Does the passage of time effect a photons entanglement with another?

Question

I recently read an article about "Delayed-choice entanglement swapping". Here is an excerpt from the article:

Delayed-choice entanglement swapping consists of the following steps. (I use the same names for the fictional experimenters as in the paper for convenience, but note that they represent acts of measurement, not literal people.)

1. Two independent sources (labeled I and II) produce pairs photons such that their polarization states are entangled. One photon from I goes to Alice, while one photon from II is sent to Bob. The second photon from each source goes to Victor. (I'm not sure why the third party is named "Victor".)

2. Alice and Bob independently perform polarization measurements; no communication passes between them during the experiment—they set the orientation of their polarization filters without knowing what the other is doing.

3. At some time after Alice and Bob perform their measurements, Victor makes a choice (the "delayed choice" in the name). He either allows his two photons from I and II to travel on without doing anything, or he combines them so that their polarization states are entangled. A final measurement determines the polarization state of those two photons.

The results of all four measurements are then compared. If Victor did not entangle his two photons, the photons received by Alice and Bob are uncorrelated with each other: the outcome of their measurements are consistent with random chance. (This is the "entanglement swapping" portion of the name.) If Victor entangled the photons, then Alice and Bob's photons have correlated polarizations—even though they were not part of the same system and never interacted.

Question: Does the passage of time (from our perspective) really matter? Each photon itself is traveling at the speed of light, which I believe should make time have very little, if any, affect on it. I would think that measuring a photon at X time and Y time from our perspective would be the same exact time from the photons perspective. Therefore, wouldn't it make sense that "modifying" a photon at Y time would have an affect on a measurement taken at X time? After all, it would seem as if we are looking at the same exact photon...

   0   <-- same time from the photons perspective
  / \
 X   Y <-- different times from our perspective

Answer 1

Please believe me that if the experiment were done not with two pairs of entangled photons, but with two pairs of entangled electrons, the results were similar, except that the wave-function of two entangled fermions is antisymmetrical instead of symmetrical. So, the light velocity plays no role here.

I recommend you look at the equation (2) in the article "Experimental delayed-choice entanglement swapping" in quant-ph/1203.4834,

http://arxiv.org/ftp/arxiv/papers/1203/1203.4834.pdf.

You see in this formula first of all that the polarization state of two photons can be expressed in the Bell-base, which contains four vectors, |Ψ+〉, |Ψ-〉, |Φ+〉, and |Φ-〉. Now, since we have two pairs of entangled photons, the authors of the article prove that the state of these four photons can be expressed as shows the equation (2).

From now on, everything is a trick. If Victor has some apparatus that allows the measurement of his two photons in the Bell-base, then he gets one of the four states I mentioned above. The 4-photon wave-function COLLAPSES on one of these states, and because of the entanglement between the four photons, the state of the pair Alice's photon and Bob's photon, also collapses on the corresponding state.

However, WITH measurement or WITHOUT measurement, we can represent Victor's photons in the Bell base. The measurement done by Victor only gives us the information which one of the 4 possibility we would obtain on the respective pair that came to him. Thus, we can compare with the result of Alice and Bob. If Victor doesn't do this measurement we can't compare, s.t. the results of Alice and Bob seem to us uncorrelated.

But there is one more thing, and fundamental. It makes no difference who measured first, Alice and Bob, or Victor. These entangled particles DON'T CARE about space and time. For them, the question which particle was MEASURED FIRST has no meaning, it is always as if they are measured simultaneously. They have a way to arrange that their answers, a way that escapes our understanding. To us, it seems as if they communicate by superluminal messages. But we cannot lay hand on such messages.

Again, these particles behave according to another type of world that our space-time world. It is for us to investigate and try to understand it.

Did I help with my explanations?

Sofia