Wednesday, July 27, 2005

Another Aspect of reality

After thousands of requests I got from my readers around the world (sic) I will try to explain one of the darkest corners of Quantum Mechanics: The EPR paradox, Bell's inequalities, the Aspect experiment, reality and locality in Quantum Mechanics.

The story consists of 2 parts. First, the original EPR paradox stated by Einstein, Podolsky and Rosen in 1935, where they argued that QM is not complete as a theory. Second, Bell formulated some inequalities that relate to the paradox and they can be experimentally tested. Aspect in 1983 performed the experiment and proved that Einstein was wrong, and that Bell's inequality is violated.

Usually people when they try to explain physics they come up with a real world example, an analogy, that non-scientists can grasp in order to make themselves understood. Although I do not completely agree with the approach, since it reduces the complexity by taking away critical facts, I will use an example here which is OK as long as one realizes the restrictions that apply.

In their paper they proposed a thought experiment that goes something like that. Imagine you and a friend are magically given each a piece of paper and that each paper has inscribed a positive integer on it, and you are told that the numbers on each paper is random, under the condition that their product is always 24. Then you drive to the east coast and your friend drives to the west coast. When you read the paper, say the number 12, you instantly know that the number written in the other paper is 2. Similarly, if you repeat the experiment and you finally read 6, you instantly know that your friend's paper reads 4, etc.

The point here is to realize that the 2 properties (the numbers) are random yet they have to satisfy some combining condition that you know ahead of time. This is ok as long as the numbers are predetermined and written on the papers beforehand. However, the problem arises because Quantum Mechanics says that the number you read is determined at the exact moment you read the paper (i.e, after you travel to the east coast). Hence at the same moment the other number on the other coast is determined afterwards and at the same time you conduct your experiment, i.e. when you read the paper. This means that a faster than light signal (forbidden by relativity) is somehow transmitted from one side to the other. This is the EPR paradox.

In their paper they attempted to resolve the paradox by introducing the so called hidden variables; that despite what QM says, there are some hidden variables that pre-determine the value of the numbers at their origin point. Bell later on he derived an inequality that expresses exactly this fact. And Aspect proved that it was all wrong.

Here we must distinguish between causality and locality. Causality means that something is happening before its cause (e.g. faster than light speed); locality means that there is a "spooky action at a distance" that allows something to be affected instantly by something on the other side of the universe. The experiment proved that Quantum Mechanics violates locality but not causality.

In reality instead of numbers in pieces of paper people use photons with polarizations (the direction that the vector is pointing). What they do is they generate e.g. photons that must have opposite polarizations, so if one is up the other has to be down and vice versa. However the initial state of the photon is random, it can be either. And EPR say the state is determined in the birth of the photons, while QM says it is determined at the instant of observation of either photon.

So, it remains to be seen how the experiment proved how QM was right after all.

To be continued...