Are Uncertainties in Measurements Important?

Question

In the first lecture of MIT's Classical Mechanics Prof. Lewin highlights the importance of uncertainties in measurements by quoting "Any measurements, without the knowledge of uncertainty is meaningless." He measures the length of a student and an aluminium bar both in their vertical and horizontal positions respectively and notes their lengths in centimeters and calculates the difference between the two positions. Question:Is it so important to make such serious considerations while making measurements? Do professional physicists make such considerations when making real world measurements? Aren't we well equipped to just ignore these uncertainties?

Answer 1

Do you even know what you mean by "ignoring the uncertainties"? I don't.

You may neglect uncertainties sometimes. That doesn't so much have anything to do with a particular measurement of a quantity $x$ being exceptionally precise, but with putting that measurement in a calculation / comparing it with another measured quantity $y$ that has a much larger uncertainty. We can then argue that, using the actual uncertainty $\sigma_{\!x}$ of $x$, the final result won't be notable different from the result we'd get assuming $\sigma_{\!x}=0$.
But that doesn't mean we ignore $\sigma_{\!x}$: we might later on compare $x$ to another quantity $z$ that's known with even smaller uncertainty than $x$ is. To give an example in numbers, let $$\begin{aligned} x =& 37.5088(46)\:\mathrm{m}, \\y=&37.41(30)\:\mathrm{m}, \\z=&37.5067351(93)\:\mathrm{m} \end{aligned}$$ These measuments clearly are all in agreement. We might have decided to neglect the uncertainty of $x$ when comparing it to $y$, because $y$ is much more uncertain. But if we had decided to ignore it we would then have faced the comparison $$ 37.5088\:\mathrm{m}\pm0\ \overset{?}=\ 37.5067351(93)\:\mathrm{m} $$ from which we would have had to conclude that $z$ disagrees with $x$, with great significance!

Answer 2

Two recent examples of where an understanding of your uncertainties would be the superluminal neutrino report and the possibility of the 120 GeV Higgs.

If the experimentalists have no sense of the ability of their machines to report accurately then neither result should be taken very seriously. It is only the apparently very good knowledge of the OPERA detectors that have stopped those scientists from being laughed at...

There is no way a human being is 'well equipped' to personally measure neutrino velocities.

Answer 3

Scientific data tells us what is probably true, not what is definitely true. It is so because we can never create absolute conditions which can ideally mimic the theoretical conditions. Scientists often deal in hypotheses, probabilities and theories rather than stating something is an absolute fact. Even when evidence points toward a specific conclusion, scientists often avoid labeling that conclusion as a fact so that if new knowledge is obtained, they can revise their conclusion.

This link could be of help to you.

Answer 4

I think the more interesting question to ask is if there is something fundamental about uncertainties?

You are free to ignore uncertainties if your calculations match experiments to the order you are interested in. In my view, a theory is at its strongest when supported by experiments.

Answer 5

For the purpose of solving problems in physics class, uncertainties are not that important, as the solution will usually be stated to 2,3, or 4 significant figures. However, it is important to understand the concept of uncertainty to be able to do lab work, and to understand if your data are reasonable or not. Uncertainty is usually mentioned in the beginning of textbooks, to be quickly forgotten, but professional physicists actually use uncertainties. Engineers often report their parts with tolerances of +- 0.01 cm, for instance, and in this context, uncertainty is important, because the part will actually be different from the nominal size. For instance, G, the universal gravitational constant and g, the gravitational acceleration of Earth, both come with uncertainties. g = 9.80665..., and the last two digits are usually written in parentheses as uncertain.