Tom Roberts wrote:
> ***@gmail.com wrote:
> > Tom Roberts wrote:
> >>***@gmail.com wrote:
> >>>Entering the slit does not change
> >>>it's vertical momentum.
> >>This is QUANTUM MECHANICS, and the slit most definitely DOES affect its
> >>vertical momentum
> >
> > You are implying that the incoming particle exchanges momentum with the
> > slit edges. Unless you can show how such an interaction is mediated,
> > then that's just nonsense. The slit cannot disturb the electron state
> > as the slit consists of empty space.
>
> You are supposed to read what I write. As I said, the EDGES of the slit
> are not empty space, and the EDGES of the slit and the material outside
> the edges most definitely do interact with the electrons that "pass
> through" the slit. These interactions affect the vertical component of
> momentum of the electron. <shrug>
What you said was all wrong. This is a thought experiment and you can
assume all apparatus material is 100% opaque (note: what a silly red
herring you raise).
>
> >>-- how else do you think a diffraction pattern arises?
> >
> > Well for starters, if you knew which slit the particle went through you
> > don't get any diffraction pattern AT ALL.
>
> Stick to THIS discussion. There is a single slit. And there _is_ a
> diffraction pattern.
I did, you just misunderstood. It doesn't matter if it's n slits or 1
slit, you DON'T get interference if you know which slit the particle
entered through. That's right, to even assume that it came through the
single slit requires a position measurement and once you do that you
DON'T get any interference at all.
Repeat: To know if the particle even enters through a single slit
requires a position measurement on that particle, and once applied, you
don't get interference and the probability distribution follows the
classical analogue.
If you don't understand that then you need to re-educate yourself
rather quickly.
> For a multi-slit experiment in which one knows which
> slit the particles went through, there _IS_ a diffraction
> pattern, [...]
>
> You _REALLY_ need to learn basic quantum mechanics before attempting to
> discuss it.
That is absolutely wrong. For if it was I could form a
Proposition 1:
"The particle enters either slit 1 or slit 2"
and compute the probability distribution on the screen a priori. That
calculated distribution has NO INTERFERENCE. If you apply position
measurements on the particles before hitting screen, to know which slit
they came from, then you don't get any interference AT ALL. Don't you
know that? If you DON'T apply position measurements then you get
interference. Obviously, having the knowledge of which slit particles
entered through prevents interference completely. Acquiring this
knowledge disturbs particle state due to photon-particle momentum
exchanges (but that is only technical point).
Fundamentally, if you look at the slits then you can say particles
entered either slit 1 or 2 BUT if you don't look then don't say it
entered either slit 1 or 2.
>
>
> > After measuring one of the electrons you can start to deduce
> > the path it necessarily must have taken to have gotten there [...]
>
> This is not possible -- C.f.Feynman's integral over all possible paths
> -- there is no "path it necessarily must have taken to have gotten
> there", there are many different possible paths (with different
> amplitudes for each).
>
> I repeat: this is QUANTUM MECHANICS. For an electron observed
> after the material containing the slit, there is nonzero
> probability that it tunneled through the material and "missed"
> the slit entirely. You do not, and CAN NOT know over which
> path any given electron traveled, THIS IS QUANTUM MECHANICS --
> you cannot know what you don't measure (and making measurements
> perturbs the system being measured).
>
> You _REALLY_ need to learn basic quantum mechanics before attempting to
> discuss it.
You started off with "stick to this discussion" and now you are
invoking absurd off-topic experimental technicalities. This is a
THOUGHT experiment and you can assume the apparatus material is 100%
opaque.
Repeat, if you look at the slits then you can say particles entered
either slit 1 or 2 (no interference) BUT if you don't look then don't
say it entered either slit 1 or 2 (interference).
>
> >>In the region before entering the slit the particles are in a state with
> >>sharp vertical momentum, but in the region after the slit the state no
> >>longer has a sharp vertical momentum. <shrug>
> >
> > How much momentum do the slit edges end up with after the partcle has
> > passed through? How was this energy exchange mediated?
>
> How much is variable, and not sharp. This is mediated by electromagnetic
> interactions between the electron and ALL of the charged particles in
> the material surrounding the slit. Please go back and actually READ what
> I wrote. And go READ a textbook on quantum mechanics, as you quite
> clearly do not understand the subject.
I did read a textbook on QM, and obviously you have PROFOUND
misunderstandings on this subject.
1. You don't understand that applying position measurements on particle
prevents interference.
2. Unless you apply a position measurement, then you can't say it
enters slit 1, 2 or slit n.
[snip]
> > There is nothing wrong with this "mental picture" at all so long as you
> > consider teleological statements with probability, not certainty.
>
> Not true. That picture is just plain wrong in the quantum realm.
> Electrons simply do NOT behave like "little cannonballs". <shrug>
Can't you read? There is nothing wrong with this "mental picture" at
all so long as you consider *teleological* statements with
*probability*, not certainty.
>
> > The sum over histories formulations says that the particle IS a little
> > cannon ball [...]
>
> Not true. You _REALLY_ need to learn basic quantum mechanics before
> attempting to discuss it.
Can't you read?
The sum over histories formulation says that the particle IS a little
"cannon ball" and that it ends up a little "cannon ball", but the
probability of getting there is the sum of the amplitude of all
possible little "cannon ball" paths (varying complex phase of amplitude
by action of that path) then simply squaring absolute value of that
sum. This approach is 100% *consistent* with any other formulation.
I suspect I overestimated your capabilities in this field. Aren't you
supposed to be a post-grad?