Re: the two slits versus schrodinger's cat

From: Greg Gerardin (g.gerardin_at_danka-studio.com)
Date: 08/18/04 

Date: Wed, 18 Aug 2004 14:42:53 +0200

"Bjoern Feuerbacher" <feuerbac@thphys.uni-heidelberg.de> a écrit dans le
message de news:cfv3qm$5q9$1@news.urz.uni-heidelberg.de...
[snip]
> >>>And what's an Hilbert space? Is it more like a mathematical object, or
a
> >>>quantum object? (ok I should check this out by myself)
> >>
> >>A mathematical object. Are you familiar with vector spaces?
> >
> > I'm familiar with nothing.
>
> That's unfortunate. In order to *really* understand concepts like the
> superposition of states, one should understand both vector spaces
> and complex numbers.

I understand complex numbers. Well I have a clear view of what is it, but I
(obviously) don't know the maths to use them.

Anyway, I don't beleive one must understand the maths of physics in order to
have a good picture of the physics itself (as long as others do the maths
and explain the phenomenon to folks like me). That reminds me of Einstein
complaining at some point that he didn't have the maths to formulate its own
theory!

I beleive that intuition and visual abstracted mental representations are
extremely powerful human capacities, and those capacities are at the source
of a lot of radical scientific discoveries (.. like GR). I can make myself
a correct picture the space-time continuum without understanding the lorentz
transformations. Just like I think have a good idea of what is a
superposition of states.

>
> > Basicaly, i'm just a graphic designer and a programmer (got few
scientific
> > *basis* tho.. i have studied vectors (newtonian/euclidiean) back in the
> > college days -> arrows representing forces...hmmm... kinda like
geometry
> > applied to physics... but i don't think it's related to "vector spaces",
is
> > it?
>
> The mathematical concept of "vector space" is a generalization of that
> concept.
>
> A Hilbert space is a vector space with an inner product (also known
> under the name "scalar product"; have you ever heard that in college?)
> which is complete, which means that every Cauchy series in it converges.
> There, now I probably have confused you completely. ;-)
>
>
> >>>But... but if i see a trace on the left, I know that the photon went
> >>>through the left slit,
> >>
> >>No. Why do you think so?
> >>
> >>The photon could also have gone through the right slit and turned around
> >>there to travel onwards in a different direction. Photons don't have
> >>to travel straight. According to the path integral interpretation of
> >>QM, they instead go on *all paths at once*!
> >
> >
> > oh well, ok! I see your point, even tho I don't see why the photon would
> > turn just like that without any reason (since the experiment is in a
> > controlled environnement)
>
> As I said: according to the path integral interpretation, photons
> go on *all* paths, no matter how many direction changes there are in
> midway.
>
> If you want to interpret this in the wave picture: before the wave
> "hits" the slits, it is a plane wave - so that one *could* say that
> all the photons in it travel in the same direction (straight towards
> the barrier with the slits) (and essentially that would only be
> right in the mean, since, as I said, the photons essentially travel on
> *all* paths "at once"). But after the slits, there is no longer a plane
> wave, but *spherical* waves emanating from the slits! So obviously at
> least some of the photons are travelling into a different direction now,
> i.e. they have *changed* their direction of travel at the slits (or,
> bit more accurate, *all* photons have now a probability amplitude to
> travel into all these different directions at once).
>
> You could also try reading up on "Huygen's principle". That is not
> relevant for photons, but perhaps will help you try to understand the
> intimate connection between plane and spherical waves, which is crucial
> for understanding the double-slit experiment in the wave picture.
> <http://www.physlink.com/Education/AskExperts/ae471.cfm>
> <http://www.mathpages.com/home/kmath242/kmath242.htm>
> <http://id.mind.net/~zona/mstm/physics/waves/propagation/huygens1.html>
>
>
> >>>same thing if I see a trace on the right... and if i see an
> >>>interference pattern, I know that the photo went through both slits...
?
> >>
> >>You don't get an interference pattern from one single photon.
> >
> >
> > Ok i understand this now. That's really what I had wrong in the first
> > place. I though that the pattern was directly caused by the wave and
its
> > interference.....!!
>
> Well, the pattern *is* essentially caused by the wave and its
> interference. But it is *not* caused by one single photon, but only
> when a lot of photons are "playing together".
>
>
> > (that was stupid when I think about it now) Now I got it
> > allright. The wave describes the probability of the photon to manifest
> > itself (as a particule) somewhere in space...
>
> Yes, that's right. And that's why the pattern of observed photons is
> an interference pattern!
>
>
> [snip]
>
>
>
> > Thanks for everything, you really helped my clarified those concepts of
wave
> > functions, states, etc..
>
> Glad I could help. :-)
>
>
> Bye,
> Bjoern

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