On Tue, May 23, 2006 at 01:56:11AM +1200, Russell McMahon wrote:
> 
> Good ol quantum mechanics has wrought utter havoc with our conceptions 
> of reality. Fortunately the vast % of people don't know this :-). Not 
> only is QM not understandable but it demands that it be 
> ununderstandable and even goes so far as to demand (Copenhagen 
> flavour, not necessarily all) that even the concept of understanding 
> what happens between emission and detection is meaningless.
> 
> Our oh so solid reality is built, it seems, on a totally 
> ununderstandable and indeed meaningless foundation. yet QM predicts 
> results with an accuracy that is astounding. It is thoroughly 
> empirical in nature. If we assume that this happens then it must 
> follow that xxx. And they did and it did so they do. And nobody knows 
> why. Or, QM says, ever can. And even the concept of understanding why 
> is meaningless.
 
This is completely untrue of people who had reasonable dealings with QM
beyond popular reports (many of which sensationalist to the point of
doing more harm than good). I don't mean do downplay the philosophical
difficulties related to quantum measurement, but these difficulties are
tangential to QM itself, which is no less meaningful than any other
theory, and in fact is more consistent and often makes better sense than
Newtonian mechanics.

As an example, which I hope I won't botch, consider the principle of
least action. One of the most aesthetically pleasing formulations of
classical mechanics is Hamilton's principle, which states that an object
moving from A to B will choose the path on which the action (roughly an
integral over time of the difference between the kinetic and potential
energies) is minimal.

This method is very powerful mathematically an gives a lot of physical
insight, but there is one thing about it which is very disturbing - the
integral depends on its starting and finishing points, A and B - how can
the object moving along supposed to know where it is supposed to end up?
This is exactly the kind of teleological thinking that was supposed to
be abandoned by Newton.

The solution to this problem was solved by Feynman when he formulated
the quantum equivalent of the action principle (a.k.a. the path
integral) - the action now lives inside a trigonometric function, and
instead of finding the path along which the action is minimal we allow
the object to follow all possible path, and simply sum over the
trigonometric function.

For processes that take place on the quantum scale, this sum can indeed
become quite formidable, but a physically interesting result can be had
when you try to apply this method to macroscopic objects. Far from the
minimal action path, the trigonometric function oscillates rapidly, and
essentially destructively interferes with itself, while on the classical
path the action doesn't change and Hamilton's principle is regenrated
simply as constructive interference, and without the object's behaviour
depending on its future.

I know it is easy to get excited about all the non-trivialness QM has to
offer to the unaccustomed mind, but please don't confuse triviality with
meaning.

Yair.
-- 
http://www.piclist.com PIC/SX FAQ & list archive
View/change your membership options at
http://mailman.mit.edu/mailman/listinfo/piclist