Atom identity

[Erasmus00]

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 [math] e^{i\phi}[/math] 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

 

[math] \Psi = \psi_1(x_1)\psi_2(x_2)+\psi_1(x_2)\psi_2(x_1) [/math]

 

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.

 

[math] \Psi = \psi_1(x_1)\psi_2(x_2)-\psi_1(x_2)\psi_2(x_1) [/math]

 

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.

[sanctus]

thanks that cleared it up.

[Qfwfq]

Qfwfq, could you explain this in more detail, or link us to some document that does?......

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:

These experiments suggest that not only are individual protons different from one another,

and:

but the same proton differs from moment to moment from itself

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 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 ([math]e^+[/math], 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.

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.

 

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.

Which does not imply much about indistinguishability.

[Little Bang]

Craig, so I guess in your mind the standard model adequately explains the electron and proton? In my opinion if we ever explain the electron proton pair it will not be as particles.

[Qfwfq]

In my opinion if we ever explain the electron proton pair it will not be as particles.

Indeed that isn't the adequate explanation. Fields or billiard balls? Neither fish nor fowl.