This entry is about a question I have about the delayed choice quantum eraser. It follows the description given in Brian Greene, The Fabric of the Cosmos, Ch 7. around p196.
In figure 1 a photon source (e.g. a laser) shoots out a beam of monochromatic photons which are divided into two beams by the beam splitter, a half-silvered mirror. The two beams strike the screen which is, say, a piece of film that records each photon strike as a white dot on black. The beams strike from two angles so the peaks and troughs in their waves interfere, producing alternating light and dark bands on the screen.
Even if the laser is set to shoot one photon at a time, the quantum mechanical probability wave of that single photon goes along both paths and interferes with itself.
In figure 2 we stick in some detectors. If either detector is turned on, it will tell us if the photon went down that path. No longer is there a probability of both paths and there is no interference pattern recorded on the screen.
In figure 3 we insert "down converters" into each path. A down converter takes in a photon and spits out two entangled photons of about 1/2 the energy (frequency). We send the "signal" photon on to the screen. We could look at the location of the idler photon to see which path the signal photon took. But for now we send the idler photon to a device called a quantum eraser. The half silvered mirror "M" makes it impossible for detectors C and D to tell if the idler came in on path 1 or 2 and so impossible to tell which path the signal photon followed, "which-path" information is "erased", so we expect an interference pattern on the screen. This has been shown experimentally.
In figure 4 we stick in detectors along paths 1 and 2. If either is turned on, we can tell which path the idler photon took, and therefore which path the signal photon took, and therefore the interference pattern should disappear.
In figure 5 we note that we don't need the extra detectors A and B. By removing the eraser mirror (compare to figure 4) the paths 1 and 2 go straight across into detectors C and D, we can tell which path the idler photon followed and therefore which path the signal photon took, and therefore the interference pattern should disappear. Put the mirror back and the interference pattern should be detected.
So far this is all pretty much per Brian Greene's book, makes sense, and has been observed experimentally.
But, here is where my confusion comes:
In figure 6 we put the quantum eraser on Alpha Centauri, nearly 5 light years away. The photons on paths 1 and 2 are going to take 5 years to get to the quantum eraser.
We run the experiment. Do we see an interference pattern or not?
There are three options:
OPTION ONE: Maybe we see an interference pattern if and only if my friend is going to put in the mirror 5 years from now. If so, my friend can signal from the future. He puts in the mirror M and causes interference if Microsoft is above $5,000 on the Alpha Centauri stock exchange. I know 5 years earlier. (In fact if we bounce the idler photons back from Alpha Centauri and set up the eraser on Earth, could we not set up a paradox? I can leave the mirror "M" in place myself 10 years after measuring the interference.)
OPTION TWO: On the other hand, maybe we never see an interference pattern, because we can in principle determine which-path information by removing the mirror 5 years from now. But then what if my friend chooses not to remove the mirror 5 years later. No device will actually measure the path so what caused the interference pattern to go away? But experiments show interference.
OPTION THREE: Or, maybe we always see an interference pattern, because perhaps it only matters if which-path information can be determined at the time the signal photons hit the screen. But what if 5 years later my friend on Alpha Centauri removes the mirror M. He can now measure and prove which path every signal photon actually followed 5 years ago. He proves each photons did take one or another path, there was nothing to interfere, and there should have been no interference pattern 5 years ago. But I have a piece of film with bands on it.
OPTION1 allows signals from the future
OPTION2 differs with experiment
OPTION3 allows me to measure both interference and which-path for the same photon. It can be measured to have gone only down only one path, but interferes - with what?
It seems clear that options 1 and 2 are out, leaving option 3. So, what is that saying?
If the eraser is ON and the light path is shorter to eraser than to the screen, interference.
If the eraser is OFF and the light path to the eraser is shorter than to the screen, no interference.
Regardless of whether the eraser is ON or OFF if it's further than to the screen, interference.
Next...
Set up a situation where the eraser is off, and can be shifted back and forth: further or closer than the screen. Make the eraser one light year away (+/-) and make the beam going to the screen bounce off a mirror 1/2 light year away and come back to Earth so the detector can be here on Earth.
Now, a light year away, by shifting the eraser back and forth across the 1-light distance threshold, I can cause photons just about to hit the screen (after having already traveled 1/2 light year out and 1/2 light year back) to interfere or not. Can't I now signal instantaneously from 1 light year away?
