Natural Science Forum / Physics / Research / December 2008

(snip, I wrote)

I would say that we mostly understand it, but not completely,
maybe asymptotically is about right.

For one, what ever happened to quantum gravity?

http://en.wikipedia.org/wiki/Interpretation_of_quantum_mechanics

There was an article a few years ago, something like the greatest
hoax ever pulled on students is teaching the Copenhagen
interpretation of quantum mechanics.  I don't remember where
I saw it, and some web searching didn't find it.

-- glen

Both, in fact.

Consider the following thought experiment:

Let one photon pass through the slits,
and register on the photographic plate (off centre).

The plate must have acquired a transverse momentum,
from the transverse momentum component of the photon.
The screen with the double slits must have acquired
an equal and opposite transverse momentum,
since momentum is conserved.
(and the photon is no longer present)

Jan

You can feel nothing of the kind.
All you can feel is a force.
The rest is (mistaken) interpretation.
You should try not to confuse observation
and interpretation,

Jan

On Nov 14, 5:53 pm, il...@abv.bg wrote:

You are right in general, but not in the idealized experiment being
considered here. The interaction with the slit is considered elastic,
hence energy and momentum magnitude conserving.

Your reasoning is flawed here, and your conclusion is false. Of course
the interaction changes when the slit is narrowed; there is now more
barrier material for the electron to bounce off of than before. And
delta-p increases because both the Schroedinger equation and the
Heisenberg uncertainty principle say so.

Again, your argument and conclusion here are flawed. For an isolated
system, even in special relativity, 4-momentum is conserved as a
whole, including its individual components. The key word here is
isolated.

Hope this helps.

Igor

(snip of electron and slit question)

Well, you can just take the problem back one level.  You can't
determine the position and momentum of the slit (or one side
of the slit) exactly.  If you have a slit such that you can measure
the momentum transfer, you won't know the position of the slit
very accurately.  In such case, you could know which side of
the slit the electron scattered from, but the uncertainty
in scattering position would destroy any interference
pattern from the electron wave.

True for any slit localized well enough to see the electron
interference pattern.

In that case, you could detect the ejected electron, determine
which part of the slit it was from, and again lose the
interference pattern.

-- glen

I think what you describe is just a very real wave (the electron as
wave) which does not correspond to Copenhagen probabilistic
interpretation.

Why then the electron wave interacts with the whole slit (I dont know
how many atoms) but on the screen with just one atom.

Ilian

============ Moderator's remark   ==========================

It is well known that Schroedinger's initial interpretation of
the particle-wave function does lead to severe contradictions to
experiment which can only be resolved by Born's interpretation
of the wave function as a probability amplitude!

On 19 Ноем, 19:32, nos...@de-ster.demon.nl (J. J. Lodder) wrote:

One may

You have omitted the impulse of the source.

Ilian

Thus spake ilper@abv.bg

You are right. The uncertainty in momentum of the particle is
counterbalanced with an uncertainty (normally unmeasurably small) of the
momentum of the slit material. When either is measured, the uncertainty
in the other is removed. This reduces the problem to an EPR type
entanglement problem. The measurement is required to be able to define a
state of definite momentum, and to thereby to apply the law of
conservation of momentum in a meaningful way. As with ordinary EPR, it
is impossible to think of this classically in any clear way.

Ehrenfest's theorem applies to the expectation of the measured value.

Regards

It's comments like this that get me wondering if I misunderstand what
the wave function is. I went back to Landau & Lifshitz, Messiah, Schiff
and even Wikipedia, and just as I thought, it is the the
amplitude-squared of the WF that is related to what gives the
statistical results of measurements, and the WF is postulated to
completely describe the dynamical properties of a system at any given
time, in rough analogy to the classical Hamiltonian or Lagrangian. I
don't understand the WF to be the picture described above.

It is getting the information out of the WF that is the tough part. All
the states available to a system can be found, but exactly which state
the system is in cannot be known precisely at a given time and must be
determined probabilistically. There are two references I think give
thoughtful descriptions of the WF:
Messiah's Quantum Mechanics, Ch. II, Sec. 10
and
Landau & Lifshitz's Quantum Mechanics - Non-Relativistic Theory, Ch. 1 -
particularly section 2.

Aside: the Dirac formalism is more sophisticated (system states defined
by vectors in Hilbert space), but it does lead us back to the same WF
with the above same properties.

I don't see why it is impossible to speak of QM trajectories.
Trajectories are described through scattering theory; the paths of
particles are calculated probabilistically--a non-scattered particle
travels in a straight line.  A bubble chamber photograph verifies the
existence of these particle trajectories.

On 29 Nov, 23:51, Arnold Neumaier <Arnold.Neuma...@univie.ac.at>
wrote:

Thanks a lot. I have found the article.

The question I raised in my first post on the thread 'For quantum
physicist only' is in my opinion far from being answered. It was
argued here that the impulse of a deflected particle is compensated
for by the impulse of the material of the slit (by almost all of the
authors except Charles Francis).

As I see there are 2 possibilities:

1. The particle on its 'trajectory' interacts with just one atom from
the edge of the slit (unknowingly why with the edge exactly). The
particle changes its impulse and the atom takes an opposite impulse.

However this opportunity is impossible because than the minimal change
of the impulse wouldn’t depend on the width of the slit.

In this sense if there are approximate trajectories (and if they are
many of them thru the slit delta x < lambda) the particle could not
'see' the other edge of the slit. As I am not well acquainted with de
Mott analysis I don’t know if there are approximate trajectories in
the case of empty space.

In this connection another question arises: if we can observe the
trajectories in a slit (in bubble chamber) would there be broadening
of delta p observed after the slit?

2.The particle being a wave (or if one prefers showing its wave
properties) interacts in the range of its wavelength (unknowingly why
but never mind) with the material of the slit.

A) this interaction must happen very selectively - just with atoms
from the edge of the surface (dp depends only on the utmost outside
width of a real slit). This selectivity needs also to be accounted
for.

B) it must be accepted that WF is not associated with a group of
undependable particles and has no probability meaning but some real
physical nature.

C) even if WF has real physical nature (or even not) I’m very
disturbed by the fact that WF will interact (or better impart
interaction of the order lambda) on the slit edges but wont show a
trace of such on the screen.
Igor Khavkine had answered to this that the change in the screen is
macroscopic whereas this (these) on the slit is not.
I would be indebted if he can explain what is meant by this (maybe
macroscopic=observable).
And than where is the boundary between macroscopic and microscopic?

D) One should explicitly note that from the point of view of classical
wave theory there is no at any means exchange of impulse between the
wave and the walls of the slit (good old Huygens principle).
So Schrödinger function also doesn’t take/give any impulse to/from the
slit (if it is to be attributed any physical reality to it). The
material doesn’t interact with the wave it just blocks the waves and
don’t let them interfere further and restore the falling plane wave