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Another option is to write X as a subscript, i.e. m_X ± u_X.
Notationally very consistent, which is nice.
But suppose that in an elementary lab I hang a spring, and measure the
elongation x that occurs when I hang a mass m1 (due to gravitational
acceleration g). I then wish to predict the natural angular frequency
when a different mass m2 hangs on the spring. All quantities have
associated uncertainties. Is anyone really going to write the equation
m_omega = sqrt((m_m1*m_g)/(m_m2*m_x)) ?
Do we need to notate the fact that in lab, we don't actually work with
the distribution mean, but instead an estimate of the distribution mean?
The +- notation is no help at all.
To put another way, I am NOT asking about how people like to notate
uncertainty of a specific measurement.
Another option is simply to write A ± B and then explain that A isNearly useless for teaching the mathematics of uncertainty propagation.
the nominal value of the distribution X while B is the corresponding
uncertainty.
You really need a notational system that preserves a reminder of the
referenced quantity.
On the other hand, using capitalization to distinguish between the
variable and the distribution is dead on arrival for physics. Do you
suggest that multiple measurements of a pendulum period T be represented
by t_1, t_2, t_3?
for teaching the mathematics of uncertainty propagation.