needed.

 

[A. Neumaier]

Well, I took the Frank Wilczek view.

But since only you and Steven Weinberg know how quantum field theory works deep down, let me ask you this, is the electric field of a charge really there?

When you "accept" something to be "real" or "valid", especially in physics, what criteria do you use?

It is observable, hence exists according to universal agreement among physicists.

According to my criteria, things exist on a scientific level if they are (in principle)
measurable, whereas unmeasurable things are taken to exist only if they are
_necessary_ for the explanation of a phenomenon.

Thus electric fields exist according to the first criterion, while quarks and quasars
exist according to the second. Virtual particles dont' exist since they don't satisfy
any of the criteria.

 

[A. Neumaier]

Well, I took the Frank Wilczek view.

The Nobel lecture by Frank Wilczek at
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1150826/

talks near the beginning about the traditional virtual particle picture:
''Loosely speaking, energy can be borrowed to make evanescent
virtual particles''.

Note his qualification that indicates that this cannot be taken
seriously. He also says why - because one encounters divergences by
taking them seriously. Then he gets more serious and shows how
renormalization fixes the problems, though he does not say that this
comes at the cost of making the virtual particles infinitely heavy
(and hence again physically meaningless). But this can be read in any
textbook on QFT.

Later, he slips back into the traditional jargon since it
provides a vivid intuition about Feynman diagrams -- especially
for the many nonexperts in his audience, but again he does so
with a careful, explicit caveat:
''(I'm being a little sloppy in my terminology; instead of saying
the number of virtual particles, it would be more proper to speak
of the number of internal loops in a Feynman graph.)''

Towards the middle he mentions lattice discretizations, and how they
cope with the problem in a nonperturbative way by not invoking virtual
particles (i.e., formally correct, a loop expansion) at all.

 

[tom.stoer]

Let's make an simple example: in classical mechanics we all agree that a body is described by its mass m and its moment(s) of inertia I; and in some sense we could conclude that m and I do "exist" (I mean not the symbols "m" and "I" but m and I in some physical sense); we never talk about it because it's so obvious :-)

Now let's focus on quantum field theory and virtual particles. A virtual particle is described by
- a propagator, e.g. 1/(p²-m²)
- its vertices, some "tensor" V
- a rule how to integrate over the whole stuff

If we compare this to classical mechanics and if you insist on the existence of virtual particles it should be possible to explain how to translate these mathematical rules into "physical entities". We can do that for m and I, we can explain what they mean, we can measure them, we can construct objects with given m and J... So we seem to know what they "are".

Now please try the same for 1/(p²-m²).

I guess you end up with nothing else but
- a symbol "1/(p²-m²)"
- a rule what to do in a certain calculation

Is this really sufficient to say that they "are there"?

 

[kexue]

It is observable, hence exists according to universal agreement among physicists.

According to my criteria, things exist on a scientific level if they are (in principle)
measurable, whereas unmeasurable things are taken to exist only if they are
_necessary_ for the explanation of a phenomenon.

Thus electric fields exist according to the first criterion, while quarks and quasars
exist according to the second. Virtual particles dont' exist since they don't satisfy
any of the criteria.

But you can not see the electric field, only a charge gets repelled or attracted! I say that the electric field is a quantum field and the virtual particles it produces transmit the force.

Again, we can not see it, but the same goes for the electric field.

Only my quantum field with its virtual particles gives one coherent and intuitive picture of nature and explains a host of phenomena and is also a view that is shared by many physicists.

And how about criteria three, if something can happen in quantum physics it happens. The energ-uncertainty relations allows the production of virtual particles last time I checked.

 

[A. Neumaier]

I know QED and QCD both in the canonical and in the PI approach. Both approaches are nearly equivalent, and both are mathematicaly ill-defined :-) Nevertheless I think that the formal definition of H together with some kind of regularization seems to be closer to mathematical rigor then Z[J]. But - as I said in another post - canonical qantization does not (always) require to invent something exp(-iHt). It depends on the questions you are asking. For the spectrum the exponential is not needed.

Indeed. But

-- if you can't define exp(-itH) then you don't have a complete physical model since then you cannot talk about states at finite times.

-- if you know the full spectral information, i.e., a representation on which the Hamiltonian is diagonal, then you get a nonperturbative definition of the exponential for free since in the diagonal representation, the exponential is just multiplication by
exp(-itE).

 

[A. Neumaier]

But you can not see the electric field, only a charge gets repelled or attracted! I say that the electric field is a quantum field and the virtual particles it produces transmit the force.

