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Why should two sub-atomic (or elementary particle) - say electrons need to have identical static properties - identical mass, identical charge? Why can't they differ between each other by a very slight degree? Is there a theory which proves that?

Imagine an alien of size of order of Milky-way galaxy examining our solar system with a probe of size of 10's of solar system dimension and concludes that all planets are identical.

Qmechanic
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Gsv
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    Theories do not prove anything. They can be either confirmed i.e. be consistent with the data, or falsified. The data we have up to now are consistent with the hypothesis that all electrons have the same properties, and beautiful predictive theories are being used to explore more details experimentally. If ever an experiment comes up with data that shows differences in individual electrons/particles then one can discuss the issue. – anna v Jul 03 '11 at 07:57
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    anna has nailed it. However, FYI, the theoretical reason for believing electrons are identical is that they are excitations of the same field. And as such, they can not differ. I think there's already some question and answer about that around somewhere. – Raskolnikov Jul 03 '11 at 08:46
  • As You can see on any color CRT, there are red, green and blue electrons! :=) Nature is very economic! It saves on everything which would make differences. – Georg Jul 03 '11 at 09:26
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    The idea is that we can't, using current technology, measure any differences between two electron in rest. I don't think there is even an experiment to distinguish between two electron (or more). Using your alien galaxy metaphor, that dude won't have any tool to tell if there is any difference between the planets (The same way as we can't tell if we are, in fact, only a small atom of a much larger galaxy). There might be a difference and once such a difference will be measures, theories will be updated (or thrown away). – Yotam Jul 03 '11 at 10:35
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    There is only one electron in the world see (http://en.wikipedia.org/wiki/One-electron_universe). So the answer to the question is trivial. Of course all electrons are identical (all = one) ;-) – Fabian Jul 03 '11 at 18:13
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    I think the strongest experimental evidence about electrons being identical is the fact that, in an assembly, their statistics do not follow the Maxwell–Boltzmann law, but instead the Fermi–Dirac law, which only makes sense for indistinguishable particles. – Edgar Bonet Jul 04 '11 at 09:23
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    Yes, the notion of identical particles was imposed by experiments. – Vladimir Kalitvianski Jul 04 '11 at 09:43

2 Answers2

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One good piece of evidence that all particles of a given type are identical is the exchange interaction. The exchange symmetry (that one can exchange any two electrons and leave the Hamiltonian unchanged) results in the Pauli exclusion principle for fermions. It also is responsible for all sorts of particle statistics effects (particles following the Fermi-Dirac or Bose-Einstein distributions) depending on whether the particles are fermions or bosons.

If the particles were even slightly non-identical, it would have large, observable effects on things like the allowed energies of the Helium atom.

Dan
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  • Nice answer +1. Indeed, many calculations produce crucially different results for identical versus distinguishable particles. – Lagerbaer Jul 04 '11 at 23:25
  • This would have been my answer too. I think these experiments prove that electrons either are fundamentally indistinguishable or have some bizarre electron-only interaction keeping them apart. – Kasper Jul 04 '11 at 23:49
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    Furthermore, I'd point out that electrons are excitations of a pervasive field. They are the same because they're made of the "same stuff". – genneth Jul 05 '11 at 10:31
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    I'm not even certain that there is more than one electron particle (although, that would seem to imply a definite fixed end to time so that the field excitation can bounce back and forth). – Brian Knoblauch Jul 06 '11 at 19:35
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    @Brian Knoblauch: It would also imply an equal number of electrons and positrons. – Dan Jul 06 '11 at 19:38
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Regarding to this question about Is the electron of carbon identical to that of hydrogen? How to prove it? the answer should be a little bit different from the usual answer. Electrons in the same state have the same energy amount and the same electric charge. Since they have a magnetic moment too they are separable in this parameter. And now the clue.

Electrons of different speed as well as of different bond to a nucleus are separable too. And as an add-in, electrons with relativistic velocity have shielded charges. So the answer, that electrons are not separatable is true only in a first thought.

Community
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HolgerFiedler
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