A Do virtual particles interact with each other?

1. Dec 16, 2015

friend

Do separate instances of virtual pair production interact with each other. Say you have a virtual pair production of an electron and a positron; they separate and then come back together. What happens in the event that there is another occurrence of a virtual electron/positron pair production nearby the first? Can the electron of the first pair annihilate with the positron of the second pair? I suppose this would mean that the positron of the first pair is left to annihilate with the electron of the second pair, or perhaps some other positron of perhaps a third pair. Is there an electric potential between them? Is there a gravitational force between them?

More generally on average for all possible virtual particles of the vacuum energy, does the vacuum energy in a small volume of space have a force on an adjacent volume of space that pulls or pushes it? Is this due to the effects mentioned in the paragraph above? Thanks.

2. Dec 16, 2015

Staff: Mentor

Virtual particles aren't even real - they are just a pictorial representation of terms in what's called a Dyson series:

Another interesting thing is the series diverges. How to handle such is a story in itself that sheds light on many things in QM including where quantitisation comes from:

Thanks
Bill

3. Dec 16, 2015

friend

As I recall, the vacuum energy is precisely that which is causing the universe to accelerate in its expansion. It's also called the cosmological constant, dark energy, the zero point energy, virtual particles, quantum fluctuations, etc. Doesn't this exactly mean that the virtual particles of the vacuum energy are causing adjacent parts of space to move away from each other (ever so slightly)? Doesn't this also mean that on the average that all the virtual particles in one differential volume of space are interacting with the virtual particles in an adjacent volume of space to moving these volumes away from each other? This seems like an obvious logical deduction. I don't know what the exact mechanism is for creating more space between the volumes that move away from each other. One thing is clear, if there is more space, then there are more virtual particles in that space.

4. Dec 16, 2015

Staff Emeritus
That's false. (Didn't Bhobba just tell you that?) There is no such thing as "more virtual particles" since they cannot be counted - you are never in a number eigenstate of them - and aren't even real.

5. Dec 17, 2015

friend

As I recall, and please correct me if I'm wrong, I remember reading somewhere, or perhaps in a video lecture, that fermions add negatively to the cosmological constant and bosons add positively (or is it visa versa?) One causes the universe to expand the other to contract. I agree that you can never really count how many virtual pairs there are in a volume of space. That would be like counting how many points of space there are in that volume. But if virtual pairs have any effect at all, then it would seem that more space would have more of them. Otherwise their density would decrease and have less effect on expansion. But that's not what we see. I guess what I'm asking is whether there is any thought that virtual pairs are a properties of space? I suppose that would be the same as asking whether the fields of QFT are a property of space? Thank you.

6. Dec 17, 2015

marz

I am confused by repeated statements that virtual particles are not real. If they were not real, then could someone please explain to me why did Steven Hawking use them to show that black holes evaporate ???

7. Dec 17, 2015

stevendaryl

Staff Emeritus
The calculation that shows that black holes radiate didn't use virtual particles, as I understand it. Hawking's description in terms of virtual particles was his attempt to give an intuitive way of thinking about it, but I don't think it was rigorous.

8. Dec 17, 2015

Staff: Mentor

He didn't. Here's what he did say: http://www.itp.uni-hannover.de/~giulini/papers/BlackHoleSeminar/Hawking_CMP_1975.pdf

I'm posting the link above mostly to make a point about the enormous gap between what you read in the popular press and the real thing; you may also want to give http://math.ucr.edu/home/baez/physics/Relativity/BlackHoles/hawking.html a quick read.

9. Dec 17, 2015

friend

Does the confusion about virtual particles arise only when talking about curved spacetime? Is it the case that the vacuum energy can be consistently described in terms of virtual pairs by all observers in flat spacetimes?

10. Dec 17, 2015

Staff: Mentor

The confusion arises due to the loose language used:
http://www.mat.univie.ac.at/~neum/physfaq/topics/virtreal

A Nugertory often says - anything you read about QFT outside a QFT textbook is likely wrong.

Its challenging and confronting when that happens, and you will find a number of very long threads that basically goes nowhere on it. The reason is people do not want to give up what they have read because it means they have to start their understanding again from scratch. They wiggle and squirm quoting this author and that.

