Identical Particle - Revision history

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‎Taxonomy

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‎In the Beginning

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‎Taxonomy

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‎Full Title or Meme

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‎Context

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‎In the Beginning

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 * 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.
-**For example virtual particles were used in Feynman diagrams to get the full gamut of all possible paths.
+**For example virtual particles were used in Feynman diagrams to get the full gamut of [[All Possible Paths]].
 ==In the Beginning==

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 ==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. The founder of the big bang has suggested that there was just one truly energetic photon that begat all of the reset.<ref>G. Lemaitre, ''The Beginning of the World from the Point of View of Quantum Theory'' https://www.nature.com/articles/127706b0</ref> Dirac shared that view with Lemaitre.<ref>Thomas Hertog ''On the Origin of Time'' (2023) ISBN 9780593128442</ref>
+# There was just energy, lots of it. All of it as photons, that is, as each boson has no independent identity. The founder of the big bang has suggested that there was just one truly energetic photon that begat all of the reset.<ref>G. Lemaitre, ''The Beginning of the World from the Point of View of Quantum Theory'' https://www.nature.com/articles/127706b0</ref> Dirac shared that view with Lemaître.<ref>Thomas Hertog ''On the Origin of Time'' (2023) ISBN 9780593128442</ref>
 # There was a fairly simple plan about how aggregations of energy could be arraigned.
 # Particles (Fermions) condensed out of this massive amount of energy by some mechanism that result in all matter and essentially no antimatter.

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 * 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==

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 ==Full Title or Meme==
-Fermi–Dirac statistics applies to [[Identical Particle]]s. In this context, “identical” means that the particles have the same mass, charge, and other intrinsic properties. Electrons fit this criterion because they are indistinguishable from one another.
+Fermi–Dirac statistics applies to [[Identical Particle]]s. In this context, “identical” means that the particles have the same mass, charge, and other intrinsic properties. Electrons fit this criterion because they are indistinguishable from one another at least in the context of the electrons bound to an atom.
 ===Taxonomy===

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 ==Full Title or Meme==
-Two [[Particle]]s that cannot be distinguished from one another, even in principle cannot be considered to have individual identities.
+Fermi–Dirac statistics applies to [[Identical Particle]]s. In this context, “identical” means that the particles have the same mass, charge, and other intrinsic properties. Electrons fit this criterion because they are indistinguishable from one another.
 ===Taxonomy===
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 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 molecules,composite subatomic particles (such as atomic nuclei), as well as atoms and molecules.<ref>Simplified from data in Wikipedia, ''Identical Particles'' https://en.wikipedia.org/wiki/Identical_particles</ref> 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.
-Pauli exclusion principle
+===Pauli Exclusion Principle===
-In statistical mechanics
+===Fermi–Dirac Distribution[[[
 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.

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 ==Full Title or Meme==
-Two [[Particle]]s are considered identical when one cannot be distinguished from one another, even in principle.
+Two [[Particle]]s that cannot be distinguished from one another, even in principle cannot be considered to have individual identities.
-In other words, each [[Particle]]  can be distinguished from the others, at least in principle.
+In other words,if each [[Particle]] can be distinguished from the others, at least in principle, then that particle can have an individual identity.
 ===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.
+* 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.
+* Virtual particle = any particle that can be imagined, but not observed.
 ==In the Beginning==
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 # Fermions can have individual identity as we know from the statistics that they follow (Fermi-Dirac statistics).
 # Energy does not like to be naked. When it is, as a photon, it tries to find a home where it is not naked.
+#

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 ==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.<ref>Simplified from data in Wikipedia, ''Identical Particles'' https://en.wikipedia.org/wiki/Identical_particles</ref> 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 [[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 molecules,composite subatomic particles (such as atomic nuclei), as well as atoms and molecules.<ref>Simplified from data in Wikipedia, ''Identical Particles'' https://en.wikipedia.org/wiki/Identical_particles</ref> 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.
 Pauli exclusion principle