Daily Archives: September 15, 2008

Quantum Entanglement

Alice and Bob are very anti-social electrons. For financial reasons, they have to share a house (a helium atom). Due to their antisocial nature, they come to a condition where both of them never are in the same spot (state) at the same time. We’re interested in their spin, (political spin). If we ask one of them what their spin is, a question that technically would be phrased like “is your spin aligned with the y-axis?”, the answer we must get is “with” or “against”. That is all the answer they can give. And if we then immediately go and ask the other the same question, we will have to get the opposite answer. If Alice answered “with”, then Bob will answer “against”.

This all assumes that Alice and Bob are in their “ground state”, which is the worst financial condition (lowest energy) possible. If one of they hae a little cash, they could be in an “excited state” and they could end up with the same spin. But in that case, they would still have to be found in different positions (and with different energies). For example, Alice could be downstairs eating while Bob is upstairs sleeping.

The physicists say that these sort of living together difficulties arise because electrons are fermions: anti-social quantum creatures in that two of them are never found in precisely the same quantum state. This is called Fermi-Dirac statistics, or the Pauli exclusion principle. Fermi, Dirac and Pauli are three physicists. “Statistics” from the fact that when you make computations using “statistical mechanics,” you have to count up the number of ways a certain situation can be achieved, and if the particles can’t fit into the same state it reduces the number of ways. Fewer ways makes that situation less likely. Statistical mechanics forms the foundation of thermodynamics, the science of temperature, pressure, volume and all that.

So electrons are fermions. This is a good thing. The reason that gravity doesn’t pull you down to the center of the earth is because the electrons in your shoes can’t fit into the same quantum states as the electrons in the stuff you’re walking on. The same principle keeps neutron stars from collapsing into black holes. Hooray for fermions!!!

The helium atom has two electrons. While two electrons cannot be in the same state, all electrons are identical in that they all have negative charge and are attracted to positively charged things. In the case of the helium atom, the nucleus is positively charged and the two electrons are attracted to it. They can’t escape, but they can’t be in the same state either.
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