I am currently studying General Relativity and I am using the book by Schutz.
I encountered a problem when I was reading about the gravitational redshift experiment. Here is the website (it is not the book, but it depicts the exact same experiment):gravitational redshift experiment
I cannot figure out the meaning of the $O(v^4)$ term in the equation of the total energy of the particle when it reaches the ground, as measured by the observer on ground:
I don’t know what $O(v^4)$ is supposed to mean. What is the context of it? I’ve done some searches on Google but I can’t seem to find any explanations. Any help would be so great!