Bartosz Milewski on Nostr: You're tossing a pair of coins: The probability of both ending up in the same state ...
You're tossing a pair of coins: The probability of both ending up in the same state is 1/2--it's two out of four possible outcomes, HH, TT, HT, TH. But if the coins are identical, how do you distinguish between HT and TH? Well, no two coins are identical. Even the tiniest of imperfections will make them different in the eyes of Nature.
But what if you do this experiment with a pair of helium atoms? You can't have any imperfection in an atom--they are truly identical. The analog of coin-tossing is to give them the choice of two equally probable quantum states. It turns out that the probability of two helium atoms ending up in the same state is not 1/2, but 2/3. There are only three possibilities: both in the first state, both in the second state, and one in each state. This is truly bizarre! It's as if there was only one helium atom multitasking for two.
Because of this weird statistics, called the Bose-Einstein statistics, helium atoms (or bosons, in general) tend to aggregate, as if they were attracted to each other. This can sometimes lead to macroscopic effects, like super-liquidity in helium, coherent light in lasers (photon are bosons), or superconductivity (bosonic Cooper pairs).
Electrons are even weirder--they obey the Fermi-Dirac statistics. Two electrons (or fermions, in general) can never be in the same state. It's as if the result of tossing two coins was never two heads or two tails. They resist very strongly if you try to squeeze them into the same state. On a macro scale, this is why we have neutron stars. Neutrons are fermions, so even the tremendous gravitational pull can't make the neutron star collapse (unless it forms a black hole, in which case all bets are off).
But what if you do this experiment with a pair of helium atoms? You can't have any imperfection in an atom--they are truly identical. The analog of coin-tossing is to give them the choice of two equally probable quantum states. It turns out that the probability of two helium atoms ending up in the same state is not 1/2, but 2/3. There are only three possibilities: both in the first state, both in the second state, and one in each state. This is truly bizarre! It's as if there was only one helium atom multitasking for two.
Because of this weird statistics, called the Bose-Einstein statistics, helium atoms (or bosons, in general) tend to aggregate, as if they were attracted to each other. This can sometimes lead to macroscopic effects, like super-liquidity in helium, coherent light in lasers (photon are bosons), or superconductivity (bosonic Cooper pairs).
Electrons are even weirder--they obey the Fermi-Dirac statistics. Two electrons (or fermions, in general) can never be in the same state. It's as if the result of tossing two coins was never two heads or two tails. They resist very strongly if you try to squeeze them into the same state. On a macro scale, this is why we have neutron stars. Neutrons are fermions, so even the tremendous gravitational pull can't make the neutron star collapse (unless it forms a black hole, in which case all bets are off).