thank you brilliant for sponsoring this video this is the Heisenberg's
uncertainty principle at least a version
of it not only does it make the atom
stable but it allows you and me to exist
but wait a second what exactly does it
say well here's how my teacher explained
it to me if you look at this photo taken
by a high-speed camera of a moving
tennis ball you know exactly its
location but do you know where it's
going I'm like no it's a photo so it
could be going in any direction I have
no idea meaning I have no clue about its
velocity but what if I took a long
exposure photo of that same tennis ball
ooh ooh now I know it's going in this
direction and by looking at the blur I
can estimate its speed as well which
means now I have a much better estimate
of the Velocity but notice now I don't
know where the location of the ball I
don't know where the ball is so I've
lost the location um information of that
ball in other words if the uncertainty
in finding the location of an object is
very tiny then the uncertainty in
finding the momentum of the object
because the momentum is given by its
velocity that is very large but if you
know the velocity or the momentum very
nicely its uncertainty is very small
then there will be huge uncertainty in
the position of the ball and guess what
elementary particles like electrons
behave in a similar way if you find its
position exactly you wouldn't know where
it's going you wouldn't know anything
about its momentum on the other hand if
you find its momentum exactly you
wouldn't know anything about its
position if you take the uncertainty in
the position and the momentum together
they must have a minimum value and that
minimum value happens to be h/ 4 Pi
which is the uncertainty principle now
for a long time I thought that this
makes so much sense like so much
intuitive sense but then I realized
there's a problem with the analogy you
see if you go back to that photo I can
actually figure out the velocity of the
ball over here you know how instead of
using a still camera I use a high-speed
video camera and then I just look at the
next frame and by looking at the next
frame I will know which direction the
ball is going and I can figure out this
distance and calculate the velocity
higher the frame rate better my
calculation so this is just a
technological limitation I can figure
out the velocity but Heisenberg's
uncertainty principle it is not a
technological limitation another
explanation I heard was that hey if you
try to figure out where the electron is
you have to bounce off light on it and
when you do that you're going to disturb
the electron disturbing its momentum and
that's why you'll have no idea about its
momentum when you learn about its
position but again the problem is the
uncertainty principle has nothing to do
with measurement it is much more subtle
so for a long time I thought I will
never get a rigorous intuition behind
what's really going on over there that
is until I read five lectures and then
my mind was truly blown so the hope of
this video if I do it right is not just
to understand the principle but to
actually ReDiscover it intuitively so
that we understand in our bones and guts
and will make perfect sense and I think
fan helped me do that so I'm sharing it
with you so if you're ready for this
let's begin so where do we start fan
says we need to First understand the
idea of wave particle duality and I'm
like wait a second I know what that
means right I mean electrons for example
are both waves and particles at the same
time right and fan says no not quite
mean what what what do you mean well fan
asks mahes if you have an animal that
flies like a pigeon but also has a face
like that of a mouse and the fur that of
a mouse would we say that animal is both
a pigeon and a mouse at the same time no
no it's not it's a different animal alog
together it just shares some common
properties with these two but it's a
different animal Al together right
similarly an electron has certain
properties that are similar to that of
the traditional particles for example
they come in lumps he says so you will
always find an electron in one
particular location you can count one
electron two electron three electron
they're not spread out or anything like
that okay which is very similar to how
particles are they come in lumps like
the grain of grains of sand or a tennis
ball or other things like that but the
electrons are not particles why because
they do certain things that normal
particles don't do for example if you
were to set up an experiment with the
two holes which is the double SE
experiment and shoot electrons through
them you will get something which you
wouldn't expect from grains of sand or
tennis ball you'll get a pattern that
looks like this think about it how does
that make any sense normal particles
don't do that therefore electrons are
not normal particles but this pattern is
an interference pattern that you get
from waves and therefore this means
electrons also have properties like they
interfere they defract properties that
we associate with traditional wav
but does that mean they are waves no
because remember waves do not come in
lumps they are continuous they are at
multiple locations at the same time but
electrons come in lumps which means they
neither waves waves nor particles
they're their own things fan says they
act screwy in their own way which sounds
disappointing right but here's the good
news electrons are screwy just like how
protons neutrons or even photons and
other other things are they're all
screwy in the same way so the physics
for them is pretty much the same we call
them Quantum objects so they are neither
particles nor waves they share certain
properties with particles or waves but
they are neither of them this is the
whole idea behind the W particle duality
okay so since Heisenberg's uncertainty
principle applies to Quantum objects our
next question would be how do we deal
with the momentum and the position of
quantum objects so let's start with the
momentum fan ask do you want just a
formula to calculate momentum of such
Quantum objects or do you want some
intuition behind it I'm like of course
give me the intuition right so for that
F says let's go back in time a little
bit um around 1900s where we thought we
understood what light was we celebrated
thinking that light is an
electromagnetic wave we understand
Optics is soled almost all the physics
is soled nothing else remains to do only
to realize a little bit later that there
were certain experiments like the
photoelectric effect or the black body
radiation where we could couldn't
