The latest issue of Discover, which I do not have in front of me, mentioned something about scientists discovering that negative knowledge, or the actual decrease of knowledge, is possible. It was a short article and it had something to do with Heisenberg’s uncertainty principle and the various spins of pairs of electrons.
I didn’t quite grasp the idea presented but the author offered an example to help us with the concept.
Let’s say there are two cards: the Ace of hearts and the Ace of spades.
Tom and Mary each pick one card face down. Tom looks at his card. By doing so, he knows not only what his card is but also what Mary’s card is.
Now let’s say they pick cards face down. Before looking at them, Tom hands his card to Mary. Now it is impossible to determine who picked what card.
Therefore, the article claimed, knowledge is LOST. Huh? How so? I’m having a hard time wrapping my brain around this concept. The knowledge is unknown and it remains unknown. It wasn’t gained, but to be lost wouldn’t it imply that either Tom or Mary knew something at one point? What exactly was lost in this transaction?
The idea, I believe, is that which card was picked is not actually determined unless the system is observed and the waveform collapsed. It’s not that you don’t know which card you picked, it’s that you picked both, and the actual choice happens when you observe it (simplistically speaking). If you make it impossible to observe by mixing up the two cards (again, in a perfect quantum system where it’s impossible to trace which card was which) or destroying them, you’re destorying that information.
The basic problem here is a failure of analogies. Any classical analogy to a quantum-mechanical system will either not make sense classically, or it will not be analogous to the quantum process in question. I don’t know enough about this particular situation to say which it is, in this case.
Without having read about the matter, here’s my WAG. (<- Note!)
First of all, assume bad Science journalism. (Very common.) The author probably didn’t understand the distinction between loss of information (the amount of information decreasing) and negative information.
Examples of loss of information are far easier to come by than given in the OP. E.g., take an encyclopedia, burn it, flush the ashes down the toilet, etc. The amount of information in your house has gone down, but not negative.
On a quantum level, things “fluctuate”. Some fluctuations might accidently create an encyclopedia. (The odds are tiny to say the least.) But by symmetry, if such a fluctuation were to occur, there must be a counter fluctuation in the system somewhere else so the net information remains the same. The counter fluctuation would have negative information.
Now, quantum fluctuating cards, let alone encyclopedias, are too large to realistically hope to observe in a lab. But pairs of electrons will do nicely. OTOH, the amount of information such a pair can represent is barely non-zero.
http://www.physorg.com/news5621.html
"While all this might appear to be very mysterious,Dr Michal Horodecki is quick to point out that the idea of negative information can be put on a rigorous scientific footing. “We can quantify information in terms of how much stuff I need to send you before you get to know something. In the case of negative quantum information, you can get to know something without me sending you any quantum particles. In fact, you will gain the potential to learn more quantum information in the future.” "
I found the article. Page 14. Here’s a snipet for it:
“In physics, this game can be played using pairs of electrons in place of cards. Electrons can spin in what are called singlets. One spins in one direction; the other spins in the opposite. They are said to be entangled because, in teh bizarre world of quantum mechanics, neither electron has a definite spin until one of them is measured. At that instant, both particles immediately seetle in to their respective spins. Put another way, each electron has an equal chance of being measured while spinning in one direction or the other. Unlike playing cards, which can be glanced at and remembered, the electron pairs cannot be observed without nullifying their delicate duality. So if (tom and mary (I apparently changed their names in the OP)) each have half a singlet, and Paul gives away his electron, the correlation is irevocably lost. The fragile, solipsisitic nature of quantum states allows for negative information.”
So where is this negative information coming from again? By whose reference point is information lost and how could it be lost when it was never gained in the first place?
Here is the account from Oppenheim, one of the folks who worked on the experiments showing quantum information can be negative. I read this when it came out in early august and it really is very readable and understandable in the real world.