For context I have an undergraduate degree in Natural Sciences but am tasked with teaching some physics to 13 year olds to whom I have to explain the concept of mass.
As far as I can distill it mass is how much stuff there is. However, this feels slightly misleading as it suggests an amount which is a different concept either measured in moles or as a dimensionless number. In terms of different particles having different masses there is only one thing to count yet their masses differ. This is of course because of the Higgs but I can’t explain that to a class of 13yos :/
Should I just stick to the simple but slightly wrong definition or is there another way of distilling it?
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It’s actually a pretty messy concept, so don’t feel bad at fumbling for an explanation!
“Mass” can mean a number of different things depending on the context, and it just so happens we believe that they are all the same.
**Inertial mass** is one of the two most common intuitive definitions. This is “how hard something is to move” – namely, if you push on it with a certain force, how fast does it go? As with anything else in physics your experience on Earth is somewhat complicated by other factors, but a decent proxy would be imagining putting your object on a cart on a level surface and trying to pull it. Something with more inertial mass is harder to pull.
**Gravitational mass** is the other common one. This is basically “weight”. If you need to get into *weight* versus *mass*, the only real difference is relative to your current gravitational field. An object might weigh less on the Moon, but if one ball is twice as massive as the other, it will be twice as heavy on any planet, even if the absolute weight (gravitational force) varies. In short, gravitation mass is “how hard does gravity pull on this thing”.
Wikipedia [has more to say](https://en.wikipedia.org/wiki/Mass#Definitions) here, too.
It’s actually a very interesting quirk of physics that, as far as we know, these two quantities are the same! There is no obvious reason that this should be true, but it seems to be so. Objects are yanked on by gravity *exactly* in proportion to how hard they are to move, resulting in every object moving (accelerating) equally quickly when pulled on by gravity. (This was the original breakthrough that Galileo and Newton are known for.)
Well, you won’t really be able to talk about anything more than the classical introduction. So lets talk about that:
Classically mass means nothing which we only have 1 object in motion. But objects don’t want to change their motion, we call that inertia. When two objects collide they will move apart at different velocities. Velocity isn’t conserved nor is it random. Similar “something” objects split the out velocities evenly while different objects split it differently.
Ok, idea! Lets try a linear model we weight the velocities with some number. So now we introduced a way to say that an object is twice as “much” as another. And so will be move half as much. And as it turns out this is enough. Velocity is kinda conserved once you weight them with this new mass thing, its called momentum. Mass states how much an object refuses to change its motion. At least classically.
But of course this raises question like: is inertial and weighted mass (due to gravity) the same? Of course they are and its not a happy coincidence. What mass is has to come from some theory of space, it does we call it special relativity. This classical introduction is an empirical way of looking at mass and not really coming from anywhere apart from someone one day tried adding weights to velocities and figured that this new quantity is conserved and named it momentum. Is mass more than this? Yes. Does it have to be? Not really, this classical interpretation is fine. At first these are understandable and useful. Trying to build it up from QFT and SR is not that useful.
Don’t introduce mass, only when it’s required. You can obviously show how without momentum you just can’t solve some problems. And introduce the idea of mass to show how it solves the problem.
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