Parent is not talking about the "distinction between distance and time" but about the multipliers that come into play into their equations (which are artificial and based on the base units selected).
The distinction between feet and seconds is just as real as the distinction between distance and time, and is much more real than the distinction between feet and meters. Look at the parent's literal words and pretend you did not already know what's going on.
I'm well aware of the practical value and conceptual clarity of natural units. They are just not being explained well in this thread. "What the teacher really meant was..." is not a good defense when the student doesn't understand.
> The distinction between feet and seconds is just as real as the distinction between distance and time
There is a "real" distinction between [light]seconds of distance and seconds of time, but it's a difference in what is being measured, not in how it is quantifiable. Measuring them with the same units doesn't imply that they are perfect substitutes, any more than one could arbitrarily replace an ounce of gold with the same weight of feathers; in practice, they are non-interchangeable enough that gold is even measured with a different type of "ounce". Likewise with spacetime: for most purposes human non-physicists think about, they are completely non-substitutable. So practically, it works well to use a "Troy" sort of system for one. But it's a purely human distinction.
> but it's a difference in what is being measured, not in how it is quantifiable. Measuring them with the same units doesn't imply that they are perfect substitutes
I agree! Please read my comments carefully. I am not arguing against the usefulness or deep conceptual importance of natural units! I am critiquing the terrible explanations being given in this thread.
> Likewise with spacetime: for most purposes human non-physicists think about, they are completely non-substitutable. So practically, it works well to use a "Troy" sort of system for one. But it's a purely human distinction.
No! Space and time are not interchangeable in any universal sense even if they are universally linked by a symmetry. A space-like interval and a time-like interval cannot be interchanged with each other by a Lorentz transformation. The distinction between space-like and time-like intervals is observer independent.
Would you agree that if there was a unit for 299,792,458 meters called 'q' then the "speed of light" could be expressed as 1 q/s? Then e = m*c^2 is e = m x 1 or e = m (but the units of q^2/s^2 are still there, just the arithmetic is simplified)
I am not arguing against natural units. I use them daily, and they are more than just practically useful. I am critiquing bad explanations for their interpretation and justification.
"are physically related such that, in a sense..." I didn't say they were equivalent, I said they were connected. You can't transform a time-like interval into a space-like one, but you can transform one time-like interval into another such that the separation on time increase and the separation in space decreases.
There's only so much clarity you can fit into a HN comment.
I'm well aware of the practical value and conceptual clarity of natural units. They are just not being explained well in this thread. "What the teacher really meant was..." is not a good defense when the student doesn't understand.