Re: Duplication Thought Experiment Involving Complementarity

From: George Levy <GLevy.domain.name.hidden>
Date: Sun, 08 Sep 2002 12:37:14 -0700

  Stephen

Your point is well taken. We can sample and send the original Kirk every
microsecond. It would take one millisecond to send one thousand Kirks,
each copy sufficiently different for QM purposes, but not different
enough for each Kirk to consciously know the difference.

I should have kept my units the same throughout (i.e., 6.6257 square
kilometers) instead of alternating square miles and square kilometers.
Can any one of you recognize this number?

I would like to discuss another difference between the thought
experiment and QM. The thought experiment provides a discrete grid
comprising 1024 points. As a result, Kirk can occupy any one of 1024
discrete points. His position uncertainty is discrete. On the other
hand, the uncertainty generated by QM events is continuous.

George

Stephen Paul King wrote:

> Dear George and Friends,
>
>
>
> Could you modify your story to take into consideration the "no
> cloning" theorem of QM? Basically it states that it is impossible to
> copy the quantum mechanical information of a system. On the other
> hand, we might assume the Banach-Tarsky paradox derived from the use
> of the axiom of choice and consider that each of Kirk's clones were
> diferent enough that their QM information had no overlap and that each
> could be generated from some arbitrary original "Kirk".
>
> ----- Original Message -----
>
> From:George Levy <mailto:GLevy.domain.name.hidden>
>
> To: everything-list.domain.name.hidden <mailto:everything-list.domain.name.hidden>
>
> Sent: Saturday, September 07, 2002 7:39 PM
>
> Subject: Re: Duplication Thought Experiment Involving Complementarity
>
>
> 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 Sun Sep 08 2002 - 12:39:23 PDT