units

 May 2, 2021

22:31

Oh – and, picked up Gravitation by Misner, Thorne, and Wheeler the other day. Yes it is a very large and heavy book. So there’s a bit in there about “geometricized units” that says, for instance, you can refer to mass in a geometric unit such as kilometers so long as your units and conversions line up. In this case, multiply by G/c^2 to “switch” from mass units to distance units. For example, the mass of the Sun could be said to be 1.477km. This, incidentally, is half the Schwarzschild radius. 

So going back to something I was typing up here the other day but didn’t post – let’s say we treat time, distance, and mass units as “cancellable”. Then what’s the total for various types of measurement? For instance speed = m/s so that’s 1-1 = 0. Acceleration is m/s^2 so 1-2 = -1. I believe that works out like this: 

-1: acceleration, frequency

0: speed, force

+1: distance, time, mass, momentum, energy, torque

+2: area, angular momentum

correction

 May 1, 2021

23:04

Whoops, that was not correct. It’s true that the time dilation due to gravity is the same as what it would be due to velocity for an object at the escape velocity, there is still a combinatorial effect – meaning that if something falls to “here” from really far away, then the dilation it has (compared to an observer still at the place where it fell from) will include both dilation factors. (and, it looks like, not exactly their product, since nothing’s ever that straightforward in GR)