Are All Electrons Entangled with Each Other?

[metroplex021]

I have a couple of questions about entanglement and decoherence!

1. Sometimes you read that, strictly speaking, all electrons are entangled with one another. But can that be right?! Isn't it at least the case that electrons have to have interacted with one another in the past in order to be entangled?

2. I have been reading about how the environment can cause entanglement to disappear very quickly. Since molecules always occur in environments, doesn't that means that the
spin entanglement that exists between two electrons in an atomic bond will likewise be destroyed? But how then do we explain how the atoms in the molecule stay bonded?

Any thoughts much appreciated!

 

[mfb]

1. Sometimes you read that, strictly speaking, all electrons are entangled with one another.

Not in a relevant way.

But can that be right?! Isn't it at least the case that electrons have to have interacted with one another in the past in order to be entangled?

Well, they do interact, as all electrons are charged.

2. I have been reading about how the environment can cause entanglement to disappear very quickly. Since molecules always occur in environments

You can have an isolated molecule in a vacuum.

, doesn't that means that the
spin entanglement that exists between two electrons in an atomic bond will likewise be destroyed?

No, as long as there is no interaction with them (like incoming light of the right frequency, or collisions with other molecules, or whatever).

But how then do we explain how the atoms in the molecule stay bonded?

You don't need entanglement for that.

 

[Demystifier]

1. Sometimes you read that, strictly speaking, all electrons are entangled with one another. But can that be right?! Isn't it at least the case that electrons have to have interacted with one another in the past in order to be entangled?

All particles of the same kind (e.g. all electrons or all photons) must have symmetric (for bosons) or antisymmetric (for fermions) wave function. This means that all particles of the same kind are entangled. This kind of entanglement does not require interaction, but usually does not have observational consequences.

2. I have been reading about how the environment can cause entanglement to disappear very quickly. Since molecules always occur in environments, doesn't that means that the
spin entanglement that exists between two electrons in an atomic bond will likewise be destroyed? But how then do we explain how the atoms in the molecule stay bonded?

First, decoherence of object by interaction with environment is quick when the the object is big. An atom is not big, so decoherence of atom is not so quick.

Second, not all coherent properties are destroyed by environment. It depends on the exact nature of interaction with the environment. For example, all interactions with environment are local in the position space, so atom will usually be found at a definite position (not in a superposition of different positions). But most interactions are not sensitive to the spin of the particle, so interaction usually does not destroy the spin-coherence.