# Are atoms unique?

Do atoms have any uniquely identifying characteristic besides their history?

For example, if we had detailed information about a specific carbon atom from one of Planck's fingerprints, and could time-travel to the cosmic event in which the atom formed, would it contain information with which we could positively identify that they two are the same?

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As far as I know, atoms don't have any practical uniquely identifying characteristic, not even history. –  DumpsterDoofus Feb 17 at 23:40
My mention of history was intended to eliminate the use of outside knowledge of an atom's origin. Its history is of course not in any way recorded within the structure of the atom itself...as far as we know :) –  Charles Burns Feb 17 at 23:52
A great article presenting the issue in time-less QM - lesswrong.com/lw/pl/no_individual_particles. The whole sequence is well worth a read lesswrong.com/lw/r5/the_quantum_physics_sequence –  Luaan Feb 18 at 12:10
Suggestion to title (v1): Are atoms identical? –  Qmechanic Feb 18 at 12:20

Fundamental particles are identical.

If you have two electrons, one from the big bang and the other freshly minted from the LHC, there is no experiment you can do to determine which one is which. And if there was an experiment (even in principle) that could distinguish the electrons then they would actually behave differently.

Electrons tend to the lowest energy state, which is the innermost shell of an atom. If I could get a pen and write names on all of my electrons then they would all fall down into this state. However since we can't tell one electron from another only a single (well actually two since there are two spins states of an electron) electron will fit in the lowest energy state, every other electron has to fit in a unique higher energy level.

Edit: people are making a lot of comments on the above paragraph and what I meant by making electrons distinguishable, so I will give a concrete example: If we have a neutral carbon atom it will have six electrons in orbitals 2s1 2s2 2p2. Muons and tauons are fundamental particles with very similar properties to the electron but different masses. Muons are ~200 times more massive than electrons and tauons are ~3477 times more massive than an electron.

If we replace two of the electrons with muons and two of the electrons with tauons all of the particles would fall into the lowest energy shell (which can fit two of each kind because of spin). If in theory these particles only differed in mass by 1% or even 0.0000001% they would still be distinguishable and so all fit on the lowest energy level.

Now atoms are not fundamental particles they are composite, I.E. composed of "smaller" particles, electrons, protons and neutrons.

Protons and neutrons are themselves composed of quarks. But because of the way that quarks combine, they tend to always be in the lowest energy level so all protons can be considered identical, and similarly with neutrons.

To take the example of carbon, there are several different isotopes, different number of neutrons, of carbon (mostly $^{12}C$ but also ~1% $^{13}C$ and ~0.0000000001% $^{14}C$ {the latter which decays with a half life of ~$5,730$ years [carbon dating] but is replaced by reactions with the sun's rays in the upper atmosphere}).

If we take two $^{12}C$ atoms, and force all of the spins to be the same. This is not too difficult for the electrons of the atom since the inner electrons do not have a choice of spin because every spin in every level is already full. So only outer electrons matter. The nucleons also have spin.

With our two $^{12}C$ atoms with all of the same spins, we now have two indistinguishable particles which if you set up an appropriate experiment (similar in principle to the electrons not being able to occupy the same state) we will be able to experimentally prove that these two atoms is indistinguishable.

Are atoms unique?

No.

Do atoms have any uniquely identifying characteristic besides their history?

Their history of a particle does not affect it*. No particles are unique. Atoms may have isotopes or spin to identify one from another, but these are not unique from another particle with the same properties.

would it contain information with which we could positively identify that they two are the same?

Yes only because we could positively identify that this carbon atom is the same as almost every other carbon atom in existence.

*Unless it does, in which case it may be considered a different particle with different properties.

