The Heisenberg Uncertainty Principle Explained Intuitively



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in the first year of my physics degree I
had a birthday party and 30 people came
in the last year of my physics degree I
had a birthday party and five people
came now it’s not like physics turned me
into a mega bitch or anything like that
at least not that I know of but as the
years went on I became more and more
serious about my studies I stopped going
out with friends meeting new people and
I spent most of the day night alone in
my room integrating equations the better
my grades got the more my social life
suffered this is just an example of one
of life’s many trade-offs but trade-offs
aren’t just unique to us they play a
pretty big role in the way the world
in this video we’re going to talk about
the uncertainty principle and you’ll see
that whether we’re talking about
position momentum good grades or a
social life it all follows the same
logic there are some things you just
can’t improve without messing up
something else the most well-known
version of this is probably the
Heisenberg uncertainty principle from
quantum mechanics and while we will get
to that today
the uncertainty principle is a lot more
general let’s start with something
simpler say there’s this little old lady
now you’ve been watching her for a week
and you notice that on Sunday she goes
to the market now can you conclude that
every Sunday she goes to the market well
not really
you’ve only see her do it once now you
watch her for another week and a low and
behold on Sunday she goes to the market
so it’s tempting to say that she goes to
the market with frequency once per week
but it’s still not enough you need more
time to draw an accurate conclusion
after a year of careful surveillance
you’re pretty sure that she goes to the
market with frequency once per week but
what if the next week she goes to bingo
instead or what if she needs more cat
food and goes twice really you need an
infinitely long time to be 100% sure
that Mildred frequences the market once
per week obviously you don’t have an
infinite amount of time so the frequency
of Mildred’s market trips can never be
known to 100% accuracy there’s this
trade-off between knowing the frequency
and spending time this is a version of
the uncertainty principle and variables
that have this trade-off relationship
are called conjugate variables and
more well known pair of conjugate
variables our position and momentum this
is one version of the Heisenberg
uncertainty principle and it states that
the uncertainty in position and the
uncertainty in momentum are always
greater than or equal to this constant
here basically we can never measure both
the position and momentum of an object
to 100% accuracy we’ll come back to the
equation in a bit but first let’s talk
about the intuition the way my quantum
physics professor introduced the
uncertainty principle was imagine you’re
trying to find the location of a
basketball but the only way you can do
that is by throwing tennis balls at it
and measuring where they bounce back if
you managed to hit the basketball sure
you know where it was but now it’s moved
keep the imagery in mind for this next
bit Heisenberg was a German physicist
who loved classical music and was a
pretty accomplished piano player oh yeah
and he won the Nobel Prize for the
creation of quantum physics one day he
was performing a thought experiment he
wanted to see if he could measure both
the position and velocity of an electron
to measure the velocity of something you
just need to measure its position twice
and divide by the time it took between
each measurement so it seems silly that
you could measure something once but not
twice right but the most direct way of
measuring where something is is to shine
light on it and from the reflected light
calculate its position we do this every
day when we look at things photons hit
the object and reflect them back into
our eyes then our brain figures out
where it is from the image produced on
the retina so Heisenberg imagined
looking at an electron under a
microscope firing a photon at it and
figuring out the position of the
electron but in order not to move the
electron he would need to hit it with a
photon of really low energy now quantum
particles have a property called wave
particle duality where they behave as
both particles and as waves so while
they can be thought of as particles they
also have a wavelength and frequency
radio waves have the longest wavelength
30 centimeters or more and they’re great
for capturing images of stars and
planets but they’d be hopeless at
producing a good image of say your face
you would just get a blur see you can’t
get better focusing power than the
wavelengths that are forming on the
image the 30 centimeter radio waves can
only make images of details
least 30 centimeters big if you made the
wavelength smaller to about a millimeter
then you get a much better image
so if heisenberg wanted to get a clear
image of an electron say to within a
micron he’d need to decrease the
wavelength of the photon to within one
thousandth of a millimeter but the
energy of a photon is given by this
equation where e is the energy and
lambda is the wavelength so you can see
that as the wavelength gets smaller the
energy gets bigger if we decrease the
wavelength allowing us to get an
accurate description of its position the
photon has to be of such high energy
that it hits the electron too hard and
moves it if we hit the electron with a
photon of low energy and then hit it
again we can get an idea of the velocity
but the images will be too fuzzy to
measure its position with decent
accuracy this is a conundrum position
and momentum are conjugate variables you
can’t gain information about one without
losing information about the other now
let’s come back to our equation
hopefully now it makes more sense these
triangles main uncertainty and this X
means position and this pain means
momentum this h-bar on two is a teeny
tiny little constant don’t worry about
the exact value right now the important
thing is that it’s greater than zero so
the equation tells us that the
uncertainty in position and the
uncertainty in momentum is always
greater than zero basically we have to
have some uncertainty somewhere as we
saw from Heisenberg’s experiment this
had nothing to do with the equipment he
was using unless we find a way to make
wavelength shorter without increasing
energy we’re screwed now for those of
you who need a mathematical description
to go with the intuition don’t worry
it’s coming when einstein concluded that
light behaved as particles this french
guy named Dubrow made this outrageous
totally not founded on anything claimed
that all particles must behave like
waves too and he was right the
wavelength of an electron is just
Planck’s constant divided by its
momentum therefore the momentum of a
wave can be represented by a wavelength
so say we know the exact momentum of an
electron we can represent it as a
beautiful infinitely long
wave but the position of the electron is
also described by this wave the area
under the curve represents the
probability of it being there and we can
see that we have basically no idea where
it is
but waves have this cool property that
when you add them together they
interfere and create a new wave so say
we’re presented with this wave that
describes the electrons position and
momentum now the electron is much more
localized and we have a way better idea
of where it is but this wave is made up
of a sum of a lot of different
wavelengths and remember that wavelength
and momentum are practically
interchangeable so then we no longer
have just one momentum value we have
loads so in gaining information about
the position of the electron we’ve lost
information about its momentum position
and momentum are just two of the loads
of different conjugate variables
Heisenberg’s mentor Niels Bohr gave this
relationship between conjugate variables
a proper name complementarity the deeper
meaning is that there are some pairs of
complementary properties that just can’t
be measured or observed simultaneously
trade-offs are built in to the laws of
nature of the particles that make up our
universe and our lives so next time you
think you can have your cake and eat it
you probably can’t I’m often asked how I
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thanks for watching guys I hope this
video helps you understand the
uncertainty principle a bit better this
video is part of a quantum physics
series I’ve got going on at the moment
which I’ve put for you at the end of
this video like subscribe all that other
stuff that youtubers are meant to say
and I will see you next time bye
English (auto-generated)


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