Quantum cheese gremlins, and why Einstein didn’t like them

Quantum mechanics is odd. There’s no getting around that. It’s not the kind of thing that is intuitive to our monkey brains. But that doesn’t mean its mysteries are too hard for us to understand.

Here is a monkey that knows much about science, but nothing about quantum mechanics.

One of strange things to come out of quantum mechanics is called non-locality. It was something that led Einstein to denounce quantum theory as incomplete. But experiments have confirmed that it really is something that happens in our universe.

In this article, I’ll try to explain why quantum theory disagrees with any that Einstein would approve of. This requires a story, and also a little maths. But I’ll keep the maths as simple as possible.

So, on with the story. There are two friends, Alice and Bob. They are both members of a cheese club, which sends them a piece of cheese every week. Sometimes they get the same cheese. Sometimes they don’t. They wonder if there is some correlation between the cheeses they get, or if they are chosen completely independently.

An 11th century Arab cheese club.

To find out, they look at the two most important characteristics of cheese: whether it is mature and whether it is hard.

They can’t be bothered with some complicated ranking of how mature and hard the cheese are. So each week they just record their answers to the questions “Is it mature?” and “Is it hard?” with a simple ‘Yes’ and ‘No’. Then they have a chat to see if their answers are the same or different.

After many weeks, they see how many times their cheeses had the same hardness. If it was 100% of the time, then they always either both get hard cheese or both get soft. If it is 0%, they one got hard whenever the other got soft. For 50% it just seems random whether they get the same or not.

Let’s call this percentage hh, because it looks at the hardness of both Alice and Bob’s cheeses. They’ll also calculate mm, which looks at whether their answers to the maturity question are the same.

They can also calculate hm, which compares Alice’s answer to the hardness question to Bob’s answer for maturity. Why do they do this? Why not? They have the data, they might as well do maths with it!

Similarly, they calculate mh. This is the same as the above, but the other way round. It compares Alice’s hardness to Bob’s maturity.

Now they have numbers, what will they do with them? A guy called J.S. Bell found that adding numbers like this can give you a quantity that really helps to understand these correlations. One such simple sum is the following

CHSH = hh + hm + mh - mm .

Don’t be put off by the lone minus sign at the end there. It’s job is to confuse the numbers, not you. The sum is called CHSH because this isn’t Bell’s original version, but is one by some guys with these initials.

John S. Bell at CERN.

What is the biggest value that Alice and Bob could ever expect this sum to be? That would surely come when hh, hm and mh (the ones being added) are all maxed out to 100%.

We’d also want mm to be 0%. That’s the one getting subtracted, so we want it as small as possible. And if it was as low as 0% the CHSH sum would come out at 300%. Mathematically, it would be impossible to go any higher than this.

But Alice and Bob’s cheeses cannot reach this mathematical limit. There are some hidden rules that get in the way.

The number hh tells us how the hardness of Alice and Bob’s cheeses are related. Then hm and mh tell us how this is related to the maturity of their cheeses. By following these clues, we can deduce something about mm.

This is the mathsy bit. Good luck!

For example, suppose Alice got a hard cheese one week. If hh, hm and mh are all 100%, we can show that Alice and Bob’s cheeses will be mature.

We start with the fact that hh is 100%. If Alice’s cheese is hard, this means Bob got a hard cheese too. And because mh is also 100%, Bob’s cheese being hard means that Alice’s is mature. Similarly, since hm is 100%, we can deduce that Bob’s is also mature. So there you go! Just what I said. Both mature.

Now follow the same logic through for weeks when Alice got a soft cheese. You’ll find that hh, hm and mh all being 100% mean that both cheeses are mild.

In both examples, Alice and Bob’s answers to the maturity question are the same. So mm must also be 100% whenever hh, hm and mh are all 100%.

Plugging these numbers into the CHSH sum, it ends up as only 200%. The rules make it fall short of the mathematical bound of 300%.

So what are these hidden rules? Can we get around them?

Suppose Alice and Bob were lazy, and couldn’t be bothered to answer two whole questions every week. So instead they randomly each choose whether to answer the hardness question, or the maturity question.

