Can Vacuum Fluctuations Lead to Electron-Positron Annihilation?

[asimov42]

Hi everyone,

I had a related, more complicated post in another thread - I hope it's ok to post a simplified and slightly different question here (posting as a layman):

Let's say I have an electron traveling alone in the vacuum, when a vacuum disturbance (fluctuation) occurs nearby. If the disturbance has the correct form, say, an electron-position pair, could the positron annihilate with the original electron? (leaving the remaining electron) The positron would have to have negative mass to ensure conservation of mass/energy.

So, the overall question, could something like the above occur? I've been careful to specifically stay away from the term virtual particle.

Any help would be greatly appreciated, as I think there are a number of concepts I'm getting confused. Thanks all!

 

[bhobba]

Any help would be greatly appreciated, as I think there are a number of concepts I'm getting confused. Thanks all!

And you will continue to be confused in applying classical pictures to QFT. It can't be done. Don't try. As I mentioned in another thread virtual particles do not actually exist nor is a particle traveling along in a vacuum a valid picture in QFT. Vacuum fluctuations are in the same category.

If you want to understand QFT there is no choice but the long slog of studying a proper textbook:
https://www.amazon.com/dp/B00MN96BHW/?tag=pfamazon01-20

Just to elaborate a bit further since many sources will tell you vacuum fluctuations exist and are responsible for things like spontaneous emission and the Casmir effect. Such is not strictly true because they can be explained without that concept. Its simply a name given to certain things in the math, but some people take it too literally and that leads to all sorts of problems.

For example see the following:
http://arxiv.org/pdf/hep-th/0503158v1.pdf

Thanks
Bill

 

[bhobba]

I have been looking for some more detail on this point because in the popular press, and even some professional literature, this idea of the reality of quantum fluctuations of the vacuum is very pervasive leading to queries like the OP posed. Yet if you study QFT you find its not like that at all.

The best I could come up with is an article by Professor Neumaier who is a very well respected science advisor on this forum:
http://arnold-neumaier.at/physfaq/topics/vacfluc

As he explains it is simply a formal property of a quantum system:
'But the vacuum fluctuations frequently associated with vacuum polarization are not fluctuations in time, of virtual particles popping in and out of existence from the vacuum (as popular sources on the internet assert), but formal properties of the quantum formalism. And ''observable consequences'' does not imply a cause and effect relationship -- Vacuum fluctuations cause nothing, hence have no effect. It is their presence in the equations that has some observable consequences.'

As I said in another thread anything you have read about QFT outside a QFT textbook is likely wrong - quantum fluctuations is simply another example.

Thanks
Bill

 

[Nugatory]

Let's say I have an electron traveling alone in the vacuum, when a vacuum disturbance (fluctuation) occurs nearby. If the disturbance has the correct form, say, an electron-positron pair, could the positron annihilate with the original electron? (leaving the remaining electron)...could something like the above occur?

You are confusing yourself by thinking in terms of the "original" electron. The particles are indistinguishable, so you are describing a situation in which we look at the system and find one electron, then look at it a moment later and find one electron. There's nothing strange or surprising about that; it happens all the time.

 

[Nugatory]

This thread was temporarily closed for moderation and is now reopened. @asimov42, if you want more clarification or have further questions... Ask away!