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Science, Maths & Technology

Uncertain principles

Updated Thursday 3rd August 2006

Get to grips with Heisenbergs uncertainty principle

Daniel Craig as Heisenberg from BBC TV's Copenhagen Copyrighted image Icon Copyright: BBC

Quantum mechanics does away with the deterministic view of the future. It is no longer cause and effect. So what can we know about the world? It was the belief of the classical physicists that it was possible to know the position and velocity of a particle as accurately as one would wish.

After all, if you are travelling at 30mph and you are sat on your bicycle then you know these things at the same time. But they and you are wrong. In quantum mechanics there is a fundamental limit to the accuracy that can be achieved, no matter how good the measuring device.

In 1927 Heisenberg made a startling discovery. Quantum theory implies a limitation on how accurately certain pairs of physical variables could be measured simultaneously. Using some of the matrix mechanics that had been proposed by Max Born, Heisenberg realised that position and momentum (the relationship between mass and velocity) were non-commutable; you could not precisely know them both at the same time.

Hence, there is no way of accurately locating the exact position of a sub-atomic particle unless you are willing to be uncertain about its momentum. But there is no way you can be certain about momentum without being uncertain about position. It is impossible to precisely measure them both at the same time.

So, you might ask, how can I drive my car at 50mph at 26 degrees latitude and 99 degrees longitude? Well, the value of the constant that determines the uncertainty about either position or momentum is so small (in fact, it is Planck’s constant: 6.62620 x 10-34 Js) that it has a negligible impact in this world. So, no need to worry too much about this particular uncertainty.

This article was first published in 1999

 

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