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Could you explain a bit more about your third paragraph? How does being able to differentiate between electrons effect how many of them fit in a given shell? –  Robert Feb 18 at 4:44
The 1s shell is the lowest energy state. If I have two electrons that I can tell apart (because of spin), then they both fit on this shell. Howeve a third electron would have to be identical to one of the first two and move to a higher shell. See en.wikipedia.org/wiki/Pauli_exclusion_principle –  user288447 Feb 18 at 6:41
This is a correct answer. It is interesting, though not directly related to the question, to state that because of the existence of isotopes, ensembles of atoms do give a signature of their history. spaceflightnow.com/news/n0201/13decay –  anna v Feb 18 at 7:15
Correct. The 2001 Nobel Prize was awarded for the creation of an Bose-Einstein Condensate of atoms. A BEC consists of identical particles, so there's also experimental confirmation. –  MSalters Feb 18 at 8:15
I find this sentence "If I could get a pen and write names on all of my electrons then they would all fall down into this state." kinda iffy, they could simply not care about their names. I would explicitly say, that the points is, the Pauli's principle say no two identical electrons can occupy the same "slot". Inventing virtual electron characteristics to make them distinguishable is kinda murky area IMO. –  luk32 Feb 18 at 8:29

Does position count as a characteristic? If so, then yes, atoms do have unique characteristics.

Edit: Perhaps I should rephrase this. If position counts as a characteristic, then yes, atoms do have unique characteristics.

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If you have a new question, please ask it by clicking the Ask Question button. Include a link to this question if it helps provide context. –  Ali Feb 18 at 1:29
@Ali this isn't a new question, though. –  David Z Feb 18 at 4:21
@DavidZ You're right. –  Ali Feb 18 at 11:19
If he's right ... just delete your erroneous comment?? –  Joe Blow Feb 19 at 13:51

I'm going to add to user288447's answer, with which I concur, by adding that the evidence for this comes from Thermodynamics (at least that's where I learned about it, the principle is reflected everywhere). If the identity of individual particles mattered, then the way that entropy changes when you separate a group of particles from each other would be very different. This is only reiterating what's been said, that you can't construct an experiment that distinguishes particles from each other, but what fascinated me when I learned this is that you can also say "experiment has consistently shown that particles with the same properties are indistinguishable."

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(I'd love to go into more detail, but my Thermo book is at the bottom of a large stack and I'm supposed to be doing homework.) –  krs013 Feb 18 at 9:17
I would change your last statement to "experiment has consistently shown", since experiments can't prove anything. –  corsiKa Feb 18 at 22:07
@corsiKa I'm not sure if I agree with that, though I see your point. It may not be correct of me to apply a finite number of experiments to all particles, but I do think that it is proof. What alternative is there? –  krs013 Feb 19 at 6:20
There is no alternative: proofs cannot be. You can only ever disprove a hypothesis. With peer consensus and being consistently confirmed via experimentation, a hypothesis may be elevated to a theory. Consider the theory of gravity: we have not proven anything about gravity, but we have consistently shown via repeatable, falsifiable experiments that our various hypotheses remain... err... nondisproven? You can prove things in mathematics, but not in physics. –  corsiKa Feb 19 at 17:38
I would consider reading the answers physics.stackexchange.com/q/31068/1954 as well as the Wikipedia articles on Hypothesis and Scientific Theory. There is also a quote by Albert Einstein: "No amount of experimentation can ever prove me right; a single experiment can prove me wrong." –  corsiKa Feb 19 at 17:40
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At the atomic level, atoms have very few distinguishing characteristics. These are the result of different number and amounts of electrons, protons, neutrons, etc. as outlined in the periodic table of the elements. However, when talking about a specific element like carbon, there is no difference between a carbon particle created 4 billion years ago or one created today. The measurable characteristics of carbon are tied directly to the number of electrons protons, neutrons, etc., and its geometry. A carbon particle made today has the same composition and geometry of a carbon particle made any time in the past. Since their properties are the same and independent of the method used to create them, they are indistinguishable, and poses no history. The only way we could know that they were created at different dates, would be from information obtained outside of the particles.

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