The physical nature of the system imposes a definite limit upon how precise this can all be. We'll see the car touch the finish line, push the stopwatch button, and look at the digital display. In this classical case, there is clearly some degree of uncertainty about this, because these actions take some physical time. We measure the speed by pushing a button on a stopwatch at the moment we see it cross the finish line and we measure the speed by looking at a digital read-out (which is not in line with watching the car, so you have to turn your head once it crosses the finish line). We are supposed to measure not only the time that it crosses the finish line but also the exact speed at which it does so. Let's say that we were watching a race car on a track and we were supposed to record when it crossed a finish line. Though the above may seem very strange, there's actually a decent correspondence to the way we can function in the real (that is, classical) world. The more precisely we measure time, the less precisely we are able to simultaneously measure energy (and vice versa). ![]() The more precisely we measure position, the less precisely we are able to simultaneously measure momentum (and vice versa). In other words, we cannot simultaneously measure both properties within each equation to an unlimited level of precision. If the uncertainty in any of these measurements gets very small, which corresponds to having an extremely precise measurement, then these relationships tell us that the corresponding uncertainty would have to increase, to maintain the proportionality. delta- t: This is the uncertainty in time measurement of an object.įrom these equations, we can tell some physical properties of the system's measurement uncertainty based upon our corresponding level of precision with our measurement.delta- E: This is the uncertainty in energy of an object.delta- p: This is the uncertainty in momentum of an object. ![]()
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