Are atoms/particles unique/undistinguishable?

Are all hydrogen atoms undistinguishable from each other? (discounting isotopes and ions), all unique? several different models?

Ditto for all other atoms of course, I am starting at hydrogen just because being simpler they should have less room for variations.

How about subatomic particles? Are protons/neutrons/gluons all the same? unique?

Hydrogen atoms can be distinguishable, but the distinguishing marks aren’t permanent. Two different hydrogen atoms might, for instance, be in different energy levels, but it’s not too hard to change the energy level of an atom, and if you got them to the same energy level, they would again be indistinguishable.

Likewise, two molecules will be indistinguishable, if they have the same arrangement of atoms and are in the same energy level. But molecules tend to have a lot more energy levels available to them than atoms, so it’s more likely that they’ll be different. And very complex molecules often don’t actually have exactly the same arrangements of atoms as each other, even though they might be referred to by the same name.

Of course, particles smaller than atoms will be indistinguishable, too, or at most, be distinguishable only by some easily-changed property. So two electons, for instance, might have spins in opposite directions, but if you flip one over, then they’ll be indistinguishable.

You can sort subatomic particles into the bosons and fermions, with the bosons having integer spins and the fermions having half-integer spins.

In practice, the difference means that any number of bosons can share the same quantum state, or loosely, can be in the same place as one another without interacting. Photons can cross photons. This is the principle behind lasers.

No two fermions can occupy the same space, which is why electrons sort themselves out into rigidly defined orbitals around atoms.

So some particles are even more equal than other particles.

Other than spin, however, I believe that all particles of a type are identical. (Unless some quantum mechanical principle that I’m forgetting is in operation.)

And as Chronos says, all atoms are interchangeable for one another.

My understanding is that particles are constrained by whatever underlying theory we’ll find so that each must be exactly the same fundamental entity as all its compatriots. Only conglomerations can have differences. And identical conglomerations, as in the same isotropes of atoms, must also be equivalent.

I think without splitting hairs the answer is yes, they are indistiquishable. That said for my knowledge all that’s been said so far is also correct.

Fundamental particles are indistinguishable. That’s what leads to quantum statistics. Bosons are those which carry the trivial representation of the symmetric groups under exchange of particles, and fermions are those which carry the signum representation. If it were not the case that all electrons are indistinguishable, they couldn’t be exchanged and so would not carry any such representation, and similarly for photons.

I don’t know why you are quoting me since I think I was agreeing with you <b>mathochist</b>

Backing you up, man, not contradicting.

More accurately, no two identical fermions can be in the same quantum state at the same time.

Spin is just another quantum state of the electron in an atom, of which there are 4 (called the quantum numbers). An electron is an electron, and can be either spin up or spin down (ms = +1/2 or - 1/2).

Yes, I was aware that spin is a quantum property, which is why I made the comment. But there are some pretty obscure and esoteric quantum properties and I was using the famed SDMB CYA parenthetical formulation. (Originally developed by Feynman, Alpher, Bethe, and Gamow at a drunken Princeton colloquium under an enraged Einstein’s window, I believe.)

Yeah, but the statement about spin was confusing. It’s like saying there are two kinds of dogs-- sleeping dogs and awake dogs. “Sleeping” is a state, not something intrinsic in any particular dog.

Thanks to all for the responses. Then we have that:

Particles are undistinguishable

so are atoms

so are molecules

(and I am guessing so are cristals)

With each level of increasing complexity, there is more room for variation in their states but they are still fundamentally identical.

Does this break at some point for specific reasons other than just the increased complexity that makes it less likely that all the states are the same?

Polymers? DNA strands?
Are viruses (of the same type, of course) indistinguishable from each other?

I think the point is that increased complexity gives you more room for items that are of different structure that might be cataloged as ‘similar’. DNA strands, for instance, have enormous room for variability because of the DNA code… (the way that they spell out protein sequences in the G, C, T, A letters etc,) and some DNA strands might be ‘damaged’ because one of their elements is not constructed properly, but if two DNA strands spell out the same sequence, are both in perfect condition, and in the same location, then it’d be very hard to tell them apart I think. Viruses I think you get into tougher territory. Two viri born of the same infected cell (and thus constructed according to a parent virus ‘recipe’) would presumably have an identical DNA payload barring a mutation. However, I’m not sure if they’d have the same protein sheath around them, or if those are more like snowflakes, no two sheaths quite the same.