In figure 1 a photon source (e.g. a laser) shoots out a beam of monochromatic photons which are divided into two beams by the beam splitter, a half-silvered mirror. The two beams strike the screen which is, say, a piece of film that records each photon strike as a white dot on black. The beams strike from two angles so the peaks and troughs in their waves interfere, producing alternating light and dark bands on the screen.
Even if the laser is set to shoot one photon at a time, the quantum mechanical probability wave of that single photon goes along both paths and interferes with itself.
In figure 2 we stick in some detectors. If either detector is turned on, it will tell us if the photon went down that path. No longer is there a probability of both paths and there is no interference pattern recorded on the screen.
In figure 3 we insert "down converters" into each path. A down converter takes in a photon and spits out two entangled photons of about 1/2 the energy (frequency). We send the "signal" photon on to the screen. We could look at the location of the idler photon to see which path the signal photon took. But for now we send the idler photon to a device called a quantum eraser. The half silvered mirror "M" makes it impossible for detectors C and D to tell if the idler came in on path 1 or 2 and so impossible to tell which path the signal photon followed, "which-path" information is "erased", so we expect an interference pattern on the screen. This has been shown experimentally.
In figure 4 we stick in detectors along paths 1 and 2. If either is turned on, we can tell which path the idler photon took, and therefore which path the signal photon took, and therefore the interference pattern should disappear.
In figure 5 we note that we don't need the extra detectors A and B. By removing the eraser mirror (compare to figure 4) the paths 1 and 2 go straight across into detectors C and D, we can tell which path the idler photon followed and therefore which path the signal photon took, and therefore the interference pattern should disappear. Put the mirror back and the interference pattern should be detected.
So far this is all pretty much per Brian Greene's book, makes sense, and has been observed experimentally.
But, here is where my confusion comes:
In figure 6 we put the quantum eraser on Alpha Centauri, nearly 5 light years away. The photons on paths 1 and 2 are going to take 5 years to get to the quantum eraser.
We run the experiment. Do we see an interference pattern or not?
There are three options:
OPTION ONE: Maybe we see an interference pattern if and only if my friend is going to put in the mirror 5 years from now. If so, my friend can signal from the future. He puts in the mirror M and causes interference if Microsoft is above $5,000 on the Alpha Centauri stock exchange. I know 5 years earlier. (In fact if we bounce the idler photons back from Alpha Centauri and set up the eraser on Earth, could we not set up a paradox? I can leave the mirror "M" in place myself 10 years after measuring the interference.)
OPTION TWO: On the other hand, maybe we never see an interference pattern, because we can in principle determine which-path information by removing the mirror 5 years from now. But then what if my friend chooses not to remove the mirror 5 years later. No device will actually measure the path so what caused the interference pattern to go away? But experiments show interference.
OPTION THREE: Or, maybe we always see an interference pattern, because perhaps it only matters if which-path information can be determined at the time the signal photons hit the screen. But what if 5 years later my friend on Alpha Centauri removes the mirror M. He can now measure and prove which path every signal photon actually followed 5 years ago. He proves each photons did take one or another path, there was nothing to interfere, and there should have been no interference pattern 5 years ago. But I have a piece of film with bands on it.
OPTION1 allows signals from the future
OPTION2 differs with experiment
OPTION3 allows me to measure both interference and which-path for the same photon. It can be measured to have gone only down only one path, but interferes - with what?
It seems clear that options 1 and 2 are out, leaving option 3. So, what is that saying?
If the eraser is ON and the light path is shorter to eraser than to the screen, interference.
If the eraser is OFF and the light path to the eraser is shorter than to the screen, no interference.
Regardless of whether the eraser is ON or OFF if it's further than to the screen, interference.
Next...
Set up a situation where the eraser is off, and can be shifted back and forth: further or closer than the screen. Make the eraser one light year away (+/-) and make the beam going to the screen bounce off a mirror 1/2 light year away and come back to Earth so the detector can be here on Earth.
Now, a light year away, by shifting the eraser back and forth across the 1-light distance threshold, I can cause photons just about to hit the screen (after having already traveled 1/2 light year out and 1/2 light year back) to interfere or not. Can't I now signal instantaneously from 1 light year away?
posted by Eric Holstege at 2:15 PM
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