Difference between revisions of "Identical Particle"
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The working hypothesis, the postulates and consequences. | The working hypothesis, the postulates and consequences. | ||
| − | # There was just energy, lots of it. | + | # There was just energy, lots of it. All of it as photons, that is, as each boson has no independent identity. |
# There was a fairly simple plan about how aggregations of energy could be arraigned. | # There was a fairly simple plan about how aggregations of energy could be arraigned. | ||
# Energy does not like to be naked. When it is, as a photon, it tries to find a home where it is not naked. | # Energy does not like to be naked. When it is, as a photon, it tries to find a home where it is not naked. | ||
Revision as of 22:01, 30 May 2023
Full Title or Meme
Two particles are considered identical when one cannot be distinguished from one another, even in principle.
Taxonomy
For the purposes of this page:
- particle = any piece of matter or energy that is small enough for quantum effects to be observed.
- wave or wavelet = any view of a particle that emphases its wave-like characteristics.
- virtual particle = any particle that can be imagined, but not observed.
In the Beginning
The working hypothesis, the postulates and consequences.
- There was just energy, lots of it. All of it as photons, that is, as each boson has no independent identity.
- There was a fairly simple plan about how aggregations of energy could be arraigned.
- Energy does not like to be naked. When it is, as a photon, it tries to find a home where it is not naked.
Context
In Quantum Mechanics two particles (or two waves) that can be considered identical include, but are not limited to, elementary particles (such as electrons), composite subatomic particles (such as atomic nuclei), as well as atoms and molecules1,composite subatomic particles (such as atomic nuclei), as well as atoms and molecules.[1] For example, all of the electrons bound to an atom are indistinguishable and so there is no set of state variables that can be identified with a particular electron.
In statistical mechanics
Assume you have two particles A and B in states 1 and 2. If the two particles are distinguishable, then by exchanging the particles A and B, you will obtain a new state that will have the same properties as the old state i.e. you have degeneracy and you have to count both states when calculating the entropy for example. On the other hand, for indistinguishable particles, exchanging A and B is a transformation that does nothing and you have the same physical state. This means that for indistinguishable particles, particle labels are unphysical and they represent a redundancy in describing the physical state and that is why you would have to divide by some symmetry factor to get the proper counting of states.
https://www.feynmanlectures.caltech.edu/III_01.html
Solutions
For this page the distinction that is important in the statistical rules that apply. Maxwell-Boltzmann distribution is used for solving distinguishable particle and Fermi-Dirac, Bose-Einstein for indistinguishable particles.
Particles which exhibit symmetric states are called bosons. The nature of symmetric states has important consequences for the statistical properties of systems composed of many identical bosons. These statistical properties are described as Bose–Einstein statistics.
Particles which exhibit antisymmetric states are called fermions. Antisymmetry gives rise to the Pauli exclusion principle, which forbids identical fermions from sharing the same quantum state. Systems of many identical fermions are described by Fermi–Dirac statistics.
References
- ↑ Simplified from data in Wikipedia, Identical Particle https://en.wikipedia.org/wiki/Identical_particles
