Re: QFT question

"Bjoern Feuerbacher" <bjoern.feuerbacher@xxxxxxxxxxxxxxxxxxxxx> wrote in
message news:d7mgun$aj6$1@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx
| FrediFizzx wrote:
| > "Bjoern Feuerbacher" <bjoern.feuerbacher@xxxxxxxxxxxxxxxxxxxxx>
wrote in
| > message news:d7k05n$l5s$1@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx
| > | FrediFizzx wrote:
| > | > "Bjoern Feuerbacher" <bjoern.feuerbacher@xxxxxxxxxxxxxxxxxxxxx>
| > wrote in
| > | > message news:d7f6rf$c4n$1@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx
| > | > | FrediFizzx wrote:
| > | > | > "Bjoern Feuerbacher"
<bjoern.feuerbacher@xxxxxxxxxxxxxxxxxxxxx>
| > | > wrote in
| > | > | > message news:d77h73$p3c$2@xxxxxxxxxxxxxxxxxxxxxxxxxxxxx
| > | > | > | FrediFizzx wrote:
| > | > |
| > | > | [snip]
| > | > |
| > | > |
| > | > | > | Photons are excitations of the EM field in the sense that
the
| > more
| > | > | > | photons there are, the higher the energy contained in the
EM
| > field
| > | > is.
| > | > | >
| > | > | > What happens when the number of photons is zero?
| > | > |
| > | > | Then you still have a non-zero EM field: zero-point
fluctuations.
| > | >
| > | > Sorry, the expectation value of the E and the B fields are zero.
I
| > | > quote from Milonni's "The Quantum Vacuum: An Intro. to QED"
page
| > 41.
| > | >
| > | > "In the vacuum state, and in all stationary states |n>, the
| > expectation
| > | > values of the electric and magnetic fields vanish:
| > | >
| > | > <E(r, t)> = <B(r, t)> = 0 (2.38)
| > | >
| > | > since <n|a|n> = 0." Where E, B and r are vectors.
| > |
| > | Err, I didn't talk about the expectation values.
| > |
| > | Please notice also that for every *excited* stationary state (i.e.
for
| > | every state with a definite photon number!), these expectation
values
| > | vanish. If you want to have a state for which the expectation
values
| > | do *not* vanish, try coherent states.
| >
| > So what? That is not the point here.
|
| Au contraire, that is precisely the point here: that in states of the
| electromagnetic field with a given number of photons (including the
| ground state!) the electromagnetic field strength is not zero,
| although the expectation values are zero.

We are talking about *no* photons. Give me a reference where someone
has measured this non-zero EM field strength when n = 0.

| > | > However, the expectation value of the square of the electric
field,
| > | > <E^2(r, t)> is non-zero.
| > |
| > | Indeed. Don't you think that that's a clear indication that there
| > | still
| > | is an electromagnetic field, although the expectation values of E
and
| > | B themselves are zero?
|
| I notice you chose to ignore that.

Is it really still an EM field? Try to measure it. Or show me a
reference where someone else measured it.

| > | > | > The way you are saying it, it sounds like photons could be
| > | > | > excitations of photons.
| > | > |
| > | > | I don't think that what I said sounds like that.
| > | >
| > | > You even say it again above. "An excitation of an excited
state..."
| > |
| > | Don't you see the difference between "excitation" and "excited
state"?
| > |
| > |
| > | > When n = 0 there are no photons and no excitation.
| > |
| > | Indeed. So what???
| >
| > That is the whole point of this exercise. Photons are excitations
of
| > the quantum vacuum and not of an EM field.
|
| That does not follow in any way from what you said above!

No photons; no EM field. Period. If there is an EM field then there
are photons and n > 0.

| > If you want to claim the
| > quantum vacuum has an EM field that photons are excitations of, then
| > measure it and tell me what its value is. Bet you get zero.
|
| Do you *really* want to claim that in the vacuum state, the
| electromagnetic field is exactly zero? You *do* know that the
| electromagnetic field is described in QED as an infinite set of
| coupled harmonic oscillators, and that harmonic oscillators in quantum
| theory have a non-zero oscillation amplitude even in the ground state,
| don't you?

Whoa! Where do you get this "coupled" from? That is my line. ;-)
Reference for that, please. Yes, I know about quantum harmonic
oscillators just fine.

FrediFizzx

.

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