The equation E=mc^2, written in spray paint on a garbage crate.

Possibly the most famous equation in physics, and it's everywhere, even in graffiti! Image: neighborhoods.org.

But what does this equation actually mean – and why is it so important in physics? It all comes back to relativity, the hallmark of Einstein’s contributions to physics.

This famous equation describes the “mass-energy equivalence” principle: basically, that energy (E) is related to mass (m) and vice versa, and the speed of light (c) is just a constant that separates them. This doesn’t mean that you can convert between the two: what is does mean is that energy is mass, and vice versa. They’re just two different names for the same idea, and this equation tells us how much energy would be released if an object of a certain mass was completely destroyed.

So, this means that the two are inseparable. If a particle has energy (motion, heat, light) it must also have mass (so light particles – photons – have mass!) and vice versa, so that even a really heavy boulder has energy. However, confusingly, if a particle’s energy becomes mass (for example, in a particle collision where two light particles produce a whole load of heavier ones) that energy is considered to be a “more mobile kind of mass” – this is to obey the conservation laws, which hold that both energy and mass must be conserved. Again, the same is true in reverse.

But why is this particular equation so important? Well, for one thing, it’s simple! A lot of physics equations are a combination of Greek symbols and complex mathematical functions, which really don’t make sense unless you’ve done university-level physics. It’s really rare for there to be an memorable equation, and E = mc^2 fits the bill!

However, that’s not all there is to it. Mass-energy equivalence is a big part of a lot of physics calculations, in particular those used in special relativity. In this case, the observer sees a different amount of energy depending on where they are (the train appears to be going faster if you’re standing, rather than if you’re driving alongside) but since energy has to be conserved across all possible frames, the mass must be contributing to the overall energy amount. And, yet again, vice versa.

One small equation – one big leap for physics!



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