# Entangled Electrons

What attribute would help determine in a spaghetti of tangled-entangled electrons, which two are the respective entangled electron pairs, since obviously there is an attribute other than charge or spin which entangles them..

As the charges are separated, a field force is presumably created between them.

There's also the communication of 'spin attributes' between distanced entangled electrons, might this be related to a fluctuation in the lines of force (whether magnetic or dielectric)?

This may be unanswerable, since manipulating instantaneous transmission signals as vibrations in lines of force between entangled electrons would be worthy of a Nobel, and I expect no Nobelists here, just thinkers.. Plus, we may not have measurements of I'm asking about.

You seem to think of entanglement as a property of individual particles. That is not true:

Let $\mathcal{H}$ be the Hilbert space of states of a single particle (electron, photon, whatever, doesn't matter). Then the space of states of two particles is given by the tensor product $\mathcal{H}\otimes\mathcal{H}$, and the space of states of $N$ particles is given by $\bigotimes_{i = 1}^N \mathcal{H}$. A state $\lvert \psi \rangle \in \bigotimes_{i = 1}^N \mathcal{H}$ is called entangled if it cannot be written as the product of individual states, i.e. if there are no $\lvert \psi_i \rangle \in \mathcal{H}$ such that

$$\lvert \psi \rangle = \lvert \psi_1 \rangle \otimes \dots \otimes \lvert \psi_N \rangle$$

And that's it. This does not tell you anything about the state other than that there are no definite states of the single particles from which the entangled state would arise. In particular, there is no property of the individual particles that would imply entanglement, since entanglement precisely means that there are no well defined individual particle states in an entangled state.

There is also no communication happening in the naive sense. For a two-particle entangled state, $\lvert \psi \rangle = \lvert \psi_1^A \rangle \otimes \lvert \psi_2^A \rangle + \lvert \psi_1^B \rangle \otimes \lvert \psi_2^B \rangle$, a measurement of a single particle simply "collapses" the state into either $\lvert \psi_1^A \rangle \otimes \lvert \psi_2^A \rangle$ or $\lvert \psi_1^B \rangle \otimes \lvert \psi_2^B \rangle$. In a QM interpretation with collapse, this seems to require some sort of communication (though you'd be hard-pressed to even say how that "signal" could ever be transferred), but in non-collapse interpretations (e.g. Many Worlds), there is no need for communication in the naive sense, since the state simply evolves happily ever after, and we are now just also entangled with it.

But whatever interpretation you may or may not adhere to, there is nothing in the math requiring anything like an actual signal of any kind to be sent through the electric field or whatever.

• Wow this was great! You really know the detail necessary for me to ask clarification in lay terms; For instance, if their is no property to allow these like charges to attract, what then is their motive force for the duet entanglement? And the 'communication' I speak of is the bit of information i heard regarding a distanced 'formerly joined and entangled' electron which will reverse spin accordingly to the manipulation of the other.. – David Jul 30 '14 at 21:57
• I'm not sure what you mean by "motive force". For the second thing, the particles do not reverse spin. It is simply that their shared state is collapsed from the superposition of two states into a specific one through the measurement of one particle. There is no well-defined spin of either of them prior to measurement, and thus no reversal. – ACuriousMind Jul 30 '14 at 22:28