Re: [Phys-l] Complementary principle in jeopardy?

[John Denker <jsd@av8n.com>]

On 06/15/2011 09:24 AM, Savinainen Antti wrote:
> Hi all,
>
> I suppose some of you have seen these news already about a new
> Science article:
>
> <http://www.physorg.com/news/2011-06-quantum-physics-photons-two-slit-interferometer.html>
>
>  One author states that:
>
> "But mostly, we are all just thrilled to be able to see, in some
> sense, what a photon does as it goes through an interferometer,
> something all of our textbooks and professors had always told us was
> impossible."
>
> Interesting! Any comments?

Comment #1:  "The" complementarity principle is not in jeopardy.
Not at all.  Not even close.

Comment #2:  As always, if you mis-state the laws of physics, you
can find violations of the mis-stated laws.

Comment #3:  The previous comment is not as trivial as it might
sound.  There are lots and lots of mis-stated laws floating
around.  Overthrowing the mis-stated laws of physics is very
different from overthrowing the real laws of physics.

IMHO, when doing this sort of thing, it is important to be upfront 
about what is being done and what is not being done.  There is
every chance that you will be misunderstood and misquoted, but
you don't want to be responsible for any part of that.

For example, just a few days ago in this forum, some folks implied
that E/ω was some sort of "adiabatic invariant" for a harmonic
oscillator.  I described an experiment for which E/ω was clearly
not invariant ... not just a Gedankenexperiment, but an easy-to-do
real-world experiment.

One of the skills required of scientists and of teachers is to
be able to tell the difference between scientific thinking and
non-scientific thinking.  Therefore it is worth studying the
methods that people use to "prove" bogus results. 
 -- Some of the bogus methods are all-too-familiar, such appeal 
  to authority ("it's in the book by Arnold") or proof by example:
  ("somebody did an experiment once where E/ω was invariant").
 -- Some of the bogus methods are more original and ingenious
  ("sin(2ω) is not sufficiently differentiable").

The fact remains, there are right ways and wrong ways to state
Liouville's theorem.  If you state it in terms of a certain 
type of area in phase space, the theorem is valid and quite
general ... but if you state in terms of E/ω, not so much.

So it is with the two-slit photon experiments, and with the
uncertainty principle in general.

Forsooth, the Liouville theorem and the uncertainty principle
are  *intimately*  related.  AFAICT any apparatus that violates
the one could be used to violate the other.  The two variables
that appear in the canonical commutation relation
   [x, p] = i ℏ                 [1]
are exactly the two variables that define the axes in phase
space.  Note that the right answer involves [x, p] not [E, ω]
... and involves a set of neighboring trajectories in phase
space, not a single trajectory.

It is sometimes claimed that 
   if you make any attempt to measure which slit the photon 
   goes through, it destroys the interference pattern.   [2]
This qualitative claim is a very far cry from the quantitative 
fundamental equation [1].

The fact remains, there are lots of ways that you can learn
/something/ about x and /something/ about p simultaneously.
For photons, and for harmonic oscillators (which are essentially
the same thing), Glauber states are a familiar example of states
that have minimal uncertainty in phase space, with only modest
uncertainty in x and p simultaneously.
  http://nobelprize.org/nobel_prizes/physics/laureates/2005/

In fact the AC electricity that comes out of a wall socket is
not a state of definite p, or definite x, or definite E ...
but instead is well described as a Glauber state, where the
RMS voltage is very large compared to the uncertainty in the
voltage.

So, to directly address the recent two-slit experiment:  They
have done a "weak" measurement of x in conjunction with a
"weak" measurement of p.  This is entirely consistent with
the fundamental quantitative laws of physics such as [1].
It is of course inconsistent with the qualitative claim [2]
and innumerable other mis-statements.

====

The annoying and disappointing thing about the recent paper
  http://www.sciencemag.org/content/332/6034/1170.abstract
is that the very first sentence of the abstract perpetuates
a mis-statement of the fundamental law.

I assume the experiment was valid and reproducible;  I just
object to the way the result was presented.  The proper and
traditional scientific practice is to explain how a novel
result is consistent with the rest of what we know (which
this result) ... rather than claiming it is inconsistent 
with the rest of physics (which it isn't).  A result can be
novel and interesting without being inconsistent with the
rest of physics.

I don't like hype.  It's a sign of immaturity and insecurity.
It's unscientific.