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Note that this "high temperature" approximation does not distinguish between fermions and bosons. The discrepancy in the partition functions of distinguishable and indistinguishable particles was known as far back as the 19th century, before the advent of quantum mechanics. It leads to a difficulty known as the Gibbs paradox.
The name boson was coined by Paul Dirac [3] [4] to commemorate the contribution of Satyendra Nath Bose, an Indian physicist. When Bose was a reader (later professor) at the University of Dhaka, Bengal (now in Bangladesh), [5] [6] he and Albert Einstein developed the theory characterising such particles, now known as Bose–Einstein statistics and Bose–Einstein condensate.
If a system shows measurable differences when one of its particles is replaced by another particle, these two particles are called distinguishable. Bosons Bosons are particles with integer spin (s = 0, 1, 2, ... ). They can either be elementary (like photons) or composite (such as mesons, nuclei or even atoms).
Bosons are one of the two fundamental particles having integral spinclasses of particles, the other being fermions. Bosons are characterized by Bose–Einstein statistics and all have integer spins. Bosons may be either elementary, like photons and gluons, or composite, like mesons. According to the Standard Model, the elementary bosons are:
For fermions the expectation value of the distance increases, and for bosons it decreases (compared to distinguishable particles). [ 2 ] The exchange interaction arises from the combination of exchange symmetry and the Coulomb interaction.
The treatment of identical particles is very different for bosons (particles with integer spin) versus fermions (particles with half-integer spin). The above N -particle function must either be symmetrized (in the bosonic case) or anti-symmetrized (in the fermionic case) with respect to the particle numbers.
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By analogy, if in an alternate universe coins were to behave like photons and other bosons, the probability of producing two heads would indeed be one-third, and so is the probability of getting a head and a tail which equals one-half for the conventional (classical, distinguishable) coins.