Entanglement, Measurements, and Interactions

[JasonWuzHear]

Hello, I'm trying to better understand entanglement in the context of measurements and interactions.

(1.) Are uncertainty and entanglement linked together? Are the eigenstates of an observable entangled since a measurement of one of them collapses the wavefunction to a single eigenstate, making all the coefficients of the other eigenstates 0?(2.) Consider a very sensitive measuring tool that measures the spin of one of two spin-entangled electrons (their total momentum is 0). Is the entanglement of one of the electrons then transferred to the measuring device (now the measuring device is entangled with the other electron) assuming the wavefunction does not collapse yet?(3.) In general, is the entanglement transferred until the wavefunction collapses? Does the wavefunction collapsing transform/transfer any uncertainty?(4.) Is it possible to create a device that can measure states of a particle based on gravitational interactions? Assuming all particles make a measurement when they interact, what keeps massive particles from continuously collapsing from continuously interacting with other massive particles, also assuming gravity is continuous? With other forces assuming they're continuously interacting?

My thoughts: Interactions do not necessarily cause wavefunction collapse. In the case that they do not, there is some form of entanglement transfer.

Thanks!

 

[Nugatory]

My thoughts: Interactions do not necessarily cause wavefunction collapse. In the case that they do not, there is some form of entanglement transfer.

That's a fair summary, and it identifies one of the awkwardnesses of collapse interpretations: just why is it that sometimes we get collapse and sometimes we just get entanglement between the participants in an interaction? This is basically the concern that led Schrodinger to pose his famous cat/cyanide/box thought experiment - he wasn't seriously suggesting that the cat was entangled with the radioactive sample and both alive and dead until we opened the box, he was pointing out that quantum mechanics didn't clearly say that the cat would be either alive or dead even before we looked.

Google for "quantum decoherence" and search this forum for a more modern take on the subject.