Why Do Universal Constants Show Up and Why Can We Get Rid of Them?

Often times, the same constants show up in our theories over and over again. This may seem mysterious at first, but what exactly does this tell us about the universe? Typically, these constants end up being nothing more than conversion factors, allowing us to connect two quantities that originally seemed completely separate. For, example, in special relativity, light travels the same distance in the same amount of time in every inertial reference frame. This tells us that space and time are fundamentally linked and we made a bad assumption that they were two disconnected things. We see similar trends in other theories, like quantum mechanics and statistical mechanics. But if these constants are nothing more than conversion factors, then there's no reason to keep them around to clutter up our equations! We just have to choose units for the relevant quantities in our theory which will allow us to get rid of the constants. This is known as using "natural units" and is done quite often in theoretical physics.

However, not all theories agree on what units certain quantities should have. For example, the units of distance and time in general relativity seem to be inverted from those that are found in quantum field theory if we set all universal constants to one in both theories! To alleviate this, we can't completely get rid of all of the constants in both theories.

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