explain what was going on using the wave
theory this is where folks like Mox plun
and uh Einstein Albert Einstein came
along and they realized that light must
be coming in chunks as well must be
coming in lumps as well the quantum
nature of light was discovered by these
folks because of these experiments this
is your photons and the energy of the
photons they hypothesized has to be
given by this particular equation e
equal to H new where is the energy of
the photon H is the Plank's constant and
U represents the frequency of light well
earlier it was just a hypothesis but
then experiments like photic effect
actually confirmed that this must be
true okay now at this point fan asks
smes do you see something interesting
over here and I'm like no this is a
usual equation I know about it what
would I see fan says if you at De Bry
okay or de brogle however you want to
call him okay then you would notice that
hey hey hey hey new is the frequency
right frequency of any wave is given as
C / Lambda and I'm like yeah so what
well now if you bring the C on the other
side you get e divided by C on the left
hand side and I'm like yeah so what well
from the classical electromagnetic wave
theory the momentum of an
electromagnetic wave is given by E
equals c sorry Eid by C do you remember
this mahes I'm like yeah I kind of
remember this we did a video on it a
video where we showed why light has
momentum even without mass we showed
that uh the light's momentum comes from
its energy you don't have to watch that
video I'm not fishing for views but we
derived it intuitively over there so you
can check it out if you need to do that
but this comes from classical physics
okay but anyways de Bry what he says
what he looks at it and says that hey
that means I Now understand that the
momentum of these Quantum Light
particles whatever you want to call them
that should equal the planks constant
divided by the wavelength I have an
expression that connects the momentum
and the wavelength why he got excited
was because he said look if light which
we thought was a wave happens to have
particle properties maybe particles like
electrons which we thought to be
particles may also have wave properties
and might also have wavelength
associated with it so maybe this
equation also works for electrons that
was the hypothesis that de Bry put
forward again back then it was a
hypothesis but today we have verified it
that this is true so this works not only
for photons but all Quantum objects and
that means if you want to find the
momentum of any of these like say
electrons this is how you find it you
take the flanks constant and divide by
the wavelength and that's how you
calculate the momentum of the object at
link is also in the description all right Heisenberg is waiting for us so
this is how we think about momentum for
Quantum objects but now comes the last
question how do we think about position
for the quantum objects that's the last
piece of the puzzle and for that fman
says again we have to go back in time a
little bit okay once we put forward this
hypothesis that these electrons for
example can have wavelength a question
was asked if electrons have wavelength
they should also have a wave equation
right where is the wave equation and
that's where Irving shinger says hold my
cat he comes back in a year with the
wave equation which we call today the
shinger wave equation this equation
looks scary and maybe it's a topic for a
future video but what's important is
that it encapsulates all the properties
of these Quantum objects actually not
all some properties like spin was not
captured very well anyways then comes
the big question what does that equation
even mean I mean think about it if you
solve this wave equation and you get a
wave say that looks like this for an
electron what does that wave represent
right because it's not the electrons are
wiggling up and down no no no this
itself is the electron then what do
these Peaks and values even mean that
was the big question well we call these
Peaks and valleys we the symbol that we
use to repres represent the Peaks and
valys is Sai and we realize that maybe
Sai doesn't the the Peaks and The
Valleys don't really mean anything but
we also realize that if you take a
square of these Peaks and valleys then
that gives you the probability of
finding the quantum object at that
particular location and I'm like but
what does that mean what do you mean
fman okay fan says M look at these
locations okay okay what's the value of
s over here the amplitude it's zero this
means the probability of finding the
electrons over here is zero so if you
were to shine light on this electron to
try and locate it there's no chance that
you would find the electrons in these
locations on the other hand look at
these locations the S value is very high
so the probability of finding the
electron over there is very high so if
you were to shine light on this electron
there's a very good chance you'll find
the electrons over here and this is the
weirdest thing about Quantum objects
they don't really have a position until
you measure it it's not like you don't
know where the position is no no no we
know that the position can be anywhere
here and here it's inherently
probabilistic it has nothing to do with
our measuring tools they don't have a
position until you measure it okay so if
you put it all together we Now
understand how to think about momentum
of such Quantum objects and we Now
understand how to think about position
of such Quantum objects as well and now
let's put these two together to build
the uncertain principles ourselves so
fan what do we do next fan asks mes can
you imagine an electron which has a
specific value of momentum and I'm like
yeah if it has a specific value of
momentum it's moving at a constant
velocity I'm imagining it like this and
finally it's like no no no mahes you're
still thinking classically see these are
quantum objects right so if they have a
specific value of momentum they should
have a specific value for wavelength so
a better way to imagine this is a wave
of a specific wavelength and this wave
would extend all the way to infinity and
I'm like wait a second wait a second I
get that electrons have wavelength so
we're drawing a wave but why does it
extend to Infinity why can't I have why
can't I represent it this way well
because look the wavelength here and the
wavelength here is different right the
wavelength over here is infinity
actually but we said that this electron
should have one value of wavelength
everywhere which means the Ron should
look somewhat like this it should extend
all the way to Infinity everywhere in
