5 ms·
This is a great paper from NIST that gets into some of the problems with the limit of ‘dimensionlessness’ in metrology and the SI, and in particular issues like
by jameshart 2mo ago
This is a great paper from NIST that gets into some of the problems with the limit of ‘dimensionlessness’ in metrology and the SI, and in particular issues like the fact that Hertz is considered a coherent SI unit but radian isn’t.
https://www.nist.gov/publications/dimensionless-units-si https://www.nist.gov/publications/dimensionless-units-si
A key takeaway:
> one conclusion that is not
optional is that the unit hertz cannot be regarded as a
coherent unit of the SI, in contrast to its designation in the current form of the SI, where cycles are ignored and Hz
may be replaced by s^−1
- hasley 2mo agoReally interesting read, thank you! One thing I found especially interesting: They argue that you can express the (complex) exponential function exp(x) as a power series with powers x^k. They do not say it explicitly, but if we assume the power series comes from a Taylor series, then the k-th factor 1/(k!) is the derivative evaluated at x=0. And the k-th derivative has exactly the unit needed to cancel the unit of x^k. So, all summands of the series are unitless and hence the exponential function's argument is unitless. This argument would hold for any function which can be written as a series like this. I am wondering whether this is actually a "problem" of the derivative operator.