Conservation laws

Some fundamental constraint relationships are called conservation laws.

Stuff does not get lost

Until 1905, physicists thought you could never gain or lose mass. You do need to be careful to find all everything in your experiment, to measure its mass. So, you do need to be working with a closed system.

This is the conservation of mass.

Everything has mass: some things are also electrically charged. For those that are, the conservation of charge is another constraint relationship that says how the world is, again in a closed system.

How much motion is not lost either

Momentum measures how much motion something has.

momentum = mass × velocity

Work in a closed system and the total momentum does not change: you can share it out among the things in the system. Another constraint relationship, that's the conservation of momentum.

This seems a little more removed from the lived-in world, perhaps because it's not easy to build a momentum-meter. You might think you always have to calculate the quantity.

The most famous one of all

The conservation of energy demands calculations, and so is furthest from the lived-in world. Many of the quantities that you measure to feed into the calculations don't even seem to have any obvious similarities. That's probably one good reason why it took so long to find the law, and maybe why it’s hard to understand what's going on.