First, quantum physics tells us that as you move to smaller and smaller scales, some important physical quantities become “pixelated.” Things that appear to be continuous (smooth and gradual) at the macroscopic scale are in fact discrete and chunky at the microscopic scale. In other words, they are limited to distinct, well-separated values. For example, the usual laws of physics would say that the energy embodied in a swinging clock pendulum could take on any possible value depending on how fast and how high it is swinging. However, we’ll see that a tiny clock pendulum in the quantum realm cannot swing at just any energy, but is restricted to certain, discrete energy values.
At first glance, this may seem less revolutionary than it really is. In our digital age, we’re accustomed to things being restricted to small steps. If you go to turn up your home stereo, for example, you will raise it in small, incremental steps as indicated by little clicks or a progress bar, or even by enumerated values. Likewise, we’re used to seeing low-resolution digital photographs looking pixelated when stretched too big. If you bring an image up on a computer display, and then zoom in further and further and further, you often see that what appeared to be smooth was in fact composed of many small dots.
The difference between these everyday examples and quantum granularity is that the quantum version is inherent and unavoidable. It can never be overcome. In principle, there is nothing to stop us from developing a computer display or a printer with better and better resolution. At the quantum scale, however, smaller pixels are simply not available.
In the quantum realm, many physical quantities turn out to be discrete, or pixelated, in nature.
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