When they have their chat to compare answers, they’ll only be able to do one comparison. If they both looked at hardness, then their data for that week will contribute to hh. If Alice looked at hardness and Bob at maturity, it would be hm, and so on.

Now what if the cheese club knew in advance what would be measured? They could send out cheeses with the same hardness on hh weeks, and so ensure hh is 100%. They could also make sure that hm and mh weeks lead to these being 100%. But on mm weeks, they could make sure that the maturities are always different. Then mm would be 0%, and the CHSH sum would be able to go beyond the 200% limit, all the way to 300%.

This would be perfectly possible if Alice and Bob made their choices months beforehand, and made them public. But if they decided on the day, after the cheese was already delivered, it becomes a bit less possible.

For the cheese club to carry out their plan now, they’d need a little gremlin who waits and see what Alice looks at, and then run to Bob’s house to mess with his cheese. If Alice and Bob measure at the same time, the gremlin would have to move instantly, even faster than the speed of light!

The hidden rule is simply that cheese gremlins who can travel faster than light do not exist. Which seems reasonable.

An artistic interpretation of gremlins affecting Bob’s cheese, which seems to be black this week. The pointing man is presumably from the cheese club. Alice is not depicted.

This principle is more properly called local realism. It stems from Einstein’s theory of relativity, which prohibits anything, even information, travelling faster than light. Einstein would not like any theory for which it seemed like those sorts of shenanigans were going on.

But quantum mechanics is such a theory!

Suppose our cheeses were quantum, and the properties we are measuring are what are known as complementary observables in quantum mechanics. This means that you cannot measure one without preventing the possibility of measuring the other. So if you find out that a cheese is hard, the cheese completely forgets whether it was mature or not. That information is no longer anywhere in the universe. But if you look at whether it is mature, it does not want to reveal its ignorance. So it will give you an answer, randomly chosen, that bears little resemblance to whether it was originally mature of not.

The idea of measuring only one property every week, which may have seemed quite lazy when we had normal cheese, now makes sense for quantum cheese. You know that only the first measurement gives a sensible answer. You know that the second gives nonsense. So you only measure once for each cheese.

So now let’s say that the cheese club always sends out cheeses so that the hardness is the same, and the maturity is the same. If Alice chooses to look at the hardness, and find that her cheese is hard, she instantly knows that Bob’s cheese will be hard too.

Since Alice knows all about Bob’s cheese, it’s like she looked at his cheese too. And because she looked at the hardness, the maturity of his cheese becomes random. Somehow, just by looking her own cheese, she instantly effects Bob’s.

Similarly, if Alice looked at the maturity of her cheese, the hardness of both her and Bob’s cheeses become random.

This shows an important thing about quantum correlations: Alice’s choice seems to influence Bob’s result. The quantum cheese acts as if there really are infinitely fast cheese gremlins!

This seems to violate Einstein’s theory of relativity. But actually, it obeys it in spirit. Since Bob has no idea what his cheese should look like, he doesn’t know if (and how) Alice’s measurement changes it. So we cannot use quantum cheese to send useful information faster than light.

Even so, there is some philosophical friction between relativity and quantum mechanics. And that’s why Einstein didn’t like it.

To see if this strange effect, which we call quantum non-locality, really exists in the universe, we have to do an experiment. An experiment means we need to measure something, and that’s where the CHSH sum comes in.

Harnessing quantum locality, it is possible to engineer a situation for which the CHSH sum should come out higher than 200%, even when Alice and Bob make their choice immediately before measurement.

This will have to be a bit more complex than the example above. Some correlations between hardness and maturity need to be thrown too. But it should get all the way up to 241%. Not 300%, for some reason, but certainly beyond the 200% limit for universes without cheese Gremlins.

If we do the experiment and this result is found, we show that the universe truly is one that Einstein wouldn’t be happy with.

We have measured it. Many times. We have made sure that the gremlins really would need to travel faster than light to make it happen, and it still happens. Non-locality is here to stay. We don’t fully know what it means, and we still aren’t happy with interpretations which suggest stuff moving faster than light. But nevertheless, it exists. And, most importantly, we can use it to build cool stuff. Stuff like quantum computers.