Again, we can not see it, but the same goes for the electric field.

Only my quantum field with its virtual particles gives one coherent and intuitive picture of nature and explains a host of phenomena and is also a view that is shared by many physicists.

And how about criteria three, if something can happen in quantum physics it happens. The energ-uncertainty relations allows the production of virtual particles last time I checked.

Being able to see something was never a necessary criterion for existence.
If you only accept that something exists when you see it, you'd conclude that the
moon has only one side, and that the Earth is hollow (since its interior can't be seen).
This is ridiculous. In any case, this is not the scientific view.

The established view is not seeability but measurability. Virtual particles cannot be measured by their very definition, since they are internal lines in the perturbative description of a scattering amplitude of which, again by definition, only the in and
out behavior is measurable.

Moreover, the virtual particle view is not coherent. There is no theory how the state of a virtual particle changes with time, not even in the simplest situations. Virtual particles make sense only at a very superficial level comparable to a billiard ball view of quantum particles. Both are very inadequate to describe reality.


Criterion 3 is not something that can be checked, thus it is not a criterion. How do you know when a virtual particle has happened (whatever this means)?

Finally:
People are sometimes invoking Heisenberg's uncertainty relation that
allegedly allows the violation of conservation of energy for a very
short time, thus apparently making room for seemingly nonphysical
processes. However, the uncertainty relation is based on the existence
of operators satisfying the canonical commutation rule, and while
there are such operators for spatial position and spatial momentum,
there are no such operators for time and energy, or for 4-position
and 4-momentum. Indeed, there is no time operator in either quantum
mechanics or quantum field theory, and since the energy operator (the
Hamiltonian) of a physical system is always bounded below, it cannot
be part of a pair of operators satisfying the canonical commutation
rule. Therefore the time-energy uncertainty relation is without a
formal basis.

 

[kexue]

The Nobel lecture by Frank Wilczek at
http://www.ncbi.nlm.nih.gov/pmc/articles/PMC1150826/

talks near the beginning about the traditional virtual particle picture:
''Loosely speaking, energy can be borrowed to make evanescent
virtual particles''.

Note his qualification that...

Well you know, I asked him what he thinks about virtual particles. He gave a beautiful answer, which was

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.

And as I said before somewhere in this thread, if Prof. Wilczek is inclined to include that concept of virtual particles in his inventory of reality, so may I.

You can see them as not "real" (whatever that means!), that is perfectly fine, too.

 

[kexue]

The established view is not seeability but measurability. Virtual particles cannot be measured by their very definition, since they are internal lines in the perturbative description of a scattering amplitude of which, again by definition, only the in and
out behavior is measurable.

That is not the definition of virtual particles. That what people always try to make the definition of virtual particles, internal lines of Feynman graphs, artefacts of perturbation theory and so on.

Here for the third time is the definition of virtual particles by PF member selfadjoint

Here's the idea. In quantum mechanics nothing is really real unless you can observe it or measure it. In order to be observable, a particle has to have some minimum amount of energy for some minimum amount of time; this comes out of the uncertainty principle that says the product of those two things has to be bigger than a certain number.

So it's possible to conceive of a particle whose energy is not big enough or whose lifetime is not long enough to permit a true quantum measurement, but still both of them could be greater than zero. The world could be full of such particles, and the measurements would never show it.

Well, quantum field theory takes those particles seriously. It says they interact with observable particles, for example they make the electron which emits and absorbs them a bit heavier, and a bit more sluggish in motion, than it would be if they didn't exist.

Furthermore, QFT says that the virtual particles are the ones that carry the forces. For example with photons, the "real" photons make light, and other forms of electromagnetic radiation, but the virtual photons carry the electric force; a charged particle is charged because it emits virtual photons. And the other bosons, that carry the weak and strong forces, behave the same way. Real particles interact with each other by exchanging virtual bosons.

This is the story quantum field theory tells, and the justification, the reason you should at least consider beliving in it, is that it makes fantiastically correct predictions. That bit above where I said that interacting with virtual particles made the electron sluggish? It's called the anomalous moment of the electron, and the prediction, based on virtual particles, matches experiment to six decimal places.

And again, to say that classical field moves a charge or the virtual particles of a quantum field, one explanation is as "real" as the other, both we can't see, but we only can measure how the charge moves.

 

[A. Neumaier]

Well you know, I asked him what he thinks about virtual particles. He gave a beautiful answer, which was

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.*

And as I said before somewhere in this thread, if Prof. Wilczek is inclined to include that concept of virtual particles in his inventory of reality, so may I.

