Entanglement with an Extinct photon?

A recent paper by Megidish et al suggests it is possible to create an entanglement with a photon that no longer exists! The paper, titled ‘Entanglement Between Photons that have Never Coexisted’ documents an experiment of entanglement-swapping between two pairs of photons (http://arxiv.org/pdf/1209.4191v1.pdf.)

Basically they created two entangled photons. Entanglement means that the two photons instantly affect each other even though they are separated by large distances. While spooky and difficult to explain, this is the accepted reality of physics. Then they allowed one photon to expire. Then they created another entangled pair (photons 3 and 4). Next they swapped the second photon into entanglement with photon 3, and released photon 4. They found that photon 4 was entangled with photon 1, even though the two had never existed at the same time. If this is true, then it raises all sorts of new weirdness for quantum mechanics.

The conclusion is that, ‘This is a manifestation of the non-locality of quantum mechanics … in time.’ The authors presented two explanations for their results, both involving temporal causality (but in different directions): (a) that ‘measuring the last photon affects the physical description of the first photon in the past, before it has even been measured. Thus, the ”spooky action” is steering the system’s past.’ And (b)  the measurement of the first photon is *immediately* steering the future physical description of the last photon. ‘ (emphasis added).  I don’t disagree with the experimental evidence, but I do think the authors have overly dramatised their findings and rushed their interpretations without thinking through all the explanations.

However there is a much simpler explanation that does not require retrospective temporal causality.

First, consider that a particle can have two states of some variable. That variable could be spin, polarisation, etc. (In this experiment they used polarisation.) Label those states BLACK and WHITE. Second, accept that entanglement involves two particles synchronising their states, and having the means to continue to maintain that synchronisation over large distances: this is the spooky part of entanglement. For the present purposes we don’t have to worry about exactly *how* that entanglement occurs, but merely accept that it does. Third,  accept that such synchronisation involves the entangled particles taking complementary states. (This does appear to be the case in the experiment, but it is not totally clear). In this experiment that would correspond to photon 1 taking BLACK, and photon 2 taking the WHITE state.

Then destroy photon 1. Thereafter create two new photons 3 and 4, and entangle them together in a complementary way. Since we are talking about states like polarisation, the absolute orientations will not necessarily be the same as the first pair: call them RED and GREEN for convenience.

Next, swap the entanglement so that 2 and 3 and entangled, and release photon 4. At this point we need a fourth assumption, that the state of photon 2 has been preserved and dominates the 3-4 pair. This is a reasonable interpretation of the experiment. Then, since photon 2 is WHITE, photon 3 adjusts from RED to become BLACK. Now we need a fifth assumption, that in the entanglement-swapping process the released photon 4 also has to transform to a complementary state, i.e. cannot stay GREEN. This is  a sensible assumption for conservation reasons. This means that photon 4 changes from GREEN to WHITE and exits the entanglement.

Now,  compare the first and last photons: photon 1 was BLACK and photon 4 is WHITE. So it is true, photon 1 has influenced the future state of photon 4, in the sense that 4 has become complementary to what 1 used to be.

Thus photon 4 is (inversely) correlated to photon 1, with photon 2 being the temporal carrier of the state.

Finally, note that correlation does not necessitate causality.

Therefore, there is no positive reason to accept the paper’s conclusion that entanglement can occur across time.

Update 16 Oct 2012

This experiment showed that photon 4 had properties complementary to what photon 1 used to have. So what? Some take this view that this constitutes entanglement. However entanglement is usually understood as a two-way effect, where EITHER particle can affect the other. Entanglement involves bi-lateral causality. In this case the effect is decidedly ONE-SIDED in both the object (photon 4) and direction of time. The paper makes no claim that photon 4 resurrects the dead photon 1. Nor is there any evidence provided that the future photon 4 influences the initial creation of photon 1.

The results cannot be interpreted as bi-lateral causality, and hence the observed effect is merely correlation rather than true entanglement.

Interpreting the results as superposition across time, is a position of belief not necessity.

 

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