# Energy conservation+superpositions=entanglement?

A particle in a quantum harmonic oscillator can be in a superposition of energy eigenstates, and so the energy is not well-defined. However, energy is still conserved, so if I understand it correctly the "uncertainty" in the superposition's energy must be matched by uncertainty elsewhere in the Universe. is this entanglement we're talking about here, or is there another explanation for how energy conservation works here?

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kith
A particle in a quantum harmonic oscillator can be in a superposition of energy eigenstates, and so the energy is not well-defined. However, energy is still conserved, so if I understand it correctly the "uncertainty" in the superposition's energy must be matched by uncertainty elsewhere in the Universe.
The uncertainty associated with a superposition state of a certain system isn't related to other systems in any way.

On the other hand, if you have two systems in an entangled state, you cannot assign definite state vectors to the individual systems in the first place. Look up the difference between "pure" and "mixed" states if you are interested in this.

or is there another explanation for how energy conservation works here?
If you don't have a definite energy, energy conservation refers to the expectation value of energy.

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The uncertainty associated with a superposition state of a certain system isn't related to other systems in any way.

On the other hand, if you have two systems in an entangled state, you cannot assign definite state vectors to the individual systems in the first place. Look up the difference between "pure" and "mixed" states if you are interested in this.

If you don't have a definite energy, energy conservation refers to the expectation value of energy.
OK. Collapsing the wavefunction can cause a dramatic change in the expectation value of the energy, though; how is that energy accounted for?

Thanks.

kith
OK. Collapsing the wavefunction can cause a dramatic change in the expectation value of the energy, though; how is that energy accounted for?
First of all, bringing your system into contact with a measurement apparatus makes it an open system, so its energy need not be conserved. Naturally, one would try to use a full description including the apparatus and see what happens there. But then, you unfortunately run into all the well-known problems of the foundations of QM.

Also that the expectation value changes dramatically when you perform a measurement happens already in classical statistical mechanics. I'm not saying that QM is completely analogous but if the state somehow encodes subjective information, this behaviour is not so surprising.

OK, I've got it I think. It reminded me of the classic entanglement problem where an atom emits two circularly-polarized photons in opposite directions: angular momentum conservation forces the two particles to have opposite polarizations. I think there's still an "entanglement" argument to be made in there somewhere, but I'll think about it some more. Thanks!

kith