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Q&A Unusual way to write spacetime coordinates/metric: Is there any downside?

There is no problem with the approach you suggest: it's equivalent to deciding to use seconds and light-seconds as your units for space-time four vectors instead of light-meters and meters. (I actu...

posted 3y ago by dmckee‭  ·  edited 3y ago by dmckee‭

Answer
#2: Post edited by user avatar dmckee‭ · 2021-01-10T22:55:13Z (about 3 years ago)
  • There is no problem with the approach you suggest: it's equivalent to deciding to use seconds and light-seconds as your units for space-time four vectors instead of light-meters and meters. (I actually prefer that when I want to connect to human scaled measurements.)
  • But ... most professionals work in "natural" units meaning that they basically just agree not to write down factors of $c$ (and of $h$ and $G$, though that doesn't come up in special relativity) at all. It is understood that because you know what physical quantity is represented by each symbol you can figure out how to restore the constants if needed. This is sometime described a *"setting $c$, $h$, and $G$ to one"*, though I find that this phrase doesn't explain the procedure very well to newcomers.
  • The result is that the question you're considering is interesting to physicists only during a relatively narrow window between starting to grapple with relativity and adopting the professional viewpoint.
  • I don't personally like to add yet another option to the several scheme that are already to be found in common texts (and I considered linking the XKCD comic on Standards).
  • There is no problem with the approach you suggest: it's equivalent to deciding to use seconds and light-seconds as your units for space-time four vectors instead of light-meters and meters. (I actually prefer that when I want to connect to human scaled measurements.)
  • But ... most professionals who use relativity regularly (cosmologists, particle physicists, etc.) work in "natural" units meaning that they basically just agree not to write down factors of $c$ (and of $\hbar$ and $G$, though that doesn't come up in special relativity) at all. It is understood that because you know what physical quantity is represented by each symbol you can figure out how to restore the constants if needed. This is sometime described a *"setting $c$, $\hbar$, and $G$ to one"*, though I find that this phrase doesn't explain the procedure very well to newcomers.
  • The result is that the question you're considering is interesting to physicists only during a relatively narrow window between starting to grapple with relativity and adopting the professional viewpoint.
  • I don't personally like to add yet another option to the several scheme that are already to be found in common texts (and I considered linking the XKCD comic on Standards).
#1: Initial revision by user avatar dmckee‭ · 2021-01-10T22:49:23Z (about 3 years ago)
There is no problem with the approach you suggest: it's equivalent to deciding to use seconds and light-seconds as your units for space-time four vectors instead of light-meters and meters. (I actually prefer that when I want to connect to human scaled measurements.)

But ... most professionals work in "natural" units meaning that they basically just agree not to write down factors of $c$ (and of $h$ and $G$, though that doesn't come up in special relativity) at all. It is understood that because you know what physical quantity is represented by each symbol you can figure out how to restore the constants if needed. This is sometime described a *"setting $c$, $h$, and $G$ to one"*, though I find that this phrase doesn't explain the procedure very well to newcomers.

The result is that the question you're considering is interesting to physicists only during a relatively narrow window between starting to grapple with relativity and adopting the professional viewpoint. 

I don't personally like to add yet another option to the several scheme that are already to be found in common texts (and I considered linking the XKCD comic on Standards).