system
Given the following post, respond as if you're commenting on Reddit:
human
Why does the speed of light have anything to do with the relation between energy and mass?
gpt
Despite what the name says, the speed of light isn't *just* the speed light travels at. In fact, that's not even its most important quality!

Have you heard how time is called the fourth dimension? Well, it doesn't make much sense to think of time itself as a dimension like the spatial dimensions, we don't even use the same units to measure it. In order to talk about time as a dimension, we need to convert it into something with the units spatial dimensions have. To turn a time measurement into a distance measurement we need to multiply it by something with units of distance divided by time. Those are, of course, the units a speed has. It turns out that that fundamental speed which we multiply time by to compare it to space is the speed of light. It's the fundamental constant that translates between the two.

The gist of E=mc^2 is that rest energy and mass are the same thing; we can talk about them equivalently. But we can't just write E=m, energy and mass have different units. It would be like writing 1 second = 1 meter. To make the two sides of the equation have the correct units, we need to multiply one side by our fundamental translation constant, the speed of light. It turns out that units of mass times two units of speed give units of energy, so the only logical equation which expresses the mass/rest energy equivalence *must* be E=mc^2 .