Re: [Phys-L] Delay in photoelectric effect?

[John Denker <jsd@av8n.com>]

On 09/16/2014 11:30 AM, Savinainen Antti wrote:
> It is again a time in the year when I'm teaching early quantum 
> mechanics for the IB and Finnish syllabus HS students.

OK.

> We just finished discussing the photoelectric effect and a question
> arised: does the lack of time delay in the process really mean "no
> time whatsoever"? 

The question embodies a misconception, as discussed
below.

> Could it be that the time delay is so small that
> it cannot be measured using the available technology?>  Or is it really
> a process which takes exactly zero time? My physical intuition
> (well, for what it's worth) would suggest that it would take *some*
> time, although clearly much less than classically anticipated.

Here's the deal:  The photoelectric effect, as the 
term is generally understood, involves photons that 
are monochromatic, or nearly so.

There is an energy/time tradeoff principle.  This is
not identical to the Heisenberg uncertainty principle
but similar in structure.  So, to the extent that we
can measure the interaction-time at all, the photoelectric 
effect is imperfect, and to the extent that we can talk
about the photon energy (aka frequency) at all, the
timing is imperfect.  In particular, a very-nearly
ideal photoelectric interaction would take a very
long time on average ... definitely not zero time.

As I have said before, the usual hand-wavy story about
"quantum leaps" is just wrong.  Planck warned people
from Day One that the evidence did not require energy
to be quantized.  Einstein ignored Planck's advice
and took the quantization idea literally, especially
in his photoelectric paper, and got a prize for doing
so, but it's still not the right way to think about
it.  Really not.

Energy is not quantized.  This should be obvious at the
level of dimensional analysis, based on the dimensions
of Planck's constant ... i.e. the quantum of action,
i.e. area in phase space.

We should focus attention on phase space.  Even then,
phase space is not quantized in the sense of being
discrete.  Planck's constant is the /unit of area/
in phase space, much like a radian is a unit of
angle, even though angles are not quantized.

Measuring area in units of ℏ tells you the number
of /basis/ states involved.  However, basis states
are not the only states!  By way of analogy, in 
ordinary space, the x-axis, y-axis, and z-axis are
not the only vectors.

This is real physics, with directly observable consequences.
In Fourier-transform NMR, for example, it is routine to
apply a more-or-less monochromatic tipping pulse for
/half/ the time it would take to cause a transition
from one energy eigenstate to another.  There's even
a name for this:  It's called a π/2 tipping pulse.
It can be used to put the system into a state halfway 
between two basis states (in the energy eigenstate
basis).

Explaining quantization to high-school students in the 
context of the photoelectric effect is not easy.  I'm 
guessing that they don't know what the relevant basis 
states are, and even if they did they would have a 
hard time imagining a superposition state halfway in 
between.

Possibly constructive suggestion:  Switch to a different
system.  I would be tempted to start with a two-state
system.  Photon polarization is a possible example,
amenable to classroom experimentation.  I'm assuming
you don't have a pulsed-NMR machine lying around.  If 
your basis states are RCP and LCP, then X-polarization
and Y-polarization are halfway between basis states,
yet are perfectly well behaved, and easily achievable 
with quarter-wave plates.

Then, if you want to take this to the next level,
where there is a large number of basis states, like
the photoelectric system but not quite so complicated,
consider the coherent states of a harmonic oscillator.
This has plenty of real-world applications.  The AC
electricity that comes out of the wall socket is best
described as a large-amplitude coherent state ... not
even remotely similar to a photon-number eigenstate.

This system is described, with pictures and computer
animations, at
  https://www.av8n.com/physics/coherent-states.htm
That includes a discussion of the fact that a lot of 
the stuff that people assume is quantized is not in 
fact quantized.