# The Heisenberg Uncertainty Principle Explained Intuitively

## Transcript

This episode is sponsored by Skillshare

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

works

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

Mildred

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

too

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

[Music]

English (auto-generated)

## Description

https://skl.sh/upandatom4An intuitive explanation of the Heisenberg Uncertainty Principle of quantum mechanics.Hi! I’m Jade. Subscribe to Up and Atom for new physics, math and computer science videos every two weeks!*Follow me* @upndatom

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*Quantum Physics Series:

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*Sources*

The Blackhole Wars – Leonard Susskind

Quantum Mechanics: The Theoretical Minimum – Leonard Susskind

http://newt.phys.unsw.edu.au/jw/uncertainty.html

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