Quantum Information for Quantum Cats (3)

Unbearable Whimsicalness of Quantum Being

In classical mechanics (which in this case is synonymous with our common sense), sufficiently precise measurement would yield practically complete specification of the state of an object. Let us, as an example consider an arrow at fixed location which can be rotated in a plane. Once you fix the reference of orientation, let's say the perpendicular direction "up", the state of the arrow is specified by the angle \theta . Whoever measure the angle of this arrow, it is naturally \theta everytime he measures.

Let us imagin that the arrow is very small, say as small as one milionth meter, which is also called one nanometer. The arrow is now govered by quantum mechanics. Craziness of creaps in. A small arrow of this scale is referred to as spin.

The quantum arrow here is not a ficticious object of our invention. An atom or an electron are naturally existing quantum arrows. They bear magnetic moments, and their north pole can be identified as the direction of the arrow.

Now let us consider a situation where somebody places this quantum arrow in the direction \theta. Following the convention of the business, We refer this somebody as Alice. Now what will happen if somebody else, named Bob comes in and measure the direction of the arrow? The answer is that it is not necessarily \theta, but can be anything with a certain probability. Not only that, but that probability changes according to the wishes of Bob! There are certain rule even in this arbitrary craziness: The answer can never be \theta+180 degree however Bob wishes. In fact Bob's discretion is rather limited. He can hope for an angle \phi, and can obtain either \phi or \phi+180 degree as an answer with certain probability which he has no control.


On Intuitive Understanding of Quantum Craziness

However crazy the quantum mechanics appear to our intuition, we might argues that it is sufficient that the rule exist in mathematically consistent manner, and if we can always operatively follow the rule to get experimentally verifiable results. This type of atitude, a mix of agnosticism and pragmatism, is in fact the mainstream in the practitioner of quantum mechanics. This is probably a historical consequence of the dominance of one of the founder of quantum machanics, Niels Bohr and his disiples usually referred to as Copenhagen School. However, it apears to be a human nature to aspire for an understanding of everything including all mysteries in humanly understandable way. This instict for intuition has been represented by Albert Einstein in the early stage of quantum mechanics, and he has mounted a repeated chanlege to Copenhagen interpretation of quantum mechanics. This traditonally had no practical effect on the application of quantum mechanics, thus regarded as a metaphysocal debate. But anti-Copenhagen realism has kept alive by a small minority of physisists, among whom David Bohm is famous for the discovery of "Aharonov-Bohm effect", a profound discovery of pratical consequences, but really brought about by his pholosophical line of thinking. This is clearly an example of a heresy's ocasional enriching power. I do not know whether recent "many world interpretation" also falls into this type of potentially productive category or just a counter-productive philosophizing. Those who are into the sociology of science (or just academic gossip) might better look at this, not that trivial pratical joke of so-called post-modern science wars (or whatever that was called).