Monday, July 9, 2007

A Newton's 1st Law Thought Experiment

One of the most powerful weapon that a physicist can have is the thought experiment, or gedankenexperiment, which was the original German term coined by the physicist Hans Christian Oersted (which you should subsequently meet: he discovered that a compass, when placed near a wire with electric current, is deflected, the first known link between electricity and magnetism!).


The powers of the thought experiment are immense: some of these experiments can never be performed (e.g. a bucket of water suspended in an entirely empty universe!), but nonetheless thinking about them reveal some very important loopholes in thought. The bucket of water thought experiment (see: Mach's Principle) and the arguments of Newton and Mach helped formulate General Relativity for Einstein. Einstein, Podolsky and Rosen's famous thought experiment, known as the EPR Paradox is another example of a thought experiment that helped bring to attention the failings of theories, and to re-order our thinking.


I'm going to present a very simple thought experiment that leads us naturally to Newton's 1st Law. Newton's 1st Law states that any object in a uniform state of motion will continue in that state of motion unless acted upon by a force. This means that any object will go on doing whatever it was doing (either travelling in a straight line, or remaining stationary) unless someone or something decides to do something about it.


This fact is by no means straightforward to deduce: when a horse pulls a cart, the cart starts moving, but when the horse stops pulling, the cart stops moving. In fact, this fact was so difficult to deduce, that for many years the thinking was that a force was required to produce and to sustain motion (of course, you would know that the reason the cart stops moving is due to friction).


I hope you see the difference here: before Newton came along, people were questioning the reasons for motion, and many believed that motion was a result of a force. But Newton realised that motion itself has no reason. An object that is moving uniformly continues to move uniformly because that is the way of the universe. Only changes in motion could be explained by the presence of a force.


One way to arrive at this conclusion is a very neat thought experiment that really impressed me when I first encountered it. It is so simple that there is no denying the accuracies of its conclusions and the correctness of Newton's 1st Law.



So, imagine a ball rolling down a ramp. If we make the ramp really really smooth, like bowling alley smooth, and drop the ball off from a certain height, you can ascertain that the ball ascends to somewhere around its original height. One thing you can be sure: the ball never stops somewhere along the bottom of the ramp.


I hope you can see where this is going. We just have to make the ramp longer:

And by the same argument, the ball should rise up to its original height again. And now, the prestige of the trick!



If we were to have an infinitely long ramp, what would the ball do?


Naturally the ball wants to return to its original height, as we have argued in the previous two diagrams, but in an infinitely long ramp, the ball has no choice but to roll on forever! And thus, what we have shown from a simple thought experiment is that uniform motion is a natural state, and if undisturbed, goes on forever.


Of course, thought experiments in no way prove anything. The EPR Paradox mentioned earlier was cited as a way of debunking Quantum Mechanics, because it gave incredulous results in theory that goes against "common sense". But, when physicists actually got around to performing the experiment cited in the EPR paradox, the results that came back totally went against what scientists had long considered to be irrefutable.


But nonetheless, they are extremely useful ways of thinking about physics and reality.

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