# Virtual particles coming into existence

## Main Question or Discussion Point

from what i understand they pop into and out of existence because + 1 - 1 = 0 and because quantum mechanics... and thats the same reason we have matter in the first place, right? because we had anti matter and matter (from virtual particles, right?) in the beginning of the observable universe...

are these the same processes? am i completely misunderstanding what a virtual particle is? im wondering... if more matter was created then anti-matter in the beginning then why arent virtual particles creating more matter than anti matter right now?

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strangerep
am i completely misunderstanding what a virtual particle is?
Yes.

Virtual particles are not real. They are part of a diagrammatic method to calculate scattering amplitudes in quantum field theory. I.e., artefacts of the mathematics of perturbation approximations.

There's an endless number of older PF threads about virtual particles, much of it frustrating. Nevertheless, you should probably search back through some of these before growing your own.

strangerep,
I've wondered about these artifacts of the math.
When a pair of virtual particles appear in the math, are they subject to the same math as if a pair real particles?

If a similar pair of real particles separated from a single point, one might observe that point to continue to be coincident with the pair's subsequent center of mass. This would suggest that the angle between the two velocities was 180 degrees and the separation point was at rest with respect to the observer.

If one observed both particles moving away from their separation point at an angle unequal to 180 degrees, this would suggest that the separation point had some velocity with respect to the observer so that the pair's COM would have a velocity relative to the appearance point, and so not continuing to be coincident with it..

Now, if the "separation point" above is replaced for virtual particles by whatever the generating math entity that does so, does the math also follow to account for a this generating entity to include a velocity attribute at the event of creation of a virtual pair?

Or is the math for virtual pairs like c... where all virtual pairs are defined or assumed to emerge from a point at rest with respect to all observers? I suspect this might be so because I'm thinking that otherwise the math would be assuming an absolute space from which all virtual pairs appeared, and any subsequent velocity between the pair's COM and the point of separation could be attributed to absolute relative motion of the observer, therefore violating fundamental assumptions of relativity.

Or is the math for virtual pairs just verbal / logical / categorical and not subject to the usual implied mechanics / geometry?

I hope you understand what I mean...

Nugatory
Mentor
Now, if the "separation point" above is replaced for virtual particles by whatever the generating math entity that does so, does the math also follow to account for a this generating entity to include a velocity attribute at the event of creation of a virtual pair?
The question cannot arise because you cannot observe virtual particles - if you could, they wouldn't be virtual.

It's easy to say what virtual particles are not (pretty much anything you've been told outside of a QFT text is wrong) but not so easy to say what they are. You could do worse than https://www.amazon.com/dp/B00MN96BHW/?tag=pfamazon01-20, but the mathematical price of admission is fairly steep.

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ShayanJ
Gold Member
Sorry for inetrrupting but because I'm not a native speaker, I sometimes have problem interpreting some sentences.
You could do worse than https://www.amazon.com/dp/B00MN96BHW/?tag=pfamazon01-20, but the mathematical price of admission is fairly steep.
Does this mean that you think that book treats the subject in a bad manner?

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Nugatory
Mentor
Does this mean that you think that book treats the subject in a bad manner?
I think the book treats its subject matter very well. A reader who lacks an adequate math background will find it difficult to understand, but that will be true of any treatment of QFT.

The question cannot arise because you cannot observe virtual particles - if you could, they wouldn't be virtual.
I was careful to restrict "observation" to the case of real pairs. The purpose of mentioning the real pairs was to establish the idea of the geometric locations of the point of separation and COM of the real pair, in preparation for asking about the analogous values or relations of the math artifacts.

The question can arise because I am asking something about the math of virtual particles, not observations of them. I am asking if when the virtual particles arise in the math, does the model give them an attribute of a point of origin (a separation point from which they emerge) and whether that point of origin may have an attribute of velocity allowing the geometric line between the virtual pair to not cross their point of origin... this has nothing to do with experiments or observation or their existential reality; only asking at a very high level if the artifacts in the math have these kind of modeled properties in the math itself.

The "Properties" section of the Wikipedia entry for Virtual particle includes these phrases:

"Virtual particles occur in combinations..."
"...appear to occur close to one another in time..."
"...calculated in terms of exchanges of virtual particles..."
"...four-momentum q..."
"...kinetic energy may not have the usual relationship to velocity–indeed, it can be negative"
"...virtual particles of larger mass..."
These suggest that the math includes some aspects of location, time, distance, velocity, mass, momentum, kinetic energy, and mass, perhaps different than their classical counterparts but still acting as values and relations in the model. Clearly none of these are observed, but the math is using these to model something and it seems that these properties must answer about how the model itself represents the pairs conceptually geometrically.

