The heisenberg uncertainty principles has
to be one of the coolest and also one of the
most misunderstood and abused ideas in physics.
So before I explain it you, I want you to
pick which of these 3 statements you think
is the uncertainty principle.
This isn’t to embarrass you, it’s because
it really helps to know where your preconceived
understanding is flawed to be able to fix
it so please please do it, it’s for your
own good.
Even if you don’t know the principle or
none of these seem perfect, just pick the
one that sounds most right to you, and in
the corner of the video you can find a poll
where you can enter your guess.
Please pause the video now to read these and
decide.
All right, I hope you’ve made your choice.
Maybe you’ll be surprised, but both 1 and
2 are very flawed.
They demonstrate quite fundamental misconceptions
about quantum mechanics.
But worse, they make it sound like the heisenberg
is about measuring- here’s the thing, it’s
not about measurement.
The principle works whether or not we ever
measure the particle.
Before I explain that, let me try convince
you the other two options are just not right.
Option 1 first.
The really big issue with this option is it
says quantum particles really have a position
and momentum, just like in classical physics;
but they’re just shy about it.
This is not at all what quantum mechanics
says.
What quantum says is, a particle doesn’t
just have one place or speed they’re going
at, instead.
Instead, while they’re not observed, they
can be in what we call a superposition of
many places, and many speeds.
But, say you go to measure it.
You can only measure one thing about the particle,
so let’s say you’re measuring the position.
You’re not going to see it in all of these
places.
It will just be in one- and it will pick which
one, randomly.
So that’s one reason the first answer is
wrong.
When you measure a particle, it doesn’t
tell you a range of places or any other information
about where it is, it just turns up in one
single place.
And what’s worse is, you can’t measure
it again and hope to see one of those other
spots.
Now it’s not in a superposition anymore,
if you measure it again, it will certainly
be in this place.
In the language of quantum mechanics, a measurement
collapses the state- so the particle is no
longer doing what it was before.
So it’s pretty meaningless to now measure
the speed to try and deduce anything about
the particle’s speed before you measured
anything.
No, you’ve ruined the original state.
I mean you can measure the speed, and just
like with position, it will tell you just
one speed, but that is in no way the speed
the particle was really going or even related
to the superposition of speeds of the particle
originally.
So in summary, the particle didn’t have
just one speed orposition.
But if you measured say it’s position, it
would only tell you one of places, and which
one is random.
Plus you couldn’t ask it again to get more
information, because it’s no longer in a
superposition of places.
And worse, you can’t even ask the same particle
about its momentum now.
The value you get is unrelated to the original
superposition of momentum.
On the other hand this option says the particles
really have one speed and one position.
And That you can get some range of information
about the particles position, and that you
can then also go ask about momentum too.
What about the second option.
This has got to be one of the most popular
explanations of the uncertainty principle
and it’s just so confusing, because it’s
completely unrelated the uncertainty principle.
The principle is not about some very specific
set up for measuring position.
Implying that it is leads people to ask the
very sensible question, ‘well why don’t
we just come up with a better device?’
The heisenberg uncertainty principle is not
about measurement at all.
I’ll explain in a sec, but first let’s
address the issues of this one.
It has some pretty similar misconceptions;
that the particle really has one position
and momentum and that we’re trying to outwit
the particle to find them both out.
It also seems to say that the ‘uncertainty’
is from knocking the particle or some other
way of disturbing the particle via measurement.
The uncertainty has nothing to do with measurement.
It’s about the range of the different speeds
in the superposition.
This range is the ‘uncertainty’ referred
by the principle.
But uncertainty is an unfortunate term for
it.
Uncertainty makes people think there is a
speed, but we’re uncertain about what it
is.
But no, quantum mechanics is so much weirder
and more exciting than that than that, I mean
this second option is basically classical.
There’s pretty much nothing there that you
won’t expect from real life.
Quantum mechanics is not what you’d expect
from everyday life.
So let me explain the real heisenberg uncertainty
principle
As I was saying before, the particle is in
a superposition of many places, but usually
it’s not equally in all of the places.
Some places are weighted more heavily, which
means that if you were to measure it, it’s
more likely to turn up in one of these places.
But we’re not going to measure it.
Ok?
There’s no measurement in this entire thing.
Just to make that clear.
Now let’s say a particle is most likely
to turn up in a certain areas.
There’s a way to mathematically describe
the total size of these likely areas.
We’ll use the symbol delta x.
So a particle could have a really small delta
x, which means that it’s mostly in a superposition
over a small area.
Which again means, if we were to measure where
it is, we could make a pretty good guess about
where the particle will turn up.
This is probably why the term uncertainty
is used to describe delta x, because it measures
how much uncertainty we’d have about the
result if we were to measure.
I just don’t like to use that word because
of the connotation that it really was in one
place, but we didn’t have enough knowledge
to know where.
No.
Even with all the knowledge that quantum mechanics
says is possible for anyone, there’s still
this randomness when you measure.
Ok, we can similarly talk about the momentum.
The particle is in this superposition of speeds.
So which speeds are weighted the most heavily?
Again, you’ll find it’s some range, and
you quantify the size of that range mathematically
the same way and call it delta p.
Now we have the stage set for understanding
that famous misused equation.
What it says is, in quantum mechanics delta
x and delta p can’t both be as small as
you want.
See, if delta x was really really really really
small, but so was delta p, their product would
be very small, but that’s no good- it has
to be bigger than this number.
This is significant because while it’s true
that in quantum we know the particle is in
a superposition, we might have wanted to minimise
how bad that is.
We might have thought, well at least if the
particle won’t just go at one speed, we
could come up with a way to really really
narrow down the range of speeds in the superposition.
And then, even if we have to accept the particle
is in a superposition of many places, at least
we can make it mostly in one small area.
Then this particle has almost one speed and
almost one position at a time is almost a
classical particle.
So it will almost act like we want it to.
But the heisenberg uncertainty principle destroys
that possibility.
There’s no way to make a particle almost
classical in position and almost classical
in momentum.
One or both have to give, and the world is
quantum, not classical, no matter what we
wish.
If you’re new here and you’ve made it
to this point, I’m honestly impressed.
I’m sure plenty of the points that seemed
really odd or were poorly explained.
But if you’re interested in knowing the
details then you can start here.
For everyone else, you get a small break from
homework just this time because I want to
make a video soon that talks about how the
heisenberg uncertainty comes about naturally
from all the things we’ve already talk about,
and I want to get onto that video very quickly.
