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It's possible that this question is too soft or even quite senseless for this forum, but I will ask nevertheless.

Everyday (macroscopic) things, like a grandfather's pendulum clock or the grandfather himself have age, which can be determined in several (not independent) ways:

1, testimony of birth - when a child is born or clock made, someone makes a dated record of this event and archives it. This is useless, however, if we are not sure that the examined person is identical with the recorded one (in other words that the birth record or identity card is his). Since electrons (or atoms) are indistinguishable particles, this method cannot be used.

2, signs of aging - as clock or man age, various irreversible changes accumulate, and it is possible at least estimate their age. We can measure state of electron or atom, but it doesn't make sense to speak of how long ago the state (like excitation) has been changed.

3, historical style period - pendulum clocks made in the 18th century look different from those made in 2013 (and there are no pendulum clocks made before Christiaan Huygens). Electron or atom created in glacial period or Triassic are the same as those created a while ago.

Does it make a sense to speak about age of electron or atom?

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No. It doesn't make sense to speak of the source either: – Brandon Enright May 4 '13 at 20:57

The fact that electrons are identical particles doesn't mean you can't separate one from another and keep track of which is which. They can be told apart according to their positions, energies, and momenta. Say I stick a $\beta^-$ source a foot away from a Geiger counter and I get a click. I know that the electron I detected was 1 ns old (c=1 ft/ns). This one was differentiated from the other nearby ones by its MeV energy.

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I see that our answers disagree on the last point. Perhaps you're right, there is some possibility of keeping track of an electron, but this can't be done for a "macroscopical" amount of time, i.e. for example you can't say how old is an electron of my body... – Bzazz May 4 '13 at 21:07
@Bzazz: I can trap an electron in a magnetic field for any desired length of time. The limitation is that if you get it mixed up with other electrons, you won't be able to keep track of which was which. – Ben Crowell May 4 '13 at 21:21
Exactly, an electron "alone in a room" is trackable, while in the matter it is not. – Bzazz May 4 '13 at 22:01

I suppose the key point for a good answer is to use the fact that, say, electrons are not only identical but also indistinguishable one from the other. This means that certainly points 2. and 3. of your post cannot be applied. It's intuitively plausible, instead, that one can track an electron, for example produced in a nuclear reaction, and follow it for some time. Then, since you know the reaction it was born in, you know its age. Unfortunately this is also not correct because of uncertainty principle: you can never know if the electron you have observed is the same as the one observed before because (very roughly speaking) after every measurement you lose track of it.

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