We use radio telescopes on Earth because of the atmosphere, right? It blocks the more energetic wavelengths but not radio waves and microwaves. So, since radiation like x-ray and gamma radiation are more energetic, wouldn't it be better to get those data instead of radio (I mean, having avoided t...

I have a quantity that is calculated with two measurements, but I only have a tabulated standard deviation for one of the measurements. How would I calculate the error on the calculated quantity? The form is as follows: $\frac{a - b}{b}$. I have an std on $b$. The problem is that I'm not sure how...

We know that $d/dx$ is the generator of translation in the sense that $$e^{ad/dx}f(x)=f(x+a)\tag{1}$$ which can be easily be proved from the Taylor series of $f(x+a)$. Studying the very basics of conformal group/transformations suggest that the generator of scale transformation, at least in 3D, i...