Negative information (was: Help support non-crazy scientist?)

Gruff <gruffstar@xxxxxxxxxxxxxx> kirjoitti 14.06.2007:

Back the non-ironic point though, yes, I think negative information is
a non-classical concept*, but it would be interesting to see if there
was a case that made sense from a human perspective.

Well, there would seem to be a fairly simple analogy that only depends
on having an isolated system:

Suppose that I have two otherwise identical balls, one of which is red
and the other one blue. I give you a bag containing one of them, and
keep the other one in my pocket.

Now, clearly, the bag contains information about the color of the ball
in it. To be specific, it contains exactly one bit. _You_ don't know
the information yet, since you haven't looked inside the bag; but you
have the bag, and the bag contains the information, so in a sense you
do possess that one bit of information.

Here the bag with the ball here is analogous to an undisturbed quantum
system, just like the box in the famous Schroedinger's Cat thought
experiment. For quantum systems, the isolation is required to keep
the quantum state from collapsing. But for our purposes, we don't
really need the system to be in a non-classical state; all we need is
for it to be isolated.

Now, the other ball, which I have in my pocket, clearly also contains
information about the color of the ball in the bag. In fact, it also
carries one bit of information -- but it's the same bit as the one
carried by the ball in the bag! In statistical language, we'd say
that the colors of the two balls are correlated. We (or at least you)
don't know which ball is which, but we know that, whatever color the
ball in my pocket has, the one in the bag has the other.

You could, if you wanted, think of this as a classical analogy of
quantum entanglement. It's not quite the same thing, but I've heard
people who know more about quantum mechanics than I do say that the
analogy isn't entirely bogus. For the difference, try googling for
the term "Bell inequality". In any case, it's good enough for us.

Now suppose that, before you look into the bag, I take the other ball
from my pocket and, without showing it to you, slip it into the bag
and give it a good shake. Since the balls are indistinguishable
except for their color, you'll no longer be able to tell which of them
was in the bag to begin with. The information that you possessed is
no longer there. The two bits cancel each other out. In a sense,
I've just sent you a signal carrying minus one bit of information.

Of course, all of this relies on the bag with the ball being an
isolated system. As soon as you peek into the bag and see the color
of the ball in it, it doesn't matter what I do with the other ball;
you'll still know what you saw. But then, the same is true for
quantum systems as well; as soon as you measure them, they collapse
(from your viewpoint, anyway) and no longer behave the same.

But as long as you resist the temptation to peek, I can first send you
a bit of information and then, if I so choose, unsend it by sending
you a "negative" bit to cancel out the first one. If that's not an
example of negative information, I don't know what is.

--
Ilmari Karonen
To reply by e-mail, please replace ".invalid" with ".net" in address.
.

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