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Wednesday, August 31, 2005

Deterministic Universe (step five) Superposition, Copenhagen Interpretation, and Schrödinger's Cat

Superposition is a principle of quantum theory that describes a challenging concept about the nature and behavior of matter and forces at the atomic level. The principle of superposition claims that while we do not know what the state of any object is, it is actually in all possible states simultaneously, as long as we don't look to check. It is the measurement itself that causes the object to be limited to a single possibility.

Recently, one of Einstein's young friends, Abraham Pais, reported that around 1950 Einstein had asked him if he really believed that the moon existed only if he looked at it. Einstein asked this question because he disagreed with a lot of the most important and influential physicists of his time, about the interpretation of that area of physics known as quantum physics that deals with the behavior of objects in the microphysical, subatomic, world. Many of these physicists were committed to an interpretation from which it follows that nothing - the moon included - exists unless it is being observed. Einstein wanted to know whether Pais was on his side or theirs.

The development of quantum theory is one of the greatest scientific achievements of the twentieth century. However science is still figuring out the question of why it works. Unlike classical physics, quantum theory discards causality, declaring that events on the subatomic level simply happen.

Einstein refused to believe in a reality that precluded cause and effect. "God does not play dice with the universe." he declared. He especially objected to the theory's insistence that particles, forces, and events seemed to come into existence only when a measurement or observation was made.

The rules of quantum mechanics tell you statistically where the particles will hit the screen, and will identify the bright bands where many particles are likely to hit and the dark bands where few particles are likely to hit. However, for a single particle, the rules of quantum mechanics cannot predict where the particle will actually be observed. What are the rules to determine where an individual particle is observed? The probability statements made by quantum mechanics are irreducible in the sense that they don't exclusively reflect our limited knowledge of some hidden variables. In classical physics, probabilities were used to describe the outcome of rolling a die, even though the process was thought to be deterministic. Probabilities were used to substitute for complete knowledge. By contrast, the Copenhagen interpretation holds that in quantum mechanics, measurement outcomes are fundamentally indeterministic.

What happens to the particle in between the time it is emitted and the time that it is observed? The particle seems to be interacting with both slits and this appears inconsistent with the behavior of a point particle, yet when the particle is observed, one sees a point particle. Physics is the science of outcomes of measurement processes. Speculation beyond that cannot be justified. The Copenhagen interpretation rejects questions like "where was the particle before I measured its position" as meaningless.

When the particle is moving through the slits, its behavior appears to be described by a non-localized wave function which is traveling through both slits at the same time. Yet when the particle is observed it is never a diffuse non-localized wave packet, but appears to be a single point particle. The act of measurement causes an instantaneous "collapse of the wave function". This means that the measurement process randomly picks out exactly one of the many possibilities allowed for by the state's wave function, and the wave function instantaneously changes to reflect that pick. This causes the particle to appear to switch between statistical and non-statistical behaviors.

Erwin Schrödinger proposed a similar analogy to show how superposition would work with an everyday example. Called Schrödinger's Cat, a cat is placed into a steel chamber. In the chamber, exists a very small amount of a radioactive substance. If even a single atom of the substance decays during the test period then the cat will die. An observer cannot know whether an atom has decayed, and consequently, cannot know whether the cat is alive or dead. It is only when we break open the box and learn the condition of the cat that the superposition is lost, and the cat becomes dead or alive. This situation is sometimes called quantum indeterminacy or the observer's paradox: the observation or measurement itself affects an outcome, so that it can never be known what the outcome would have been if it were not observed.

Copenhagen Interpretation held that in quantum mechanics, measurement outcomes are fundamentally indeterministic. Einstein would object, stating that the cat would not become dead or alive once it were observer. The cat will be dead or alive, however we will not know its condition until observed. Similarly, I use the Copenhagen Interpretation and Schrödinger's Cat to explain that electrons will continue to act -- based on Physical Law -- even if we do not, or cannot, observe how they act. Though we cannot measure outcomes they are still determined from antecedent causes.


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