the universe so now think about its
momentum okay so since I know its
momentum perfectly because it has one
specific value of momentum Delta p is
zero there is no uncertainty in momentum
but what about its position where will
you find this electron if you are to
measure it well for that the probability
it depends on the amplitude square but
look now the amplitude is the same
everywhere
which means the probability of this
finding this electron is the same
anywhere in the universe in other words
the uncertainty in finding this electron
is infinity because I can find it
anywhere in the universe this is the key
that Fineman says yes this is
nonsensical but if you try to create a
quantum object which has one value of
momentum so that there's no uncertainty
look you inevitably end up with having
infinite uncertainty in its position not
because you don't know its position no
no no now the probability of finding
that you know electron is the same
anywhere that's why the uncertainty goes
haywire and becomes Infinity right now
let's try to think about a more
realistic Quantum object so we need to
localize it a little bit more I need to
narrow down its position which means I
have to decrease its uncertainty how do
I do that well again think about it if I
have to narrow it down I have to make
sure the waves have zero amplitude at
some places how do you do that well fan
says just add more waves to it with
slightly different wavelength wait why
what does that do well because it has
slightly different wavelength there are
certain locations where the waves of the
Peaks and the W you know valleys will
line up over here in these places the
amplitude will be much higher but there
will be also other places where the
Peaks and The Valleys line up like this
in such cases they will destroy each
other destructive interference and when
we do that we'll now end up with a new
wave that kind of sort of looks like
this I know it looks ugly but look what
we have done because now there are
places where the amplitude is very high
and other places where the amplitude is
low I have narrowed it down so this is
much better than before when it comes to
position but it comes at a cost you see
because to narrow it down to narrow down
the position I had to add two waves of
two different wavelengths that means now
this object has two values for momentum
what does that mean that means if you
are to now measure this particular
electron's momentum there's a 50/50%
chance of having it to be either one of
them in other words narrowing down the
position decreasing the uncertain the
position automatically has now increase
the uncertainty in momentum it's no
longer zero you can see right in front
of your eyes it has nothing to do with
measurement that's how the quantum
objects work and if you want to narrow
it down even further when it comes to
position you add even more waves you can
do that but if you add more waves you're
going to increase the uncertainty in the
momentum even further decreasing one
increases the other beautiful isn't it
and by the way I know these are ugly
drawings so here's an audacity
simulation over here if I add two waves
of slightly different wavelength look I
can find I can destructively interfere
them so that I can narrow down the
positions high probability of finding
the electrons here but if I add even
more waves see I'm narrowing it down
even further in the limiting case I can
add so many waves of different different
wavelengths such that I will get I will
I will get one specific location where
there's a high amplitude and almost zero
amplitude everywhere else now this is a
highly localized electron the
probability of finding the electron is
super high in this region that means the
uncertainty has gone down down
dramatically but because I've added so
many waves of different wavelength it
has so many values of momenta that means
its uncertainty in the momentum has gone
up so this is it this is the uncertainty
principle nothing to do with the
measurement nothing to do with our
instruments but inherently how Quantum
objects work just think about this try
to create a quantum object in your head
which has a perfect value for momentum
and a perfect value for position it's
not possible
okay and that's the uncertainty
principle that's why if you take their
product it should have a minimum value
Heisenberg said and that minimum value
happens to be H divid 4 Pi we can derive
this as well intuitively which we'll
probably do in a separate video but at
least we got the essence of it right
finally f one how does the uncertainty
principle stabilize the atom well if you
go back to the classical model of the
atom where the electron is going around
the proton say in the hydrogen atom then
this can cannot work because the
electrons are charged particles so
charged particles when they accelerate
they should lose energy to radiation
which means as it loses energy it should
plummet into the proton but that doesn't
happen why nobody had a real answer for
this but Heisenberg's uncertainty
principle can help us understand why
that cannot happen the simple answer is
electrons are not simple particles they
are quantum objects so think about it
this way the uncertainty in the position
of the electron is pretty much the size
of the atom right if the atom is so big
we know the electron has to be somewhere
over here and not somewhere over here so
there's a high chance of finding the
electron over here so its uncertainty is
over here now if there if the electron
were to plummet towards the nucleus
towards the proton then its uncertainty
would reduce and if the uncertainty in
the position becomes very small its
uncertainty in the momentum would become
very large meaning the electron would
now have much larger velocity which
could actually Propel it
outwards and that that's why because of
that undefined very large momentum it
will not be able to S it will not
actually fall into the nucleus it will
come right back up so the uncertainty
principle ensures electrons do not lose
energy and fall into the nucleus it's
the principle because of which electron
has to be having some energy and stay
away from the nucleus and that's the
reason why today we think of it in terms
of an electron cloud the uncertainty
principle saves the atom it stabilizes
the atom and allows everything to exist
including you and me so what do you
think about this do you think you now
have a much better intuition for the
uncertainty principal and much better
appreciation for it as well if you did
let me know and uh yeah stay tuned And
subscribe if you want more Quantum
mechanic stuff it's coming soon see you