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classical mechanics explains behavior of large objects, while quantum mechanics describes very small objects, such as subatomic particles. In his example during class, he described water in both ways. In a classical sense, when we pour water from a can, it comes out as one continuous stream. However, if we looked at it at the quantum level, we would find that the water molecules are moving one by one- they are separate, not continuous. It just helps to make the distinction. Also, a variable can be any number in classical mechanics, but is limited to a certain few numbers in quantum mechanics.
Classical mechanics describes how large objects act and their corresponding behavior. Classical mechanics typically represents a continuous function because the object is so large that it can be present in a continuous field. Quantum mechanics, meanwhile, describes the behavior of small objects which it accepts energy in small, discrete amounts. In the example of water being poured from a flowering can, water is explained by both classical and quantum mechanics. When the water is initially being poured out, there is a lot of water in the can so there is a continuous stream of water coming from the can (classical mechanics). As the amount of water in the can lessens, it becomes quantized because clusters of the water molecules fall out until one discrete water molecule falls out of the can (quantum mechanics). Therefore, the water being poured out of the can at the small scale isn't continuous anymore.
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