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In Wikipedia it is mentioned that position and momentum can be entangled as well as spin and polarization etc. I assume etc. is charge etc. I understand how if you measure spin up on one of a pair you get spin down on the second of the pair.

What happens to the other particle in an entangled pair if I measure the momentum, position or charge of one of the particles?

Is there a momentum up and down or charge up and down analog?

http://en.wikipedia.org/wiki/Quantum_entanglement

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Momentum conservation holds also for quantum mechanics. Energy and momentum conservation are used in studying elementary particle interactions continuously.

In a two body reaction the momenta are correlated, but unknown before measurement. After measuring the momentum of one of the particles, if the masses are known, one knows the momentum of the one that was not measured/observed using momentum conservation.

A prime example was the discovery of the neutrino, which was discovered by imposing energy and momentum conservation on the reaction. Within the accuracies of the experiments the neutrino mass was of order zero, though later, neutrino oscillations showed that neutrinos have a small mass, currently given by upper limits.

By the way, "entanglement" is a fancy way of talking of correlations, and is misleading, since there is nothing mysterious about conserving momentum energy and quantum numbers.

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  • $\begingroup$ Does that mean it's not the same type of entanglement? $\endgroup$
    – Jitter
    Commented Nov 12, 2013 at 6:36
  • $\begingroup$ Just to be specific, if I have an entangled electron pair and I measure the momentum of one electron will it always be equal to the other electron or can it vary? $\endgroup$
    – Jitter
    Commented Nov 12, 2013 at 6:53
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    $\begingroup$ @LukeHutchison If you accelerate you introduce a new interaction , which means a new wavefunction and the entanglement is broken. If it is a two body decay , for example a pi0 into two photons, and they leave the interaction point with a momentum, the gammas are entangled. If the pi0 four vector is known, then measuring one gamma no matter how far away, from the interaction point, the momentum of the other far away one is known with the accuracy of the experimental measurements of energy and momentum. $\endgroup$
    – anna v
    Commented Apr 28, 2019 at 6:07
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    $\begingroup$ That is why continuous variables are not useful for qubits or whatnots, and one prefers measuring the spins, for example. Measuring the spin of one gamma gives the spin of the other ( the pi0 has spin zero) because they are entangled in the same wavefunction., but it is a yes or no measurement, where experimental errors have a much smaller effect. $\endgroup$
    – anna v
    Commented Apr 28, 2019 at 6:07
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    $\begingroup$ @LukeHutchison Not massless, they can have mass, but they must not accelerate, because accelerataion means a new interaction adding energy. In general if all the four momenta of all the input and output particles are know they will be known until they interact. Two body states can be used for information purposes for entanglement, but momenta, since they are continuous and form probability distributions of their four vectors according to the qm solution, are not useful for information processes. spins are because there is a countable state of how a spin is oriented versus the motion. $\endgroup$
    – anna v
    Commented Apr 29, 2019 at 10:50

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