[extropy-chat] HISTORY: Solved & Unsolved Riddles

[scerir]

[Dirac]

"Each photon then interferes only with itself."
"Interference between two different photons can never occur."

[John K Clark]

Well, if you fire a bunch of photons at 2 slits you get the same pattern
if you send them one at a time as you do if you send them all at once; 
the only difference is the pattern takes longer to form. If they 
interfered with each other you'd think there would be a difference.

[me]

The reason why I wrote that Dirac's second statement is
wrong is simple. There are dozens of experiments showing the
two-independent-photon (so called second-order)interference.
In example this one:
http://arxiv.org/abs/quant-ph/0208174
Of course the condition for the interference is always the same:
indistinguishability. That is to say: no possiblity of knowing 
which photon came from which source.

The first statement by Dirac seems also wrong to many authors
(Glauber i.e.) because it is very difficult - within the QM
statistical interpretation, where are just particles and
probabilities - to understand what kind of *physical* 
self-interference may happen. In any case this self-interference
is almost unobservable in a single (one) photon event. 
You can just infere, or deduce, something like that (maybe
using the Mach-Zehnder interferometer?). But you cannot prove,
or show, directly, self-interference or, in general, non
locality, with a single, individual photon. So, to me,
that self-interference is just a beautiful koan, like 
the sound of one hand clapping. 

A propos, there are also weird two-slit esperiments in which
a light beam is divided by a (random) shutter in such
a way that the two slits are never open *simultaneously*.
Nevertheless you get the interference.
Consider a diaphragm, with two slits, slit 1 and
slit 2. Each of these slits can be opened, or closed,
by a shutter connected with a separate counter.
A weak alpha-particle emitter is placed between
the two counters. Imagine that, in the beginning
of the experiment, both slits are closed.
If an alpha-particle strikes one of the counters,
the slit connected with this counter is opened,
and the counters cease to operate, and a light-source
is turned on, in front of the diaphragm, and this
light-source illuminate a photographic plate placed
behind the diaphragm. Following qm rules, we can write
         psi = 1/sqrt2 (psi_1 + psi_2)
where psi_1 is the wavefunction describing the system
when the slit 1 is open (psi_2 when the slit 2 is open).
Thus, from the theory, we get the usual interference
pattern, on the photographic plate behind the diaphragm.
But if we keep our eyes opened, and we observe which slit
is open (slit 1, or slit 2) then, in accordance with the
'complementarity' principle, and the 'projection' postulate,
a reduction takes place, and no interference pattern
appears on the plate.
The above interesting 'gedanken' experiment is due to
L. Janossy, and K. Nagy, [Annalen der Physik, 17, (1956),
115-121]. Btw, Janossy and Nagy thought it was possible
to perform such an experiment, but they also thought
it was impossible to get that interference.

After useful considerations by Leonard Mandel [J. Opt.
Soc. Amer., 49, (1959), 931] at last R.M. Sillitto and
Catherine Wykes [Physics Letters, 39-A-4, (1972), 333]
performed the Janossy and Nagy experiment and found a marvelous
interference when just one photon was present in their
interferometer, at a time, and when their electro-optic
(not random) shutter was switched several times during the
time-travel of each photon.
In terms of photons the condition for interference
is that the two paths lead to the same cell of phase space,
so that the path of each photon is intrinsically indeterminate
(the usual 'welcher weg' issue).
Of course, the shutter (random or not) must switch in a time
which is less than the uncertainty in the time arrival of
the photon.

[John K Clark]

But the transition is never smooth, in the 2 slit experiment the photons
act like waves until they hit the photographic plate, then they don't 
produce a smudge at you'd expect a wave to do, they make a point as 
you'd expect a particle to do.

[me]

The notion of the *smooth* transition within the wave-particle duality 
or complementarity (in deeper terms: localization and superposition 
are complementary) may be quantified by the inequality V^2 + K^2 = 1, 
relating the fringe visibility V, and the path knowledge K. This 
inequality is verified in many different experiments. (And suggests 
a limited, finite amount of information ...). 

An excellent gedanken experiment was presented by Zurek (and also
Wootters?) this way
        
              |
         |    |
       s       d
         |    |
               d
              |
              |

there is a single slit and then a double slit, but their
axes are not in line, so you can calculate that 99 per cent
of the photons passing through the single slit also
pass through the upper slit (in the two-slit apparatus).
Still you get a little interference.

Now I must stop, it is too late here :-)