From: scerir (scerir@libero.it)
Date: Mon Jan 20 2003 - 02:19:55 MST
Damien Broderick:
> Here's a half-baked notion I put up for demolition or development:
In general MWI is 'useful' as a tool, a gedanken interpretation.
Unfortunately there are many MWI. So you have to choose your own.
(In other worlds I already chose different interpretations.)
The best one, but I'm not an expert, states that those worlds
interfere untill measurements are performed. When measurements
are performed the splitting (branching) occurs.
Thus, in our world, in a double slit set-up, the branching occurs
when we observe what is going on. If we make an early observation
we cause the branching and we do not get the interference pattern.
I.e. if we observe the electron going through slit one, we can not
observe the second (real, eh!) electron going through slit two.
To observe, of course, means to use an (irreversible) device which
can tell you 'which path','which slit'.
Before observation there is no MWI, because there are no 'relative'
states. (Here I suppose that 'osbervation' and 'measurement' are
the same thing.)
> You agree to open the shutter at 8 pm on the day of the next Lotto
> draw iff the winning numbers are 3, 15, 27, 28, 31 and 45.
Here you mean a quantum Lotto, I suppose.
Of course there is a difference between a quantum and a normal Lotto,
a quantum and a normal roulette. The difference is linked to the
quantum superposition principle (etc.).
But there is a general 'philosophical' difference too.
Let us suppose that Alice is spinning a normal roulette and Bob moves
his hand. From classical physics we get there is no relation between
the output, the number Alice gets, and Bob's hand. (Ok, we can also
think that classical physics is non-local ...., but we avoid this.)
Now let us suppose that Alice is spinning a quantum roulette. Quantum
physics is not deterministic and (maybe) also non-local. So there
might be a relation between the output, the number Alice gets,
and Bob's hand.
> Is it the case that in those universes where this number set doesn't win,
> versions of you will all see punctate recordings on the detector, while in
> the n million fewer universes where it *does* win, you'll all see an
> interference fringe? Or does the presence of a closed shutter in most
> universes obliterate interference in *all* worlds?
In our (present) world, the winning numbers of our quantum Lotto are
3, 15, 27, 28, 31 and 45, the shutter is open, you get the interference
pattern. In another world the losing numbers are 3, 15, 27, 28, 31 and 45,
the shutter is closed, you do not see the interference pattern. Or not?
> In the 1 in n million test universes where fringes do show, you'll invest
> in a ticket and be rich the next day. Better than *none* of you
> winning...
It is also possible that in some universe there is a time reversal, due
to the time symmetrical Schroedinger equation. Hmmm.
> (As I recall, the mere possibility of closing the shutter forces the
> non-interference, but maybe that gets finessed in this approach?)
Yes the orthodox QM interpretation says that the mere possibility of
reading a pointer, the mere possibility of realizing 'which path',
the mere presence of a device, the mere possibility of getting
some inormation force the non interference. But this is wrong.
The effect is physical, of course. It has been shown (in the two slit
electron interference) it is due to the asymmetrical spread of the
wavepacket, because of photon scattering.
Wootters and Zurek ["Complementarity in the Double-
Slit Experiment: Quantum Nonseparability and a
Quantitative Statement of Bohr's Principle", in
Physical Review, D19,(1979)]showed that photons
still have a 'wave-like' behaviour even if the path
is predicted *almost* certainly (99%). This gedanken
experiment is very interesting. Their apparatus
is a single-slit + a double-slit + a screen.
Greenberger and Yasin wrote in mathematical terms the Complementarity
Principle as
p^2 + n^2 =1
where p is the predictability of the path (in the double-slit
experiment) and n is the visibility of the interference fringes.
Thomas V. Marcella wrote a beautiful paper about
http://www.iop.org/EJ/S/UNREG/abstract/0143-0807/23/6/303/
"quantum interference with slits", a truly quantum mechanical
treatment, or it seems so. (Wheeler gave another treatment
in 1978).
'Young's experiment and the finiteness of information'
Caslav Brukner, Anton Zeilinger
Phil. Trans. R. Soc. Lond. A 360 (2002) 1061
http://arxiv.org/abs/quant-ph/0201026
Young's experiment is the quintessential quantum experiment. It is argued
here that quantum interference is a consequence of the finiteness of
information. The observer has the choice whether that information manifests
itself as path information or in the interference pattern or in both
partially to the extent defined by the finiteness of information.
This archive was generated by hypermail 2.1.5 : Tue Jan 21 2003 - 17:10:21 MST