Dear Dr. Iva,
Do you have any idea where all the things I lose go? I had a theory that they just spontaneously tunneled into a wall, or floor, or something. Then one of my friends had to tell me that the possiblilty of that happening is one in ten to the ten to the thirty-thousand. Since my old theory doesn't seem very likely anymore, what happened? Hmmm... maybe it was tears in the space time continuum, or itty bitty tiny black holes, or gremlins, or...?
You are right to realize that there is no way a macroscopic object would be able to tunnel through a wall. Still, your problem can be explained in terms of quantum mechanics. Quantum mechanics is based on the idea that associated with each particle is a sort of "information wave" that lets us know where the particle might or might not be at any given moment. These information waves move just like water waves, earthquake waves, or stadium waves.
Imagine a pebble dropped in a pond. Close to the spot that the pebble fell in the rings are sharply defined. Then as time goes on the rings spread out, and eventually fade back into the pond. This effect is called dispersion. A wave will spread out and flatten as time goes on.
The way an information wave determines a particle's position is really quite simple. The particle is most likely to be in a spot where the wave has a high amplitude. You can see that if the wave has a sharp peak, the particle is almost certainly right in the center. However, if the wave function flattens and spreads, the particle might be in the center, or off to the side, or just about anywhere.
Scientists believe that wave functions only have effect on microscopic objects, but there seems to be plenty of evidence that they affect small items like pens and keychains and socks too. When you first set down your car keys on your desk, you can be pretty sure that they will still be there if you look at them a minute later. Come back in an hour, and they will probably still be there, but they might not. As time goes on, their information wave will spread and flatten, and by next week your keys could be just about anywhere.
The oddest thing about quantum mechanics is that YOU can change the shape of a particle's wave function just by observing the particle! If you set your shoes on the floor of your bedroom and stare at them you know exactly where they are. It is as if their wave function was infinitely peaked right there. If you stare at them all month the wave function will never spread. Those shoes won't move an inch. But step out of the room and go watch the evening news for an hour, and your shoes just might not be there when you get back. Yes, I know you will have remembered that you put them right there in the middle of the floor, but somehow, there they are, under the bed! Once you find them again, their wave function peaks sharply and the cycle starts over.
It isn't like your shoes physically got up and moved under the bed. It's just that as time goes on the probability that you will find them under the bed grows closer and closer to the probability that you will find them in the middle of the floor. Those shoes really aren't anywhere until you find them. This explains how you can look for a certain object in the exact same place three or four seperate times and not see it there, only to find it right in front of you on your last try.
Another reason that things get lost has to do with their potential function. When the potential is high, that means it takes the object a lot of energy to be in that spot. If the potential is low, the object doesn't need as much energy to be there. Everything in the universe is intrinsically lazy, so naturally things tend to go to places where they have lower potential.
Many household objects have a particular potential function associated with the floor plan of a house. Here is a sample potential function for socks.
It is easy to see from this diagram that socks get lost in the wash so often because the potential for socks in a washing machine is so high compared with the potential for the washroom floor.
There are ways to avoid all these quantum problems. You can be sure to only use classical objects. Unfortunately, in classical mechanics, large objects are often treated as simple point masses. This would mean that even though you could always determine exactly where your socks are, they wouldn't fit very well.
Any Way You Slice It
Dear Dr. Iva,
How does a banana work?
The banana is truly a highly complex tool. Scientists are not sure that they fully understand it, even after centuries of study. The banana was first used by the African tribes in what is now known as the Banana Republic. They would challenge a rival tribe to battle, and then spread rumors among their enemy that they had discovered the secret of the banana and would use it against them. Most often the opposing tribe would come to the designated battle field, pleading for mercy, as the banana, when used correctly, is considered to be one of the most powerful weapons known to primitive peoples. Of course, after the other tribe had surrendered, the first tribe would laugh and tell them that they were all crazy for thinking they had actually figured out how the banana works, hence the term, "going bananas".
It has recently been proven that any cross section of a banana can be approximated by a regular conic section. It is hypothesized that the volume of a banana can be calculated by slicing it up into a number of circles, measuring the area of each circle, summing the areas, and multiplying it by the thickness of a slice. As the number of slices approaches infinity, the volume of the banana can be found with as much accuracy as required. This is known as a Reimann Sundae, after the mathematician who got credit for developing the method.
But although we can understand a lot of things about the banana, exactly how it works remains a mystery. Perhaps some day science will be advanced enough that we can understand this perplexing problem.