have you asked yourself a question to
what extent can you be certain an
object's position and momentum.
Probably not, but this can be answered by
the uncertainty principle of quantum
mechanics.
Werner Heisenberg stated that the more
precisely the position is determined the
less precisely the momentum is known and
conversely which means the more
uncertain you are about its position the
less uncertain you are about its
momentum and vice versa. To understand
this, we must discuss the basic concepts
of quantum mechanics. There is a ball
hidden side of one of these three cups.
It could be in this cup, this, or this.
This represents multiple states in which
the ball is in these states could be the
object's position momentum and many more
but for this case its position these
states have a probability that are not
necessarily equal the most probable
state is not always the state the ball
is in right now the ball is in a
superposition of being in all of these
three cups at once once observe it
collapses into one state in random
another way of visualizing this is by
this ball game very few charts give you
random results but multiple trials give
you a pattern this can be represented by
a probability density the higher the
peak, the more probable it is to find it
there. The uncertainty principle can be observed
When you point a laser through a
narrowing slit, you get this probability
density. if you narrow the slit, you expect the
spot to narrow but at a certain point it
starts to spread what just happened was
in to limit its paths you decrease
uncertainty in position and therefore
uncertainty of momentum should increase
since momentum is a vector quantity
direction matters this is called a
single slit diffraction another concept
is the wave particle duality everything
acts like a particle and a wave this was
first observed in light and was later
observed on electrons.
macroscopic objects have wavelengths too. it is
calculated by the de broglie wavelength
formula a particle has no definite
momentum but has a definite position and
the wave has a definite momentum but no
definite position we can add waves of
multiple trials to have a smaller wave
packet this can be represented by a wave
function the square of the wave function
is a probability density it does us how
probable it is for a particle to be in
that state to increase certainty in
position we add more weights and thus
have a large uncertainty in momentum and
to decrease certainty in position you
can add less waves
why don't we observe the uncertainty and
wavelength on macroscopic objects it is
because the Planck's constant is so
small if the volume of the Sun equals 1
the new plan constant has a volume of
this bone it is undetectable and
insignificant on large objects but is
significant on microscopic objects we
can never be fully certain at once
position and momentum or the other will
be infinite one thing's for sure we're
certain that we're uncertain