You can see them as not "real" (whatever that means!), that is perfectly fine, too.

You don't seem to notice the nuances in his answer.

He says ''When... I am inclined' ... On the other hand ... '' (showing an ambivalence in his
views), and then mentions the need of ''a little boldness'' (i.e., closing the eyes to the difficulties in maintaining the picture on a more detailed level), and that it is a matter of taste (i..e, not of scientific knowledge, which is impersonal and hence independent of taste), and finally concludes by saying that science cannot be well represented in terms of ordinary language so that one must make compromises -- which are , of course, a matter of taste.

On the scientific level, the taste no longer plays a role, and physicist have no difficulty agreeing about the meaning. But on the level of illustrating it for a casual sender of an email query who, by the formulation of the query, can be seen not to be an expert,
taste plays a big role.

He knows what he is talking about, while you just seem to pick a view by your taste, without realizing that by doing so you are leaving the scientific level.

 

[A. Neumaier]

That is not the definition of virtual particles. That what people always try to make the definition of virtual particles, internal lines of Feynman graphs, artefacts of perturbation theory and so on.

Indeed, those who understand quantum field theory make this the definition. It is the _only_ grounding that virtual particles have in the formalism of QFT. That's why people always try to drive home this point, even to a persistent unbeliever like you. We never give up hope early...

Here for the third times is definition of virtual particles by PF member selfadjoint

Here's the idea. In quantum mechanics nothing is really real unless you can observe it or measure it. In order to be observable, a particle has to have some minimum amount of energy for some minimum amount of time; this comes out of the uncertainty principle that says the product of those two things has to be bigger than a certain number.

So it's possible to conceive of a particle whose energy is not big enough or whose lifetime is not long enough to permit a true quantum measurement, but still both of them could be greater than zero. The world could be full of such particles, and the measurements would never show it.

Well, quantum field theory takes those particles seriously. It says they interact with observable particles, for example they make the electron which emits and absorbs them a bit heavier, and a bit more sluggish in motion, than it would be if they didn't exist.

Furthermore, QFT says that the virtual particles are the ones that carry the forces.

Well, this is vague talk, far from a useful definition. How do you know that the claim is correct that ''they make the electron which emits and absorbs them a bit heavier''?

To give this claim any sort of substance, one must turn to a proper definition, namely the one in terms of internal lines of Feynman diagrams. If you don't do that, QFT is completely silent about virtual particles. The same holds for the second claim that ''QFT says that the virtual particles are the ones that carry the forces.''

This is the story quantum field theory tells, and the justification, the reason you should at least consider beliving in it, is that it makes fantiastically correct predictions. That bit above where I said that interacting with virtual particles made the electron sluggish? It's called the anomalous moment of the electron, and the prediction, based on virtual particles, matches experiment to six decimal places.

If you look at derivations of this prediction in standard textbooks, you'll find that the only relation they have to virtual particles is through internal lines of contributing Feynman
diagrams, while there is no relation to what, above, you consider to be the definition of a virtual particle.

As long as you cannot check for yourself the adequacy of definitions and proofs you should be much more modest with your corresponding claims!

 

[kexue]

You don't seem to notice the nuances in his answer.

No I did not. Thanks for pointing out.

If you look at derivations of this prediction in standard textbooks...

Have you read the reply of Peskin to my question "are virtual 'really' there?" The guy wrote a little book, too, which some call standard.

Have you read Zee's textbook, page 27 where he states "That the exchange of a particle can produce a force was one of the most profound conceptual advances in physics"?

Or have you even read what Curtis Callan and Gerad t'Hooft answered to my question "are virtual particles really there?" Or Witten and Suskind? Or Pollitzer? (Matter of fact, I have more quotes that argue in my favor, but I stopped posting them since it makes people just angry or they read into them what they like anyway. Also, posting personal emails on a open discussion is not so nice. I'm not Julian Assange.)

Granted, no one of these people understands quantum field theory at that level you do, but still I would consider their opinion.

You say I have not understood quantum field theory. As it seems you have not even understood the basic principles of quantum mechanics! So let me break it down for you.

According to quantum mechanics, no objects are "real" in the same sense as in classical physics; only probabilities of individual outcomes and the formulae to calculate them are "real" and predictable. No quantity characterizing a quantum physical system exists prior to the measurement. However, if you consider correct formulae for observable probabilities "real", then the virtual particles are "real" as well. Represented as internal lines (propagators) of Feynman diagrams, they are essential building blocks of the formulae for the probability amplitude.

