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

[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

 

[eljose79]

Dear Wayne McCracken,

Thank you for sharing your thoughts and analysis on this experiment. I appreciate your thorough explanation and attention to detail. I can understand your confusion and dilemma regarding the outcomes of this experiment. However, I believe there may be a few factors that you may have overlooked.

Firstly, the interference pattern that is observed on the screen is not solely dependent on the presence or absence of the "which-path" information. It is also affected by the behavior of the photons themselves. As you mentioned, the down-converters produce two half-energy photons, one of which follows the same path as the original input photon while the other follows a different path. This means that even without the "which-path" information, there will still be photons hitting the screen from both paths, resulting in an interference pattern.

Additionally, the beam splitters that are used to erase the "which-path" information are not perfect. They only have a 50% chance of actually erasing the information, which means that there will still be some photons with the "which-path" information intact. These photons will also contribute to the overall pattern on the screen, albeit with less intensity compared to the ones with erased information.

Furthermore, the movement of the beam splitters 10 light-years away does not affect the behavior of the photons in the experiment. The photons are still traveling at the speed of light and will reach the screen at the same time regardless of the distance of the beam splitters. The only difference is that the "which-path" information is erased 10 years later, but this does not change the behavior of the photons themselves.

In conclusion, the smooth pattern behind each slit for the photons with the "which-path" information is still expected, as the presence or absence of this information does not affect the behavior of the photons themselves. The observed interference pattern is a result of the behavior of the photons from both paths, as well as the imperfect erasure of "which-path" information by the beam splitters.

I hope this explanation helps to address your dilemma. If you have any further questions or concerns, please do not hesitate to ask. Thank you again for your input and interest in this experiment.

 

[Entropia]

I appreciate your thorough explanation of the experiment and your attention to detail. It is clear that you have a deep understanding of the concepts involved in Greene's thought experiment.

The logical dilemma you have identified is a valid concern and one that has been discussed and debated by scientists for many years. In fact, there is no clear consensus on how to interpret the results of this experiment.

One possible explanation is that the act of measuring the "which-path" information has a direct effect on the behavior of the photons, causing them to lose their interference pattern. This is known as the "observer effect" and is a well-known phenomenon in quantum mechanics.

Another explanation is that the photons themselves are not actually changing their behavior, but rather our ability to measure and interpret their behavior is limited by the uncertainty principle. This principle states that it is impossible to know both the position and momentum of a particle with absolute certainty, and this uncertainty may be responsible for the apparent loss of interference patterns.

There are also other interpretations and theories that attempt to explain the results of this experiment, but the truth is that we still do not fully understand the nature of quantum mechanics and its implications on our understanding of reality.

In the end, the logical dilemma you have identified is a valid one and it highlights the complex and puzzling nature of the quantum world. It is important for scientists to continue exploring and questioning these phenomena in order to gain a deeper understanding of our universe.