Reading Summary Guidelines
• Do for each section of assigned reading (e.g. 2.1) before class on the day
assigned. Bring them to class for reference.
• Use WORDS, not equations
• Keep it short! 5-15 lines.
• Focus on the big picture of the text.
• Take in ADDITION to notes.
“Meh” Example: Error and Uncertainty (first two paragraphs).
Experiments are designed to test a hypotheses or theoretical prediction. In order
to determine this, every experimental result must have an uncertainty. The
uncertainty can be compared with the difference to draw a conclusion.
Particles called neutrinos were measured by the OPERA experiment to be
exceeding the speed of light, moving 454 miles 0.0000000060 seconds faster than
light. We need to know the uncertainty in this measurement to determine if
neutrinos really move faster than light.
Better Example: Error and Uncertainty (first two paragraphs).
If an experimental result is just a bit different from a theoretical prediction, the
natural question to ask is whether that difference is due to an actual physical
effect or just experimental error. Scientists use estimates of the uncertainty in
experimental results to determine whether a difference between experiment and
theory could be explained by possible measurement error.
“Meh” Example: Differences vs. Uncertainty
Error is the difference between an experimental result and a true value. Discrepancy is the
difference between an experimental result and a theory being tested. Difference is the
difference between two experimental results. Uncertainty, or “possible error” is the amount
that the measurements could be off, which should not depend on the theory. In the OPERA
experiment, the difference was bigger than the uncertainty, so they originally thought their
results differed significantly from theory. However, it turned out that their uncertainty estimate
was too low, so really, their results did not differ significantly from theory.
In our class, when difference is bigger than uncertainty, this means there is a significant
difference. It should be noted that in more rigorous contexts, statistical tests can be used rather
than this simple comparison.
Better Example: Differences vs. Uncertainty
The difference between an experimental result and a theory, prediction, or other result can be
referred to as error, discrepancy, or difference, depending on context. For example if an
experiment measures the value of 𝜋 as 3.30, the error is 3.30 – 3.14 = 0.16. The uncertainty,
also known, confusingly, as “possible error” is based on your measurement tools and
methodology: it’s how far off you could be because of measurement problems. For example if
you measure pi by using the width of your thumb to measure the diameter and circumference
of a circle, your uncertainty is probably very large (say, for example, 0.5) because the method is
not very accurate.
In the example above, the difference is not significant because the 0.16 difference is smaller
than the 0.5 uncertainty. That is, the experiment is still consistent with the theory because the
difference could be explained by measurement error. In this class, we’ll determine whether a
difference is significant or now by simply seeing whether it is bigger than or smaller than the
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