Re: [Phys-L] Photons and radio waves

[John Denker <jsd@av8n.com>]

On 10/06/2013 08:48 AM, Savinainen Antti wrote:
> a colleague asked my why photons are seldom, if ever, mentioned in
> the context of radio waves. It seems to be an interesting question.
> On one hand, it is clear that radio waves can be understood as very
> low-energy photons (lVERY arge wavelength when compared with visible
> light). On the other hand, one could think that radio waves do not
> easily exhibit their photon-like nature. Are there experiments which
> could be used to empirically show that radio waves are photons (not a
> good expression but you know what I mean...) in the same way as light
> is? For instance, how to observe the photoelectric effect or the
> Compton effect with very low-energy photon?
>
> My guess is that almost everything one wants to do with radio waves
> can be done using Maxwell's theory of electromagnetism.

First of all, note that even at optical frequencies, light is not
nearly as quantized as the popular literature would have you believe.
Yes, there are energy eigenstates, and yes, these states have quantized
energy ... but these are not the only states!  They are not even the
only basis states.  For details, see
  http://www.av8n.com/physics/coherent-states.htm

At lower frequencies, such as audio or RF, even if you have energy
eigenstates, the spacing between energy levels is so small that
almost nobody is interested.  In particular, the spacing is small
compared to kT at room temperature.  The relevant conversion factor
is 
    21 gigahertz per kelvin.
That is Planck's constant -- or rather the inverse thereof -- in 
practical engineering units.

Almost every radio I own nowadays operates in the GHz band (phones,
computers, et cetera).  That used to be called the microwave band,
and I suppose it still is, but nowadays it's also considered plain
old RF.

I mention this because if you combine GHz frequencies with millikelvin 
temperatures, then the quantization of the radio can become quite
significant.  Been there, done that.

  Again I say "can become" rather than "necessarily becomes" because
  at any frequency and any temperature, you might decide that the
  energy eigenstates (quantized) are less interesting than the coherent 
  states (non-quantized).  As a familiar example:  The spin-up and
  spin-down basis states of an atom are definitely quantized, but the 
  free-induction decay in a pulsed-NMR experiment is best described
  in continuous, non-quantized terms.

  You can build a photon counter if you want.
  You can also build a voltmeter if you want.
  One of them has quantized energy levels; the other does not.
  Much depends on how you choose to carry out the measurement.

============

All this applies to all of physics, not restricted to the electromagnetic
field.  If you want an example of the same physics in a different domain,
consider a playground swingset.  It is a harmonic oscillator.  As such,
it has quantized energy levels.  However, the motion that you actually
see is more conveniently described as a coherent state.  In particular,
the correspondence principle applies more directly and more conveniently
to the coherent states.  The quantum-mechanical coherent state behavior
is virtually indistinguishable from the classical behavior.