So in my QFT course, my professor said that you can set $c$ and $h$ bar$\hbar$ to 1. And he gave us an example:
$$E = mc^{2}$$
And then set $c = 1$:
$$E = m$$
This seems completely ludicrous to me to do. Doesn't it change the result? Why can this be done and why isn't it wrong?
I mean, $E = mc^{2}$ gives you one answer and $E = m$ gives you another, completely different answer!