atom identity

Hi there are atoms of a paticular element say hydrogen for example exactly identcal or are they as individual as we are, in other words are there some very minor differences between...

From ten feet away they appear identical. The point, if the components of the proton keep getting smaller we will be unable to tell just like the sand grains from ten feet.

Appear but are not.

If it were only an appearance in the case of atoms, if it were enough that we can't tell, how would you explain superfluidity? Could it be that superfluididy is observed only by those that can't tell the difference between the individual atoms?

I don't have a clue. Apparently the discussion has gotten above my head.

He's basically saying that there is observed physical phenomena that would not be possible under your premise.

Qfwfq, could you explain this in more detail, or link us to some document that does? My understanding of superfluids and conductors – a very superficial appreciation of BCS theory – is that the phenomena have to do with bosonic interactions of quarks and electrons with quarks and electrons in their containers/barriers or conductors. While not requiring that quarks or electrons are distinguishable, this explanation does not preclude that they must be.

I’m aware that the exclusion principle can be stated, roughly, as “no two fermions may have the same quantum numbers”. This implies that, if two fermions were different in some way unrelated to position (ie: having differing in some undiscovered attribute), they could occupy the same space at the same instant. This is not observed, and would suggest dire “super-degenerate” consequences for the universe if it was. However, I’m unaware of any requirement by the formalism of quantum physics that implies that additional, undiscovered quantum numbers, exempt from the exclusion principle but detectable by some interaction, may not be added to the model – nor any requirement that such attributes must be added.

In short, I don’t believe that the formalism precludes its own modification.

This is pretty deep stuff. I’d appreciate guidance from people with better physics educations and comprehension than me.I don’t think this follows logically from the premise. The conclusion that electrons (which, unlike protons, are fundamental particles under the Standard Model) are indistinguishable can surely be credited as better than “a clue” as to their true construction. The claim that it is not seems akin to the statement “that I have stated a hypothesis which has not been experimentally demonstrated to be incorrect implies that the hypothesis must be incorrect, and an experimental demonstration of that just not yet performed”, a logical non sequitur.

I think Dirac commented brilliantly on the possibility that electrons really, ultimately, are indistinguishable in the sense we’re discussing, when he speculated that if we accept the formally defensible assertion that a positron (, the antiparticle of an electron) is actually an electron traveling backward in time, and that through a variety of interactions, an electron may transform into a positron and vice versa, then there may actually be only one electron/positron in the universe! Though a frivolous speculation, it nonetheless conveys the bizarre nature of quantum physics.The quark model – part of the Standard Model – wants to say the proton, a baryon, is made of exactly 3 smaller fermions – 2 u and 1 d quarks – and a virtual (literally) zoo of bosons.

Given that the Standard Model describes the proton as such a menagerie of virtual particles in constant complex interaction with 3 real ones, it’s vexing to explain how we can make any claim that protons are indistinguishable from one another. Strictly speaking, I believe we can only say that protons are indistinguishable to every ordinary technique for distinguishing them. Some extraordinary techniques can – if this were not the case, we would have no experimental support of the quark model. Most of these extraordinary techniques consisted of accelerating particles such as electrons to very high speeds, colliding them with protons and neutrons, and measuring their velocity when the “emerged”. These experiments suggest that not only are individual protons different from one another, but the same proton differs from moment to moment from itself – reminiscent of Heraclitus’s famous river.

Finally, note that just because the Standard Model considers quarks and other fundamental particles fundamental, does not mean that no theoretical investigation of the possibility of them being composites of yet more fundamental particles doesn’t exist. String and preon theories are examples of such investigations. So far, however, these speculative theories have yet to produce any compellingly experimentally verified predictions, unlike the celebratedly successful Standard Model.

Bosonic and fermionic statistics are expressions of indistinguishable particles. If particles were, even in principle, distinguishable, there wouldn't be bosons/fermions. Many experimental consequences follow from this. If I have more time a little later, I'll type up a longer explanation. But now the ALCS is on.
-Will

ALCS?