The only difference in "reality" between virtual and asymptotic particles is that the asymptotic particles may "exist" eternally while the life of virtual particles is, by definition, transient. Because the virtual particles only live temporarily, their energy and momentum don't have to satisfy the usual E^2-p^2.c^2=m^2.c^4. In a real setup, no particle exists eternally, so every particle in the real world is, to some extent, virtual.

And also let me stress something, which I think we settled in this thread before you stepped in:the question about reality is surely philosphical. Whether you say it is 'just a tool' or it is 'real' is to some degree a matter of taste when it comes to virtual particles.

I say that something that predicts and explains with astonishing precision many empirical observations and which is allowed or even demanded by the laws of (quantum) physics, and in addition gives a beautiful, coherent and intuitive picture of how nature works, I say this is real!

Virtual particles are`really there', whether explicitly (in perturbative
calculations) or implicitly.

 

[nismaratwork]

But you can not see the electric field, only a charge gets repelled or attracted! I say that the electric field is a quantum field and the virtual particles it produces transmit the force.

This isn't a website about what you say based on a LACK of information. You don't prove a hypothesis by increasing vagueness...

Again, we can not see it, but the same goes for the electric field.

Only my quantum field with its virtual particles gives one coherent and intuitive picture of nature and explains a host of phenomena and is also a view that is shared by many physicists.

Your field? Oh, and "many physicists"... that many is a weasel-word. http://en.wikipedia.org/wiki/Weasel_word

And how about criteria three, if something can happen in quantum physics it happens. The energ-uncertainty relations allows the production of virtual particles last time I checked.

re: bolded... QM doesn't say that, although you could argue for that the MWI does... not in the same universe however. Beyond that, you just go back to a meaningless argument that everyone in this thread has trashed, A. Neumaier most recently. Virtual Particles are just a function of the approach you take, and shouldn't be confused with nature.

I'd say you're pushing a personal theory, but you don't have a theory, just a critical misapprehension.

 

[tiny-tim]

Zee & Peskin

Have you read Zee's textbook, page 27 where he states "That the exchange of a particle can produce a force was one of the most profound conceptual advances in physics"?

That is what Zee is saying, yes.

Zee dislikes virtual particles so much that he only mentions them about 10 times in the book, apparently each time as a shorthand for an internal line or similar concept.

Have you read the reply of Peskin to my question "are virtual 'really' there?" The guy wrote a little book, too, which some call standard.

Peskin is not talking about the same virtual particles as you or we are.

He is not talking about quantum field theory at all.

He is simply describing transfer of momentum … which of course is real!

Everyone agrees that a field is real, even though it's ghost-like. It has energy, it has momentum, it has various other attributes. And when it gives momentum to a particle, clearly it loses momentum, and that loss (or gain) of momentum is a genuine change in a genuine real physical attribute of the field.

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.

(similar to visualisation of real photons as "condensing out" of the electromagnetic field)

This has nothing to do with quantum field theory.

It does not even have anything to do with ordinary quantum theory, except for his stipulation that the momentum must be quantised (which makes it not only real, but also capable of being considered a particle) …

in other words, his description of the reality of this transfer of momentum stands perfectly well on its own (with quantisation added or not added to it, according to taste) …

he is talking only about transfer of momentum, and is calling it a "virtual particle"

(equivalent to the single virtual particle in an "H"-shape diagram)

 

[weejee]

Only exponentials of bounded operators can be defined by a Taylor expansion.
The general case is nonperturbative, using either Cauchy's integral theorem or the
Hille-Josida theorem.

Could you elaborate on this? For ordinary numbers, if we define the exponential in terms of a Taylor expansion, the radius of convergence is infinite. I wonder what is different for operators?
(I acknowledge that even if exp(-iHt) itself is well-defined in terms of a Taylor expansion, defining the expectation value <exp(-iHt)> using the same approach can easily fail.)

 

[tiny-tim]

kexue, the only mention Peskin makes of virtual particles is …

To describe this transfer of momentum, we say that a
"virtual photon" passes between the positive charge and the electron.
The virtual photon carries

Energy < (momentum) x c

so formally it has negative mass. There is even a sense in which it
is transferred instantaneously or even goes backward in time, although other electrodynamic effects add to this one so that there is no violation
of causality.

