Uncertainty of Measurements [1/10] |
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One of the fundamental principles of experimental science is that no real measurement is infinitely precise, but instead must necessarily include a degree of uncertainty in the value. | ||

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Uncertainty of Measurements [2/10] |
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This uncertainty which is present in any real measurement arises from the fact that any imaginable measuring device--even if designed and used perfectly---can record its measurement only with a finite precision. | ||

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Uncertainty of Measurements [3/10] |
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One way to understand this fact is to realize that in order to record a measurement with infinite precision, the instrument would require an output capable of displaying an infinite number of digits. | ||

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Uncertainty of Measurements [4/10] |
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By using more accurate measuring devices, uncertainty in measurements can often be made as small as needed for a particular purpose, but it can never be eliminated completely, even as a theoretical idea. | ||

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Uncertainty of Measurements [5/10] |
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In dynamics, the presence of uncertainty in any real measurement means that in studying any system, the initial conditions cannot be specified to infinite accuracy. | ||

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Uncertainty of Measurements [6/10] |
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In the study of motion using Newton's laws, the uncertainty present in the initial conditions of a system yields a corresponding uncertainty, however small, in the range of the prediction for any later or earlier time. | ||

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Uncertainty of Measurements [7/10] |
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Throughout most of the modern history of physics, it has been assumed that it is possible to shrink the uncertainty in the final dynamical prediction by measuring the initial conditions to greater and greater accuracy. | ||

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Uncertainty of Measurements [8/10] |
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Thus, in studying the motion of a rocket, for example, one could know the final position of the rocket ten times as accurately by specifying the initial conditions at launch ten times as accurately. | ||

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Uncertainty of Measurements [9/10] |
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It is important to remember that the uncertainty in the dynamical outcome does not arise from any randomness in the equations of motion--since they are completely deterministic--but rather from the lack of the infinite accuracy in the initial conditions. | ||

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Uncertainty of Measurements [10/10] |
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The unspoken goal of experimental science has been that as measuring instruments become more and more accurate through technology, the accuracy of the predictions made by applying the dynamical laws will become greater and greater, approaching but never reaching absolute accuracy. | ||

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