Starting with acceleration

You can feel and measure accelerations directly

You were born on a planet where acceleration is omnipresent – both in the natural and in the made world. Release a stone held out in your hand and it accelerates. The same applies to amusement park rides where the ride container often falls in a controlled way. Watch a jet take off and it too accelerates, as it does when it lands (but now the acceleration is negative – more on that later). However, in all these cases you're noticing the acceleration from a detached point of view. How about getting closer to the action?

Catch a wave and you feel the lurch of acceleration as you take off on your surfboard. Sit in the jet and you also feel the lurch, as you do if you're in the fairground ride when it's released. You can feel these lurches – no need to keep your eyes open. That's because we've evolved on a planet where there is a gravitational field, and so we've developed acceleration sensors. These are built into the inner ear, and they act primarily as orientation sensors, so you can figure out which way is up. The gravitational field, acting on the masses in these sensors, along with every other mass in the vicinity, deflects them. Change the orientation and you change the direction of deflection. But you can also deflect them by accelerating your head. The origin of motion sickness is a mismatch between visual and accelerometer inputs. Sit in deep in the hull of a ship and your eyes tell you that there is no acceleration – but your inner ears are sending exactly the opposite message.

Someone on the shoreline will also expect you to be experiencing acceleration, as will another sailor on a vessel sailing a parallel course. Perhaps the acceleration is something that Alice, Bob and Charlie, from their three different points of view, will always agree about. It's not likely that they'll agree about your velocity – but more on that later.