Maybe this would be better suited for philosphy.se, if so, then let me know and i'll move it, but this seemed like a reasonable place to start.

Let's start with my motivations for asking such a bizarre question. I was watching a river flowing some years back when I started considering the individual water molecules that made up this river and where these particles would end up (in this case lake superior, and then eventually the ocean). So I had this idea, this river had a bunch of hydrogen atoms and a bunch of oxygen atoms, but each one of these particles was it's own particle. That is: each atom is surely its self and not another atom, and so I would say that each particle is unique. However, they're not, or are they? Each hydrogen atom is exactly the same(?), it has 1 proton and 1 electron. So fundamentally, two particles are exactly the same, yet they are unique. How do i remedy this paradox?

One answer I have thought of is this, sure each hydrogen is a proton and an electron, but two hydrogen atoms have different protons and electrons (they don't share the same proton or electron). So I would say the two hydrogen atoms are different. While they each have an electron and a proton, they are different electrons and protons and so the hydrogen atoms are different and not unique. but what if we go smaller?

Are there any differences between two separate electrons? These are fundamental particles, they consist only of themselves. So what is the fundamental difference between two separate electrons? If I lose my favorite electron when I vacation in florida, and then i try and find that electron later will i ever be able to tell which was my electron?

Is the only difference between two fundamental particles their location and momentum? Is there no way to keep track of a particle and know with certainty which, in a sea of particles, is the particle we're keeping track of?


Statistical mechanics of fluids and gases has been developed to account for situations where there are many individual particles which can not be individually traced. I think the philosophical basis for statistical analysis is that one deals with separate particles, each having an element of randomness in their trajectories due to unknown past histories and quantum fluctuations.

However, another way of looking at this is the "one-electron universe". Richard Feynman received a phone call one day in 1940 from John Wheeler, who postulated that "all electrons and positrons are actually manifestations of a single entity moving backwards and forwards in time." See Wikipedia article: http://en.wikipedia.org/wiki/One-electron_universe.

Also, see the Wikipedia article on identical particles: http://en.wikipedia.org/wiki/Identical_particles

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  • $\begingroup$ Cool! Thank you for the resources, I'll look into these. I think i've heard that Feynman story before... powerful stuff. $\endgroup$ – Paddling Ghost Apr 16 '15 at 21:53

Indeed, every fundamental particle is precisely the same. I think Griffiths quantum book is the one that uses the evocative phrasing "not even God can tell them apart".

This is not just philosophy, it actually has important consequences. When we do many-body physics and thermodynamics, we often talk about the total number of states of the system. For instance, if I had three distinguishable atoms--red, blue, and green, and I had to put them in order, I could organize them in (Red, blue, green) or in (Red, green, blue), etc. There are six ways to do this. But if my system had two red atoms and one green atom--if two of them were indistinguishable. Then I only have three options, corresponding to the placement of the green atom. And if all three atoms are red, I only have one possible configuration. Since the number of possible configurations becomes important when we discuss entropy, this enters into physical quantities. This occurs in classical mechanics, but it's a bit of a fudge ("Gibbs factor").

In quantum mechanics, it gets even more interesting, since there are some particles (bosons) where identical particles can share a state, and others (fermions) where they cannot. These two types of particles behave very differently at low temperatures, because the kind of configuration-counting I did earlier goes very differently depending on whether I can put more than one atom in each slot, so to speak.

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  • $\begingroup$ Very interesting. That quote is disturbing to me. "Not even God can tell them apart." ahhhhhhh. Why does this disturb me so? regardless, thanks for your answer. It defnietly shed some light on the issue. $\endgroup$ – Paddling Ghost Apr 16 '15 at 21:55

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