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1

During an experiment I collected a $x,y$ table of data that are expected to satisfy a linear relation $y=kx$. For any $x_i$ I have an associated error/uncertainty $\delta x_i$ and the same applies to the $y_i$'s. What is the best thing to do in order to have a good estimate of the parameter $k$ and the associated error $\delta k$? The typical solution to ...

0

From 2018 (most probable date at the moment), with the redefinition of the International System of Units (SI), the Planck constant will have an exact, permanent, value, with zero associated uncertainty, assigned according to the latest (2018) adjustment of the fundamental constants made by the CODATA group (see related answer here).

-2

No. In sensible units, Planck's constant reduced is exactly 1. Its accuracy cannot be improved in any meaningful sense. In non-sensible units such as humans sometimes use around the house, Planck's constant is a mishmash of mass, length and time units. Since the mass unit (the kilogram) is not defined physically, it must be measured, and that measurement ...

2

If you are measuring y at some value x, and both quantities have uncertainty, then in principle you should show the uncertainties on both axes. In some circumstances you might omit the x error bars. This would be the case if the y value depends on x such that $$\Delta y \gg |dy/dx| \Delta x,$$ where $dy/dx$ is your best estimate of the gradient of $y(x)$. ...

9

Following on from Jon's comment above, this is from the NIST Website (Dated June 21, 2016), discussing a more accurate measure of the kilogram, and the involvement of Planck's constant. A high-tech version of an old-fashioned balance scale at the National Institute of Standards and Technology (NIST) has just brought scientists a critical step closer ...

6

Planck's constant's accuracy can indeed be increased. As detailed by this website, there are five main different ways of calculating Planck's constant, each with varying levels of uncertainty. Approximately every four years, a organization called CODATA (more specifically, its Task Group on Fundamental Constants) publishes the most up-to-date values for ...

0

If we know-and we are sure about-the relationship between y and x: If $y=f(x)$, you must propagate the uncertainty of $x$ to $y$. That is, since $y$ is analogous to $x$, then the uncertainty in $y$ is analogous to the uncertainty of $x$. So, you use a method that you can find in detail in Taylor's book "An Introduction to Error Analysis: The Study of ...

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