When I was about 10 years old, I measured the length of a snake.
He was 5'10" when he breathed in, and 6'2" when he breathed out.
So there was some irreducible inherent uncertainty about the
length.
When I took high-school chemistry, they tried to teach me that
the uncertainty of a measurement was set by the smallest graduation
on the instrument being used. I wasn't buying it.
When I got to college, they had us do fancy experiments that
involved counting photons (from a dim light source or from
radioactive γ decay), where the uncertainty was clearly and
directly set by the physics aka the statistics of the situation.
These were not simple experiments.
Also we did low-noise electronic design, limited by Johnson
noise. Again, not simple.
Almost all physics since 1898 has made heavy use of probability
and statistics:
-- entropy, as in thermodynamics
-- statistical mechanics: diffusion, electrical conductivity,
thermal conductivity, viscosity, et cetera.
-- entropy, as in information
-- quantum mechanics
The main exception is relativity, which is post-1898 but not
particularly statistical.
So the question is: Does anybody have a favorite *simple*
experiment where the uncertainty is limited by the physics
of the situation -- e.g. shot noise, thermal noise, quantum
noise, or some other property of the thing being measured --
not by technical limitations or roundoff error.
By simple I mean suitable for high-school physics course.
There are a lot of activities that use coin-tossing and
dice-rolling to /simulate/ the physics, which is fine as
far as it goes, but right now I'm asking about measuring
the physics itself.
I'm sure there are better examples, but to get the discussion
started let me mention one of my all-time favorites, namely
the "yardstick drop" experiment to measure reaction times.
This can be carried out at any level from 4th grade on up.
There is a lot of inherent scatter in the data, certainly
not limited by the graduations on the yardstick.
This example is interdisciplinary, since it uses basic
physics to measure something that isn't basic physics,
i.e. reaction time.
Has anybody got something better they could recommend?