2022 Nobel prize for physics was for three scientists who worked on entangled particles. As a researcher working on the same field, I would like to write about it for a general audience. This is the first part of Entanglement story.
Classical to Quantum
What is the absolute truth about the matter in this universe? Does it depend on your approach, like a magic 8 ball that gives you different answers each time? Or is it universal that we can predict the future of every system if we have sufficient information? Until the end of the 19th century, things were pretty straightforward. If you know the position and velocity of a particle (or a ball), you can predict its future with certainty. Most of our mechanical systems are designed with this classical world understanding. Take the case of a projectile motion. When you throw a stone into the air, depending upon the angle, your initial force and the speed and direction of the wind, one can estimate where it will end up.
But classical physics started breaking down when you approach some limits.
When the particle is so tiny (microscopic) or too cold, quantum effects started dominating its behaviour.
When the particle velocity is close to the speed of light, or if it is travelling near a heavy object, relativity plays a different role in its behaviour.
Relativity is another topic altogether. Our interest today is the first effect. The microscopic particle cannot be considered as a particle only. It has a characteristic wave associated with it. This is called wave-particle duality. Due to this effect, one cannot determine the velocity and position of a particle deterministically. In other words, there is an inherent error when you measure the position and momentum (velocity X mass) of a particle. This is the famous “Heisenberg’s uncertainty principle”.
The wave associated with each particle is called its wavefunction. It defines many of its properties like energy, momentum, spin etc. Now, things get messy when you add many particles and their interactions.
Let us say there are two particles. Typically, the total wave function of the system of two particles can be written as a product of two individual wave functions. But one can construct situations that this is not true. Such states are the so-called Entangled states.
Initially, entangled states were described as a threat to quantum physics by Albert Einstein. He pointed out that this non-separability does not seem to be affected by the positions of the particles. Thus there will be correlations even if the particles are far apart. In the famous EPR paper, the authors took a simple example of an entangled state and how it can violate the uncertainty principle.
The correctness of the theory is judged by the degree of agreement between the conclusions of the theory and human experience. This experience, which alone enables us to make inferences about reality, in physics takes the form of experiment and measurement. It is the second question that we wish to consider here, as applied to quantum mechanics. - Einstein, Podolsky and Rosan
And you might have heard his famous remark “spooky action at a distance”. Even though the particles are well separated, the measurement on one particle reveals some information about the state of the other. This violates the famous “locality”.
Suresh and Ramesh walk into two separate bars
Let us say Ramesh and Suresh are the entangled particles. Their entanglement is on the colour of their drink. If Suresh takes a red drink Ramesh will opt for a blue one. If Ramesh is having a Red drink, Suresh will choose the blue. Their quantum state is
QRS= RED X BLUE + BLUE X RED
This is simple if they are going to the same bar. One can see what other is taking and have an informed choice. But what if they are far apart and can’t communicate instantly? This is when things get wired.
They seem to have the correlation maintained, no matter what the distance between them is. How do we know this? When you only follow Suresh into each bar, you can find that he is picking up blue and red drinks, rather randomly. However, if you keep the record and match it with Remesh, the uncanny correlation comes back.
The hidden variable theory
Physicists in the middle of the 20th century were puzzled by this conundrum and tried to come up with a different solution that brings back sanity. One approach was that the wave function has a hidden variable that is not accessed by the measurement. This hidden variable decides the state of each particle.
In their example, let’s say they have another friend, let us call them Bobby and Mona, with them. Bobby and Mona share a random list of drink options which they enforce on Ramesh and Suresh. That way, you can explain the strange correlation.
There were two problems with this. One, we don’t know what is the variable that is hidden. Another issue is that we can perform the measurement differently, and still can obtain the wired correlation. Let’s say Ramesh and Suresh go to bars that have only PINK and YELLOW drinks. Now, the wavefunction according to the new bar settings is
QRS= PINK X YELLOW + YELLOW X PINK.
This is possible since waves can be in a state of superposition (I am planning to write a separate article on superposition only, let me know if you are interested) . You can mix two colours to get another. Similarly, they can go to bars with different coloured drinks, but the correlation remains. One caveat, if Ramesh goes to the RED/BLUE bar and Suresh goes to the PINK/YELLOW bar, they will see less or no correlation at all.
Bell’s theorem
The debate continued for more than a decade until a physicist named John S Bell from Northern Ireland derived an expression that tests the hidden variable theorem. Folks, here I want to convince you of the scientific rigour and importance of falsifiability. Any theory, however beautiful or convincing it is, should have testable predictions. I have written a piece on the same here. So the effort of the physicist is not only deriving the laws of nature, but also the conditions and parameters for which the theory's prediction must hold. If these are violated in an experiment, the theory is wrong.
Bell derived a parameter formed by the measurement outcomes ( the list of drink colours for Ramesh and Suresh.) which has an upper limit value of 2 if we consider normal quantum mechanics with hidden variable theory. If the measurements violate the Bells inequality ( as the theorem is commonly known) it tells that there are no local hidden variables and the quantum mechanics is inherently non-local.
It took more than 40 years to conclusively violate Bell’s inequality and prove the existence of non-local correlation. And that is what the Nobel prize for physics this year is all about. Let me stop here. I will continue the story in another newsletter issue. Let me know your thoughts in the comment box.