And two viri of the same ‘strain’ but found in very different places, I wouldn’t be too surprised if there wasn’t an actual genetic difference between them - but the DNA tests that mark the strain would still be the same
Does all that make any sense??

Crystals, to a point. Pure crystals of the same size, yes. But one doesn’t need to work for De Beers to know that a 20 carat blue diamond is distinguishable from a 1 carat colorless diamond :slight_smile: Different size and impurities.

Polymers are a bit like crystals in that a chain of polyestyrene with no impurities will be identical to all other chains of polyestyrene in the world except for size. The ends of the chains are the same, the repeating unit making up the length of the chain is the same; the length varies.

Polymers formed by more than one monomer have more variation. Polymers with cross-chain links, even more.

DNA strands are still molecules; specifically, they’re polymers made up of 4 monomers. Each chromosome is formed by two parallel strands of monomers, linked by hydrogen bonds. Each of the DNA strands in my cells is different from her same-cell companions, but (except for mutations and ova) all my cells have identical collections of DNA strands. For a male, all his cells (except mutations and ova) will have identical Y-chromosomes.
Crystals and polymers aren’t really identical but they have a lot of repeatability. We describe their repeatable properties and relevant irrepeatable ones (for example, the impurities that make a diamond blue would be relevant for a chemist or physicist, not necessarily for a jeweler).

Well, yes for crystals, polymers and DNA I meant identical (at an atomic level) pairs of each.

I presume that at some point of complexity, the variations on internal states are such that identical items don’t behave identically. For example, two identical enzymes are approached by respective identical molecules but a reaction might occur in one and not in the other because of different internal states (bond stress, whatever). Right?

Yes, identical superstrucures are indeed identical. The thing is, they become increasingly less likely to actaully occur in nature. A perfectly pure crystal, if it exists at all, would be only found in a lab.

Take semiconductors. They start off (mainly) with a pure Si crystal. Except, of course, it isn’t really pure. We just say it’s pure because the impurities are at a low enough level that we can expect two different crystals to behave in much the same way. But you can always make your demands strict enough so that they wouldn’t behave in the same way.

Even if two DNA strands have the exact same sequence, they’re probably (as in, 99.999…9% likely) still going to be distinguishable. One might be bent in a particular place, or twisted a little bit tighter or looser, or any of a host of other differences. Strictly speaking, they’d be in different states, and you could convert a DNA molecule from one state to another, just like you could with an individual atom. The problem is that by the time you get to a system as complicated as a DNA molecule, there is going to be such an incredibly large number of states that it’s going to be, for practical purposes, impossible to get two different molecules into exactly the same state.

Sorry, I knew I came off a bit touchy.

You could have two different isotopes of the same element…chemically the same, but distinguishable by mass and radioactive decay. No way to distinguish members of the same isotope though.

Hmm… good point, and like everything else that could propogate up the chain. Two seemingly identical DNA chains, for instance, except that one of them happens to have an atom of carbon-14 in it. Until suddenly - BAM, the radiocarbon atom explodes like a tiny little bomb, turns into nitrogen (I think,) and the rest of the molecule gets twisted into a new shape.

(Is that sort of thing still thought to be a significant contributor to genetic mutation?)

Right. Can be geometry (most bonds can rotate quite freely), can be electronic states (are all the electrons paired or not), can be that the electronic states and the basic geometries are the same but one group still has enough energy to reorganize (i.e., to react) and the other doesn’t.

My favorite:

in order to react, two molecules must have the same total spin (a molecule and a radical or a molecule and an ion are different cases). For most molecules, the state of lowest energy is one where all the electrons are paired, so the total spin is zero: that’s called a singlet state (because it leads to a single line in certain scans).

O2 in it’s basic state has two unpaired electrons, it’s a triplet (three lines in the same scans). So the most abundant form of O2 can’t react with the majority of the things it encounters. Give the O2 enough energy to get those two electrons together and then it can react with pretty much anything.