Double Slit Paradox: A Wave-Particle Mystery

[shlosmem]

Let's take a pair of particles A and B that are in a quantum entanglement state, and shoot them in different directions. Along the way, one of them will pass in the famous screen of the two slits, say B. According to the known experiment, if we put a detector in one of the slits, we will lose the wave feature of the particle.
Since both particles are quantum entanglement, one position can be deduced by measuring the other - therefore, the collapse of the wave of B will cause the collapse of A. If the time taken for A to reach a screen is shorter than the time taken for B to reach the detector, it will be found that the presence of the detector caused the collapse of the wave at A before the detector acted at all - ie a backward effect in time.
What's more interesting is what will happen if we will pass (a lot of) B's through a spiral path, so we can look at A's effect on the screen - a none wave pattern, and have the detector removed before the B's approaches the slit (and vice versa). What we will see on A's screen in that case? did we get a paradox?

 

[PeterDonis]

Since both particles are quantum entanglement, one position can be deduced by measuring the other

That depends on what particular properties of the particles are entangled. You have to specify that as part of the scenario. Is it the spins that are entangled? (That's the most common case in actual experiments.) Is it their momenta? Or something else?

Only if the particles' positions are entangled can measuring one's position tell you about the position of the other. But it's actually extremely difficult to have a state where the positions of two particles are entangled, that is useful for doing experiments.

the collapse of the wave of B will cause the collapse of A

If you view "collapse" as simply a mathematical procedure to be followed once you know the measurement results, that's fine.

But if you view "collapse" as a real process happening, then whether there is such a process depends on which interpretation of QM you adopt, and interpretation discussions belong in the interpretations forum. For discussions in this forum, we stick to the minimum necessary to use the math of QM, which means you cannot think of "collapse" as an actual process.

If the time taken for A to reach a screen is shorter than the time taken for B to reach the detector, it will be found that the presence of the detector caused the collapse of the wave at A before the detector acted at all - ie a backward effect in time.

This requires treating "collapse" as a real process, which, as above, is interpretation dependent and cannot be a basis for discussion in this forum.

What's more interesting is what will happen if we will pass (a lot of) B's through a spiral path, so we can look at A's effect on the screen - a none wave pattern, and have the detector removed before the B's approaches the slit (and vice versa).

I'm not sure what you're describing here. I would suggest finding an actual textbook or paper that describes the sort of experiment you are interested in, and giving that as a reference.

 

[DrChinese]

Let's take a pair of particles A and B that are in a quantum entanglement state, and shoot them in different directions. Along the way, one of them will pass in the famous screen of the two slits, say B. According to the known experiment, if we put a detector in one of the slits, we will lose the wave feature of the particle.

... did we get a paradox?

Just to add a detail to PeterDonis' excellent answer:

Entangled particles generally do NOT produce a typical double slit pattern. Therefore there is no paradox even before you get into the other important details. See Zeilinger's Figure 2, which exactly reproduces your scenario.

https://pdfs.semanticscholar.org/3644/6f15507880c629e06391adf9d21aa6d76015.pdf

"Because of the perfect correlation between the two particles, particle 2 can serve to find out which slit particle 1 passed and therefore no interference pattern arises."

 

[vanhees71]

It is fully impossible to answer the question without specifying precisely (a) the state in which the particles are a prepared and (b) the setup of the entire experiment and (c) what's meausured on each of the two particles. One lesson QT teaches us is exacty this: You need to carefully specify all this to make sensible descriptions of Nature. As soon as you do that and you stick to the physics alone (as @PeterDonis told you above, the question whether there's a collapse or not is not part of physics but part of interepretations of QT). Here we discuss only, what's observed given a precise description of points (a)-(c). Before this is not given, it's not possible to discuss anything in a sensinble way. The (not quite legal) link to the RMP article by Zeilinger in the previous posting is excellent. One should however not quote a single sentence out of that without the context involving the points (a)-(c) above. Zeilinger's paper has the advantage that it always provides this minimal requirement for being able to sensible talk about anything in (quantum) physics!

 

[shlosmem]

DrChinese Thank you for your great answer. I will try to read the article. Meanwhile, I will appreciate it if you can tell a bit more about the fact you mentioned.

"Because of the perfect correlation between the two particles, particle 2 can serve to find out which slit particle 1 passed and therefore no interference pattern arises."

Does it mean that there will be no interference pattern even if the two particles are not measured but both pass similarly through (a different) double-slit screen?

 

[DrChinese]

Does it mean that there will be no interference pattern even if the two particles are not measured but both pass similarly through (a different) double-slit screen?

For the setup you are suggesting*: Yes. They will show no interference pattern.

The way to get an interference pattern is to perform additional processing on the photon so that the entanglement ceases. Of course that defeats your objective.

*This is assuming a setup where you have 2 entangled photons emerging from a PDC crystal. Each photon is sent to a double slit setup. Those photons will not be coherent in the usual sense necessary for creating an interference pattern.

Please keep in mind that what PeterDonis and vanhees71 say is correct as well. Their explanation goes deeper than mine, but I think my example more closely matches what you are zeroing in on. Basically: whenever you think you can beat nature with some paradox, a neat little "gotcha" appears. And that happens in your case, as I understand what you are thinking.

