Thanks to Babbel for helping support this episode.
Hey Crazies.
Just about everyone that's heard of quantum mechanics has heard the following phrase:
"The electron can be in multiple states at the same time."
But what if I told you that's a lie?
Quantum particles are never in multiple states at the same time.
They're only ever in one state.
It's just that most quantum states don't make sense to us.
The quantum spin of an electron is the quintessential example to use here,
but that can get... confusing real fast.
It's like a ball that's spinning.
Except it isn't a ball.
And it isn't spinning.
So to keep this explanation as simple as possible, we're going to remove all that baggage.
Like the photon, we're going to be traveling light.
Agh.
(Laughing)
No electrons. No quantum spin. No none of that stuff.
We're talking about balls in the land of make-believe.
Actually, I probably don't want to say balls a million times today.
We're going to be talking about orbs in the land of make-believe.
These orbs come in two different textures: smooth and rough.
But texture is on a spectrum measured by the coefficient of friction.
I know, but this isn't the real universe. It's a metaphor. Just go with it.
Okay, we'll see where this goes. Thank you.
These orbs are not stuck in their state.
We could send a rough one through a polisher and it would become smooth.
We could send a smooth one through a roughener and it would become rough.
So, if we wanted to, we could change the state of any of these orbs.
Generally though, we're not trying to do that.
But what if they're not just orbs? What if their quantum orbs?
You might imagine a third state that's both smooth and rough at the same time,
something we'd call a quantum superposition.
Visuals like this are misleading though, for multiple reasons.
First, they give us the impression that these new combination states are somehow multiple states at the same time,
which they're not.
That's not how this works.
That's not how any of this works.
Even quantum superpositions are single states.
We might not intuitively understand them,
but they're single states nonetheless.
Second, visuals like that make it seem like there's only three states available
when there's actually an infinite number of possible states.
There are infinity minus two possible examples of this kind of state.
It's not the weird one. These two are.
Quantum superpositions are the norm.
To understand what's going on here, we need to do a little review of how vectors work.
[Title Screen: Vector Spaces]
If you're not familiar, vectors are just quantities that have a direction.
They're usually represented as an arrow like the velocity of this cookie.
Let's pause the animation for a moment
and say this cookie is traveling at five miles per hour this way.
If we impose an xy-plane on the picture, we can define a couple special vectors:
one along the X direction and one along the Y direction.
These are what we call "basis vectors"
because they're the basis of any vector in the xy-plane.
Surprisingly, the name makes sense.
We can write any vector in the xy-plane as a combination of these two basis vectors.
For the velocity, that might be three miles per hour to the right and four miles per hour up.
The set of all vectors that can be written in terms of these basis, vectors is called a "vector space."
There are all kinds of vector spaces, some more abstract than others.
See, vectors are just a mathematical tool, and sometimes tools can be used in unexpected ways.
You know, like opening a walnut with a sledgehammer.
Anyway, the coordinates we used for the cookie measure location,
so we call it position space.
Or, since it's the default, sometimes we just call it space.
It might be the only space you see in introductory physics, but there are plenty of other options.
In my master's thesis, I used momentum space to model electrons in a white dwarf.
But even momentum is an obvious vector, so it's not too much of a stretch.
Quantum mechanics uses vector spaces on things that aren't vectors.
Speaking of which, let's get back to our quantum orb.
What if we chose one direction to be smooth and the other direction to be rough?
Instead of texture being on some kind of linear spectrum like Nerd Clone suggested earlier,
the texture state of our orb would be a vector in this abstract vector space.
If it's in the smooth state, it looks like this.
If it's in the rough state, it looks like this.
These two vectors are the basis vectors for our texture space.
They're also called the eigenstate because... Whoa! Whoa! I'm going to stop you right there.
That's a whole other video.
We need to stay focused on the topic at hand.
[Title Screen: Quantum States]
What quantum mechanics does is it opens up more options to a physical property.
It takes the state of any quantum particle and treats it like a vector in an abstract vector space.
Any state of any particle.
The length of a state vector is always equal to one, but the angle can change.
That means many states are available to it, not just two.
These are only the two basic states.
The rest of them look like this, all infinity minus two of them.
There's only ever one state arrow though, so it's only ever in one single state.
To take this point home, let's look back at the velocity of our cookie from earlier.
It doesn't point along either axis, so it has components along both.
Would you say this cookie is in two different velocity states at the same time?
No, of course not.
It's in a single state:
Five miles per hour in whatever direction it's moving.
Another way to look at this is that there's nothing special about this particular xy-plane.
I could have just as easily drawn it like this or even like this.
It doesn't matter.
If the coordinates looked like this, the cookie's velocity is only along the X direction.
Did it suddenly drop from multiple states to a single state?
No!
It was in a single state the whole time.
