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Wikipedia says:

Quantum superposition is a fundamental principle of quantum mechanics that holds that a physical system—such as an electron—exists partly in all its particular, theoretically possible states (or, configuration of its properties) simultaneously;[...]

What interests me is what happens when location is the state that is superposed. If an electron exists in two locations at once, as a result of quantum superposition, does that mean that the mass of the universe has increased so long as the superposition exists?

So in other words, does it follow that effectively two electrons exist during superposition? Why or why not?

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No, the electron is just one. You just have an indetermination on its position. About the metaphysical implications, this is not physics, as the word says. –  Bzazz Jan 22 '13 at 17:38
    
He isn't actually asking any metaphysical question here, although there are metaphysical questions that one might ask about superpositions generally (and not just ones in position or momentum space). –  Niel de Beaudrap Jan 22 '13 at 17:40

4 Answers 4

up vote 1 down vote accepted

In QM you have only the one electron, but according to the Copenhagen interpretation (which is positivist) we can only know what we measure, and we may not measure position/momentum with equal precision as they are complementary. This is usually interpreted popularly that there is indeterminancy of position or the wave nature of the particle. The first cannot be quite right as one expects Heisenbergs uncertainty principle to hold even if measurements are not taking place, and neither is the second - it is neither particle nor wave, as traditionally envisaged, but something else entirely.

In QFT, we no longer have an electon, but an electron field. The excitations of this field represent electrons in different positions. But in a sense the excitations could be said to exist globally in the field.

According to Heisenbergs uncertainty principle you can have variation in mass/energy with respect to time. So yes, the energy does vary, but there is still a conservation law of some kind.

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It is better to say that there are two sources of one electron. You can find it here OR there when there are two sources (two slits, for example).

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In the Schrödinger picture one can see that the wave-function $\psi(t)$ remains normalized under the action of the time evolution operator, and since the probability of finding an electron is $$P(t) = \int_\text{All space}\mathrm{d}V \, \psi^*(t)\psi(t) = 1$$ there is always exactly one electron.

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According to QFT all electrons in the universe are the same electron in superposition do to the electron moving thru the time parameter like another special dimension, "but to broaden this scope" no particles exist at all (just field quanta).

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How would this explain the self-interference pattern of the double-slit experiment? Your description sounds a bit like a path-integral approach except that you only have a particle in one place at a time. –  Brandon Enright Feb 3 at 6:23

protected by Qmechanic Feb 4 at 8:48

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