Heisengberg's Uncertainty Principle

[mikey4444]

Can anyone explain in a relatively simple manner, that non-scientific people would understand, exactly what Heisenberg's uncertainty principle is ?

A simple example of how it might be used would also be welcome.

[jim360]

I think maths is a mixture of invention and discovery. We invent the language to describe maths, to be sure. But sometimes it leads us to places we never expected. Take complex numbers as an example. They were discovered and not invented, in the theory of cubic equations, they just kept showing up again and again. Discovery, not invention. Some things may just be invention, e.g. the unified theories that seem to fit nicely but don't (yet) match experiment, or JTP's least favourite physical topic of Supersymmetry - but not always!

[jake-the-peg]

Oh interesting Jim

I rather thought complex numbers were invented in Italy in the 16th century as a tool to solve 3rd order polynomials

Why do you say they were 'discovered' ?

[jim360]

Because they first appeared before they were "invented", e.g. in the solution to x^3=x. Which is solved by x = 1, 0, -1 or by some weird thing that gave the cube root of the square root of -1 plus its reciprocal or some such. For a lng time no-one accepted that it was a real thing (since even negative numbers were thought of as "imaginary") so the square root of minus one was "discovered", so to speak, about a hundred years or so before anyone thought to do anything new with it. I will need to check the dates but I think we're talking a couple of generations at least from first appearance to first calculations using complex numbers. That length of time between things suggest that in some sense it was a discovery, at least to me.

[Khandro]

You are right jim, i m [humble] o, not only is maths a mixture of invention and discovery, so is everything relating to human advancement. Tycho first believed that the planets were held in place by some form of transparent orbs, eventually he realised that there were no orbs, but the planets floated in space, but then it took the Kepler to replace orbs with orbits, then his measurements led him to believe that orbits were not circular, but elliptical, because circles are constructs drawn by humans with compasses - which is geometry, (I love the realisation of that concept) but I think he figured out that if you don't know what form the ellipse takes, you may as well, for working purposes, stick with circles, he knew that these were man-made geometric constructs but continued with their use until he could show otherwise, thereby turning geometry into physics; brilliant!