Spacetime tells matter how to move; matter tells spacetime how to curve.
— John Wheeler
Up to this point, we have thought of mass as a single thing - however, we can break it into two, as such:
This is the magnitude of gravitational force between two objects.
This is an object's opposition to a change in motion. When we use equations for momentum and
What's the difference?
While gravitational mass and inertial mass relate to two different concepts, they are numerically equivalent and the physics with regard to each is identical - this is what the equivalence principle means. Gravitational mass and inertial mass can be thought of as one and the same, and are completely interchangeable.
So, what's the point?
Why make the distinction if we immediately state that they're identical again? Well, it has some very interesting implications on the way we see and think about the world around us.
Frames of Reference
Imagine two people, Alice and Bob, standing inside of two identical rooms. Alice's is situated on Earth and is completely stationary - whereas Bob's room is inside a rocket in the middle of space. This means that currently, if both Alice and Bob tried to drop a ball in their rooms, Alice's ball would fall to the ground but Bob's ball would remain floating.
However, if Bob's rocket was accelerating forwards at exactly
One more example would be if Bob's rocket stopped moving, and Alice's room was in freefall on Earth - like a falling lift (or "elevator" for you American oddballs). Again, Alice and Bob would observe the same physics relative to their respective frames of reference - both would experience the exact same sensation of weightlessness. If you were in a room in freefall, you would feel the exact same as an astronaut in the International Space Station (well, other than the rapidly growing terror of a crash landing)!
A spacetime diagram shows the movement of an object through space and time. It represents space, a temporal dimension, as a physical dimension by giving time its own axis in addition to the spatial axes.
For example, a spacetime diagram for 1D space (e.g. only moving horizontally through space) would look like this:
If you traced out the path an object takes as it progresses through time, you would get its worldline - a line which represents how the object moves through both space and time. A vertical worldline represents a stationary object, whereas a slanted worldline would represent a moving object. A curved line would therefore represent an object with changing velocity, i.e. accelerating.
Since the speed of light would be one light-second per second, a diagonal line with gradient