Converting equations in Natural units to SI?

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Discussion Overview

The discussion revolves around converting equations from natural units, where hbar and c are set to 1, into SI units that include these constants. Participants explore methods for performing these conversions, particularly in the context of physics equations involving energy, momentum, and mass.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Debate/contested

Main Points Raised

  • One participant inquires about a general method for converting equations from natural units to SI units, expressing uncertainty about how to approach the problem.
  • Another participant suggests multiplying values by appropriate powers of hbar and c to achieve the correct units, providing examples of conversions for mass and time.
  • A participant describes a specific dispersion relation in natural units and seeks guidance on how to convert terms involving wave vector k and energy E into SI units, particularly for a term linear in k.
  • One participant challenges the equivalence of certain units, emphasizing the need for careful consideration of dimensional analysis when converting terms involving k and energy.

Areas of Agreement / Disagreement

Participants express differing views on the specifics of the conversion process, particularly regarding the treatment of terms in equations. There is no consensus on the best approach to handle all terms, indicating that multiple competing views remain.

Contextual Notes

Some participants note the complexity of converting terms that are not straightforward, highlighting the need for clarity on the dimensional analysis involved in the conversions. There are unresolved questions about specific combinations of hbar and c for certain terms.

Who May Find This Useful

Readers interested in theoretical physics, particularly those working with quantum mechanics or field theory, may find the discussion relevant for understanding unit conversions in their equations.

lordkelvin
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How can I convert an equation in units where hbar = c = 1 into an equation with hbar and c in SI units? I searched around a bit and wasn't able to find anything (I'm probably not asking the right question). Is there some general way to do it rather than just intuition from having seen the equations before with hbar and c in them?
 
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Simply multiply the value with appropriate powers of hbar and c to get the correct unit.

You have 1MeV as a result and want a mass? It is 1MeV/c^2. You have 1/MeV as result and want a time? It is hbar/MeV. And so on.
 
I have a dispersion relation that involves some constants (and it's in natural units so no c or hbar shows up). I'd like to plot E versus k using this equation with k and E in SI units.
There are some terms with k^2/(2m) so I can just multiply those by hbar^2, but then there's another term that is only linear in k which I don't know what to do with. I would like to be able to multiply it by some combo of hbar and c but I have no way of knowing whether it's right. So I have a term that is in units of 1eV of inverse length, what do I multiply by? hbar*c?
 
if you have [k/m] = 1/(m*kg), this is not equivalent to an energy with hbar=c=1.
Or do you have a simple k? Well, [k]=1/m, so [k*hbar*c]=1/m Js m/s = J.
Correct, multiply by hbar*c.
 

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