Over the years, I've given many references and resources on quantum entanglement on this blog (check here for one of the more comprehensive references). Now, obviously, many of these sources are highly sophisticated and not really meant for the general public. It is also true that I continue to get and to see question on quantum entanglement from the public. Worse still, the Deepak Chopras of the world, who clearly do not understand the physics involved, are bastardizing this phenomenon in ridiculous fashion. But the final straw that compelled me to write up this thing is the episode of "Marvel Agent of Shield" from last night where the top brass of HYDRA was trying to explain to Bakshi what "quantum entanglement" is and how Gordon was using it to teleport from one location to another. ABSURD!
So while this is all brought about by a TV series, it is more of a reflection on how so many people are really missing the understanding of this phenomenon. So I intend to explain this is very simple language and using highly-simplified picture to explain what quantum entanglement is. Hopefully, it will diminish some of the false ideas and myth of what it is.
Before I dive into the quantum aspect of it, I want to start with something that is well-known, and something we teach even high school students in basic physics. It is the conservation of momentum. In Figure 1, I am showing a straight-foward example of conservation of linear momentum case, a common problem that we give to intro physics students.
In (a), you have an object with no initial linear momentum. In (b), it spontaneously splits into two different masses, m1 and m2, and go off in opposite directions. In (c), m1 reaches Bob and m2 reaches Alice. Bob measures the momentum of m1 to be p1.. Now, this is crucial. IMMEDIATELY, without even asking Alice, Bob knows unambiguously the momentum of m2 to be p2 simply via the conservation of linear momentum. He knows this instantaneously, meaning the momentum of m2 is unambiguously determined, no matter how far m2 is from Bob. When Alice finally measures the momentum of m2, she will find that it is, indeed, equal to p2.
Yet, in all the years that we learn classical physics, never once do we ever consider that m1 and m2 are "entangled". No mystical and metaphysical essays were ever written about how these two are somehow connected and can "talk" to each other at speeds faster than light.
Now, let's go to the quantum case. Similar scenario, outlined in Figure 2.
Here, we are starting to see something slightly different. We start with an object with no net spin in (a). Then it spontaneously splits into two particles. This is where it will be different than the classical case in Figure 1. Each of the daughter particles has a superposition of two possible spin states: up and down. This is what we call the SUPERPOSITION phenomenon. It was what prompted the infamous Schrodinger Cat thought experiment where the cat is both alive and dead. This is crucial to understand because it means that the state of each of the daughter particle is NOT DETERMINED. Standard QM interpretation says that the particle has no definite spin direction, and that until it is measured, both spin states are there!
Now, when one daughter particle reaches Bob, he then measures it spin. ONLY THEN will the particle be in a particular spin state (i.e. the commonly-described as wavefunction collapsing into a particular value). In my illustration, Bob see that it is in a spin-down state. Immediately, the spin state of other particle at Alice is in the spin-up state to preserve the conservation of spin angular momentum. When Bob measures the pin of his particle, he immediately knows the spin of the particle at Alice because he knows what it should be to conserve spin. This is similar to the classical case!
This superposition of state is what makes this different than the above classical example. In the classical case, even before Bob and Alice measure the momentum of their particles, there is no question that the particles have definite momenta all through its trajectory. Classical physics says that the momentum of each particle are already determined, we just need to measure them.
But in quantum physics, this isn't true. The superposition principle clearly has shown that in the creation of each of those two particles, the spin state are not determined, and that both possible states are present simultaneously. The spin state is only determined once a measurement is made on ONE of the particles. When that occurs, then the spin state of the other particle is also unambiguously determined.
This is why people have been asking how the other particle at Alice somehow knew the proper spin state to be in, because presumably, before any measurement is made, they both can randomly select either spin state to be in. Was there any signal sent from Bob's particle to Alice's to tell it what spin state to be in? We have found no such signal, and if there is, it has been shown that it will have to travel significantly faster than c. No matter how far apart the two daughter particles are, they somehow will know just what state to be in once one of them is measured.
This, boys and girls, is what we called quantum entanglement. The property of the quantum particles that we call "spin" is entangled between these two particles. Once the value of the spin of one particle is determined, it automatically forces the other particles to be in a corresponding state to preserve the conservation law.
But note that what is entangled is the property of the particle. It is the information about the property (spin) that is undergoing the so-called quantum teleportation. The particle itself did not get "teleported" the way they teleport things in Star Trek movies/TV series. It is the property, the information about the object, that is entangled, not the entire object itself. So in this example, the object doesn't jump around all over the place.
The physics and mathematics that describe quantum entanglement are more involved than this cartoon description, of course. There are mathematical rules resulting in physical constraints to the states and properties that are entangled. So you just can't pick up anything and say that you want to entangle it with something else. It just doesn't work that way, especially if you want to clearly observe the effects of the entanglement.
The important lesson to take away from this is that you can't learn physics in bits and pieces. If you simply focus on the "entanglement" aspect and are oblivious to understanding the existence of quantum superposition, then you will never understand why this is very different and mysterious than the classical case. In physics, it is not uncommon that you have to also understand a series of things leading up to it. This is why it is truly a knowledge and not just merely a series of disconnected information.