# Logical dilemma in Greene's The Fabric of the Cosmos?

1. Jan 3, 2010

### wmccrack

First, I'm afraid my description is going to be unavoidably lengthy, but I think need to explain my problem fully in order to hope for an answer that explains my dilemma properly. So if someone can follow it through to the end I'd appreciate the input.

I'm pretty sure I have understood most everything up to the experiment discussed in Fig 7.5b (Time and the Quantum - Shaping the Past) but it appears that there is a logical discrepancy in Greene's description of this experiment. More likely there is a way of looking at it that I have not thought of.

Background:
This "delayed-choice" experiment uses two "down-converters", one in each of the two pathways of a double slit experiment. Each down-converter takes a photon that has passed through one of the slits as input, and produces two half-energy photons as output, a "signal" photon that follows the path that the original input photon would have followed, and the other "idler" photon which follows a different path where it can be detected (or not as we shall see). Detection of an idler photon from one of the down-converters will of course determine that an input photon was present in that particular path and consequently determine which slit the photon went through.

In this experiment however an additional embellishment is a series of beam splitters that are used in a manner so that only 50% of the produced idler photons is detected in a manner that unambiguously indicates which path the original input photon took (which slit), and the other 50% is detected in a manner that makes it impossible to determine the original input photon's path (i.e. the "which-path" information is effectively erased).

Finally in Greene`s "thought experiment" version of this experiment, the beam splitters are moved a long way away (10 light-years in Greene's fanciful example). So that the beam splitters only operate 10 years after the original experiment is completed, and therefore the 50% erasure of information of "which-path" information occurs 10 years after the data is collected regarding the pattern of signal photons hitting the detector screen.

According to Greene, the screen's detected pattern will "show not the slightest hint of an interference pattern". But if you come back to the data 10 years later, after you know which photons have had their "which-path" information erased, and look at what happened to that subset of all of the photons, you will find that those photons form an interference pattern.

Now for the dilemma:
If, as described by Greene, all of the photons collectively formed a smooth pattern (according to calculable probabilities for where the photons will be detected on the screen), but the above 50% subset formed an interference pattern (where the "which-path" was erased), the remaining 50% (the ones where the path is still known) would have to no longer form a smooth pattern (i.e. there would be "holes" in the data where the first 50% was removed).

The problem then is that where one would expect a smooth distribution behind each slit for those photons where the path information was measured, but according to my analysis it is not smooth as expected.

If anyone has gotten this far and has an answer I then I thank you for your perseverance!!

Wayne McCracken