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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 Saturday nights 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.
Take 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 seen her do it once.
Now, you watch it for another week and
lo 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 frequencies 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.
Another more well-known pair of conjugate variables,
are position and momentum.
This is one version of the Heisenberg uncertainty principle
and it States that the uncertainty and position,
and the uncertainty and 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 manage 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 edit 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 wave length
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 at least 30 centimeters big.
If you made the wavelength smaller,
to about a millimeter,
then you'd 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 1000th of a millimeter.
But, the energy of a photon
is given by this equation
where E is the energy and the 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
it's positioned 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 mean uncertainty
and this X means position,
and this P means momentum.
This H by 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 wavelengths 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 De Broglie made this outrageous,
totally not founded on anything claim
that all particles must behave like waves too.
And it 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 sine 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 say 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 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 of 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 loads
of different conjugate variables.
Heisenberg's mentor Niels Bohr,
gave this relationship
between conjugate variables a proper name, complementarity.
The data remaining
is that there are some pairs
of complimentary properties
that just can't be measured
or observed simultaneously.
Trade-offs are built into the laws of nature,
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.
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Thanks for watching guys.
I hope this video helped 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 all the stuff
that YouTube is meant to say,
and I will see you next time. Bye.
(upbeat music)