The virtual photon is not a real particle, but it is certainly real, in the sense that the electron really does change its momentum in the encounter.​

(btw, doesn't he mean imaginary mass rather than negative mass?)

he is clearly talking only about transfer of momentum …

he denies that the virtual photon is a particle,

and the only thing to which he attributes reality is the transfer of momentum (and of course that is over the whole history of the positive charge and the electron, fine for expaining a particle causing a sudden change, but not for a particle causing the gradual curve that we actually see … which presumably is why he denies that there is a particle there )

kexue, do you say that the virtual photon is a particle?

if not, what do you say it is? ​

(and btw, you've twice mentioned "cognitive dissonance" but we still have no idea what you're going on about, and you're not saying )

EDIT: in case anyone is wondering why I've made a second post on Peskin for no apparent reason, it's because kexue made three posts in between which have since been deleted, one of which replied to my first post ​

 

[tom.stoer]

kexue, I tried very hard to explain to you that exactly this Coulomb interaction demonstrates that the whole concept of virtual particles is gauge dependent and therefore intrinsically unphysical. That means it is meaningless (nonsense) to talk about "the virtual photon"; the whole concept of virtual photons depends on the unphysical choice of a gauge which makes the virtual photons itself unphysical.

The process of Coulomb interaction of charges in QED can be explained w/o the need to refer to virtual photons at all. Chosing a different gauge means altering what a virtual photon "is" and where it appears in your calculations.

As I explained a couple of times the Coulomb potential can be explained w/o the need to refer to any kind of virtual particle at all. I gave you a detailed explanation in post #48, I gave you a very good (neutral) reference in https://www.physicsforums.com/showthread.php?t=445730 post #5,7 where you can check the details. So please either take note what we are saying.

 

[kexue]

kexue, I tried very hard to explain to you that exactly this Coulomb interaction demonstrates that the whole concept of virtual particles is gauge dependent and therefore intrinsically unphysical. That means it is .

Tom, no need to yell at me. Have you read my post 172?

Do you consider correct formulae for observable probabilities as "real"?

 

[kexue]

What Tom sees as meaningless and nonsense, is described as general feature of the world (on page 2) in this http://scipp.ucsc.edu/~dine/ph217/wilczek.pdf" of quantum field theory again by Frank Wilczek.

On page 3:...the association of forces and interactions with particle exchange... with the correspondence of fields and particles, as it arises in quantum field theory, Maxwell discovery corresponds to the excitence of photons, and the generation of forces by intermediary fields corresponds to the exchange of virtual particles...the association of forces (or, more generally, with interactions) with exchange of particles is a general feature of quantum field theory

Zee calls it one of the most profound conceptual advances in physics, Wilczek a general feature of the world

Tom says it is meaningless and nonsense, A. Neumaier says it explains nothing

Well, what do other PF members think? Please join the discussion everybody! Don't be shy.

 

[Maui]

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. [/I]

Some of the replies here suggest very strongly that the view that virtual particles really exist is not necessarily wrong, but they do not conform to some individuals' world views of how the world must be(based on their inherent classical concepts). My personal take is that we will be forced to accept much weirder 'tools' than virtual particles to describe reality at a deeper level.

Virtual particles make sense only at a very superficial level comparable to a billiard ball view of quantum particles. Both are very inadequate to describe reality.

Agreed but how do you propose we describe reality if not in classical-like, approximate concepts?

 

[Maui]

if something can happen in quantum physics it happens.

re: bolded... QM doesn't say that, although you could argue for that the MWI does... not in the same universe however.

So what is it that cannot happen to a quantum system, given enough time?

Virtual Particles are just a function of the approach you take, and shouldn't be confused with nature.

All classical models of reality are fundamentally a function of the approach you take and more or less a crude approximation to what Nature is. Good way to kill the thread.

 

[tom.stoer]

What Tom sees as meaningless and nonsense, is described as general feature (on page 2) of the world in this http://scipp.ucsc.edu/~dine/ph217/wilczek.pdf" of quantum field theory by Frank Wilczek.

...

Zee calls it one of the most profound conceptual advances in physics, Wilczek a general feature of the world

I am sorry to say that but unfortunately Zee and Wilczek (and others) are addressing laymen with a very limited picture of QFT. I am pretty sure that they would agree to most statements we are making here, namely to the fact that virtual particles are artifacts of perturbation theory and means just scratching the surface of modern QFT. It is a pitty that virtual particles (in popular science) and perturbation theory (in introductory textbooks) are so much promoted. I guess this is due to the fact that one can draw nice diagrams and is ready to do some calculations rather quickly. So one could get the impression that this is QFT - it is NOT! (even from "experts" you can hear that perturbation theory is a way to define QFT - unfortunately this is not only missleading but simply wrong in most cases; I would go even further and say that this partially hinders progress in science; looking at papers where four-loop integrals have been calculated I am wondering why wasting time with splitting hairs instead of doing something reasonable).

