# Existence of Virtual Particles

Selectron
As I understand it, according to the Copenhagen interpretation of QM, nothing can be said to exist until it is observed. I have also read that it is impossible to observe virtual particles in an experiment.

How is it then that virtual particles can be said to exist?

Kruger
They exist because there is an uncertainty in time and energy: d(E)d(t)>=h(bar)/2.
To measure an energy d(E) you need the time d(t) to measure a particle.
Particles that don't obey this inequality can't thus be measured.

Antiphon
Selectron said:
As I understand it, according to the Copenhagen interpretation of QM, nothing can be said to exist until it is observed. I have also read that it is impossible to observe virtual particles in an experiment.

How is it then that virtual particles can be said to exist?

This is a common misundertanding. CI says that particular measurable
features don't exist until they are meaured because the measurement
process forces the system into that particular state. It does not
mean that the object (quantum) does not exist until the measurement.

Virtual particles themselves can't be detected but they do have measurable
effects on atomic systems.

Mentor
Selectron said:
How is it then that virtual particles can be said to exist?

Virtual particles exist only as metaphors for certain mathematical constructions that occur when you calculate the probability of an interaction process in quantum field theory.

Briefly, when you set up the equations for an interaction between two particles, you get a complex multiple integral which cannot be evaluated by normal means. However, when the interaction is "weak" such as with the electromagnetic and weak nuclear interactions, you can do a "perturbation expansion" which is analogous to a power-series expansion which people sometimes use to evaluate tricky functions or integrals. You get a sum of an infinite series of terms. Each term is an integral of a product of several factors.

Feynman noticed that he could associate each term with a little diagram whose parts corresponded to the factors in that term, and he came up with a simple set of rules for constructing all of the diagrams (terms) associated with a particular interaction process. These of course are his famous "Feynman diagrams".

Some of these terms have energy and momentum associated with them, but do not correspond to any of the real particles coming into or out of the interaction. They do correspond to lines in Feynman diagrams, just like the real particles do. So we call them "virtual particles".

Therefore, virtual particles don't exist in the same sense that real particles do. That's why we call them "virtual", after all! Most of the conceptual problems people have with virtual particles come from trying to make them into "real" particles.

marlon
jtbell said:
Some of these terms have energy and momentum associated with them, but do not correspond to any of the real particles coming into or out of the interaction. They do correspond to lines in Feynman diagrams, just like the real particles do. So we call them "virtual particles".
I do not think this entirely accurate. Virtual particles are off mass shell (ie they do not respect the Einstein energy relationship). In terms of Feynman diagrammatics, virtual particles correspond to the INTERNAL lines of feynmann diagrams (ie lines that start at one vertex and end at another/same vertex point). Virtual particle do have momentum, so they do not have momentum-uncertainty. The HUP learns us that virtual particles really are everywhere in space. However, and this is where i disagree with you, virtual particles do NOT have a definite energy value because the very reason they exist is the energy uncertainty.

marlon

marlon
Selectron said:
read that it is impossible to observe virtual particles in an experiment.

How is it then that virtual particles can be said to exist?

Ever heard of the casimir effect ? i suggest you check out this effect on the Wikipedia website or do a general search in this forum. We have debated this issue many times before.

regards
marlon

I agree with jtbell. Arguably, one of the first uses of the virtual notion was in descriptions of radioactive decay in which, say, the electron in nuclear beta decay goes through a potential barrier. In the barrier, the wave functions are combinations of exp(+/- g*x) functions, not plane waves, where g is roughly x*SQRT(V - E), when the energy E is less than the potential V. in the barrier the KE is negative, unlike the emitted electron's + KE outside the nucleus.Effectively, the electron is sortof bound in the barrier area. It's not free, and it's not really bound, so we call it "virtual". As they often do, physicists use figurative and metaphorical language to describe the contents of tricky math and tricky physics, and that's why we have virtual particles.

In quantum dynamics of any sort, the idea of virtual particles, virtual states makes the execution and interpretaion of perturbation theory easier and clearer.

Are virtual particles real? You tell me what real is, and I'll take a crack. Similarly, what's to exist? Do messages exist between the lines?

Regards,
Reilly Atkinson

marlon
reilly said:
I agree with jtbell. Arguably, one of the first uses of the virtual notion was in descriptions of radioactive decay in which, say, the electron in nuclear beta decay goes through a potential barrier. In the barrier, the wave functions are combinations of exp(+/- g*x) functions, not plane waves, where g is roughly x*SQRT(V - E), when the energy E is less than the potential V. in the barrier the KE is negative, unlike the emitted electron's + KE outside the nucleus.Effectively, the electron is sortof bound in the barrier area. It's not free, and it's not really bound, so we call it "virtual". As they often do, physicists use figurative and metaphorical language to describe the contents of tricky math and tricky physics, and that's why we have virtual particles.

