Our garden is a mature but unruly pear tree and a few snails. To
be fair the wise old tree is surrounded by a tiny forest of littler
plants with jaggedy edged leaves and various dandelions, bluebells,
and other mystery plants with purple and pink flowers. It's only a
little green pod but resting in it for a few minutes you feel like
you've gone full Walden - until over the fence, the river past it,
the houses past that, a bright red London bus flashes past and you
remember where you are.
Today in the few minutes I was drinking my coffee in the garden -
necessarily under the old pear tree - a blue tit ventured onto the
branch right by me to demonstrate some impressive upside-down
acrobatics and chirp a lot. On one of the tinier plants one of those
jumping, claw-like spiders rushed up the stem only for the little
insect at the top to fly away at the last moment - I wondered if
the lucky creature knew how close had been the call (no, it didn't).
Beyond providing food for peckish squirrels and more peckish birds,
the pear tree was until recently covered in white blossom. I used
to go to a poetry and music night called Catweazle Club which, as
well as being the only place I've heard blues sitar, featured rather
a lot of poems about nature, the passing seasons, and so on and on.
At the time I have to say I didn't see what all the fuss was about
(sitting on my knees for an hour or so probably didn't make me
enormously receptive). But I have to admit that the sight of the
white pear blossom blowing, in slow motion, down from the branches
did get me feeling all fond of nature; I felt stirred - stirred! -
which is the most a plant has done to me so far.
Enough of that - what's all this hippy-dippy non-sense got to do
with spontaneous emission? Well most of my garden-standing time
recently has been spent thinking about matter and radiation, perhaps
inevitably since I've been reading about the history of quantum
mechanics. One thing which jumped out is that among the three great
radiation processes - stimulated emission, stimulated absorption,
and spontaneous emission - it is often said that stimulated emission
and spontaneous emission are 'purely quantum' (which is to say we've
given up trying to understand them). But I was reading a very
interesting paper by Lamb (he with the shift) called anti-photon
which made the case that stimulated emission can occur just as well
in classical systems so long as they are nonlinear. And the pear
blossom falling got me wondering if spontaneous emission could not
also have a (satisfying) explanation.
Here's the thing: it is obviously true that an atom alone in the
universe which finds itself in an energy eigenstate will remain
there - for there is no time-varying charge density or current, so
it does not radiate, and happily rotates its phase ad infinitum.
But if its state includes even a tiny amount of another energy
eigenstate, there will be a time-varying charge density, so our
atom duly radiates, and naturally loses energy and ends up in the
lower energy eigenstate. Now, the atoms we see are hardly alone in
the universe, and are constantly jostled by the electric fields of
neighbouring atoms in whatever crystal or what have you they live
in. So it seems to me that - so much as we can talk about an
individual atom's state at all - if an atom in a laser crystal for
example was to be in an energy eigenstate, it would take only a
tiny push from the constantly varying electric fields in the crystal
to introduce a tiny component of another eigenstate, and this is
enough to get the atom to radiate. So in the real world I would
expect spontaneous emission to occur; the case in which the atom
doesn't radiate seems to be rather singular and vanishingly unlikely.
It is true that in quantum electrodynamics it is shown that spontaneous
emission would happen even in this singular case - and is sometimes
explained as emission stimulated by vacuum fluctuations - but I
wonder if this case ever actually occurs in real crystals.
Enough of that - what's all this hippy-dippy non-sense got to do
with pear blossom? Well the thing that got all this going was the
homely fact that even if I stand perfectly still in the garden, the
old pear tree, the dandelions and bluebells, and the surrounding
tiny forest are all in constant motion because of the wind - and
it is this gentle motion imparted by the wind which shakes down the
blossom from the pear tree. And it got me thinking that if you lived
in an underground lab complex and had only studied theories of ideal
pear trees in a vacuum, the fact that blossom falls from the tree
without you shaking it would seem highly anomalous; classical blossom
needs shaking to fall of course, of course. But for a real tree -
a tree in that real world fabled to exist outside of the lab, outside
of the books - and for the real tree in our garden, the blossom of
course falls without my shaking it, just because the tree is gently
shaken by the wind - as all real trees are.