In calculus nobody would say that Taylor expansion is calculus; it's just one tool that applies to a certain problem space and fails dramatically for others.

But I think it doesn'tmake much sense to repeat myself (and others) b/c all why I am saying in this post has been said over and over again but has not been noticed by you.

 

[A. Neumaier]

Could you elaborate on this? For ordinary numbers, if we define the exponential in terms of a Taylor expansion, the radius of convergence is infinite. I wonder what is different for operators?
(I acknowledge that even if exp(-iHt) itself is well-defined in terms of a Taylor expansion, defining the expectation value <exp(-iHt)> using the same approach can easily fail.)

An operator series
f(A)= sum f_k A^k
can be given mathematical sense iff ||A|| is smaller than the convergence radius. if the convergence radius is infinite, this means that ||A|| has to be bounded.

 

[A. Neumaier]

kexue, the only mention Peskin makes of virtual particles is …

To describe this transfer of momentum, we say that a
"virtual photon" passes between the positive charge and the electron.
The virtual photon carries

Energy < (momentum) x c

so formally it has negative mass. There is even a sense in which it
is transferred instantaneously or even goes backward in time, although other electrodynamic effects add to this one so that there is no violation
of causality.

The virtual photon is not a real particle, but it is certainly real, in the sense that the electron really does change its momentum in the encounter.​

(btw, doesn't he mean imaginary mass rather than negative mass?)

Yes. This shows how sloppy Zeh is, and that his informal discussion cannot be taken at face value but must be interpreted in the light of actual formulas...

 

[nismaratwork]

So what is it that cannot happen to a quantum system, given enough time?

There is a difference between CAN happen, and WILL happen... either way that isn't relevant outside of the MWI.

All classical models of reality are fundamentally a function of the approach you take and more or less a crude approximation to what Nature is. Good way to kill the thread.

Except that isn't remotely what I said or meant. I was simply saying that we define real objects in nature as having criteria that virtual particles lack, not that all theories are approximations. Virtual particles aren't a theory or model of reality... they're just part of one way that you can work through a problem. As for classical models... we're not discussing any here.

 

[nismaratwork]

I am sorry to say that but unfortunately Zee and Wilczek (and others) are addressing laymen with a very limited picture of QFT. I am pretty sure that they would agree to most statements we are making here, namely to the fact that virtual particles are artifacts of perturbation theory and means just scratching the surface of modern QFT. It is a pitty that virtual particles (in popular science) and perturbation theory (in introductory textbooks) are so much promoted. I guess this is due to the fact that one can draw nice diagrams and is ready to do some calculations rather quickly. So one could get the impression that this is QFT - it is NOT! (even from "experts" you can hear that perturbation theory is a way to define QFT - unfortunately this is not only missleading but simply wrong in most cases; I would go even further and say that this partially hinders progress in science; looking at papers where four-loop integrals have been calculated I am wondering why wasting time with splitting hairs instead of doing something reasonable).

In calculus nobody would say that Taylor expansion is calculus; it's just one tool that applies to a certain problem space and fails dramatically for others.

But I think it doesn'tmake much sense to repeat myself (and others) b/c all why I am saying in this post has been said over and over again but has not been noticed by you.

It's hard to argue with someone who is utterly dogmatic, especially when their standard of proof is based on some abstract notion of collecting quotes rather than an understanding of the sceince.

 

[A. Neumaier]

Agreed but how do you propose we describe reality if not in classical-like, approximate concepts?

reality in physics (even quantum physics) is defined in terms of measurability. What is measurable in principle is real from the point of view of physics.

The relation between measurement and quantum theory is slightly nontrivial because of the probabilistic nature of the predictions, but this is not too much different from the
probabilisitic nature of measurements in classical physics.

 

[nismaratwork]

reality in physics (even quantum physics) is defined in terms of measurability. What is measurable in principle is real from the point of view of physics.

The relation between measurement and quantum theory is slightly nontrivial because of the probabilistic nature of the predictions, but this is not too much different from the
probabilisitic nature of measurements in classical physics.

re: bolded portion: Which is good, and obvious intuitively since our everyday world isn't composed of what would seem to us like quantum madness.

 

[kexue]

reality in physics (even quantum physics) is defined in terms of measurability. What is measurable in principle is real from the point of view of physics.