It doesn't matter what you quote - the answer is still the same - they do not exist. Best to grasp that now rather than go down a path that leads nowhere.

Regarding the cosmological constant issue where empty space has a certain intrinsic energy again populist accounts do not tell the full story. As usual, science advisor John Baez gives the correct explanation:
http://www.mat.univie.ac.at/~neum/physfaq/topics/virtreal

Whenever you find something that confuses do a search on what John says. He is invariably correct.

Thanks
Bill

11. Dec 18, 2015

andresB

Since the error in relating any vacuum energy to the cosmological constant seems to be very big, it might be very possible that this is dea have something wrong .

12. Dec 18, 2015

friend

which says, "virtual particles occuring in computations _must_have disappeared from the formulas by the time the calculations lead to something that can be compared with experiment."

I totally agree. I think the issue is that the expectation value of any virtual particles is zero but the variance is not. The question is whether this non-zero variance has a physical effect.

Or is it possible that I am conflating two issues. I thought the Heisenberg Uncertainty Principle (HUP) allowed for a non-zero variance in the energy for a brief moment of time of various frequency modes of the various quantum fields, even though on the average the energy is zero. Isn't this exactly what virtual particles do? If so, then virtual particles have just as much physical reality as the HUP.

13. Dec 18, 2015

Staff: Mentor

No. They are what I said they are - things that appear in Feynman diagrams which is a pictorial representation of the Dyson series.

Don't fight against it - you wont get anywhere.

Thanks
Bill

14. Dec 18, 2015

friend

If you really feel strongly about your point of view, then perhaps you can do something to change the wikipedia article on quantum fluctuations which directly says that the HUP gives rise to the "creation of particle-antiparticle pairs of virtual particles".

Or is it more the case that you object to the particle description and would accept the picture of fluctuations in the quantum fields instead?

15. Dec 18, 2015

Staff: Mentor

Did you read the link I gave? Its not my view - its what the theory says:
'Virtual particles are an artifact of perturbation theory that give an intuitive (but if taken too far, misleading) interpretation for Feynman diagrams. More precisely, a virtual photon, say,is an internal photon line in one of the Feynman diagrams. But there is nothing real associated with it. Detectable photons are never virtual, but always real, 'dressed' photons. Virtual particles, and the Feynman diagrams they appear in, are just a visual tool of keeping track of the different terms in a formal expansion of scattering amplitudes into multi-dimensional integrals involving multiple propaators - the momenta of the virtual particles represent the integration variables. They have no meaning at all outside these integrals. They get out of mathematical existence once one changes the formula for computing a scattering amplitude.'

As a further nail in their coffin perturbation theory is not the only way to do calculations in QFT - it can also be one by so called Lattice Gauge Theory. When you do it that way they never even appear. They are simply an artefact of the perturbation methods used, having no actual existence whatsoever.

The Wikipedia article is an example of what I said. People give this quote and that quote, they squirm and do all sorts of things rather than accept the truth.

How does it happen? Starting out in QFT people like comfortable visualisable intuitive pictures. They are wrong - but that's the way its usually done.

Thanks
Bill

16. Dec 18, 2015

Staff: Mentor

There's a reason why wikipedia articles are not in general acceptable sources here - some are good, some are not so good. If you check out the talk page (a good idea before you trust any wikipedia article on an advanced science topic) for that one, you will see that it is among the not-so-good ones.

Wikipedia is a great resource as long as you're aware of its limitations, and one of its limitations is that it's not very good at subjects beyond the undergraduate level. Many of the experts here (and anecdotally, specialists in many other fields) have given up on editing wikipedia articles - you can fix them, but they don't stay fixed, and unlike Sisyphus we have a choice.

Last edited: Dec 18, 2015
17. Dec 18, 2015

friend

Yes, I read it. And after doing a specific search, I found no reference for the Heisenberg uncertainty principle, no reference for quantum fluctuations, nor quantum fields. This leads me to think the entire objection of the article is to the particle picture. And I'm not sure I am saying anything contrary to that article.

