Our brains evolved to function in a world where everything is much bigger than an atom, much smaller than the Universe, and standing still compared to the speed of light. Whenever we deal with very small or very large scales of space and time or phenomena close to the speed of light, we encounter apparent paradoxes. They're not real paradoxes, just phenomena that are unfamiliar to us because of how our brains evolved.
On the atomic scale, matter and energy are inherently fuzzy. We cannot simultaneously specify the momentum and position of a particle to better than a certain precision. This fact, called the Heisenberg Uncertainty Principle, has real results. For example, since the position of a particle is inherently fuzzy, we often cannot say for certain whether it is on one side or the other of a thin barrier, even if the barrier, in theory, is impassible. Electrons and other particles can and do "tunnel" through barriers, and this effect is used in electronics.
One such barrier is the energy barrier holding particles together in an atomic nucleus. In classical physics, the barrier should either be absolutely impassible or completely ineffective. In reality, there is a finite probability that a particle will get through the energy barrier. If you think about it, radioactive decay is a strange law. It's statistical: a given nucleus has a fixed probability of decaying per unit time. A C-14 atom has a half-life of 5700 years and has about a one in ten thousand chance of decaying in any given year. It has the same chance whether the nucleus is a year old or a million years old. We don't say there's a 50% chance of an eclipse on a certain date - the odds are either 100% or zero. The statistical nature of decay is a consequence of uncertainty. In quantum mechanics, it is possible for a camel to pass through the eye of a needle, though the probability is mind-bogglingly tiny.
Another aspect of the inherent fuzziness of matter is the wave-particle duality. If we set up an experiment that requires light photons or electrons to behave as particles, they behave as particles. If we set up an experiment that requires them to act as waves, they obligingly act as waves. So are they waves or particles? They're both, and neither. Sometimes we can approximate them as particles, other times as waves, and very often neither approximation works and we have to resort to the more complex equations of physics to describe them.
The classic wave-particle experiment involves sending light through two slits. If we simply shine light at the two slits, the light from both slits interferes and creates a pattern of light and dark bands. If we set up the system so we determine beforehand which slit each photon of light passes through, we get a patch of light behind each slit and no interference pattern. If we expect the light to behave as a wave, it does. If we expect it to act as a particle, it does. This sort of behavior provides a fertile field for psychics and pseudo-philosophers of science who claim that belief can affect the outcome of experiments.
In reality, the result is (in some ways) not a whole lot more mysterious than throwing a switch and causing a train to travel down one track instead of another. By setting the experiment up so that we determine the path of the photon, we alter its state, and hence the outcome of the experiment.
One of the principal consequences of uncertainty is that you cannot specify the exact state of a particle without somehow interacting with it.
A famous paradox involving Uncertainty is sometimes called "Who killed Schroedinger's Cat?" after one of the physicists who developed the concept of Quantum Uncertainty. We lock a cat in a box with a vial of poison gas. A Geiger counter is wired to the vial; when the Geiger counter detects the decay of a radioactive atom, it breaks the vial and kills the cat. After a period of time we look into the box. Is the cat alive or dead?
Quite a few physicists hold that the question is meaningless until the observation is made; that the "state of the system" is indeterminate until the box is opened, at which point the system "collapses" to some state whose probability can be calculated using quantum mechanics. The question has an obvious relation to the ancient conundrum, "If a tree falls in a forest with no one to hear it, does the tree make a noise?"
Schroedinger's Cat is a good example of a "thought experiment," a device often used in physics to investigate the consequences of hypotheses. It is a great heuristic device that illustrates some of the paradoxes of quantum mechanics while sharpening our inquiries. But problems arise from the many people who take it too literally. These include some scientists who should know better and a lot of would-be philosophers of science who believe esse est percipi (to be is to be perceived).
Let's vary the cat-in-the-box experiment a little.
Clearly, we rapidly end up with absurdities if we assume that conscious observing determines the state of a system. What is important are the changes that occur in the system, and any physical object that is potentially capable of being influenced by the event is an "observer". The atomic decay has already been "observed" because the nucleus that decayed has changed. The system whose quantum state "collapses" is the particle in the atomic nucleus that changes during a radioactive decay. Everything else after that - the geiger counter, the vial, the cat - is classical deterministic physics. Whether a sentient being takes note is irrelevant. There is a direct experimental test of this idea. Some uranium nuclei decay by spontaneous fission. The two resulting nuclei fly apart through the surrounding material, raising a fair amount of havoc. The method of fission-track dating involves etching a mineral with acid to enhance the tracks caused by spontaneous fission, then counting the tracks to determine the age of the material. According to the "cat-is-indeterminate" school, the state of the nuclei is indeterminate until we etch the sample, but etching would not work unless there was pre-existing damage to the material.
Actually, even the tree-in-the-forest question assumes that we can know what took place in the absence of an observer. How do we know a tree fell at all? If we're prepared to say our act of observing determines whether sound exists, why not say that the forest itself exists only because we observe it? Many people recall that as small children they wondered if everybody else disappeared when they weren't looking. Some people never outgrow it.
Another interesting misapplication of the Uncertainty Principle was physicist Mohan Kalelkar's interpretation of a paradox called Newcomb's Paradox, which involves trying to guess what amount of money an omniscient being has put in one of two boxes. The paradox is that whatever strategy we use, the being can anticipate and defeat it, even though we are trying to guess the state of a system that already exists. Kalelkar asserted that the system is indeterminate, and by analogy with the famous two-slit experiment, claimed that opening the boxes determines the outcome of the experiment. This interpretation first of all forgets that the outcome is already known by the being who put the money in the boxes, and second makes the far more profound mistake of ignoring the difference in size between an electron and a dollar bill.
Created 3 February 1998, Last Update 30 August 2011
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