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Relative uncertainty is the measurement uncertainty relative to the magnitude of a particular single choice for the value for the measured quantity, when this choice is nonzero. This particular single choice is usually called the measured value, which may be optimal in some well-defined sense (e.g., a mean, median, or mode). Thus, the relative ...
Equation (2) is the means to get from the measured quantities L, T, and θ to the derived quantity g. Note that an alternative approach would be to convert all the individual T measurements to estimates of g, using Eq(2), and then to average those g values to obtain the final result.
Any non-linear differentiable function, (,), of two variables, and , can be expanded as + +. If we take the variance on both sides and use the formula [11] for the variance of a linear combination of variables (+) = + + (,), then we obtain | | + | | +, where is the standard deviation of the function , is the standard deviation of , is the standard deviation of and = is the ...
Similarly, uncertainty is propagated through calculations so that the calculated value has some degree of uncertainty depending upon the uncertainties of the measured values and the equation used in the calculation.
The uncertainty principle, also known as Heisenberg's indeterminacy principle, is a fundamental concept in quantum mechanics. It states that there is a limit to the precision with which certain pairs of physical properties, such as position and momentum, can be simultaneously known. In other words, the more accurately one property is measured ...
In physical experiments uncertainty analysis, or experimental uncertainty assessment, deals with assessing the uncertainty in a measurement.An experiment designed to determine an effect, demonstrate a law, or estimate the numerical value of a physical variable will be affected by errors due to instrumentation, methodology, presence of confounding effects and so on.
An example of a source of this uncertainty would be the drag in an experiment designed to measure the acceleration of gravity near the earth's surface. The commonly used gravitational acceleration of 9.8 m/s² ignores the effects of air resistance, but the air resistance for the object could be measured and incorporated into the experiment to ...
Δp x is uncertainty in measured value of momentum, Δt is duration of measurement, v x is velocity of particle before measurement, v′ x is velocity of particle after measurement, ħ is the reduced Planck constant. The measured momentum of the electron is then related to v x, whereas its momentum after the measurement is related to v′ x ...