Ah, so basically metrics are tensors which describe the distance between two different points from an origin, and since they're from an origin, they can both be considered vectors? Everything makes much more sense now (I was wrongly conflating the coordinate elements with indices), thanks!
So...
No worries, you've given me more than enough help! In fact, if you feel you have to abandon this thread for good, please have no hesitation (my questions seem to be increasing exponentially).
Ah so I can take the scale factor to be the function of the proper real distance between any two...
Sorry for the double post.
So a rank 1 vector can be manipulated to be represented on a 1D plane as a dot (i.e. coming straight out of the plane)? If a 1st order tensor has the three dimensions to be its one index, what is the other index of a 2nd rank tensors of the GR equations (is it...
So the scale factor a(t) describing the expansion between space isn't real? Without it then, how would we know that at some future point in time, the distance between two points at rest in an expanding spacetime has increased? Or is its purpose merely to change the metric from showing the...
So redefining time doesn't mean defining that time has no scale factor of its own? If I am understanding correctly, the set of numbers have no physical reality is analogous to how if you draw a coordinate plane on a balloon and inflate it, the actual distances between two labeled set of numbers...
Thank you all so much for your responses! I apologize the frustration that will come from my bastardized interpretation of your responses; I've never taken any lessons on differential equations or any in-depth lessons on parametrics and scalar functions.
What exactly is the redefinition of...
In the context of Friedmann's time, 1922, how did he know to make the metric scale factor, a, a function of time when Hubble's redshifts were not yet published? I understand that he took the assumption that the universe is homogenous and isotropic, but does that naturally imply that the universe...