We're not changing anything about the cookie itself, just how we represent it mathematically.
The same goes for our texture states.
No matter what states you're looking at, it's only one arrow.
It's always only one single state.
The fact that you can write it as the sum of two other vectors doesn't change anything.
The orb does not care.
Just a little note though, before we move forward.
This notation I'm using is called "brah-ket notation,"
as in bracket notation.
Each state is encased in a bracket.
When the bracket is on the right, they're called "ket vectors."
There is a such thing as a "brah vector."
Yes, it's really called that.
But it isn't important until we start taking measurements.
[Title Screen: Quantum Measurements]
If we're going to continue like this with our quantum orb,
at some point we're going to want to measure that texture.
You could feel it with your hand, but humans are a bit biased.
Plus, remember, this is just a metaphor for particles
and you can't feel particles with your hand.
So instead, we'll be using a texture detector.
Say that three times fast:
Texture detector. Texture detector. Texture detector.
If an orb is smooth, it'll come out one exit.
If it's rough, it'll come out the other exit.
So what happens if one of those superposition orbs goes in there?
Well, how does that box work? Oh, I have no idea, but it doesn't matter.
Wait, where's Nerd Clone?
I called in back up.
I'm getting teamed up on now. Great.
All that matters about this box is that it sorts orbs into two distinct categories and it never fails at its job.
On the inside the box can work however you'd like, as long as it meets those criteria.
So... let's go through the options.
We know the orbs can't split and come out both exits.
My orbs are like particles, so they're invincible.
Invincible orbs? Invincible orbs. (Laughing)
How is this still sounding like innuendo?
Anyway, we also know they can't come out neither exit because the detector never fails.
That only leaves two options:
It comes out of exit 1 or it comes out of exit 2.
A superposition orb goes into the detector and has to pick an exit.
In the process though, it's no longer in a superposition.
You remember how the polisher box could make an orb smooth
and the roughener box could make an orb rough?
Well, the texture detector can do either of those things under the right conditions.
Texture detector. Texture detector. Texture detector.
The act of measuring the state of the orb changes the state of the orb.
And this isn't because we designed our detector wrong or our technology is limited.
Any detector that meets these criteria has no choice but to affect the state of whatever it's measuring.
It doesn't matter how you design it.
Now, to be clear, neither the detectors nor the orbs are making any kind of conscious decision.
The choice is made by physical rules.
Those rules just happen to be based on probability.
The state vector actually tells us what those probabilities are,
and it does it with these numbers.
This is where those brah vectors come in.
Say, you've got an orb in this smooth state.
The chances of it coming out the smooth exit should be 100%, right?
Here's the smooth state written as a vector.
Taking a measurement looks like this:
a brah vector next to a ket vector to make a full bracket.
Squaring the answer gives us the probability,
which is 1 or 100% in this case.
We can do the same thing with the rough state.
The chances of a rough orb coming out of the rough exit is 1 or 100%.
The chances of a rough orb coming out of the smooth exit is 0%.
The same goes for a smooth orb and the rough exit.
As long as you can remember those four options, we can do this with superpositions too.
Say the orb is in this state.
What are the chances it'll come out the smooth exit?
Well, you just use the smooth brah like before.
Is it too much? (Laughing)
It is what it is. What are you going to do? (Laughing)
The brah vector comes in, operates on both terms,
we plug in one or zero where needed, square the answer,
and BAM! Probability.
You can do the same thing for the rough exit or just subtract from 100%.
OK, that's an acceptable analogy.
Thank you. So what's a quantum superposition again?
Review time!
Quantum mechanics opens up more options to a physical property using vectors.
Rather than just smooth or rough, our made-up orb can be in any state in this abstract xy-plane.
No matter what, it's always in one single state.
We just don't intuitively understand most of the options.
The coefficients of a superposition tell us the probabilities of getting one of the basis states,
specifically after passing through a detector that measures those basis states.
That's it. That's all it is.
And that's true no matter how many basis states there are.
I kept my example at two for simplicity, but it depends on the circumstances.
You could easily have an infinite number of basis states.
The point is though, if someone says a quantum particle is in more than one state at the same time,
they're either not fully embracing the nature of quantum mechanics
or they don't think you can.
So did this help you understand quantum superposition a little better?
Let us know in the comments.
Thanks for liking and sharing this video.
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who has been pledging at the Einsteinium level for two and a half years.
Don't forget to subscribe if you'd like to keep up with us.
And until next time, remember, it's OK to be a little crazy.
Thanks again to Babbel for helping support this episode.
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There are so many people in the last video saying they didn't want to get called in the middle of the night.
First of all, they shouldn't be calling you without texting to see if it's OK,
at any time of day.
Secondly, why isn't your phone on silent at night?
I'm not about to get woken up by a robocall.
Anyway, thanks for watching.