Determinism

by Areeba Abid

Determinism is the idea that if all the net forces acting on an object are known, the motion of the object can be predicted iteratively over and over forever.

The Main Idea

Newton's laws allow us to predict the motion of an object if we know the initial position, initial momentum, and forces acting on the object. Using iterative prediction, we can calculate where the object will be at any given time in the future. If this idea is extrapolated to all objects in the universe, it would seem that we could predict the future of the entire universe if we only knew the positions and momentums of every object. This idea has been taken even further to argue that humans do not have free will, because the atoms that make up our bodies simply continue to move in the paths they have been set upon by their initial conditions.

Practical Limitations

While the idea of determinism seems straightforward at first, there are actually complicated reasons that we cannot predict the future of even small, simpler systems, much less the entire universe.

One practical limitation is the fact that initial conditions (the starting positions and momentums of objects) can only be measured as accurately as our instruments allow, and after a few time steps, small inaccuracies build on each other. This means that over time, our model of the system and our predictions of its future state stray farther and farther away from the actual future state of the system. This is why iterative prediction is usually only used over small periods of time.

Another practical limitation is that we must necessarily simplify systems to be able to model and calculate them. It is impossible to account for every interaction within and outside a system, since every single particle in the universe interacts with every single other particle in the universe, resulting in an unthinkable number of calculations that would need to be done to accurately account for the net forces on a system. This introduces error that limits the long term accuracy of any calculations that we can practically carry out.

Chaos

Another type of limitation is chaos, which results in systems that are extremely sensitive to initial conditions. This means that tiny changes in initial conditions quickly lead to dramatic differences in behavior.

A Mathematical Model

What are the mathematical equations that allow us to model this topic. For example [math]\displaystyle{ {\frac{d\vec{p}}{dt}}_{system} = \vec{F}_{net} }[/math] where p is the momentum of the system and F is the net force from the surroundings.

A Computational Model

How do we visualize or predict using this topic. Consider embedding some vpython code here Teach hands-on with GlowScript

Examples

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Connectedness

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History

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See also

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Further reading

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External links

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