I do not follow here. the electron in beta decay comes out of the vacuum and exists because there was energy available that gave this electron a legitimate reason to exist, if you will. It is this process that announced the advent of QFT because of 'this electron that seemed to appear out of the atomic nucleus'

The tunneling-argument, i also do not get. Isn't energy conserved in tunneling ? The tunneling particle stays at the same energy state and tunnels into the vacuum state that is also at the same energy (in the form of its KE).

So, if energy conservation is not violated, then how can you call this electron virtual ?

A particle is virtual if :
1) it corresponds to an internal Feynman line
and
2) if it is off mass shell

Virtual particle arise in interactions between real particles or as 'vaccuum fluctuations'...

What about the Casimir effect as a proof that virtual particles do indeed exist ?

regards
marlon

marlon - My initial argument goes back to George Gamow, if I recall correctly, in the late twenties or early thirties. At roughly the same time Fermi introduced his famous phenomological 4-point interaction for beta decay, which has evolved into vector boson mediated beta decay. Electrons in beta decay show no signs of being created from the vacuum -- this from 60 or 70 years of experimental evidence, there seem always to be other leptons or hadrons around.

The argument I use applies equally well to alpha decay, which is a better example, and was the subject of the original tunneling work, Energy conservation? Important in beta decay dynamics to be sure, but not so much in interpretation. There are many nuclear physics books, Blatt and Weiskopf is always worth reading as an example, and Kemble's QM text, and oldie but goodie. Roughly speaking, first think of a scattering situation with the neutron or proton inside a nucleus being the source of the beta particle, or the internal fission of a nucleus into a daughter nucleus and an alpha particle as the alpha's source. Then, again approximately, the standard analysis of scattering through a barrier takes you where you want to go.

Think about non-rel Coloumb scattering of an electron from a central potential. You can solve the problem exactly, or you can do perturbation theory. Virtual particles play no role in the exact solution. But the perturbative solution is all about virtual particles. Go figure.

As jtbell has noted, as have I in earlier posts, it's all about metaphors.

Regards,
Reilly Atkinson

PS -- Any corrections to my inadequate recall of history would be appreciated

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dgiznya

Hawking Radiation is a sort of experiment for observing virtual particles.
If a photon pair is created from vacuum fluctuations on the event horizon of a black hole, the photon on the outside of the event horizon (virtual particle) will survive and be seen as radiation. The photon on the inside of the event horizon will not of course be seen.

Kruger
If a photon pair is created from vacuum fluctuations on the event horizon of a black hole, the photon on the outside of the event horizon (virtual particle) will survive and be seen as radiation. The photon on the inside of the event horizon will not of course be seen.

This is incorrect. Virtual photons can appear alone in vacuum, without a another virtual photon. Only virtual charged particles must occur as particle antiparticle pair, like electron and positron.

ehh, I'm confused.

Question: momentum conservation has to be sadisfied all the time. Why can then a virtual photon (from vacuum fluctuation) exist allone?

dgiznya
photons

Photons can and do occur in pairs. (Not that they have to.)
Photons are their own antiparticles.

The original inquiry regarded doing an experiment to see virtual particles.
I was trying to give and example.

Kruger
Photons don't occur in pairs in vacuum fluctuation. Why should they do this?

marlon
reilly said:
The argument I use applies equally well to alpha decay,
This is a QM problem NOT a QFT problem. You cannot compare alpha and beta decay like the way you try to do because there are fundamentally different in nature. In beta decay you really have the electron being created 'out of nothing' thanks to the present energy in the atomic nucleus. Alpha decay is indeed a standard example of QM tunneling. In QM, when the initial states evolves to the final state, a series of intermediate stages have been passed (well, you know...because of perturbationtheory and stuff...). each such intermediate state is called virtual because it does not respect energy conservation : energy becomes uncertain during a period of time as predicted by the Heisnberg uncertainty principle.

One cannot talk about virtual particles here because we are not working in a QFT-world. Ofcourse it is clear that in QFT, such transitional states do correspond to virtual particles, but my point is that alpha decay is a bad example in this context.

You can solve the problem exactly, or you can do perturbation theory. Virtual particles play no role in the exact solution. But the perturbative solution is all about virtual particles. Go figure.
I am sorry, what do you mean ? If you can solve a problem exactly, then why use perturbation theory. Besides, once you use perturbation theory (IN QM) you need to know that these virtual stages are only intermediate and they are not present in the final state. I think i am missing your point here.

regards
marlon

Marlon -- I guess I got confused: I learned QFT in a course called, Advanced Quantum Theory. As far as I know, Quantum Field Theory is still, according to most accounts, a subfield of Quantum Theory or Quantum Mechanics, if you will. But, things change...

