Quantum Lane Milestone 4: Entanglement
In the last month, we looked at some key phenomena of the Quantum world- namely, superposition, spin, and measurement. Here, we look at the last key concept necessary for sailing in the quantum world- entanglement. This has been a topic that has drawn questions and skepticism from a whole generation of physicists, most profoundly, Albert Einstein, who summed up his skepticism, calling entanglement “the spooky-action-at-a-distance”. So, naturally, don’t get down on yourself if it doesn’t make sense the first time around.
Let’s now jump into entanglement. As usual, we’ll start with the formal definition of entanglement, go word-by-word, and then dive into what entanglement really stands for.
The Starting Definition
According to Wikipedia, entanglement is defined as:
a physical phenomenon that occurs when a pair or group of particles is generated, interact, or share spatial proximity in a way such that the quantum state of each particle of the pair or group cannot be described independently of the state of the others, including when the particles are separated by a large distance.
Let’s boil this down. This definition mentions- 1: Interactions between objects, and 2: The state of these objects. What does this mean? Essentially, it describes entanglement as an interaction between two objects, which correlates their mutual properties to each other. The last part of the definition says that after this mutual interaction, the distance between the two objects is of little meaning, for the correlated properties of the object. What this means is that distance does NOT matter. The objects can be separated on the scale of an attometer, to as large as the scale of the entire Universe, and even then, their properties will be correlated (interestingly, it was this property which was not well received by Einstein, see EPR Paradox).
Can we even understand entanglement intuitively?
Well, yes and no. We can explain entanglement, but only partially. Scientists do understand why entanglement is caused, but not why it behaves as it does. Many unique quantum mechanical interpretations have been developed to make sense of it, but we haven’t nailed it down yet. Let’s try to explain what we can.
So, as told in the ‘formal’ definition, entanglement is an interaction, or rather say, a result of that interaction. And where the word ‘interaction’ comes, momentum is sure to make its way in. We see such “interactions” all the time in the classical world. In classical collisions, there is a change in the velocities of the objects, governed accurately (in ideal conditions) by what is known as the law of conservation of momentum.
Having said that, let’s travel the quantum lane. Let’s imagine a collision (an interaction) between two arbitrary objects (electrons, say). Now, when these two objects collide with one another, momentum is going to be conserved (albeit, in a modified manner). Makes sense? You could say that the two objects are correlated with each other. But, momentum in the Quantum realm, as talked about previously, is probabilistic. In other words, there is uncertainty in the momentum of any quantum objects. As a result, we cannot directly measure the momentum of each particle to precision, while at the same time measure other properties without losing information about the momentum of the object.
This is essentially what entanglement means! Entanglement is a result of the incomplete knowledge gained from measurement. The particles are now irreversibly correlated by mutual information, which from now on will continue to affect both particles. It’s interesting to note that this arises as an effect of stemming the law of conservation of momentum (a notion from classical mechanics) into the quantum world. Seeing measurement through this seemingly classical lens starts to make more sense intuitively.
Now, different interactions may result in different properties of the objects being entangled. It may be their spins, positions, or even their momenta, or you could also possibly entangle one quantum observable (technical term for the property) with another quantum observable of the objects!
Okay, I’ll admit, there are flaws here. Entanglement, while it sounds amazing, has some conduits that should be kept in mind when applied. Though some facts may seem trivial, they are of immense importance.
- We have not yet completely understood how exactly entanglement works. (In fact, the EPR thought experiment showed that entanglement could violate Einstein’s cosmic speed limit- the speed of light! But not necessarily; though information may be transmitted this way. Yet, there’s no way to verify this transmission of information. For that, you’ll need to travel much below the speed of light, which makes it sort of meaningless.)
- The idea behind this intuition does not work upon how different observables can be entangled with each other. Though the conservation law clarifies a lot of things, it is not enough. It doesn’t completely explain everything regarding entanglement.
- There is yet another flaw here, which is covered here in the next section.
Prospects of a Hidden Variable
As mentioned, quantum mechanics deals with the uncertain, which can be frustrating to reconcile with the classical world. The third flaw lies in the fact that quantum phenomena can’t be described with classical analogies and laws to a perfect degree of explanation.
The idea about entanglement being all about incomplete measurement may appear to the reader like entanglement is just waiting for us to be “seen” or “measured”. Somewhat, like after tossing a coin, the outcome of the coin flip (heads or tails) is just waiting to be seen under our hand which is covering the coin. But entanglement doesn't work like this. It’s not like the entangled property was always shared by the two objects and it was just waiting for us to be discovered. If some interaction happens on one of the objects such that the entangled observable is affected, then the corresponding observable of the other object is also affected, provided that the entanglement between the two is not broken.
Some questions may arise from this, as in how do we know that the coin flip-like incident is not taking place here. Well, the same question was asked by David Bohm (and Einstein-Podolsky-Rosen, earlier), one of the most-influential quantum physicists of the 1900s. He proposed the coin flip-like incident in the form of a quantum mechanical interpretation called the ‘Hidden Variable Theory’ or the ‘Bohm Interpretation’ of Quantum Mechanics. But, this interpretation could not pass the experimental tests. It could not compete with the results of the Bell Test.
So we see that there are quite many flaws in developing an intuition for entanglement. But, for beginners, this intuition should provide a path on which to base their further knowledge and path for the quantum lane. Also, the various intuitions can vary based upon which interpretation is kept in mind by the reader. The most profound one is the Copenhagen Interpretation, but many others are catching the eye, like the Many-Worlds Interpretation, Transactional Interpretation, etc.
With this, we come to the end of our stroll on the quantum lane. We have covered the key concepts of quantum mechanics through this series for a span of one month, and now, the reader should be quite ready to exit this stroll and start more advanced topics like decoherence and locality. This series should also make you ready and excited for all the mathematics of these concepts, because physics without its math, is just like food without its taste!
This article is part 4 of a larger series termed ‘Strolling the Quantum Lane’. To read more such articles and series, subscribe to ‘Quantum Untangled’ publication here.