Re: Duplication Thought Experiment Involving Complementarity

From: George Levy <GLevy.domain.name.hidden>
Date: Sat, 07 Sep 2002 16:39:12 -0700

Bruno Marchal wrote:

> George Levy asks recently "Could somebody incorporate complementarity
> in a thought experiment in the style of Bruno's duplication experiment?"
>
> This is an interesting proposal and I would be glad if someone manage
> to present one. Just that it is *because* duplication-like experiment
> leads
> quickly to obscurities and misleading intuitions, *that* modal logic
> appears to be a fruitful investment, even if it is not the only one.


As it stand, the comp hypothesis is only a philosophical exercise
because it does not reproduce the same phenomenon as QM in particular
the phenomenon of complementarity. Therefore, to establish a meaningful
relevance between comp and QM we must show that such phenomena can be
incorporated in comp.

The following thought experiment is an attempt to illustrate how
complementarity can be incorporated into a duplication experiment. This
experiment raises some interesting questions regarding the relationship
between the scientific MW and the philosopical plenitude.

Thought Experiment:

We are onboard the starship Enterprise, and captain James T. Kirk is
asking Chief Engineer Scotty to beam him down planet Alpha where a large
contigent of Klingon troops is attacking a human settlement mining
Dilithium crystals. There is not enough military personnel aboard the
Enterprise to engage the Klingons. Kirk comes up with a brilliant idea.

Resolutely turning toward his science officer he says, "Spock!" is it
possible to set the transporter to send two or more copies of an
original person?"

It has never been done captain, but there is no theoretical reason why
it could not be done" Spock replies with a puzzled look on his face. But
that would be a brilliant way to quickly generate an army on the planet
surface to fight the Klingons! Each copy will have to be sent to a
slightly different location to avoid having the copies materialize
inside each other. But this is not a problem. This can be done by
setting a grid on the planet's surface and set the transporter to send
each copy to a different point of the grid.

"Scotty," Kirk says, could you please modify the transporter to send a
thousand copies of myself to the planet's surface. Set up a 1024 point
grid on the planet's surface exactly centered at a Latitude of 32° 44' N
 and a Longitude of 117° 10' W. I want each point of the grid to be
spaced by approximately one meter so I won't bump into myself. Send me
to the center of the grid and all the copies to the other points of the
grid.

"What you're asking me is impossible, Captain" exclaims Scotty. "The
transporter will not let me do this!" I can't specify which of you is
the copy and which is the real you! The noise level in the transporter
is so low that the copies will be as good as the original, and there
will be no way to tell which is the copy and which is the original.
There is one more restriction. It's the grid. I can't make the grid any
size or shape that you want.

"Why can't the grid be any size or shape?" responds Kirk. Explain yourself!

"Excuse me captain" interjects Spock, can I please answer for Scotty?"

"By all means" Spock, Kirk replies, but make it short!

"It's actually very simple." Spock explains, the transporter has a beam
width which is determined by the transporter's antenna. Since our
distance to the planet is comparatively large, the transporter beam
intersects the planet's surface over an area approximately 6.6257 square
miles. Changing the shape of the antenna will result in changing the
shape of the grid. The grid can be circular, ellipsoidal, square, or
rectangular. You can pick any shape you want. However, the area of the
beam intersecting the planet is a constant. It must remain at 6.6257
square kilometers. Thus if the grid forms an elongated rectangle with
100 to 1 proportions (25.74x0.2574=6.6257), any one copy of you may
find itself anywhere within that surface up to 25.74 kilometers from
another.

Spock! Are you telling me that my location on the planet surface will be
indeterminate?

Yes Captain. And there is not much you can do about it, except to change
the shape of the gird but the overall grid area must remain equal to
6.6257 square kilometers. For the simple case of a rectangular grid, the
indeterminacy in your x and y position is complementary. Consider
yourself lucky that this positional uncertainty is only confined to the
surface of the panet and not to three dimensions. Some of your copies
might have found themselves transported into solid rock or 10000 feet
above ground.

"Thank you Mr. Spock."

Positioning himself in a transporter Kirk orders, "Scotty energize!" and
he is gone to fight his battle.

The end of the story is left to the reader to imagine how the thousand
copies of Kirk are transported to the planet, defeats the Klingons and
then, in the end, how the copies decide which ones will commit Hara Kiri
and which one will be allowed to go back to the Enterprise.

End of Thought Experiment

Caveat
I am well aware that there is a contradiction if the transporter antenna
can resolve a single point of the grid to better than 1 meter square but
cannot resolve the whole grid to better than 6.6257 square kilometers.
Let's assume that this is due to the peculiarities of the transporter
design: because of the very high power levels, the transporter makes use
of cosmic string segments to connect each of the grid point to the
transporter antenna. Thus, a single cosmic string is attached to a a
single grid point and can therefore provide a high resolution for the
point. However, the antenna which is used to control the bundle of
strings has a resolution of 6.6257 square kilometers. :-)

Questions
This thought experiment, attempt to provide a model of how MW relates to
the Comp hypothesis. Many questions arise.
1) Why is it that the Plenitude is not directly accessed by QM as
explained by comp. Why is there a need for an intermediate MW
characterized by complementarity?
2) Why is complementarity two-dimensional? Could it be
three-dimentional? or higher?
3) Is the two-dimensionality of complementarity fact-like? Are there
other worlds in the Plenitude which have a complementarity with a higher
dimensionality?
4) Is the MW only one instance in the Plenitude? How many levels do we
have to go from the scientifically determined MW to the philosophically
determined Plenitude?
5) Is complementarity anthropically necessary?

This is only a feable attempt in the generation of a physical model to
relate comp to the MW. I hope that we can improve on it through our
discussions.

George
Received on Sat Sep 07 2002 - 16:40:51 PDT