Co-movement and determining velocity

Starting a train journey

It's time to leave. You've found a window seat, farthest from the platform, and are settling in for the long train journey down to London. Still busy with getting your laptop out, you feel some gentle movement and hear a roar and then you're off – but wait a second – backwards!

After a moment's panic you realise that it's the local train on the adjacent platform that's moving off in the same direction as you, but a little faster. Look out of the other window, and you see the platform sliding away behind you, moving away from you in the expected direction.

The panic subsides.

The couple behind you had a moment as well:

Alice: That's weird, I thought we were off to Hereford.

So much about motion depends on our assumed point of view, often not questioned until we have a moment. This is often implicit, remaining unstated. As you might imagine, that can lead to difficulties.

• From our train, Alice notices the local train drawing away from us.
• Alice also notices the platform going backwards.
• A passenger, Bob, in the local train notices our train moving backwards.
• A waiting passenger on our platform, Charlie, sees both trains moving off in the same direction, but at different velocities.

So it seems that Alice, Bob and Charlie all notice different velocities for the:

• Platform.
• The local train.
• The London train.

Many velocities – depending on your point of view

Here are three separate points of view. So who is correct about the velocities of these trains and platforms?

Everyone and no-one. All three need to be rather more careful and rigorous as they seek to turn their implicit noticing into unambiguous physical statements that everyone can agree on.

You need to be careful before you can agree on measured quantities.

Understanding motion

Being at rest is just a rather special case of moving alongside something, so that its separation from you does not change with time. There's no privileged point of view in the universe, where the most important person sits, and rules on what is and what is not at rest. Instead you have to be careful to state your point of view. Only once that's done is it worth reporting on the velocities that you measure.

This shouldn't be that surprising: velocity determines changes in position in the same way that acceleration determines changes in velocity. And to determine the position of something you need to say where it is with respect to some chosen location (or point of view).

Several different choices of points of view will result in several different velocities – unless, of course, the chosen points of view are all moving along together and report each other as being at rest.

All motion depends on a point of view. These are all too often chosen without careful thought, as being obvious. Alice, sitting on a moving train will naturally describe the seats around her as stationary. Bob, sitting on a different moving train, will describe the seats in his carriage as stationary but those in Alice's carriage as moving. Finally, Charlie, sitting comfortably on the station, will describe both sets of seats as moving.

But there's still a big question – is there anything that these three will agree about?