Anyway, what about the virtual zoo of bosons? These gluons are always created and annihilated (and make up much of the proton's mass if I remember right). Saying that 2 protons are indistinguishable means that the statistical average of the the virtual gluons is the same or that they ALWAYS have the same number of virtual particles?

The American League championship series. Baseball.

Anyway, given two protons, you want to distinguish them by measuring the virtual gluon content. However, the virtual gluon content is not fixed, in fact the quark number isn't fixed either. These things are thought to fluctuate wildly. Hence, if you are shown a proton that has three virtual quarks, and then a proton with, say, no virtual quarks, you can't be sure if its the same, or another proton.

Anyway, as to bosons and fermions by definition being indistinguishable. If two particles are indistinguishable (even in principle) then this creates a requirement- the probabilities in a given physical system cannot change by switching these two particles. Since the probability is related to the wavefunction squared, this means that the wave function can (at most) pick up an arbitrary phase after switching the particles.

In 3 dimensions, we can further notice that switching two particles, and the inverse operator (switching two particles back) are the same. This means that we can restrict our phase to either +1 or -1. There are two ways to build this type of 2 particle wavefunction



Here switching particles amounts to switching the 1 and 2 labels on psi, and we get +1. These are bosons, and this is the defining characteristic of bosons- symmetric under exchange.



Here switching the particles gets a negative sign- i.e. odd symmetry under exchange. These are fermions. Notice that for the fermions we can't put both particles in the same state, or the wavefunction becomes 0.

So, in 3d indistinguishable particles can either be bosons or fermions- even or odd symmetry. However, in 2d, where the switching and the "switching back" operator are not the same, we can develop any arbitrary phase. This leads to "any-ons" and so called "braid statistics."
-Will

edit: if further clarification on anything is needed, let me know.

thanks that cleared it up.

I hope Will's input has helped, especially if his first reply went noticed more than when I said the same thing i. e. it wouldn't be enough that we can't tell them apart; this could hardly determine their behaviour, especially concerning such a fundamental thing as the whole of chemistry, could it? I hope Will's second reply (after the ALCS) helps to also show there's not much sense in which to speak of some quantum numbers being "exempt from the exclusion principle". A further remark: the very fact that you say both:and:in the same sentence should vaguely suggest that being a matter of the state of the proton for a given DIS event. Of course the description is quantum anyway so, even if the state of protons could be prepared just before each event, you'd still have a statistical distribution of outcomes. Now it may seem intuitively odd that composite bodies undergo these same implications, as their constituent parts, but the question can be broken down into a long argument which fails for bodies having differing counts of atoms and molecules and even more if they are solid and thus may differ by a much more persistent state, not to mention matters of decoherence.

BTW, the swarm of hadronic matter consists not only of bosons but also of quarks and leptons and their antis.

I'm not aware of Dirac having been the first to say it and on these grounds; in any case it has long been considered as sure as QM itself. However, the positron was predicted by interpretation of the negative energy solutions to his equation and the nexus with time and charge reversal (PCT) is a slightly later consideration in field theory. It is however somewhat lax to say "the antiX is actually an X traveling backward in time"; a much more certain interpretation is according to the sacred tenets of causality. Replace the "back in time" with "from B o A instead of from A to B" and, in configuration visual, whether A is earlier or later than B tells you which is which. For external lines of a Feynmann diagram it's a simple matter of which ones are ingoing and outgoing.

Further, a fermion doesn't become an antifermion; in the frame of this same formalism the same boson-fermion vertex can represent both pair creation, pair anihilation, or emission or absorption of the boson by a fermion. It won't be the same fermion in the case of a weak boson in the sense that "it changes" from one type of fermion to another, but a neutral boson can't change it from electron to positron.

Which does not imply much about indistinguishability.