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May 27, 2020 at 12:43 comment added user87745 @AlfredCentauri Yeah, as you can see, things like $E^2=m^2+p^2$ also wouldn't work out unless you make $c$ dimensionless. Maybe one can argue they'd work out "numerically" but in reality, they'd remain dimensionally inconsistent unless $c$ is truly dimensionless. :)
May 27, 2020 at 12:36 comment added Alfred Centauri @DvijD.C., this is precisely what I thought when I read this (I had a comment typed) and then, I looked around here and found counterexamples. I've understood the $(c=1)$ expression to mean that $c$ is the dimensionless constant $1$, not the 1 light-second per second dimensionful constant
May 26, 2020 at 23:24 comment added user87745 This is not what is done. You set $299792458 \text{ meters} = 1 \text{ second}$. When we say $c=1$, we mean it--there is no units hiding with that $1$. ;)
May 26, 2020 at 15:29 history answered my2cts CC BY-SA 4.0