# Is there a simple explanation for Fermi-Dirac statistics?

Is there a simple explanation for fermi-dirac statistics? I can't understand how a particle can "follow" a statistic.

Orodruin
Staff Emeritus
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That is not a question of a single particle, it is a question of how a collection of identical particles behave statistically. Ultimately, this is settled by experiment, but the underlying reason half-integer spin particles follow FD statistics is laid out in the spin-statistics theorem.

So what fundamentally makes fermions and bosons different?

Orodruin
Staff Emeritus
Homework Helper
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Fermions follow FD statistics and bosons BE statistics. But that is not the question I believe you really want to ask. I believe that the question you want to ask is "Why are half-integer spin particles fermions and integer spin particles bosons?" This, again, is laid out in the derivation of the spin-statistics theorem, see, e.g., https://en.wikipedia.org/wiki/Spin–statistics_theorem , and is ultimately connected to the behaviour under the exchange of particles.

• mfb and YoungPhysicist
Thanks man. I'll check it out.

ZapperZ
Staff Emeritus
Is there a simple explanation for fermi-dirac statistics? I can't understand how a particle can "follow" a statistic.

I think your question here exhibits a deeper issue than simply the Fermi-Dirac statistics.

The world that you see around you arises out of the collective behavior of a gazillion particles. You never deal with just one, or a few particles or interactions. Now, it is impossible to know the dynamics of every single one of these particles. So instead, we find a description of their collective behavior, and we find that in many instances, this collective description works quite adequately. This is the "statistics" that we are talking about.

You also do not need to delve into quantum physics to talk about statistics of particles. The basic thermodynamics laws are based on the classical description of particles via the Maxwell-Boltzmann statistics. So even before QM, we are already well-aware of statistical mechanics.

Zz.

• mfb and YoungPhysicist
anorlunda
Staff Emeritus
I think the simple thing you seek without a course in QM is included in the spin statistics page that @Orodruin already linked.

https://en.wikipedia.org/wiki/Spin%E2%80%93statistics_theorem said:
Bosons are particles whose wavefunction is symmetric under such an exchange or permutation, so if we swap the particles the wavefunction does not change. Fermions are particles whose wavefunction is antisymmetric, so under such a swap the wavefunction gets a minus sign, meaning that the amplitude for two identical fermions to occupy the same state must be zero. This is the Pauli exclusion principle: two identical fermions cannot occupy the same state. This rule does not hold for bosons.

From that "simple" difference, the statistics arise.