Heisenberg’s Uncertainty Principle states that one cannot know
for certain two related properties of a particle, such as
position and momentum, at once,
and the more you know about one, the less certain the other becomes.
It’s incredibly important in our universe,
and explains so many natural phenomenon,
such as light diffraction, virtual particles,
why electrons don’t fall into the atomic nucleus,
and so many more.
However, many, misconceptions still surround it,
the main one being that it is caused by a flawed measuring process.
Throw out any garbage you learnt about how the uncertainty occurs,
because Heisenberg discovered that it arises due to the very nature of matter itself,
NOT by some lousy measuring or whatever.
This innate nature is what is known as “wave-particle
duality”,
meaning, matter behaves both as
a particle,
and a wave.
With the De Broglie Equation, we can measure the exact
wavelength of any given object.
But since everything in our daily lives is so massive,
this wavelength is INCREDIBLY small.
A baseball tossed up into the air only has a wavelength of about
a billionth trillionth TRILLIONTH  meters.
However, smaller particles, such as photons or electrons,
have wavelengths that are INCREDIBLY large relative to their size.
And thus,
since a wave occupies many points at once,
the particle can be in more than one position, one state, at once.
This is what is known in Quantum Mechanics
as a “superposition”.
So a particle can be at point A with momentum x,
or at point B with momentum y,
and both would be equally valid states.
The interesting thing is,
once you measure
any aspect of the particle,
such as position or momentum,
the superposition vanishes
and you're left with just that single state
Waaaaait
we just found which state the particle is in,
and thus we know all of it’s properties, right?
Wrong.
You see, position and momentum are “independent” variables:
knowing one tells you NOTHING
about the other
But why is that? Let me explain
Remember the De Broglie Equation I talked about earlier?
By using it, we can directly relate momentum to a wave,
meaning, we can represent momentum
as a wave.
For any given wave there are many possible positions,
some more likely than others based on that point's amplitude.
But if we want to pintpoint the position,
we can add lots of different waves;
so that one wave's crest cancels out another's trough
until it gets essentially flattened
and we are more and more
certain of the most likely position for the particle
But let's look back at what we did to get here
we added different waves, and as we've seen previously
a wave can be used to represent momentum; meaning
we just combined different momentums to be more certain of the position
But a particle can't have more than one momentum
once it leaves the superposition,
so which one of the momentums we added was the particle's original
momentum? There's no way to be certain
