Quantum physics tells us that
at a fundamental level,
the world behaves less like
hard billiard balls
and more like ripples in a pond.
This wave nature of reality
means that what we imagine
as distinct particles of matter
are actually quite fuzzy.
In quantum physics,
this characteristic of reality
is captured in the Heisenberg uncertainty principle.
The Heisenberg uncertainty principle plays a big role
in these very very very small scales.
So at the scale of atoms.
It's a principle that states that you cannot know
both the position and the momentum of a particle
to arbitrary accuracy both at the same time.
But,
the particle is not the only thing that can have
a wave nature.
Water waves for example,
radio waves,
any kind of waves that we see in our world
can actually have a similar uncertainty relation.
Consider sound waves.
A typical tune is composed of many overlapping frequencies
but if we play a specific note,
like Middle C,
its frequency falls within a narrow band.
The width of this band is a measure
of the uncertainty about its precise frequency.
The shorter the duration of a note,
the wider its bandwidth
and greater the uncertainty in its frequency.
The longer the duration of the note
the narrower its bandwidth,
and the more precise its frequency.
If you take a signal
which is this thick, you know,
the width is this,
and the bandwidth is this,
these two widths, if you multiply them,
is a constant.
So if you narrow this, this will increase,
if you make this fatter, this will decrease.
The mathematics is identical
to the Heisenberg uncertainty principle.
Heisenberg determined similar relationships for particles
at the quantum level.
For instance,
the uncertainty in position, written as delta x
multipled by the uncertainty in momentum,
written as delta p,
is always greater than or equal to a constant
written as h over four pi.
We can see the Heisenberg uncertainty principle
at play in the diffraction of light.
So, what we can do is we can have a little slit,
and we can point a laser through the little slit,
and we can slowly, slowly, slowly, make the size
of the slit smaller and smaller and smaller.
In the beginning,
there will be a pattern on the wall
which is basically a blob of light or a point of light
coming from the laser.
But after a certain time, when we make it even tinier,
then actually what we see is that this blob of light
kind of diffracts out into a large pattern on the wall.
This can be explained by
the Heisenberg uncertainty principle.
When we are making the size of the slit smaller,
We're trying to make sure that we are sending
the beam of light through a very accurate position size.
This in turn translates into saying that there will be
an uncertainty in measuring the momentum of
the light packet,
so this uncertainty manifests itself
as an angular uncertainty which falls on the wall
and produces this diffraction pattern.
Heisenberg extended the uncertainties
that are evident in all waves
to the realm of quantum particles.
We cannot determine where an electron is
at a particular point in space time,
and then also determine what its energy,
or what its momentum is
at the same particular space-time point.
And this is very important because
it tells us about the stability of matter.
So when we start from classical electrodynamics,
the problem was that there's the nucleus at the centre,
and the electron which is accelerating around
the nucleus at the centre,
and if it continues on this acceleration than it should go
closer and closer and closer
to the nucleus and fall into the nucleus
but that does not happen because we know that
most matter is stable and the universe is not disintegrating.
Here's where the Heisenberg uncertainty principle kicks in,
and it says that, if we know that the electron is going
closer and closer and closer to the nucleus then we know
its position to great accuracy.
And if we know its position to great accuracy,
that means uncertainty in its momentum
is increasing and increasing and increasing the more
and more closer it comes to the centre of the nucleus.
And this is not possible because an electron can only have
so much energy, as we can calculate from electrodynamics.
And because this is not possible,
we know that there is an inherent uncertainty
in where the position of the electron is.
If quantum mechanics is correct,
there is no way of measuring its position or momentum
accurately simultaneously,
it has nothing to do with the limitations of our instruments.
It's a fuzziness built into nature.
The Heisenberg uncertainty principle reflects the
fundamental nature of reality,
and it is that uncertain nature that allows for atoms,
chemistry,
and all the solid stuff of our every day world.
It does give us a new insight into reality,
it tells us that in reality things are fuzzy,
but at the same time, it also opens up a door
to many different ways of viewing that reality.
It's an extremely rich sort of doorway into what reality is.