Re: On the uncertainty principle for photons. An experimental counter

J.J.Lodder wrote:

kvblake <kvblake2...@xxxxxxxxx> wrote:
From QM follows that the position of a photon can not be determined
better than L (de Broglie wavelength).


If you think so, please show a derivation from first principles.
(and please, wavelength will do. No need to involve De Broglie)


Suppose one creates a wave in the meter range - say L=2m. Could the
photons in this wave go through a tube of radius 1 cm?


Yes. Try it.


If one registers a click of a photon counter placed inside the tube -
would this be a counterexample of QM - e.g. the position of the photon
determeined better than de Broglie's wavelength???


No, unless you supply the proof required.

You can do better than that though.
Suppose you throw a photon with sufficient energy
at an atom, and detect the resultant photo-electron.
If you see an electron you have fixed the position of the photon
to an atomic diameter, much smaller than its wavelength.


For further amusement you may note that the atom
can by a hydrogen atom in a Rydberg state,
which allows you to detect even radio-frquency waves.


Best,


Jan


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

Sorry about the delay. A huge lack of Internet connection...

I think that was a trivial fact. Nevertheless the prove I found seems
a little strange to me too.
It's from QED of Beresteckii, Lifshitz (the intro).
It's like that:
1. Min uncertainty of x -> Dx for a massive particle in its rest frame
is Dx=h/mc (under h I mean Dirac's h not Heisenberg's h->h/2PI but I
dont know how to write it with this bar up.. - that's why ...... was
confused with this 4PI - ---- the second 2 is from some preciser
formulation of DxDp=h/2)
2. Min uncertainty in the frame where the particle is moving with
energy E is then Dx=ch/E
3. For ultrarelativistic particles E almost = cp hence Dx>h/p
4. Photons are always relativistic so Dx>h/p=L (lambda as introduced
by de Broglie).


In this book also stands the following.
The above is valid for experiments from every result of which x can be
determined (I would call this experiments of class I)
If one uses impacts without probability one for the time of experiment
from each deflection of the probe particle one can judge about x. But
if deflection is 0 one can not tell anything about x (class II).

I think my experiment is from class I and yours is from class II.
================================
To Rich:

Rich L. wrote:

I think the misunderstanding is that QM does not say that the energy
of a photon cannot be captured in a volume much smaller than its
wavelength, but that the exact path that the photon travels between
source and detection cannot be measured more precisely than this. As
other replys have pointed out, the energy in a radio frequency photon
can originate from a volume with dimensions orders of magnitude
smaller than the wavelength, and when the photon is detected the
location of detection can be determined with much greater precision
as
well. It is the location of the "photon" in between these two events
that is uncertain.

Rich L.

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


If there is a source of radiowaves and I put in front of it a tube of
lenght 10 m and r=2 cm with a detector at the end and the detector
clicks I could be absolute sure of the path and Dp wouldn't also be
great provided 'c' is a constant.

.