## Automated Natural Unit Conversions in Mathematica

Introduction and Review

Natural units are a way to simplify repetitive fundamental constants in theoretical physics equations. In my research, I used three particular unit systems: geometric ($c=G=1$), natural ($c=\hbar=1$), and Planck units ($c=\hbar=G=1$). However, for me it is time consuming to convert to and from natural units. I decided that I would write an extension to Mathematicaâ€™s units package to remedy this.

A great summary of natural units goes in more detail in an excellent document here. Given a SI quantity $Q_{\text{SI}}$, the quantity in natural units is given by $Q_{\text{geometric}} = Q_{\text{SI}}/A$ for some factor $A$. For the rest of this post, I will use geometric units. Suppose that the quantity has SI units of the form

\[[Q_{\text{SI}}] = M^\alpha \times L^\beta \times T^\gamma \, ,\]then, one can find $Q_{\text{geometric}}$ with the following factor

\[A = G^{-\alpha} c^{2\alpha-\gamma} \, .\]So all we need to do to convert between the units is to find $A$.

The first thing that we need to do is write a helper function that will return the $\alpha$, $\beta$, and $\gamma$ from our previous equation. All I need to do was write a wrapper class for the UnitDimensions[] fuction that Mathematica has.

Next, I wrote a function to calculate the constant $A$.

Finally, I used a function that will find $Q_{\text{geometric}}$ by dividing $Q_{\text{SI}}$ by $A$. Afterwards, it converts the result into meters to the $n$ power as is used in geometric units.

The full version of these functions which includes geometric, natural, and Planck units is publicly available on my Github. Feel free to use it and I hope that it will save you time in your research!

Introduction and Review

I gave a presentation to a conference organized at Sigma Pi Sigma at University of Virginia.

I gave an hour long presentation to the gravity research group at University of Virginia. It specializes on content from my upcoming paper.

I gave a five minute presentation to Society of Physics Students about my research. This was to encourage first year students to get involved in research.

I had the pleasure of presenting my research to a group of first year students who are interested in scientific research. I gave an introduction to my resear...

Here is my upcoming paper describing tests of general relativity using black hole-pulsar binaries if one is found with next generation telescopes.

I spent the 2017 summer working with Marie Kasprazack, Arnaud Pele, and Adam Mullavey at LIGO Livingston through the Caltech SURF Program. I examined nonline...

I presented the results of my research at LIGO from the summer of 2017 at Caltech for the SURF final presentation.

I made this website on 10/21/2018 (though I have retroactively added some materials). I look forward to adding to it in the future!