The relation between measurement and quantum theory is slightly nontrivial because of the probabilistic nature of the predictions, but this is not too much different from the
probabilisitic nature of measurements in classical physics.

Again https://www.physicsforums.com/showpost.php?p=3030669&postcount=172" to this.

 

[weejee]

An operator series
f(A)= sum f_k A^k
can be given mathematical sense iff ||A|| is smaller than the convergence radius. if the convergence radius is infinite, this means that ||A|| has to be bounded.

Thank you for the reply.
I get the point, but I'm still unsure about one thing.

Is it that the exponential (in terms of a Taylor expansion) is ill defined for all unbounded operators, or is it still well-defined for certain kinds of them. If so, is there a criterion to distinguish them?

The reason I raise this question is that if we apply this condition strictly, even something like the time-evolution operator of a quantum harmonic oscillator is not well-defined.

 

[A. Neumaier]

I'm still unsure about one thing.

Is it that the exponential (in terms of a Taylor expansion) is ill defined for all unbounded operators, or is it still well-defined for certain kinds of them. If so, is there a criterion to distinguish them?.

The exponential is well-defined in many cases when the Taylor series does not converge.
A better definition of exp(A) is as the solution of the differential equation A'(t)=A(t)
with A(0)=1, whnever one can show that this has a unique solution.
a

 

[kexue]

I am sorry to say that but unfortunately Zee and Wilczek (and others) are addressing laymen with a very limited picture of QFT.

No Tom, they are not addressing laymen. Both are not laymen expositions. They addressing physicists.

In calculus nobody would say that Taylor expansion is calculus; it's just one tool that applies to a certain problem space and fails dramatically for others.

Quantum physics is not calculus. Again, I refer you to https://www.physicsforums.com/showpost.php?p=3030669&postcount=172", and must ask you once more: Do you consider correct formulae for observable probabilities as "real"?Here for your convenience again https://www.physicsforums.com/showpost.php?p=3019831&postcount=74" from post 74, where he states the same thing very clearly:They "are really out there" in the sense that their contribution certainly affects the amplitudes of particle transitions.

No nuances here.

 

[sheaf]

What Tom sees as meaningless and nonsense, is described as general feature (on page 2) of the world in this http://scipp.ucsc.edu/~dine/ph217/wilczek.pdf" of quantum field theory by Frank Wilczek.

On page 3:...the association of forces and interactions with particle exchange... with the correspondence of fields and particles, as it arises in quantum field theory, Maxwell discovery corresponds to the excitence of photons, and the generation of forces by intermediary fields corresponds to the exchange of virtual particles...the association of forces (or, more generally, with interactions) with exchange of particles is a general feature of quantum field theory

Zee calls it one of the most profound conceptual advances in physics, Wilczek a general feature of the world

Tom says it is meaningless and nonsense, A. Neumaier says it explains nothing

Well, what do other PF members think? Please join the discussion everybody! Don't be shy.

I'm no expert on QFT, but I've always thought of virtual particles (meaning the 'not-necessarily-on-shell' internal lines) as a heuristic to help visualise the mathematics. So I'm on the side of "they don't qualify as 'physically real' by any definition of 'physically real' which I would use". For example a real photon can make a detector click, so qualifies as physically real for me but a virtual photon cannot.

Not sure if this has been mentioned (rather a long thread !) but another aspect of the arbitrariness of virtual particles comes out in the regularization procedure. If I were to think of a virtual particle as real then I could redefine it out of existence by choosing a lower cutoff !

 

[tiny-tim]

epicycles are real?

Again https://www.physicsforums.com/showpost.php?p=3030669&postcount=172" to this.

from #172 …

I say that something that predicts and explains with astonishing precision many empirical observations

so do epicycles … so why aren't they real, on that criterion?

epicycles (which in modern language would be a geometrical approximation series, or perhaps a Fourier decomposition, of an orbit) explain orbits perfectly, and require considerably less adjustment than the renormalisation adjustment required of virtual particles!

mathematical models are supposed to predict physics … epicycles are only the most obvious members of a huge class of concepts queuing up for admission to your "reality club"!

and at least epicycles are predicted by the maths to each have a specific location …

but where are your virtual particles located? (according to the maths) ​

… and which is allowed or even demanded by the laws of (quantum) physics

i have no idea what you mean by this … surely if something "predicts and explains with astonishing precision many empirical observations", it has to be allowed by the laws of physics?

