The Nobel prize in physics 2022 went to John Clauser, Alain Aspect and Anton Zeilinger for their work on quantum entanglement.

But what is quantum entanglement? And what does it tell us about how nature works?

Suppose that I want to describe a physical object. This could be an electron, a photon (which is a particle of light), an atom or even something large like, say, a human being. I then introduce a mathematical entity called a state. The state describes, in some mathematical way, the information I have about my object. For an electron, it could be how it rotates. For an atom, it could be what kind of energy it has. And so on.

So far so good. I have an object, I have a mathematical description of its physical properties, I’m a happy physicist.

But now, let’s do something radical, extreme, something completely mind blowing. Let’s consider two objects!

This is where things can get weird.

Normally I would think that if I have one object described by some state, and then another object described by some other state, then when I regard both of the objects, I would know everything about them by just looking at the sum of their individual states. (If I have one book with some information in it, and another book with some other information in it, and I place the books next to each other, the total information is just the sum of the information contained in the individual books.)

But now comes quantum mechanics and says: whoooa, hold on, you can’t just consider two objects together like that and call it a day! What if the information about the two objects is not related to the objects taken individually, but to some kind of common, shared state? What if the information describing the state of a system is not exhausted by looking at the different parts of a system? What if the whole is larger than the sum of the parts?

Enter entanglement. It says that the information that we can have about two objects is described by a state that is not the sum of the individual states of the objects. The two objects are instead part of a shared, common – or, as it is now called, entangled – state. This entangled state means that the physical properties of the first object will somehow be connected to the physical properties of the other object.

Quantum mechanics also says another important thing. We talked about the state as something that has to do with the information that we have about an object. What do we mean by information? Well, information has to do with knowledge of the world. In order to learn something about an object we have to do some measurement of it. As happy, classical physicists we would think: “I have my mathematical state that describes the object I’m interested in, so clearly I should be able to predict the physical properties of my object by just investigating what my state predicts. I then do a measurement on my object, and, hey presto, it’s turns out to be exactly what my theory predicted!”

But it doesn’t work that way. Quantum mechanics does not predict measurement outcomes. It predicts probabilities. It says “the mathematical quantum state just predicts the probability that an object will have this or that physical property when we measure it”.

This leads to a rather weird situation, where it (depending on your philosophical inclination) looks like an object can be in many different potential configurations before measurement, but then somehow jumps from the world of virtual possibilities to the world of real physical properties when we do a measurement. This is called the collapse of the wave function (if you hear a distance meow, it’s from Schrödinger’s cat). Wave function, because that is what our mathematical states are called, and collapse, because that is what seems to happen when we do a measurement. To really understand what happens during this so-called collapse of the wave function is called the measurement problem, and it is one of the most vexing problems in quantum mechanics.

Galactic separations

But back to entanglement. Let’s look at a concrete case.

Suppose I can create two electrons that are in an entangled state. Let me now regard one of the electrons. I’m interested in something called spin. It doesn’t really matter what it is, what’s important for this scenario is that it can take on two values, which we take to be +0.5 and -0.5.

Before measurement, I don’t know if my electron will return the value +0.5 or -0.5. All I can do is to predict the probability that my electron will return the plus or the minus value. After many measurements I can see if my probability prediction was correct or not. This is where quantum mechanics shines: it really does predict the right probabilities, which have been confirmed in countless experiments.

But what about my other electron? If the two electrons are in an entangled state, something funny happens. Every time I measure +0.5 on first electron, I will discover that I always measure -0.5 for the other electron. And vice versa: If I measure -0.5 on the first electron, I will always measure +0.5 for the other electron. They are correlated, entangled, share a common state, call it what you will. The basic point is that they seem to influence each other somehow when I do a measurement. If they were not in this entangled state, then I could measure, say, +0.5 for the first electron, and then either +0.5 or -0.5 for the other electron. They would be independent of each other.

To really test entanglement, let’s do something extreme (and imaginary). Let’s send them off to opposite ends of the Milky Way. They will be roughly 100 000 light years apart when I do a measurement on the first electron. Suppose I measure +0.5. I now go to the other side of the galaxy, do a measurement on the other electron and find, lo and behold, that it’s value is -0.5!

How is this possible? How can the electron at one end of the galaxy know what happened to the electron at the other end of the galaxy?

Maybe we’re wrong? Maybe it doesn’t actually work like this? Maybe the physical properties of the electrons were actually determined when I created their entangled state? Maybe the first electron was always in the state +0.5 and the other one was always in the state -0.5?

Well, maybe it is like that. But maybe I can also test if it is like that?

This is where the so-called Bell inequalities enter. They are a set of mathematical statements concerning experimental outcomes on entangled states. They say that if there is some kind of hidden variables that predetermine the state of the electrons, and if those variables are also local (roughly meaning that the variables describing the first electron can not alter the variables describing the second electron when they are far apart), then we will see a different type of statistical correlation between our electrons compared to what quantum mechanics predicts. Notice that it’s not enough to do just one measurement. We have to do many measurements on the different possible spin configurations of the first and second electron, and then compare our list of results to see what type of statistical correlation exists between the two electrons (or rather, the big set of entangled electrons that we can create).