 

[DaveC426913]

:stepping my layperson's toe cautiously into this:
You don't get an interference pattern with a single particle (or particle pair in this case.)
You'd need to generate multiple entangled particles to establish a pattern.

* see standing caveat, in sig

 

[DrChinese]

You don't get an interference pattern with a single particle (or particle pair in this case.) You'd need to generate multiple entangled particles to establish a pattern.

I am referring to a stream of many photons, as per a usual double slit setup.

You may recall that for light - in double slit setups - there is usually a single slit that the photons go through before getting to the double slits. It's usually just a detail, but the comment is that this single slit is needed to insure that the light is coherent. If that is inserted into the OP's entangled setup, then the entanglement is essentially broken at that point. You may THEN get double slit interference, but that would be different than Zeilinger's diagram in the reference (which has no such single slit). Of course, then you would not have any correlation between which slit on one side and which slit on the other. Which again defeats the OP's idea.

Reminding everyone that the details of any quantum setup are all important as PeterDonis and vanhees71 point out. When you start talking about coherence and entangled photons, it can get very complex very quickly.

 

[shlosmem]

For the setup you are suggesting*: Yes. They will show no interference pattern.

And all without having a way to measure through which slit the photons went through.
Wow! It goes against everything I've known so far about quantum behavior.

 

[DrChinese]

And all without having a way to measure through which slit the photons went through.Wow! It goes against everything I've known so far about quantum behavior.

Consider that a typical source of entangled photons is via PDC (parametric down conversion).

In basic terms: A laser stream of photons goes in, and almost all come straight out the other side. A few of the photons are converted into entangled pairs within the crystal, and exit in a slightly different direction (about 2 degrees off from the main stream of unconverted photons coming out. These pairs are collected and used as the source for the experiment (the unconverted ones being ignored).

Because the entangled pairs originate in the crystal, their EXACT source point (where the one photon is broken into two entangled photons) can be considered "blurred". Or uncertain. Or whatever you want to call it. Regardless, those photons are not COHERENT in the same sense that the unconverted photons are. As a result, they don't produce an interference pattern after going through a double slit. For them to produce such an interference pattern, they must first go through a single slit. When that happens, the key entanglement is broken.

 

[shlosmem]

Consider that a typical source of entangled photons is via PDC (parametric down conversion).
...
Regardless, those photons are not COHERENT in the same sense that the unconverted photons are.

Your words are implied that the reason for the lack of an interference pattern is due to the technical nature of the way in which the entanglement is usually produced, but you refrain from establishing more generally that the theory states that any entanglement will brake the interference pattern.

 

[vanhees71]

It's always good to look at real experiments:

https://arxiv.org/abs/quant-ph/9903047

Obviously the biphotons from PDC are coherent enough to create an interference pattern which can be destroyed by obtaining which-way information in the double-slit experiment but also again be "erased" by postselection appropriate subensembles.

 

[DrChinese]

It's always good to look at real experiments:

https://arxiv.org/abs/quant-ph/9903047

Obviously the biphotons from PDC are coherent enough to create an interference pattern which can be destroyed by obtaining which-way information in the double-slit experiment but also again be "erased" by postselection appropriate subensembles.

Naturally, a different setup altogether than a typical setup that Zeilinger or the OP intended. Those had no coincidence counting.

 

[Cthugha]

It's always good to look at real experiments:

https://arxiv.org/abs/quant-ph/9903047

Obviously the biphotons from PDC are coherent enough to create an interference pattern which can be destroyed by obtaining which-way information in the double-slit experiment but also again be "erased" by postselection appropriate subensembles.

That is a very difficult topic as one can get the terminology mixed up and most laymen are not aware of what coherence actually means in this context. When I try to introduce this kind of quantum eraser to my students in lectures, I use the following line of reasoning: The "standard" coherence observed in a double slit is simple first-order spatial coherence. This is not a property of the light source only, but also of the experimental geometry and what has been done to the light field. It is very simple to increase this degree of coherence for any light field. You just need to filter it spatially using a pinhole. This is a simple experiment that may be performed at home. Use a spatially extended pretty bright light source on a homemade double slit and you will not find any interference pattern behind it. Filter it using a pinhole (or just place the source further away from the double slit) and the interference pattern will appear.

In that respect entangled biphotons are indeed not coherent enough to create an interference pattern. The whole magic about this kind of quantum eraser experiments is based on the simple fact that entanglement (figuratively speaking) makes it possible to shift the position of the pinhole in the example given above. One may now investigate the interference pattern of one part of the photon pair, while using the pinhole for spatial filtering on the other part of the photon pair. However, obviously this works only for the subset photons which actually passes through the pinhole, which is why coincidence counting is necessary.To the OP: If you are interested in the technical details, the issue of coherence in one property of a light field and entanglement in the complementary property and why it is not possible to have both has been discussed a while ago in a series of papers by Saleh and Teich, e.g. these (but there are more):
https://journals.aps.org/pra/abstract/10.1103/PhysRevA.62.043816
https://journals.aps.org/pra/abstract/10.1103/PhysRevA.63.063803