Why do they say love when they mean entanglement?

Distance can be so painful. We all have experienced having our beloved ones far away, either in time or space. I can only say that physical pain is milder.

Entanglement was born as the denial of distance. In the thirties, when quantum mechanics was still a child, Schrödinger was astonished to consider that quantum particles could, somehow, keep in touch even when they are separated long distances. Just because they interacted in the past, and they keep the connection.

Let us consider particles which are so dumb that they can only learn how to answer one question, and only with “yes” or “no”. All other questions are answered randomly. Let us put a couple of these particles in strong interaction, designed so that they will always provide opposite answers to any question formulated to them both. Since they can’t memorize a big list of questions, what they do is the following: the first one to be asked answers randomly, and the second answers the opposite as the first.

But now, to give the interesting twist, consider that the particles are separated a long distance. Still they can’t memorize but one question. Nonetheless, when you ask the same question to them both, they give opposite answers! Don’t call it love, call it entanglement!

By the way, what we described is the Einstein-Podolski-Rosen (EPR) paradox for spin 1/2 particles. Can we use it to send information along large distances? No. But I will leave the reader to think why.

So, these entangled pairs have some kind of connection, which Einstein called a “spooky action at a distance”. It is used extensively by scientists in order to design quantum communication and quantum computers. But I will talk about that some other day. I want to focus on the distance stuff. Entanglement seems to be the denial of distance. Is this true?

Is it rare to find entangled quantum particles? Not at all! Our electrons are strongly entangled to their neighbors, in the same atom or in nearby atoms, thus making up chemical bonds. Typically, these entanglement bonds are of short distance. You may get any block of matter and ask “how many entanglement bonds does this block have with  the rest of the universe”? The answer is normally proportional to its surface area. The reason is that electrons that live deep inside the block only have entanglement bonds to other electrons inside the block. Only the “surface” electrons are entangled to the exterior world. This is called the area law.

A soup of entangled pairs.

A soup of entangled pairs.

But the area law is not always true. Many quantum states, some natural and some engineered, have long distance entanglement bonds. Imagine a blocks in which all the electrons are entangled to a partner which is outside. Life inside that block is weird. Each electron is paired with another one which is out of your reach. So they answer questions in a weird way, which seems totally crazy to you. They are not crazy, they are in love… sorry, they are entangled to other guys which do not live nearby. The system seems random to you. Physicists consider temperature to be the most relevant source of randomness. So, for a scientist living inside such a weird block… a sensible interpretation is that, simply, it is hot. Hot. Really? Because their lovers are far away. Waw. The  metaphor really pays for itself!

But now the twist comes again! Some recent ideas, on which we are working at IFT, suggest that we should look at the relation between entanglement and distance the other way round. You may have heard that the universe is curved. Really. And that curvature is related to the gravitational pull. But you may not have heard of Einstein-Rosen (ER) bridges. If spacetime can be bent, maybe it can be cut and pasted. Why not? And then we can make shortcuts, connections between far-away places. You want to travel from Madrid to Vladivostok really fast? No worries! An ER bridge can do the trick. And this is the conjecture, which was put forward by the argentinian physicist Juan Maldacena: what if EPR=ER? What if we take seriously the area law, and decree that two entangled particles are always nearby? Indeed, this is the case for most of the time. What about the exceptions? If the particles of a given entangled pair seem to be distant to you it is because they are connected through an ER bridge, which, unfortunately, you can’t see. Thus, every time we see distant entangled pairs, perhaps we are just noticing… spacetime curvature at a quantum level.

If Einstein-Rosen = Einstein-Podolski-Rosen, then, is Podolski equal to one?

You may have dozens of objections. For example, doesn’t curvature of spacetime require mass? We do not have a full fledged quantum theory of gravity, so we don’t really know the answers. It helps solve some old problems, such as the black hole information paradox (which we will discuss some other day). But, most of all… it is really beautiful and suggestive.

So, maybe, distance does not exist at all. Maybe you should just get entangled with your beloved ones. But remember… entanglement is monogamous!

Image by RomaniM http://romanim.deviantart.com/art/1-s-and-0-s-198076497

Image by RomaniM

To know more:

Quanta magazine article on EPR=ER.

Entry on entanglement at the Stanford Encyclopedia of Philosophy

Schrödinger’s cat and quantum computers.

Original, in Spanish, published at madri+d, at the blog of the Instituto de Física Teórica (UAM-CSIC): http://www.madrimasd.org/blogs/fisicateorica/2015/10/22/103/

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But, really, what is entropy?

Entropy (1): the measure of disorder. The increase in entropy is the decrease in information.

Entropy (2): the measure of the energy which is available for work.

Problem: Reconcile both definitions.

Some people tell me that there is no problem here… Yet… I have the feeling that we call entropy to many different things because we have the intuition that, in the end, they’re all the same. My main problem: entropy (1) is an epistemological magnitude, whilst entropy (2) is ontological. Confusion between these two planes have given rise to all sorts of problems.

I should explain better: entropy (1) refers to my knowledge of the world, and entropy (2) to its substance. Yet, we might be able to reconcile them. With care, of course. Let us give an example.

Imagine a box with particles bouncing inside. We have no information at all. All possible states are equally likely. With no information, there is no work we can extract from the particles in the box. But imagine that we’re given some information, such as the temperature. Then we can extract some work, if we’re clever. Now, even more: imagine that we’re given the exact position and velocity of all the particles at a given moment. Then, again if we’re clever, we can extract a lot of work from the system! The more information we have, the more work we can extract.

So that was a purely operational view on entropy. The information content –epistemological, entropy (1)– determines the amount of work we can get –entropy (2). But the ontological view fades away… The system has no intrinsic entropy. The amount of work which is available… available for whom?

Now a problem comes… the second law of thermodynamics, the most sacred of our laws of physics, states that the entropy of an isolated system tends to grow. “But if your theory is found to be against the second law of thermodynamics I can give you no hope; there is nothing for it but to collapse in deepest humiliation”, as Arthur Eddington posed it.

Can the second law adapt itself to this view? Yes, it can, but the result is funny: For all observers, no matter their knowledge and their abilities, as time goes by, their information about an isolated physical system tends to reduce, and also the amount of work they can get from it.

Of course, isolated is key here. You’re supposed to do no more measurements at all! Then, evolution tends to decrease your information, increasing the initial uncertainties you might have. Is this statement non-trivial? I think it is, in the following sense: it excludes the possibility of some dynamical systems being physically realized.

Still, the operational point of view does not fully satisfy me yet. It states that, no matter how clever you are, the amount of work you can get from an isolated system decreases with time, since your information does. This maximization over the intelligence of people is disturbing… What do you think?