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The Heisenberg uncertainty principle

If it were possible to measure the exact position and velocity of every particle in the universe at a certain time, then by applying the basic laws of Physics we should be able to predict their state at any future time - for example, we could say how much rain would fall on Taunton on the third of January in the year 2500!

The uncertainty principle of Heisenberg states that it is actually impossible to make such a measurement

In fact, if ΔE, Δx and Δp represent the smallest uncertainty with which the energy, position and momentum of a particle can be measured and Δt the smallest uncertainty in the time of measurement, then:

Heisenberg Uncertainty Principle:      Δx.Δp = h/4π     and    ΔE.Δt = h/4π

where h is the Planck constant (6.6x10-34 Js).

Strictly the equations should be written as Δx.Δp is greater than or equal to h/4π and ΔE.Δt is greater than or equal to h/4π.

The quantity h/2π is often written as h bar (shown by a line through the h)

An idea of the development of this equation can be seen in the following simplified idea of electron diffraction. If an electron passes through a slit and is diffracted through an angle θ then sinθ = λ/Δy

Also tanθ = θc = Δvy/vo.
Therefore: Δvy/vo = λ/Δy and so ΔvyΔy = λvo
But λ = h/mv and therefore ΔvyΔy = h/m and so

ΔpΔy = h (which is close to the equation of Heisenberg!)

If Δy decreases then Δvy increases so if the electron gets through the slit its position will be known within Δy.

The concept of the detached observer of classical Physics is a myth, since a completely isolated universe cannot be observed. An observer must always be part of an experiment - otherwise there is no experiment.

The 'true' nature of a particle, or at least the modern view of it, is that it has both wave and particle properties described by the wave mechanical model of Schroedinger. This model is complex but simply states that we cannot fix the position of a particle (as in classical Physics) but can only predict the probability of it being at a given point at a certain time. It could therefore be anywhere, but is in fact more likely to be at one place than another. The square of the amplitude of the wave associated with a particle at a given point in space and time is proportional to the probability of the particle being at that point.

Further consideration of this subject is beyond the scope of this text, but it is hoped that this very brief introduction has been sufficient to demonstrate the uncertainty of Physics on a nuclear level. Remember that all the world around us is composed of waves, even ourselves.

As you read this, there is only a probability that you are there at all!

© Keith Gibbs 2013