Re: How did that field get quantized, exactly...

On Feb 12, 4:30 pm, mme...@xxxxxxxxxxxxxxxxxx wrote:
In article <1171322325.665917.91...@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>, "Edward Green" <spamspamsp...@xxxxxxxxxxx> writes:

On Feb 11, 9:16 pm, Greg Hansen <glhan...@xxxxxxx> wrote:
Edward Green wrote:
I'm trying to understand, on a simpletons' level, how the EM field
might wind up quantized so that its incremental excitations show the
characteristic E = hv .

You're no simpleton, Edward.

Oh... very well.

I admit there is some Platonic irony in my protestation, on the other
hand, when trying to understand physics I seem to swing back and forth
between the feeling that, hey, I'm a pretty smart guy, and I'll show
these people a thing or two, and, ohmigod!, there is so much and this
stuff is so dense and the people are so smart I'm never going to get
anywhere.

The reaction depends on whether at a given moment I see through the
arguments, in which case things look simple, or I don't, in which case
things look like an pathless bracken. So I make the lowest common
assumption and admit I'm a simpleton: hopefully I can at least avoid
somebody trying to prove it to me, which is far more provoking.

<...>

Thank you.

But what "confines" the EM field?

No confinement. What is the discrete spectrum of the electromagnetic
field? Without boundary conditions like a conductive cavity, the
frequencies can be anything.

I'm of two (confused) minds on this. On the one hand -- yes, the
field as a whole has a continuous spectrum, not a box in sight: on the
other -- considered as a collection of modes, each mode seems to be
"bound" in some way, like an electron is bound to a proton: the modes
act something like a mass and spring.

You may slightly "unconfuse" yourself once you'll notice that in some
of the previous posts you mix quite different "quantizations". As I
recall, you referred to the case of classical EM field within a
confined space, where you've discrete frequencies present. This is
*not at all* like the quantization of EM cavity field, where the frequency
is not quantized at all. What is quantized, is the amount of energy
corresponding to each frequency. Different beast.

This is where I break in because this is where I get muddled. It
seems that free space does this via the specific values of eps0, mu0
and their ratio.

In the case of a cavity, we can talk about the specific values of
eps and mu _of the cavity_, which depend on its structural details.
Free space OTOH has no similar structural details at whose doorstep to
lay eps0 and mu0.

None I know of.

Yes, I know, there's no firm explanation for eps0 and mu0 having the
specific values they do, shut up and calculate. But then I think "If
the values of the cavity are simply that of the vacuum plus the
contributions of the matter that makes up the cavity, the vacuum
values are a sort of 'ground level', and various cavities are 'excited
levels'. But the Casimir Effect seems to imply a sort of metamaterial
analogy of an ordinary cavity with less-than-vacuum values for eps and
mu, hinting that the observed vacuum is not a 'true' ground state. If
so, is the known vacuum held where it is via some uknown mechanism,
and is there a 'true ground state' the known vacuum could fall to, and
what would -its- values of eps and mu be? If there's anything to that
idea, then the unknown mechanism is also probably quantized, or the
vacuum would have free-fallen to that alleged 'true ground state' long
ago."

But that's as far as I can go, because AFAICT there's just no way to
find out if the thought is worth pursuing. It would require, among
other things, that we either have access to time travel to the distant
past and future to see if eps0 and mu0 change over time, and if so in
a quantized manner or smoothly, or access to other Universes for
purposes of comparison.

Well, maybe if Uncle Al can break Relativity, the usual cross-
Universal travel restrictions will go away.

That might not help either; could there _be_ no 'true ground level';
rather all possible vacuum states form a continuum? Drat. Still
"elephants all the way down".


Mark L. Fergerson

.

Relevant Pages

  • Re: How did that field get quantized, exactly...
    ... Without boundary conditions like a conductive cavity, ... of the previous posts you mix quite different "quantizations". ... contributions of the matter that makes up the cavity, the vacuum ... hinting that the observed vacuum is not a 'true' ground state. ...
    (sci.physics)
  • Re: How did that field get quantized, exactly...
    ... Without boundary conditions like a conductive cavity, ... However, getting beyond this technicality, quantization doesn't stem ... contributions of the matter that makes up the cavity, the vacuum ... hinting that the observed vacuum is not a 'true' ground state. ...
    (sci.physics)