Measured errors in Physics

Universal equations of quantities in Physics

Conformity assessment deals often with the properties of specific items.

By contrast, in the special case of measurements in Physics, the remarkable fact is that quantities of different items follow exactly (as far as we can tell) the same equations, whatever the item or level of measurement. These equations are expressions of the ‘laws of Nature’. Units of measurement in the SI obey the same equations of Physics as their corresponding quantities.

Relating different quantities

Metrological traceability in Physics is a special case where not only different measurements of one quantity made at different times by various people can be related, but remarkably measurements of different quantities can also be related to each other, through the laws of Nature. In situations where these laws of Nature are not known, for example in the ‘recipes’ of engineering or Chemistry, one does not have the same luxury as the physicist.

Testing the laws of Nature with accurate measurement

Of course the laws of Physics are constantly being tested by the most accurate measurements of physicists and there are many examples where accurate measurement lead to revisions in the laws of Nature. In that context,  it might clarify to use different symbols for a measured quantity as opposed to the quantity symbolized in the ‘model’ equation which is being tested.  This fact – that the same equations relate the physical quantities of all items – is so familiar that we sometimes forget how remarkable it is.

Thus one could imagine a physicist postulating that a particular quantity has an error (owing perhaps to some previously undiscovered physical effect rather than a mere technical error), the value of which he wants to test by experiment against some limit (e.g. is the neutrino mass really zero, or is the quantum Hall effect equation correct?).

When he measures a quantity in the lab, he will obtain a measured error of that quantity. Like any good metrologist, he will then evaluate his measurement errors; calibrate instruments; correct for known measurement errors and estimate his measurement uncertainty in the measured error before deciding whether our view of the Universe has to be up-dated.

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