I'm presently watching a lecture series on QFT in curved spacetime at PSI, here. This is a relatively easy to follow introduction. He shows that the vacuum state in flat spacetime can be a thermal state in accelerating spacetime, the Unruh effect, etc. Here he shows how fluctuations in the quantum fields can be excited due to acceleration and produce "real" particles. If I recall correctly, he even uses the language of virtual particles for at least illustration purposes.

And what I read elsewhere is that quantum fluctuations in quantum fields were stretched to enormous proportions during cosmic inflation and produced differences in density in matter that created the galaxies. How more "real" can you get? It seems all real particles were once virtual particles disassociated from their partners due to one form of acceleration or another.

18. Dec 18, 2015

Staff Emeritus
We've seen this picture before. They always fight. They know the truth - they've read popularizations. <sigh>

19. Dec 18, 2015

friend

I'm willing to accept that virtual particles are a naive interpretation of the fluctuations of quantum fields. You seem to have the education to help clarify. Perhaps you can explain it. Does the Heisenberg uncertainty principle give rise to fluctuations about an expectation value of zero, for which these fluctuations still has some physical effects? Is there or is there not a zero point energy?

20. Dec 18, 2015

Staff Emeritus
Mighty kind of you. But that's not what they are. The word "fluctuation" - the key to that sentence - is simply not right.

21. Dec 18, 2015

Staff: Mentor

The theory predicts zero point energy. Its a rather interesting value - wait for it - its infinity. This was one of the first indications of a sickness in QFT that re-normalisation is required to fix. How does renormalisation work? I wrote an introductory paper about it:

In this case however re-normalisation isnt strictly required to fix it - one can use what's called normal ordering:
https://en.wikipedia.org/wiki/Normal_order

If you go the re-normalisation route and place the cut-off reasonably at the plank scale this gives a huge zero point energy - much larger than observed. This is the so called cosmological constant problem you likely have heard about:
http://math.ucr.edu/home/baez/vacuum.html

I will also repeat a bit of advise. When you run into issues where things are unclear - like virtual particles being discussed here - you can certainly post on this forum. But if you do a search on the issue for information about it by John Baez there is a good chance you will find it and he is a source you can trust 100% for sure.

Personally I prefer normal ordering - but its still a bit of a mystery.

Thanks
Bill

Last edited: Dec 18, 2015
22. Dec 19, 2015

friend

I think what I need is an explanation of the screening effect of the electron. I'm told that the charge of an electron we see at low energies is less than the bare electron charge seen at higher energies. This is because the virtual particles of the vacuum can be polarized and lessen the true value of bare electron charge. It seems polarization would have to be strictly a particle phenomena; how can you get dipoles out of waves? Is there an alternative interpretation of the screening effect that does not involve virtual particles? Thanks.

23. Dec 19, 2015

Staff: Mentor

See my paper on re-normalisation:
https://www.physicsforums.com/insights/renormalisation-needs-cutoff/

As the cutoff goes to infinity the bare (ie un-renormalised) coupling constant goes to infinity.

II's the same thing as the cutoff in QED (ie as you go to higher energy ie as you probe smaller distances) - goes to infinity - its coupling constant also goes to infinity. Even the renormalised quantities change due to the so called re-normalisation group flow:
http://arxiv.org/abs/hep-th/0212049

That is the correct explanation. The common intuitive one is the vacuum with virtual particles popping in and out of existence get 'separated' by the field and have a screening effect that is greater as you get closer. Its intuitive and appealing - but wrong. Still for a complex subject like QFT people like appealing pictures.

Thanks
Bill

24. Dec 19, 2015

friend

I'm not sure your article is relevant. As I understand it, renormalization applies to evaluating integrals, not to the constants inside the integrals. And the running of the coupling constants with higher energy seem to all go to the same value at grand unification, and are, thus, not infinity, as you seem to say.

25. Dec 19, 2015

Staff: Mentor

Where you got that idea from I have zero idea - certainly not from my paper that I hope you read.

Re-normalisation applies to quantities like the coupling constant that blow up to infinity. The naive explanation is the screening effect of vacuum polarisation. Its wrong. The real explanation is QED only makes sense with a cut-off and quantities (called the bare quantities) depend on the cut-off.

You need to investigate re-normalisation group flow:
http://math.ucr.edu/home/baez/renormalization.html

Thanks
Bill