# Energy delta of entanglement

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1. Feb 28, 2015

### Staff: Mentor

I feel like a ping pong ball on the question of whether or not total energy of a pair of electrons changes when they become entangled or disentangled.
1. I began with a mental model similar to electrons in orbitals. Emit a photon and drop into a lower energy state until reading the ground state. A pair of electrons unentangled, emit and drop to the triplet state, then emit again and fall to the singlet (ground) state.

2. In an earlier thread, CGK elegantly showed me how to write the Hamiltonian which does not include spin states, and the wavefuncitions which do include spin.

3. In Quantum Mechanics, lecture 8, Leonard Susskind said that although entangled, there is nothing Bob can do that changes Alice's density matrix. If there was energy associated with entanglement, then if Bob became disentangled, it would change Alice's density matrix.

(2) plus (3) convinced me that there can not be an energy change associated with enganglement/disentanglement.

4. In Quantum Mechanics, Lecture 9, Susskind discussed an example. He started with an unentangled state |ud> and said that it could be expressed as a linear superposition
|ud>= |singlet>+|triplet>. Then the pair could interact with a radiation field with states |0>=no photon, |1>=photon. Start with [|singlet>+|triplet>] ⊗ |0> which then evolves to |singlet | 0> + |singlet | 1> in which the triplet emits a photon and becomes a singlet.

That brings me full circle again, in which the energy of the photon emited by the triplet is an energy delta.
So, I can argue myself into both positions on this question, entanglement/disentanglement do [or do not] imply energy changes in the system. Help please!

But going back to cgk's Hamiltonian, if there is energy associated with entanglement, why is there not a term for it in the Hamiltonian?

2. Feb 28, 2015

### jfizzix

So you have a pair of particles in some triplet state.

After a time, the two particle state decays to the lower energy singlet state.

Whether or not the particles are entangled is incidental to the change of energy. You can entangle a pair of particles with no change in energy.

One example of this would be two atoms (elastically) bouncing off of each other (in a closed system) Because the atoms interact with each other, they become entangled.

3. Feb 28, 2015

### Staff: Mentor

You say that the singlet state is a lower energy than the triplet, but that neither the singlet nor triplet are necessarily lower energy than the product (unentangled) state. That sounds contradictory.

Why would the pair initially in a product state (unentangled) fall into either triplet or singlet unless those were lower energy states?

4. Feb 28, 2015

### jfizzix

I don't think it's so much falling as it is evolving. The triplet states all have angular momentum 1 and the same energy. Two of those states are separable, and one is entangled. Depending on what sort of forces are driving this system, it can evolve from a separable state to an entangled state and back again without changing energy.

5. Mar 1, 2015

### TrickyDicky

You have to distinguish between the entangled singlet case(2-dimensional HS) that has no energy associated to the entanglement and the case involving a triplet in wich entanglement may imply energy changes/interactions.