vanhees71
Gold Member
2019 Award
Hm, after a long time I realize that there's still the possibility to find really bad articles in the English Wikipedia :-(. As already stressed by strangerep, it's simply wrong to think about the internal lines of Feynman diagrams, which are not a space-time picture of something really happening in a literal sense, but a very clever short-hand (and still very concise) notation for pretty complicated mathematical expressions to evaluate the S-matrix elements (cross sections) for scattering processes in quantum field theory. In relativistic theory, it even doesn't make sense to ask what happens "during the collision" in terms of particles. Particles are defined as asymptotic free states (let's not discuss the difficult topic what are the correct asymptotic states for theories with massless field-degrees of freedom like QED, where the true asymptotic states are not the single-particle Fock states but including coherent states of soft photons in addition). The attempt to define an observable like a "particle" or "photon" number for transient states, is doomed by inconsistencies and can lead to very misleading results. As an example in a pretty simple case, see

F. Michler, H. van Hees, D. D. Dietrich, S. Leupold, C. Greiner, Non-equilibrium photon production arising from the chiral mass shift
Ann. Phys. 336, 331 (2013)
http://arxiv.org/abs/arXiv:1208.6565

Thanks vanhees71,
I know this is a tough complex subject.

From what you wrote, I must wonder... are these artifacts of the math really mathematical or more like verbal / logical / categorical relations that augment the math, may appear as symbolic signs in the math, but are not really mathematical in current understanding of them? What I mean is that the Wiki page has a long list of physical manifestations in which virtual particles are employed to characterize and complete the current understanding... virtual particles seem to be serving as some type of quasi-mathematical placeholder for the time being.

I'll refrain from asking more... I don't have the background for the right questions.

strangerep
are these artifacts of the math really mathematical or more like verbal / logical / categorical relations that augment the math, may appear as symbolic signs in the math, but are not really mathematical in current understanding of them?
All maths is basically sequences of logical reasoning. One invents an extensive library of concise symbols and notations to decrease what would otherwise be immense verbiage.

Study some basic perturbation theory in elementary classical mechanics to see the terms.

bhobba
Mentor
From what you wrote, I must wonder... are these artifacts of the math really mathematical or more like verbal / logical / categorical relations that augment the math, may appear as symbolic signs in the math, but are not really mathematical in current understanding of them?
Its the way you interpret the math.

It results from a series expansion of certain terms (called a Dyson series) and how one pictorially interprets it in Feynman diagrams:
http://en.wikipedia.org/wiki/Dyson_series

Clem expressed it succinctly:
'Virtual particles arise as mathematical excitations if 'perturbation theory' is used in a calculation. They have no physical reality, which is why they are called 'virtual'. If perturbation theory is not used, there are usually no virtual particles.'

The Gifted Amateur book explains it very well. All I can do is refer you to it.

It is mathematically advanced but undertandable with effort. It's rather unique in that you dont need advanced QM knowledge the following background will suffice:
https://www.amazon.com/dp/0471827223/?tag=pfamazon01-20
https://www.amazon.com/dp/0465075681/?tag=pfamazon01-20
https://www.amazon.com/dp/0465036678/?tag=pfamazon01-20

There are video lectures as well:
http://theoreticalminimum.com/

It will take time, effort and concentration - but is doable. If you run into trouble (you probably will - that's practically a given) post here - that's what this forum is about. Take your time - its not a race. At the end of it you will come away with a knowledge far far beyond popularisations, many of which simply confuse.

Thanks
Bill

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hi, but spontaneous emission is no more spontaneous rather stimulated emission by the interaction of zero point energy or vacuum fluctuations- and it is verified that decay time by spontaneous emisson can be altered in cavity i.e by changing dimension around matter -indirect evidence of vacuum field indeed someway confirm existence of virtual particles-

bhobba
Mentor
hi, but spontaneous emission is no more spontaneous rather stimulated emission by the interaction of zero point energy or vacuum fluctuations- and it is verified that decay time by spontaneous emisson can be altered in cavity i.e by changing dimension around matter -indirect evidence of vacuum field indeed someway confirm existence of virtual particles-
It's not indirect evidence because if you do the calculation without perturbation theory you get the same result.

Again I repeat what the link I gave said:
'Virtual particles arise as mathematical excitations if 'perturbation theory' is used in a calculation. They have no physical reality, which is why they are called 'virtual'. If perturbation theory is not used, there are usually no virtual particles.'

Virtual means - not real - what so hard to get about that? They are simply mathematical artefacts of the formalism used. Again it's pretty clear.

Thanks
Bill

agreed - but how can we explain vacuum field, vacuum fluctuations and zero point energy ( sorry i am very dumb in this subject)

bhobba
Mentor
agreed - but how can we explain vacuum field, vacuum fluctuations and zero point energy ( sorry i am very dumb in this subject)
The standard explanation - but without the statements such as this is indirect evidence virtual particles exist.

Thanks
Bill

vanhees71