**Tags**

Quantum mechanics, Uncertainty principle, EPR paradox, Albert Einstein, Quantum entanglement, Alain Aspect

The first aspect of quantum mechanics that I want to discuss is the one that, in some way, we are most certain of. We are most certain of this aspect thanks to some remarkable experimental observations.

In 1935 Albert Einstein, together with Boris Podolsky and Nathan Rosen, published an article [Physical Review Vol. 47, p 777 (1935)] in which they described an experiment that they believed could sidestep the Heisenberg uncertainty principle. The idea is based on the entanglement of the quantum states (such as position and momentum) of two particles. Quantum entanglement implies that any particular quantum state of one particle fixes that of the other. In this way, if one would measure the position (momentum) of particle A (particle B), one would know the position (momentum) of the other. So one can them measure the position of particle A and the momentum of particle B, thereby being able to determine the position and momentum of both particles to an accuracy that could in principle acceed what Heisenberg uncertainty allows.

Although this was a profound idea, it had to wait until the 1980’s before it could be experimentally tested, through the work of Alain Aspect (using the polarisation of light instead of position and momentum) [Physical Review Letters, Vol. 49, pp.91-94 (1982)] … with surprising results.

Before that time John S. Bell reformulated the ideas of Einstein, Podolsky and Rosen in terms of an inequality for the probability of observations that can be made in such an experiment. Bell’s inequality is based on two rather innocent looking assumptions. The first assumption is that there is a unique reality. In other words, according to this assumption I am either at home or at work; I cannot be at work and at home at the same time. My tea cup cannot be full of tea and empty at the same time.

The other assumption is that all interactions are local — one thing must be in contact with something else to interact with it. If I pick up a brick I have to make physical contact with the brick. Perhaps I could use some force field, but even then the force field somehow have to be in physical contact with the brick. No “spooky action at a distance” or telekinetics are allowed.

When Alain Aspect performed his experiment he would discover that the results violate Bell’s inequality. 😯 In other words, the experiment revealed that at least one of those two assumptions must be wrong. Either there are multiple realities or there are non-local interactions.

The impact of these results is astounding. To understand why, one needs to employ a perspective of Karl Popper, which states that one can never verify a theory. At best one can only falsify theories. According to this perspective science progresses through a process of elimination. Well, if that is the case then Alain Aspect has eliminated a quarter of all possible theories with this one experiment. Remarkable progress indeed!

Of the three remaining possible combinations, the popular combination is the one that allows multiple realities while enforcing locality. This is what the Copenhagen interpretation implies. Another interpretation would be that there is a unique reality but that interactions could be non-local. To give up on both assumptions is too horrible to contemplate.

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Now if you are like me, you probably won’t believe a single word about these experimental results. How can any experiment give such a profound result? I would have wanted to know exactly how this experiment was performed so that I can understand for myself how one can draw such remarkable conclusions from the results. Well, if that is how you feel, let me try to explain in the simplest possible language how this experiment was able to come to such a profound conclusion.

The experiment was made possible by the fact that there exist certain nonlinear processes that produces two output photons out of a single input photon. These two photons are then entangled by the requiremnt that their polarisation states must be orthogonal. One can then use a polariser (or analyser) to influence one of the photons before it is observed by a detector. Assume that the polariser is oriented with an angle of 45 degrees with respect to the orientation of the linearly polarised incident light. Then each photon has a 50% probability to pass through it and be observed.

One needs to make sure that every observed pair of photons is indeed a pair of entangled photons (i.e. a pair that originated from the same input photon) and not just two separate photons that originated from different input photons. For this reason the light intensity is reduced until photons are observed one by one. Moreover, the two detectors are both connected to a coincidence counter that counts only those photons that are measured at the same time and rejects those cases where only one photon is registered at one of the detectors.

The surprising result of this xperiment is that when the two polarisers are oriented in the same direction then no coincident observations are made. This is surprising because in some cases the photons at both sides could be oriented at 45 degrees with respct to the polariser, which should imply the there is a 50% chance to see some coincidence measurements. Instead none is observed. The implication is that when the photon on one side passes through the polariser it is transformed or projected into the polarisation state that matches the orientation of the polariser. At the same time the other photon with which it is entangled will be transformed or projected into the polarisation state that is orthogonal to that of the first photon. As a result the second photon cannot pass through the polariser. So it seems that the influence of the polariser on one photon is instantaneously communicated to the other photon regardless of how far away it is from the first photon. This experiment has been repeated several times since it was first performed by Alain Aspect. Every time the same surprising violation of Bell’s inequality is obtained.

So now there are two possibilities. Either it is possible for the photons to have a non-local interaction or there are multiple realities allowing all possible orientations at the same time. At the beginning of this post I stated that this aspect of quantum is the one that we are most certain of. However, there is actually three different combinations that we can choose from. What we are however certain of is that the combination of local realism is ruled out.

I hope to come back to this remarkable experimental result and discuss the consequences.