# Monthly Archive: March 2022

## Relativistic mass

When Special Relativity is being introduced at school (if it is at all - the curriculum might depend on your country and it can change in time), one of the notions being discussed is so called "relativistic mass".

One of the consequences of relativity is that faster moving objects are harder to accelerate, which means that their inertia increases. And since it is being said from the beginning of the physics lessons that mass is the measure of inertia, it is tempting to try to explain this effect with an increase in mass. So, the notion of mass is being split into "rest mass" - the mass an object has at rest - and a "relativistic mass" - the mass of the object in motion, larger than the rest mass. The equations also become prettier right away, since if we denote the relativistic mass by $m$, we can always write $E = mc^2$, and momentum can be expressed using the formula known from classical physics $p = mv$ (versions with the rest mass also have an ugly square root in the denominator - we'll see it later). This is the life!

If you are following articles or discussions about relativity on the internet, you probably noticed relativistic mass being mentioned in multiple contexts. It is often used to explain the impossibility of reaching the speed of light ("because the mass would grow to infinity"), or sometimes someone will ask whether an object can become a black hole by going fast enough (it can't). The relativistic increase in mass is being treated as fact in such situations, as something certain.

Well, I'd like to disturb this state of affairs slightly with this article ;) Because, as it turns out, the notion of relativistic mass loses a lot of its appeal upon closer scrutiny. As a result, relativistic mass is rarely being used in academia and you can encounter it pretty much only at school, in discussions on the internet and in popular science publications. Let's take a closer look at the reasons behind that.

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