Electromagnetic field in vacuum

[scope]

hi,

just to be sure, I believe that an electron in complete vacuum, that does not interact, carries an electromagnetic field, and that this electromagnetic field is mediated by virtual photons even when there is only one electron, in vacuum, that does not interact. is that statement correct?

 

[tiny-tim]

hi,

just to be sure, I believe that an electron in complete vacuum, that does not interact, carries an electromagnetic field, and that this electromagnetic field is mediated by virtual photons even when there is only one electron, in vacuum, that does not interact. is that statement correct?

hi scope!

the phrase "mediated by virtual photons" is almost meaningless …

it's shorthand for "the spin-one creation and annihilation operators which appear in the maths of the perturbation expansion of the Hamiltonian of the electromagnetic field are those of photons"

(there's also twice as many spin-half operators, of virtual electrons)

but the photons aren't real, they aren't physically there in the field (that's why they're called "virtual"! ) …

but subject to that proviso, yes, virtual photons appear in the maths of perturbation theory even for the field of an isolated electron

 

[scope]

0-spin , do you mean that virtual photons have spin 0 instead of spin 1?

 

[tiny-tim]

oops!

oops! i don't know why i wrote that

yes, it should have been "spin-one" … thanks for pointing it out!

(i've now edited it to correct it)

 

[tiny-tim]

hi!
you told me that an electron in complete vacuum generates virtual photons in vacuum.

no, i didn't say it generates virtual photons, i said "virtual photons appear in the maths of perturbation theory even for the field of an isolated electron"

… so I wonder if there are further virtual photons for 2 electrons that do interact than for 2 electrons that do not interact at all. i thought that virtual photons are interactions and therefore further interactions means further virtual photons. what do you think? please help me! thank you!

it's a meaningless question …

there are infinitely many virtual photons in the maths (and also infinitely many virtual electrons), and none in the reality …

as strangerep says in the other thread you started …

The most important thing to grasp is that virtual photons are unphysical.
They're essentially just terms in a perturbation expansion.

You might as well ask whether, when two combatants glare at each other,
are there more virtual daggers flying between their eyes when they're close
together than when they're far apart?

It's all a bit silly, really.

 

[tom.stoer]

As I point out once a week (!) it is a common misconception here at PF that QED does contain only virtual photons. You can find a gauge which explicitly contains a Coulomb potential term w/o any virtual photon.

In addition "QED with only one electron" is mathematically ill-defined as it violates the condition Q=0 and has infinite energy.

 

[scope]

thank you, and what about the energy of the virtual photons instead of the number of them?

 

[tom.stoer]

It's meaningless as well.

A virtual photon is not "one single photon"; it's an integral over infinitly many photons each carrying an energy E and a momentum p (violating E² - p² = 0). You can associate an energy to each individual photon but this is useless; you can't associate an energy to the whole energy - it's meaningless.

 

[tiny-tim]

scope, why are you so bothered about virtual photons?

they're no more real than the fairies at the bottom of your garden, or angels dancing on the head of a pin …

of course you can find questions to ask about them, but what's the point of it all?

 

[scope]

It's meaningless as well.

A virtual photon is not "one single photon"; it's an integral over infinitly many photons each carrying an energy E and a momentum p (violating E² - p² = 0). You can associate an energy to each individual photon but this is useless; you can't associate an energy to the whole energy - it's meaningless.

and what about saying that for every interaction there is a virtual photon?
what about saying that further interactions mean a further density or intensity of virtual photons?
does that make sense?

 

[tom.stoer]

No, it doesn't make sense.

If you look at an ordinary Feynman diagram you can draw a wavy line. If the line has one end it's a real photon (interacting with a charged particle at one end); if it has two ends (on both ends it interacts with a charged particle) you may call it a virtual photon. But this is only a mathematical rule which tells you that there are infinitly many "photons" with all values for E and p you can imagine ... and with a Feynman propagator ... and that you must integrate over all E and p ... It makes sense as a mathematical construction and there are rules how to describe it rigorously but its misleading (after all these books from Feynman, Hawking, ... it remains misleading) to think about it as something like a small packet of light!