Can Free Electrons in a Vacuum Become Entangled?

[idea2000]

Hi,

Can two free electrons in a vacuum become entangled as a result of a collision between the two? I have seen examples of electrons being entangled when bonded to atoms and in other circumstances, but not in this case. Can anybody shed some light on this topic? And, more generally, when can and when can't particles be entangled, according to quantum mechanics? Thanks in advance for any help provided! =)

 

[jfizzix]

Generally, if two particles can interact with one another, they can become entangled.
This is just as true for electrons repelling other electrons, as it is for electrons bonding with protons.

Theoretically, the only time two particles can never become entangled is if the Hamiltonian describing the two factors is just the sum of the Hamiltonians for each particle. In that case, each particle's wavefunction will evolve completely independently of the other, and their joint state will always remain separable.

Conversely, if there is a term in the Hamiltonian of a pair of particles that explicitly depends on both of them (like depending on both positions for the Coulomb interaction between two charged particles), the potential for entanglement is always there.

That being said, simply having interaction between two particles doesn't mean they have to become entangled. Depending on the particular interaction, it could be that the particles entangle and disentangle over and over again. Interaction is only what makes entanglement possible.

 

[idea2000]

Hi,

After two particles become entangled, what causes the wave function to collapse? I have heard detection or interaction causes the wave function to collapse, but, if that is the case, why don't the coulomb fields of the two original electrons cause the wave function to collapse? Thanks in advance for any help! =)

 

[jfizzix]

When two particles become entangled though a measurement interaction, the set of eigenstates of one observable of one particle ("the object") becomes correlated to a corresponding set of eigenstates of a corresponding observable of the other particle ("the measurement device").

What would count as a wavefunction collapse would be that as a result of the interaction, the statistics of the measurement device correspond to single eigenstates of the object.
This doesn't necessarily explain why we see single measurement outcomes when we look at the measurement device, but beyond this point, the philosophy is still being debated.
Some say that the wavefunction "collapse" we observe is a separate phenomenon (in something like a pilot wave interpretation), while others say that we should regard our memories as records of measurement devices correlated through our interaction with the outside world (in something like a many worlds interpretation).