Monday, January 2, 2012
Science is built on experiment and critical observation. Any hypothesis worthy of consideration must allow for, or propose, tests for its validation.
However, before investing huge amounts of time and resources on actual, physical experiments, in many instance, an idea can be subjected to a gauntlet of thought (or, in German, gedanken) experiments.
These are imaginary experiments testing the implications of a hypothesis for internal contradictions or inconsistencies with established theories. They should not be confused with the process of mentally designing an actual physical experiment.
Thought experiments may ultimately help in designing real, physical experiments, but that is not their purpose. They are intended to reveal ideas that are illogical.
Gedanken experiments have a long history dating back to the earliest mathematical proofs. But, typically, they have been a tool of physicists. Among the giants of physics that have employed this methodology are Galileo, Newton, Einstein and Schrodinger.
Galileo demonstrated the power of gedanken experiments in a number of his works, including his "Mathematical Discourses and Demonstrations" published in 1628.
Rather than dropping objects of different mass from the top of the Leaning Tower of Pisa as tradition says, Galileo contrived a discussion between two imaginary characters, Salviati and Simplicio. In this exchange he exposes a contradiction in the idea that gravity causes heavier objects to fall faster than light ones.
The dialog is instructive:
Salviati - If then we take two bodies whose natural speeds are different, it is clear that on uniting the two, the more rapid one will be partly retarded by the slower, and the slower will be somewhat hastened by the swifter. Do you not agree with me in this opinion?
Simplicio - You are unquestionably right.
Salviati - But if this is true, and if a large stone moves with a speed of, say, eight while a smaller moves with a speed of four, then when they are united, the system will move with a speed less than eight; but the two stones when tied together make a stone larger than that which before moved with a speed of eight. Hence the heavier body moves with less speed than the lighter; an effect which is contrary to your supposition. Thus you see how, from your assumption that the heavier body moves more rapidly than the lighter one, I infer that the heavier body moves more slowly.
As with many gedanken experiments, the discussion ignores extraneous effects and focuses on an underlying phenomenon. If this experiment were actually performed, the effects of an object's shape and surface texture while traveling through air would obscure the fundamental effects of gravity.
Galileo ignored the effects of air resistance. He only wanted to illustrate the gravitational effect on different masses. In a vacuum a feather and a bowling ball drop at the same speed. It is irrelevant that, in the atmosphere, air resistance would retard the feather more than the ball.
Sometimes thought experiments led to paradoxes. In these cases, the individual premises of a hypothesis may seem perfectly reasonable. However, as a hypothetical experiment is thought through, step by step, contradictions are found.
These can be internal contradictions, or there can be implications which are inconsistent with everyday experience or established ideas. Some of the more revolutionary ideas of twentieth-century physics arose from attempts to resolve contradictions that could not be accounted for with conventional ideas.
The unusual behavior of matter on the subatomic scale illustrates a number of paradoxes in a branch of physics called quantum mechanics.
Trying to make sense of this behavior imposes new perspectives on how we think about observation and measurement on the atomic scale. The insights we have gained from this are profound. Without them, we would have no hope of understanding the physics of atoms and their parts.
One example, the Einstein-Podolsky-Rosen (EPR) paradox, arises in a gedanken experiment utilizing something called the Copenhagen interpretation of quantum mechanics.
As Galileo imagined measurements of the speed of different dropped objects, this thought experiment imagines measurements on subatomic systems. It describes how a measurement on one system appears to influence what happens in a second, separate system with which it seemingly has no interaction.
The Copenhagen interpretation of this phenomenon appears to violate the fundamental principle of causality. This is a seemingly simple notion, derived from our intuition, that an event must be preceded by, or be caused by, some kind of interaction. Events have causes.
On the atomic scale, interactions are accounted for by mathematical representations called wave functions. Such models are hugely successful predicting the statistical outcome of many real experiments.
The authors who first explained the EPR paradox state at the end of their published paper:
"While we have thus shown that the wave function does not provide a complete description of the physical reality, we left open the question of whether or not such a description exists. We believe, however, that such a theory is possible."
So, in this case, we have a thought experiment suggesting the mathematical model for interactions of subatomic things, though useful, is inadequate. With little success, physicists have tried beefing-up wave functions by introducing ideas of "hidden variables".
Alternatively, one can argue the EPR paradox demonstrates the Copenhagen interpretation is flawed. But, coming up with explanations that are free of paradoxes has proven formidable.
Gedanken experiments show an important way scientific knowledge of a given subject progresses, especially in its early phase. Furthermore, they illustrate the vital role of imagination in science. In the end, the final arbiter for the imagination of scientists is that their hypotheses must conform to physical reality as demonstrated in real experiments.Steve Luckstead is a medical physicist in the radiation oncology department at St. Mary Medical Center. He can be reached at email@example.com.