Exactly how is an electron created from the vacuum?

The canonical perspective is that the decaying particle is transformed into the decay products, either from a contact interaction (Fermi) or from interaction with a vector boson. The latter somewhat applies to alpha decay -- strong hadronic forces, Coulomb forces all play a role. The alpha has to penetrate a potential barrier, as does the electron once it is in play. (The idea of a potential barrier does not directly enter into the decay processes described by electro-weak theory. But it does once the nuclear stuff shows up.)

The Coulomb scattering: there are many ways to skin a cat. (I'm trying to get across the point that the 1/(E-H) terms in pert theory represent virtual particles or virtual states. So, it is entirely legitimate to think of a scattering electron as a infinite superposition of virtual electrons. Whether it is useful to do so is another matter. )

Regards,
Reilly Atkinson

marlon
reilly said:
Exactly how is an electron created from the vacuum?

Well, when i beware that this is not just a vacuum we are talking about. I mean, it really are the energies present in the actual decay that are responsible for the creation of the electron 'out of nothing'

This is just the weak interaction and to answer your question you can look at : these feynman diagrams ...

Check out the figure on the left of the four diagrams that are listed. When i refer to 'the present energies' i really mean the energy that is necessary to give the W- it's legitimate reason to exist and turn the neutro into the proton. The W- is virtual in this case because it is intermediate.

regards
marlon

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Marlon -- With all due respect, the diagram you suggest I peruse is exactly what I was talking about when I said something about a vector boson mitigating beta decay. It is virtually (sorry 'bout that) identical to a photo-pair production or photoproduction of pions, diagram. I do not see a diagram with a vacuum state included. So, what am I missing? What's the quantitative role of the vacuum in beta decay, free or bound?
Regards,
Reilly Atkinson

marlon
reilly said:
Marlon -- With all due respect, the diagram you suggest I peruse is exactly what I was talking about when I said something about a vector boson mitigating beta decay. It is virtually (sorry 'bout that) identical to a photo-pair production or photoproduction of pions, diagram. I do not see a diagram with a vacuum state included. So, what am I missing? What's the quantitative role of the vacuum in beta decay, free or bound?
Regards,
Reilly Atkinson
But why are you always asking about vacuum-states ? Are you talking about vacuum-fluctuations ? They have nothing to do with it.

Again, my point is that this beta particle seems to be created out of nothing (this is not the same as a vacuum fluctuation though) because it seems to be coming out the neutron (well, the atomic nucleus to be exact) and this is ofcourse not the case. It is thanks to the energy associated with the W- vector boson that this electron exists and respects all conservation laws at hand. That is all i ever said...

marlon

Marlon -- I'm referring to your earlier statement, "the electron in beta decay comes out of the vacuum " This, to me, is a novel idea with which I'm quite unfamiliar. All I'm doing is taking your statement literally. Hence my question: if this is true, then what specific role does the vacuum play in beta decay?
Regards,
Reilly Atkinson

marlon
reilly said:
Marlon -- I'm referring to your earlier statement, "the electron in beta decay comes out of the vacuum "

Out of the vacuum means "coming out of nothing" thanks to present energy.

To be more specific, the beta electron is the result of the neutron being converted into a proton. To respect conservation laws we need an intermediate vector boson that is 'converted' in the beta electron and the anti neutrino. hence looking at this proces, one could think of the electron being created out of the neutron or even out of the atomic nucleus. This is ofcourse not the case since that implies the electron was already present in the nucleus (this is what people first assumed for a while). thus, the electron is created out of "nothing"...

marlon

dgiznya
photon pairs

Kruger said:
Photons don't occur in pairs in vacuum fluctuation. Why should they do this?

See Physics Today August 2005 pg. 20

Kruger
Can you tell me this a little bit more precisely? What "Physics Today" you mean?

Mentor
"Physics Today" is a monthly magazine for members of the American Physical Society. You can find it in most college or university libraries, in the USA at least. Or ask one of your physics professors; he/she probably gets it.

marlon said:

Out of the vacuum means "coming out of nothing" thanks to present energy.

To be more specific, the beta electron is the result of the neutron being converted into a proton. To respect conservation laws we need an intermediate vector boson that is 'converted' in the beta electron and the anti neutrino. hence looking at this proces, one could think of the electron being created out of the neutron or even out of the atomic nucleus. This is ofcourse not the case since that implies the electron was already present in the nucleus (this is what people first assumed for a while). thus, the electron is created out of "nothing"...

marlon

If I'm not mistaken, the weak interaction interaction says that the neutron has a non-zero overlap with a proton-neutrino-electron state. This says to me that indeed the electron is "contained" in the neutron.

Regards,
Reilly Atkinson