Absolutely Small - Michael D. Fayer [5]
I have to admit to simplifying a little bit here. In two runs of the Schrödinger’s Cats experiment, you probably would not get exactly 500 live and 500 dead cats on each run. This is somewhat like flipping an honest coin 1000 times. Because the probability of getting heads is one half and the probability of getting tails is one half, after 1000 flips you will get approximately 500 heads. However, you might also get 496 heads or 512 heads. The probability of getting exactly 500 heads or 500 live cats out of 1000 trials is 0.025 (2.5%). The probability of getting 496 heads is 0.024 (2.4%) and 512 heads is 0.019 (1.9%). The probability of getting only 400 heads or 400 live cats out of 1000 trials is 4.6 × 10-11 = 0.000000000046. So the probable outcomes are clustered around 500 out of a 1000 or 50%. Knowing that you have 1000 Schrödinger’s Cat boxes with 50-50 mixtures of live-dead cats or 1000 flips of an honest coin, you can’t say what will happen when you open one box or flip the coin one time. In fact, you can’t even say exactly what will happen when you open all 1000 boxes or flip the coin 1000 times. You can say what the probability of getting a particular result is for one event and what the likely cumulative results will be for many events.
NOT LIKE FLIPPING COINS
A fundamental difference exists between Schrödinger’s Cats, or more correctly real quantum experiments, and flipping pennies. Before I flip a penny, it is either heads or tails. When I flip it, I may not know what the outcome will be, but the penny starts in a well-defined state, either heads or tails, and ends in a well-defined state, either heads or tails. It is possible to construct a machine that flips a penny so precisely that it always lands with the same result. Nothing inherent in nature prevents the construction of such a machine. If a penny with heads up is inserted into the machine, a switch could determine whether the penny lands heads or tails. In flipping a coin by hand, the nonreproducibility of the flip is what randomizes the outcome. However, a box containing Schrödinger’s Cat is completely different. The cat is a 50-50 mixture of live and dead. It is the act of opening the box and observing the state of the cat that causes it to change from a “mixed state” into a “pure state” of either alive or dead. It doesn’t matter how precisely the boxes are opened. Unlike flipping pennies, a machine constructed to open each of the 1000 boxes exactly the same way will not make the results come out the same. The only thing that can be known about opening any one box is that there is a 50% chance of finding a live cat.
REAL PHENOMENA CAN BEHAVE LIKE SCHRÖDINGER’S CATS
As described, the Schrödinger’s Cat problem cannot be actualized. However, in nature many particles and situations do behave in a manner analogous to opening Schrödinger’s Cat boxes. Particles such as photons (particles of light), electrons, atoms, and molecules have “mixed states” that become “pure states” upon observation, in a manner like that described for Schrödinger’s Cats. The things that make up everyday matter, processes, and phenomena behave at a fundamental level in a way that, at first, is as counterintuitive as Schrödinger’s Cats. However, the problem does not lie with the behavior of electrons and atoms, but rather with our intuition of how things should behave. Our intuition is based on our everyday experiences. We take in information with our senses, which are only capable of observing phenomena that involve the behavior of matter governed by the laws of classical mechanics. It is necessary to develop a new understanding of nature and a new intuition to understand and accept the quantum mechanical world that is all around us but not intuitively understandable from our sensory perceptions.
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