Natural and unnatural motions
We're programmed so that we notice change. Birds that move are much easier to pick out from the background than those that don't. However, explaining motion has proved much harder to nail. Even figuring out what needs explaining has taken millennia of discussion and theorising.
Think carefully about the following processes:
- A falling stone, getting faster and faster.
- The Moon circling the Earth.
- A stone slithering across an ice-covered pond.
- A racing cyclist powering to a sprint finish.
- A cyclist free-wheeling down a hill.
Which are natural – just what things do, if left to their own devices – and which are forced on the objects as a result of interactions with their environment? In other words, which processes need explaining and which are
just what things do? And just what is a natural environment for things?
Everyday experience turns out not to be a reliable guide to more universal truths. In some ways where we live, learn and gain our intuitions is not a very typical part of the universe. So if you want to see the bigger picture, the wider view, then you'll have to re-home the objects to find out what they get up to in a
natural environment. Then compare this environment with the one you live in, gradually adding complexity as you understand the additions that you make.
It's this necessity for re-homing the objects that is at the root of why so many find the description of the world that is developed in this episode so alien. The lived-in world seems to consist of objects whose natural motion is to come to rest, or to fall, or to rise, or some combination of these motions. Pretty much nothing seems to keep on moving unless there is some agent or agency that maintains that motion. For many centuries the theories initiated by Aristotle, based on careful observation of what things
just did, described motions in terms of
natural motions that differed for different objects. There was no simple overall pattern. That had to wait until people learnt to ask different questions about the world, seeking more unified patterns of behaviour. This required more sophisticated mathematical descriptions than were available to Aristotle, or throughout the Middle Ages, and a significant leap of the imagination. This combination of painstaking, careful analytic thinking and imaginative leaps to see the world
as it really is make this topic rather hard. It's not one to be rushed, or skimmed over. Newton was the one who built on the work of others to provide a truly comprehensive synthesis, so a shorthand for this new way of describing the world is to describe it as a Newtonian view. It's proved to be extraordinarily effective, underpinning much of the successes of the engineered environment humans have created over the last few centuries.
The motion of objects in their natural state
To arrive at a natural state of motion you need to do two kinds of stripping away:
- Stripping away appearances, so the objects are not skinned in any way.
- Stripping away contingent interactions of the object with its environment.
The idea of
skinning is a common metaphor in the technical world, from buying new cases for your mobile phone to altering the appearance of your web browser or chat client. In neither case do you alter the functionality of the appliance or software, and that's what's so useful about the metaphor. In stripping away the inessential appearances of the objects we get to their functional essence. And since physics is concerned with building a model that mimics the functions of the lived-in world, rather than producing a photo-realistic depiction, that helps.
Isolating objects from their background influences is something at which you've already developed an expertise if you've worked through the SPT: Forces topic. Every time there is an interaction, you replace it with a force as you gradually extract the object from its environment. To find out how it'll move of its own accord you need only find an environment where there are no forces – none at all. So no slip, drag, grip, tension, compression, buoyancy, gravity, electric or magnetic forces. That'll be a very empty universe. But that's good.
If you can find out how it behaves in that very simple situation then you can add in complexity later. Physics is simple: don't start by developing a complete description. It's almost always better to add in the complication later. Work out what can be left out, not what must be put in. What are the bare necessities – the essence? As it turns out – not much.
Approximating natural motion in the everyday world
Where can we find things that approximate to this simplified natural state, to make it seem more approachable?
On ice is one place. Once you're moving in that situation, it's very hard to stop. And if you're not moving it's certainly hard to get going.
In a more urban environment, in-line skates, bikes and skateboards are engineered to move as freely as possible.
Indoors, air hockey tables are one place where the not-moving remain immobile, and the moving just keep on moving. Linear air tracks in the school laboratory provide a similar experience in one dimension. Specialist dynamics trolleys, also found in the school laboratory, provide another resource.
Not very close to home, experiences in free-fall, where gravity has its way, provide rather specialised
laboratories where you can see objects falling alongside making their natural moves.
Deep space is even further from the everyday, yet may seem familiar through science fiction movies or writing.
All natural motions are somewhat like a lop-sided pendulum
In the imagined, simple world of the physicist, things just keep on going – all by themselves. Here's a rather famous
thought-experiment that supports this line of thinking. It starts from something that you can do in the laboratory: making changes that show a trend. The final step is an extrapolation to something that's just not possible in the laboratory, but which does follow the line of reasoning established there. It's a kind of reasoning by extremes, and since extremes are often agreeably simple, that can be a very profitable way to get a feel for the behaviour of a system. So the pattern of reasoning, as well as the particular result, is of value here. As the original is attributed to Galileo, who was famous for his dialogues, the reasoning is presented in dialogue form.
Pensatrice: Here's a ball. I'll release it from this height, and let it roll. Now another from the same height, down the opposite slope. Which will go faster by the time it reaches the bottom?
Cercatore: Well, both sides are the same. They're symmetrical, so I suppose it'll go at the same speed. But maybe not quite – there are bound to be some differences.
Pensatrice: OK, so without any differences in the slope, then it'll go at the same speed. Now I'm going to make a change: make the two sides different. Now I'll make one slope steeper – but still release the balls from the same height.
Cercatore: I can see some things have changed, but nothing really important so I suppose they'll reach the same speed again. We could even think about the conservation of energy to support that conclusion.
Pensatrice: So, even if I make the two sides very different, you'll still agree that it goes to the same speed – even if it has to go farther. We could even run it down one side and back up the other: the speed it loses on the way up will be exactly equal to the speed it gains on the way down, whatever the slopes. Now what if I made one side very different – a very gentle slope – so that it had to travel a very long way as it climbed and lost the speed?
Cercatore: And still very smooth surfaces? I suppose still the same height.
Pensatrice: What about if I made it travel to the other side of the universe before it started the climb?
Cercatore: Well, I suppose it would keep on going at top speed – the speed it was going at the bottom of the ramp – right up until then.
Pensatrice: And if the universe were without end?
Cercatore: Then it'd keep going at the same speed for ever, I suppose.