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:

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 = Δv_{y}/v_{o}.

Therefore: Δv_{y}/v_{o} = λ/Δy and so Δv_{y}Δy = λv_{o}

But λ = h/mv and therefore Δv_{y}Δy = h/m and so

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

If Δy decreases then Δv_{y} 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!