Alex McColgan

but this time let's bring in a little colour coding and our old friend, a 4D space-time diagram.

Hopefully you are familiar with these already, as I've done a few videos that have included them.

If not, here's a great video we did on the subject, which you should have a look at.

To recap though, just imagine that all of space has been flattened down to the one line along the bottom of our graph, while an object's motion in time is tracked along the side of the graph.

From the point of view of the barn, it is not moving in space, so we draw the arrow directly up, it is only moving into the future.

I've painted the shutting and opening of the two doors as two different colours here on the graph.

Note that they are separated by space, but they occur at the same moment in time, at least from the barn's perspective.

For our first complete perspective of this event, let's add the path of our pole.

As our pole starts moving, length contraction occurs, and the pole drops down to 20 meters.

Eventually, it arrives at the barn, and our two events occur.

Both barn doors shut at the same time, and the pole is snugly inside.

All good so far, from the barn's point of view.

But what does the pole see?

Let's make our pole the stationary object in this diagram.

After all, this is relativity, and from the pole's perspective, it is the barn that is moving quickly towards it, not the other way round.

This makes it easier to assign length contraction to the barn, which is what relativity says we should be getting.

We cannot simply add the barn to this diagram as an object that's parallel in orientation to the pole.

it just wouldn't work.

The barn, now narrower, would intersect with the pole with both doors closing and opening at the same time, so the pole wouldn't fit.

But what if we pivot our barn slightly, from this to this?