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  • Writer's pictureNoa Feldman

5 - On Quantum Entanglement and socks

*Is it your first visit here? Welcome! My name is Noa and I am a Physics Ph.D. student at Tel Aviv University. I write here about quantum mechanics for non-physicists. No background in mathematics or physics is required to read the blog, but I highly recommend reading the first four posts before reading this one, starting here.*

In the first stages of developing the quantum theory in the first decades of the 20th century, it had some opposers. Its weirdness and all of the new concepts, especially the lack of determinism - the fact that every measurement creates a collapse that is determined by fate alone - disturbed many scientists, among them Albert Einstein (even though he had an important contribution to the understanding of quantum mechanics, as we've seen in the post on the photoelectric effect).

This explanation, which requires non-determinism, is known today as "The Copenhagen Interpretation", and was established by a group of scientists working in Copenhagen at the time led by the physicist Niels Bohr. Einstein had a hard time believing it - he is famously quoted saying that God "does not play dice.". As a part of the scientific argument with Bohr, Einstein tried to prove that the understanding of quantum mechanics is impossible. Einstein, along with Boris Podolsky and Nathan Rosen (EPR), published a paper when they made a 'thought experiment' which was supposed to demonstrate a contradiction in the quantum theory, thereby proving that it is wrong. Instead, it turned out that they discovered quantum entanglement, which is one of the most interesting phenomena in quantum mechanics.

So, what is quantum entanglement? Let us perform the thought experiment that EPR suggested. It goes like this: Say I am getting ready in a dark room at home, and I take a pair of socks out of my drawer. Half of my socks are blue and half are pink, so with a probability of 50%, the socks in my hand are blue, and otherwise, they are pink.

It is important to note that I always match my socks when I fold them, so I know for sure that they have the same color. Now I take the pair apart - I take one sock in my bag and leave the other sock in my room. I don't know the color of the sock in my bag yet - for now, it is pink or blue, with a probability of 1/2 each.

With the sock in my bag, not knowing its color yet, I ride to the university on the other side of the city. Now there is one sock in my bag which has a probability half to be pink and half blue, and one sock in my room which is also with probability half pink and half blue. When I get to the university, I take my sock out of the bag, check its color, and see that it is pink. Now I understand that the sock left in my room, on the other side of the city, is also pink. So this means I measured both socks at the same time - one here with me in the university, but the other, far away in my room.

In the classical world, this is not so exciting. The fact that the sock in my room could be either pink or blue only represented my lack of knowledge. The sock always had a definite color, and by measuring the sock in my bag, I only affected myself - my knowledge of both socks. But if instead of socks I had quantum particles, and the color of the socks was in a superposition, the situation was different: That would mean that by measuring the sock in my bag, I made the sock in my room collapse as well. It doesn't matter if the other sock was in a different part of the city, the world, or the universe - by measuring one sock, I *instantly* make the other sock collapse as well.

This relation between our quantum socks is called entanglement. Before the measurement, the socks had a shared probability distribution, therefore an action on one sock instantly affected the other sock far away from it. This shared probability distribution entangled the socks together. This is the only action in physics that affects far-away objects instantly. According to everything that was known back then, the fastest we can affect a far-away object was the speed of light, and therefore the discovery of entanglement was outrageous!

EPR claimed that this phenomenon is impossible and the understanding of quantum mechanics was wrong. But quantum entanglement exists, and it was demonstrated in many experiments (the experimentalists who first demonstrated it even got the Nobel Prize in Physics in 2022). How is this working together? The fact that we cannot do anything faster than light is an important aspect of our understanding of time and causality, and it is a very important basis of Einstein's relativity theory. The answer to this is the following: even though we affected the sock in the room, we were not able to transfer any *information* to anyone in the room.

Assume we wanted to use the entanglement between my quantum socks in order to transfer information to the room. A friend is waiting for me in my dark room, holding my sock and waiting for my message. The measurement I performed determined the color of the sock, but I wasn't the one choosing whether it would be blue or pink (I only made it randomly collapse, based on the distribution it already had). So the message cannot be the color of the sock.

Even the fact that the measurement was made, that is, that I looked at the sock in my bag, is not information that I can transfer to my room using the pair of socks. When my friend looks at her sock, she doesn't know when the socks collapsed to a definite color. It could have happened half an hour ago, when I checked my bag on the way to the bus, but perhaps I haven't measured my sock at all yet, and the collapse was a result of my friend looking at her sock.

So entanglement will not allow us to communicate with far-away parties. What is it good for? It is a quantum property that does not resemble anything in our day-to-day, classical world, and therefore it is an opening and a resource for many interesting phenomena happening in the quantum world and quantum-based technologies. I will discuss it more in the next posts.

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