The outcome of a coin flip is completely random.

Only it’s not random at all.

If I’d known exactly how the coin started and what forces acted on it, and if I could

do the calculations quick enough I could have predicted the outcome.

It only looked random because there were these hidden variables I didn’t take into account.

We’ll call this classical randomness because this is the only type of randomness allowed

in classical physics, things only look random because we don’t know all the factors influencing

them.

The situation in quantum mechanics, though, is quite different.

Remember we met the wavefunction last time and we said it contains each of the possible

things the particle could be doing.

As we know, when someone or something looks, it has to just be doing one of these things.

For example, in the double slit experiment if we put detectors behind each door, we’d

see each particle going through just one slit.

But which one?

Standard quantum mechanics says that this is truly random.

Unlike in classical physics, there is no extra information you could get or extra calculations

you can do that could let you predict which it will be.

It’s not that the particle really was doing one thing all along- if you hadn’t measured

it, it would still be a superposition.

But when you do look, it has to choose only one option, and because that choice is truly

random, there is no cause for it.

There is no reason why this particle is measured at door 1 and not 2.

But!

That doesn’t mean that every option is equally likely.

Consider this example.

We do the double slit experiment again, but this time we put one of the doors a bit farer

away.

We still don’t know which door the particle went through so it must still be in a superposition

of going through both... but if we measure it, it should be more likely to go through

the closer door right?

This fact is reflected in the wavefunction through those coefficients that I’ve been

ignoring.

In this example they could be these numbers.

You interpret this as the bigger the number, the more likely the corresponding state is

to happen.

In this example, the probability that the particle is measured at the closer door is

3/4, and the farer door is 1/4.

The exact mathematical rule for this is very simple, but is a bit of a tangent at the moment,

so I’ll put that in a short video by itself.

Quantum mechanics does have an element of true unpredictability, but that doesn’t

mean that the theory is useless.

You can’t predict where one particular particle is going to go from its wavefunction, but

if there are a bunch of particles with that wavefunction, quantum mechanics let’s you

predict their overall behaviour very accurately.

There’s one other aspect of the measurement rule: that measurement causes the wavefunction

to collapse.

Say something measures a particle and finds it in a particular state.

What does the wavefunction look like now?

Remember the rule is that the wavefunction is in a superposition of all possible states.

But now, only this state is possible, so the function collapses to just this.

This actually has a dramatic effect.

In the double slit experiment, if I am measuring which slit each particle goes through that

collapses their wavefunction so that now, each particle really is just going through

one door.

That means they’re not interfering with themselves, and so we get the regular pattern,

the particles land in two bunches.

So here’s an interesting scenario.

Say Bob is measuring which door each particle goes through.

Bob sees this particle go through slit 1, so he says the wavefunction collapses to this.

But what if Bob didn’t tell Alice his result?

Is the wavefunction collapsed for her or not?

Is there an experiment she could do to tell?

Feel free to pause the video if you want to think about it.

The answer is, if one person or thing does the measurement, it doesn’t matter if no

one else knows the result, the wavefunction is collapsed.

This is a bit surprising because imagine if Alice goes and measures which slit the particle

goes through straight after Bob.

Her result looks completely random to her, just as if the particle was in a superposition.

But, this isn’t true randomness anymore.

She’ll get the same result as Bob, but since she doesn’t know his result, it looks random

just because she is missing that information.

Instead what she should do is look at the pattern on the screen.

As we said just before, because the wavefunction is collapsed, she’ll see the particles land

in two bunches.

This explains one of the big questions about quantum mechanics.

Why don’t we see quantum weirdness all the time?

Why don’t I see an interference pattern when I throw apples and don’t watch which

door they go through?

Because, even if I’m not watching, plenty of other things are.

The apple will interact with air and light and make sounds etc.

They collapse the wavefunction for me.

So Quantum superpositions are rare because they are so fragile.

We talk about quantum effects with very small particles in very controlled environments

because those particles really aren’t interacting with much, so can stay in a superposition.

And now you guys now know the two aspects of the measurement rule:

first, The outcome is random, but the probabilities come from the coefficients in the wavefunction.

And second after a measurement, the wavefunction collapses.

And so it’s question time!

First, what if there are three slits and you only have a detector at one.

What does the wavefunction of a particle that goes through look like before and after?

The second question is about what counts as a measurement.

I kind of implied that interactions with air and light count.

Do you think all interactions are measurements?

What about if a machine does a measurement and then, without storing it in memory, prints

the result, and burns it.

Is the wavefunction still collapsed?

And finally one about interpretations.

What do you think of quantum randomness?

Do you understand why physicists had problems with it?

As you may know, there are hidden variable alternatives to Quantum mechanics that don’t

have true randomness; does this make them more appealing?

Is there anything you don’t like about hidden variable theories?

Finally thank you so much for all for your answers to the slightly more philosophical

questions last time, and sorry I fell behind answering.

But it was so fun to see everyone have such different, but well considered opinions.

I’m really looking forward your answers this time.