… and in addition gives a beautiful, coherent and intuitive picture of how nature works, I say this is real!

what is beautiful or intuitive about having to assume the existence of a infinite sea of virtual particles all of which take part in every interaction, despite mostly being nowhere near the locality of the interaction?? (which btw is totally contradictory to what your hero Wilczek describes as a "characteristic core idea" of field theory: that all interactions are local (ie not at a distance))

Virtual particles are`really there' … implicitly.

whatever does that mean?!

finally (i repeat, since you still haven't answered) … do you say that your real "virtual particles" are particles?

(and if not, what characteristics or location do they have?)​

Do you consider correct formulae for observable probabilities as "real"?

how can a formula be real?

in e = mc², the energy e is real, the mass m is real, and arguably c is real …

but e = mc² is only a formula: it can be true or not true, and it can relate things that are real, but it can't itself be real

 

[kexue]

I'm no expert on QFT, but I've always thought of virtual particles (meaning the 'not-necessarily-on-shell' internal lines) as a heuristic to help visualise the mathematics. So I'm on the side of "they don't qualify as 'physically real' by any definition of 'physically real' which I would use". For example a real photon can make a detector click, so qualifies as physically real for me but a virtual photon cannot.

Not sure if this has been mentioned (rather a long thread !) but another aspect of the arbitrariness of virtual particles comes out in the regularization procedure. If I were to think of a virtual particle as real then I could redefine it out of existence by choosing a lower cutoff !

Long thread, indeed. Have you read https://www.physicsforums.com/showpost.php?p=3030512&postcount=169"?

 

[sheaf]

You refer to selfadjoint's post as an alternative to my proposal that a virtual particle is an internal line:

Here's the idea. In quantum mechanics nothing is really real unless you can observe it or measure it. In order to be observable, a particle has to have some minimum amount of energy for some minimum amount of time; this comes out of the uncertainty principle that says the product of those two things has to be bigger than a certain number.

Highlighting mine. Here he has given his definition of "real".

So it's possible to conceive of a particle whose energy is not big enough or whose lifetime is not long enough to permit a true quantum measurement, but still both of them could be greater than zero. The world could be full of such particles, and the measurements would never show it.

Referring to the defintion in the previous paragraph, these particles are not real because "the measurements would never show it".

Well, quantum field theory takes those particles seriously. It says they interact with observable particles, for example they make the electron which emits and absorbs them a bit heavier, and a bit more sluggish in motion, than it would be if they didn't exist.

Furthermore, QFT says that the virtual particles are the ones that carry the forces. For example with photons, the "real" photons make light, and other forms of electromagnetic radiation, but the virtual photons carry the electric force; a charged particle is charged because it emits virtual photons. And the other bosons, that carry the weak and strong forces, behave the same way. Real particles interact with each other by exchanging virtual bosons.

This is the story quantum field theory tells, and the justification, the reason you should at least consider beliving in it, is that it makes fantiastically correct predictions. That bit above where I said that interacting with virtual particles made the electron sluggish? It's called the anomalous moment of the electron, and the prediction, based on virtual particles, matches experiment to six decimal places.

For me, this is simply saying that if I do the mathematics, which can be heuristically described in terms of virtual particles, then I get predictions of real effects which are borne out by experiment.

 

[kexue]

Tiny-tim, I do not know what you are playing here, but have you read what I wrote boldface in https://www.physicsforums.com/showpost.php?p=3030669&postcount=172"?

I can not make it any clearer in what I think about the "reality" of "virtual" particles.

 

[kexue]

Sheaf, please read the thread at least partly before commenting. Otherwise, we go in cycles.

Virtual particles can not be measured *directly*, that's their definition, yes.

Why you should take them seriously nevertheless was brougth forward here many, many, many times.

 

[tiny-tim]

Tiny-tim, I do not know what you are playing here, but have you read what I wrote boldface in https://www.physicsforums.com/showpost.php?p=3030669&postcount=172"?

yes, i read it at the time, but it's three rambling paragraphs (ending with the extraordinary "Virtual particles are`really there' … implicitly"), and i still can't make out what it all means

people ask you very simple questions, and you either don't reply at all or you ramble on without really settling anything

writing at length in bold is no substitute for clarity

… though i think i can detect some virtual clarity!

 

[kexue]

yes, i read it at the time, but it's three rambling paragraphs (ending with the extraordinary "Virtual particles are`really there' … implicitly"), and i still can't make out what it all means

people ask you very simple questions, and you either don't reply at all or you ramble on without really settling anything

Tiny-tim, what questions you got? Maybe ones I have not answered yet.

Can you formulate them again, please? (Perhaps with minimum of one icon in this post.)