This is what Clauser, Aspect and Zeilinger tested experimentally. They didn’t use electrons, but photons, and they measured something called polarisation, which has to do with the vibrational properties of photons. What they found was that there can’t be any local and hidden variables at play that determine the outcomes of our measurements.

Quantum mechanics seems to be right.

But then we are left with the question: what does this actually tell us about how nature works?

Different camps

Let’s return to our two entangled electrons which are placed at each end of the Milky Way.

If quantum mechanics is right, the situation seems to be something like this: when we do a measurement on one of the electrons, we aren’t really measuring the individual state of the electron. We are doing a measurement of the entangled state, which is shared between the two electrons. When we do a measurement this shared, entangled state collapses to one of the two possible configurations (+0.5 for the first electron and -0.5 for the other one, or vice versa). So it’s the collapse of the wave function of an entangled state that makes the measurement outcomes of the two electrons correlated. It is this collapse of the wave function that Einstein referred to as “spooky-action-at-a-distance” (so Sabine Hossenfelder claims), since it seems to occur everywhere at once. Entanglement is just one of the most manifest examples of that.

But how it is possible for the wave function to collapse simultaneously at such large separations?

First of all, it is not possible to use entanglement to send information faster than the speed of light. In order to see the non-local correlations, we need to compare the measurements done on the two electrons. To compare the measurement, we need to send information in a normal way (over a fiber optics cable, for example). This information can not be send faster than the speed of light, and we can therefore not exploit the non-locality for superluminal communications.

The non-locality of quantum mechanics is a subtle thing that appears in the form of statistical correlations, but nonetheless it seems that a measurement at one point can influence a measurement at another point even though a signal will not have had time to travel between the two measurement points.

What all of this really means is unclear, and philosophers and physicists have set up different interpretational camps.

One camp says: well, there are non-local hidden variables, and we even have formulated a theory for that. This camp is called the Bohmian camp, and they work on something called Bohmian mechanics. But they have some problems to incorporate Bohmian mechanics (which is non-local) with quantum field theory (which is local), so people are unsure if this is the right solution.

Another camp says: when we do a measurement the wave function never collapses. Instead new worlds are created according to the different possible measurement outcomes. These new worlds are just different branches of one humongous wave function that describes everything that exists. Entanglement just looks like some kind of non-local interaction because of the way we interpret the world when we belong to one of these branches. This camp is called the Everettian, or Many Worlds, camp. Many physicists subscribe to this camp nowadays. But there are some problems here too. The meaning of probabilities becomes a bit unclear if everything happens with 100% certainty. And it seems we must allow for the idea that consciousness splits into many different states when branchings of the wavefunction occurs (which is fine with me, although the meaning of “me” becomes unclear in the Everettian world view). This camp is sometimes called the Many Words Interpretation, since their description of how probabilities emerge from the branching of the wavefunction tends to get quite, well, wordy.

Then there is another camp that says: well, maybe causal influence can somehow travel backwards in time along past light cones. This camp is called the retrocausality camp.

And yet another camp says: we have an entangled state, we do measurements on it, the wave function collapses, and it’s all good! What’s the bother really? All experiments work out fine. Before measurement we can’t really talk about what a physical state is, so let’s just roll with the perfectly fine theory that we have. This camp is sometimes called the Copenhagen Interpretation, although it is a bit hard to know what it actually means in practice.

For each of these camps, one can write an entire book that describes their philosophical position (see for example Sean Carroll’s Something Deeply Hidden and Carlo Rovelli’s Helgoland). The list I presented isn’t even exhaustive: there are many other camps.

Black holes and entanglement

What we see in all these different interpretations is that fundamental issues regarding the meaning of probability, measurement, causality and determinism appear at the forefront of the quest to understand what quantum mechanics actually means.

Maybe the question will only be resolved when we have a fully working theory of quantum gravity. It seems that quantum mechanics teaches us that there is something profoundly non-local going on in nature. But at the same time relativity theory teaches us that there is something profoundly local going on in nature. If we manage to reconcile these two insights, we might get a deeper understanding of what entanglement means.

What do I think? Maybe the solution lies buried inside black holes. The event horizon of a black hole is a kind of informational one-way membrane. Since entanglement concerns how information is shared between spatially separated measurement points, we need to answer the question what happens with that information when one entangled particle is inside a black hole and the other one is outside of it. Can we get information about what happens inside the black hole by doing measurement on entangled particles?

The quest to understand entanglement in relationship to black hole is profoundly related to the quest to understand the quantum properties of spacetime. This might lead to a change in our understand of what space and time actually is, and to what actually happens with information that ends up inside a black hole. This is research that is fruitful already today, with for example techniques used for quantum computers showing interesting links to properties of black holes (see for example John Preskill’s essay in Quanta). The link between entanglement and black holes might seem surprising, but it’s really not: it’s all about asking questions how information is encoded, transmitted and preserved in nature.

A deeper understand of black holes can thus lead to a deeper understanding of entanglement, and vice versa. That is why I smiled when a journalist who was sitting next to me at the Nobel press conference asked Anton Zeilinger what he thought about the relationship between entanglement and black holes:

But I also smiled when the Nobel committee announced this years prize, since the work of Clauser, Aspect and Zeilinger has shown us how nature works at a profound level. And that’s no small feat.