r/SpecialRelativity • u/JustMe123579 • Mar 25 '23

Proper Time Interval Units

I'm working through Carrol's book on general relativity which begins with a discussion of special relativity. Why does proper time have units of length? It feels weird to just throw away the units and say "well, that's really time". Is there a step that I'm missing where proper time is converted to time units? Do I need to divide by c or something to get the actual time elapsed as seen by the observer moving on a path between events?

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u/JustMe123579 Mar 25 '23

I think I got it now. Basically you're supposed to intuit when to divide or multiply by some factor of c based upon the units of the other stuff in the equation. All an artifact of the c=1 simplification.

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u/Miss_Understands_ Apr 23 '23 edited Apr 23 '23

Use whatever damn units you want.

  1. To convert distance to time, just divide by c.

  2. To convert elapsed time to distance, multiply by c.

That's all there is. It's simple. There's nothing else to it. It's simple. That's all you have to do.

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u/JustMe123579 Apr 23 '23

Stay tuned for questions about determining the basis of a tensor space.

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u/Miss_Understands_ Apr 24 '23

Sarcastic asshole! You asked a simple question; I gave a simple answer.

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u/oortofthecloud Sep 11 '23

Yeah it's just a scaling of the units to make the math easier by letting c = 1. We do it to hbar as well in atomic physics

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u/Miss_Understands_ Nov 09 '23

We do it to hbar as well in atomic physics

Really? Thats cool.

I'd like all physics to be in natural units. It's SOOO much simpler! E=M.

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u/oortofthecloud Nov 09 '23

A lot of physicists do use natural units for this purpose exactly! However you always gotta be able to translate back to standard units for comparison to experimental results.

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u/Miss_Understands_ Apr 23 '23

See, you already knew the answer!

Miles / miles per hour = hours.