Entangled Photon Pairs

Most recent answer: 03/24/2012

Q:
Why is an entangled pair of polarized photons a good experimental proxy for an entangled pair of spin one half fermions? According to wikipedia, this is so because the Maxwell electric field intensity E squared is a good proxy for the Born probability psi squared. But the conserved intensity is E squared minus B squared, which may not be positive.
- Sammy (age 26)
Aix En Provence, France
A:
The angular momentum states of the entangled photon pairs are exactly analogous to those of the entangled spin-1/2 particles. The polarization properties of photons are two-state systems, as are the spin-1/2 states. In particular the map horizontal photon-> spin down, vertical photon-> spin up determines the full analogy, since all other states can be formed from linear combinations of these two-state bases. So any experiment describing spin measurements on the spin-1/2 pair translates exactly into a polarization measurement on the photon pair.

Discussion of the classical fields is just a distraction here. Although it's not relevant, I have no idea what the E2-B2 comment is supposed to be about, since the energy density goes (in good units) as E2+B2.

Mike W.



(published on 03/24/2012)

Follow-Up #1: invariants and conserved quantities

Q:
Mike W: thanks for your answer about ENTANGLED PHOTONS AND ENTANGLED ELECTRONS According to wikipedia http://en.wikipedia.org/wiki/Electromagnetic_tensor the scalar Lorentz invariant F squared is E squared minus B squared in units where c is unity. If one combines this in the standard Lorentz invariant measure one gets the only invariant candidate for the Born density on three dimensional space, but the candidate is not positive definite. Sammy
- Sammy (age 26)
Aix -en-Provence
A:
Sammy- Lorentz invariants and conserved quantities are not the same. For example, energy E and momentum p are conserved, but are not Lorentz invariants.

Mike W.

(published on 03/26/2012)

Follow-Up #2: entangled photon fields

Q:
ENTANGLED PHOTONS and ENTANGLED ELECTRONS Dear Mike W: I did not ask my question well. I already knew everything you wrote about polarization and spin. I wish to know what people mean when they write that psi is a photon wavefunction. I do not think they mean the photon quantum field when they are writing on entanglement. thank you Sammy
- Sammy (age 26)
Aix en Provence
A:
Sammy- I think that in the entanglement experiments, e.g. the ones violating the Bell Inequalities, the photon quantum field is just what's involved. The classical fields are not adequate. After all, the state near one detector is nearly an eigenstate of the photon number operator, with eigenvalue one. The expectation values for the classical E and B fields are exactly zero in any eigenstate of the photon number. So clearly the information about what's going on is not in those classical values.

Mike W.

(published on 03/27/2012)