I cannot see what that has to do with my post #44. The question I raised there was merely one of terminology: having resolved a vector into components in the ##\hat x## and ##\hat y## directions, as ##\vec v=x\hat x+y\hat y## say, what are the "components"? Are they ##x## and ##y## or ##x\hat x## and ##y\hat y##?Orodruin said:My point is that the x-component in one system is not the same as the x-component in another system. Taking the x-component of a vector in system A does not give you the same thing as taking the x-component in system B. In fact, they generally have both different magnitude and obviously correspond to different directions. As such, ”the x-component” is not coordinate invariant.
I mean, ultimately it comes down to if you want everyone to necessarily write vector arrows on everything that would need it in three dimensions also for one-dimensional problems. I don’t. I expect anyone that argues for this to also start writing double arrows on top of any variable representing string tension as it is actually a rank two tensor. What you actually call things later is not as important.haruspex said:I cannot see what that has to do with my post #44. The question I raised there was merely one of terminology: having resolved a vector into components in the ##\hat x## and ##\hat y## directions, as ##\vec v=x\hat x+y\hat y## say, what are the "components"? Are they ##x## and ##y## or ##x\hat x## and ##y\hat y##?
If anyone wants to continue this sidebar, I think we should do it by PM.
A good physicist ought to use proper symbols/notations/units everywhere, especially when writing a book, or when working on a project or when explaining things to others. If one is going to not use such symbols/notations/units for something, then justification and reminder for doing it like that, must be mentioned at appropriate places. If you are studying/doing some physics on your own for your own sake, then maybe not. This makes things precise & clear for everyone, otherwise it may lead to such disasters as mentioned in post#51.Orodruin said:I mean, ultimately it comes down to if you want everyone to necessarily write vector arrows on everything that would need it in three dimensions also for one-dimensional problems. I don’t. I expect anyone that argues for this to also start writing double arrows on top of any variable representing string tension as it is actually a rank two tensor. What you actually call things later is not as important.
You are missing the point completely. Writing out the projected equation is absolutely proper. There is not a single thing inappropriate about it. Do you also want to use double arrows on string tensions? If you want to be consistent with this point of view you must. I do not know any single source that does this, you are free to find counter examples if you can.NTesla said:A good physicist ought to use proper symbols/notations/units everywhere, especially when writing a book, or when working on a project or when explaining things to others. If one is going to not use such symbols/notations/units for something, then justification and reminder for doing it like that, must be mentioned at appropriate places. If you are studying/doing some physics on your own for your own sake, then maybe not. This makes things precise & clear for everyone, otherwise it may lead to such disasters as mentioned in post#51.
You are completely missing the point that I made regarding writing justifications and reminders if one is not going to do that.Orodruin said:You are missing the point completely. Writing out the projected equation is absolutely proper. There is not a single thing inappropriate about it. Do you also want to use double arrows on string tensions? If you want to be consistent with this point of view you must. I do not know any single source that does this, you are free to find counter examples if you can.