Now let's consider a different coordinate system - one that is moving with respect to the first system.

I'd like to call the first coordinate system

**A** and the new system

**B**.

Let's choose

**B** such that it is moving with velocity 1m/s with respect to

**A** along the x-axis, and so that the origin of

**B** coincides with the origin of

**A**.

In other words,

**B**'s spatial origin is at the same place as

**A**'s spatial origin when t = 0. One second later,

**B**'s spatial origin is at the same place as x=1 in

**A**, and so on.

We can match up events in

**A** with events in

**B** like so:

A(0,0,0,0) = B(0,0,0,0)

A(1,0,0,1) = B(0,0,0,1)

A(2,0,0,2) = B(0,0,0,2)

A(3,0,0,3) = B(0,0,0,3)

...and so on.

With a bit of thought, we can write a general equation that lets us transform

*any* event from its coordinates in

**A** to its coordinates in

**B**:

A(x, y, z, t) = B(x-t, y, z, t)

We can also go backwards, from B coordinates back to A coordinates:

B(x, y, z, t) = A(x+t, y, z, t)

Now we can locate TickOne and TickTwo in

**B**:

TickOne = A(0,0,0,0) = B(0,0,0,1)

TickTwo = A(0,0,0,1) = B(-1,0,0,1)

How are we going?