New version of double-slit experiment

[universecode]

Yes, of course. That's what QM predicts in all interpretations, that's also the classical prediction for the intensity of light, and it's a result that all experiments so far have confirmed (although of course the experiments cannot be done in this hypothetical completely isolated universe - instead we calculate and validate upper bounds on the errors introduced by not being completely isolated).

Thanks, good, let's continue with our hypothetical universe and shuffle all the detectors, so they are all in different locations now. The source stays the same and continues emitting photons.
Will each detector have the same probability of detecting photons as it had before?

 

[DrChinese]

Thanks, good, let's continue with our hypothetical universe and shuffle all the detectors, so they are all in different locations now. The source stays the same and continues emitting photons.
Will each detector have the same probability of detecting photons as it had before?

Generally, the probabilities will change.

 

[universecode]

Generally, the probabilities will change.

Thanks.
Nugatory, would you confirm this answer?
You seem to be quite good at elaborating your arguments, so I just want to seal this answer before proceeding further.

 

[Nugatory]

Thanks.
Nugatory, would you confirm this answer?
You seem to be quite good at elaborating your arguments, so I just want to seal this answer before proceeding further.

So far so good...

 

[universecode]

Good, now if we return all detectors to where they were originally, will they again start observing photons each with the same probability they respectively had originally?

 

[Nugatory]

Good, now if we return all detectors to where they were originally, will they again start observing photons each with the same probability they respectively had originally?

If we've managed not to mess something up in all the moving around, yes. So far we're in accord with all interpretations of quantum mechanics and also the classical prediction for particles other than photons (and the only reason I make that exception is that there is no classical prediction for the behavior of photons).

 

[universecode]

If we've managed not to mess something up in all the moving around, yes. So far we're in accord with all interpretations of quantum mechanics and also the classical prediction for particles other than photons (and the only reason I make that exception is that there is no classical prediction for the behavior of photons).

Thanks, suppose all our detectors are around 1 light-hour away from the source and in both cases we have been observing a photon registered by one of the detectors consistently every 2 hours plus-minus 10 minutes. Would such observation contradict anything?

 

[Nugatory]

Thanks, suppose all our detectors are around 1 light-hour away from the source and in both cases we have been observing a photon registered by one of the detectors consistently every 2 hours plus-minus 10 minutes. Would such observation contradict anything?

By "both cases" you mean before we moved the detectors and after we put them back?
Not yet, as long as the source and detectors are at rest relative to one another, "around 1 light-hour away" means that the differences in the distances are small compared with ten light-minutes, "consistently" means that we ran long enough to get statistically significant results, and probably some other reasonableness assumptions that I've missed.

The non-Poisson distribution of the arrivals would be a very strong hint that that someone was turning the light on and off back at the source.

 

[DrChinese]

Thanks, suppose all our detectors are around 1 light-hour away from the source and in both cases we have been observing a photon registered by one of the detectors consistently every 2 hours plus-minus 10 minutes. Would such observation contradict anything?

We are assuming that the setup leads us to this consistent observation for the sake of the example.

 

[universecode]

By "both cases" you mean before we moved the detectors and after we put them back?

Yes

Not yet, as long as the source and detectors are at rest relative to one another, "around 1 light-hour away" means that the differences in the distances are small compared with ten light-minutes, "consistently" means that we ran long enough to get statistically significant results, and probably some other reasonableness assumptions that I've missed.

The non-Poisson distribution of the arrivals would be a very strong hint that that someone was turning the light on and off back at the source.

Thank you, excellent explanation with right assumptions.

Now, may I confirm something that I think will be very useful for anyone who might decide to read this so they can clearly understand what's going here.

The fact of switching the source on/off is completely independent from the probabilities eventually observed at each detector. Regardless of how diabolical the operator decides to behave the probabilities after sufficiently long run will tend to be the same as if there were no operator and the source was just controlled by a timer which switches the source on every two hours and then off 10 minutes after switching on?

 

[DrChinese]

Again, we are assuming your setup for the sake of discussion. We wouldn't want to get derailed on points that have nothing to do with the topic*. *which is rapidly eluding me...

 

[universecode]

nothing to do with the topic*.
*which is rapidly eluding me...

Patience is a virtue - I am sure you know that :)

Let me also make a small correction. Previously I said:
"... we have been observing a photon registered by one of the detectors consistently every 2 hours plus-minus 10 minutes..."

I am correcting that to the following:
"... we have been observing a photon registered by one of the detectors consistently within 10 minute interval past every 2 hours ..."
i.e., we receive a photon within 10 minutes past 1.00am, then a photon within 10 minutes past 3.00 am and so on.

Does this change anything we have already confirmed?

If not, then is it safe to assume that after sufficiently long run required to build appropriate statistics to estimate probabilities (which is what we do in both cases of having detectors in one or the other sets of locations) we can be certain that this is what actually happens i.e., the source is predictable in a sense that it does emit a photon within 10 minute interval past every two hours?

 

[DrChinese]

Patience is a virtue - I am sure you know that :)

So is getting to the point.

Clearly, we are willing to accept your scenario AS LONG AS there is nothing in it that leads to some violation of some other relevant issue. The longer you drag it out, the more it seems that such is what you have in mind.

Specifically: A setup in which ANY exact number N of photons is likely during some interval T at several spots is not so simple to prepare and may have significant caveats. But again, let's assume that is the expectation for the sake of discussion.

 

[universecode]

So is getting to the point.

Not in theoretical sciences! There are theorems that take dozens if not hundreds of pages to prove and every line is a key line. Rushing the argument is not a virtue here.

Let's ponder a bit about recent statements and I would like to hear views of others before moving on...

 

[diggnforgold]

Where is the original thread? I would like to know the particulars of the new take on the double slits experiment!

 

[DrChinese]

Not in theoretical sciences! There are theorems that take dozens if not hundreds of pages to prove and every line is a key line. Rushing the argument is not a virtue here.

Really? I never knew that.

The fact is that after 100 posts, we are still at the same question you had in post #1. Which is whether it matters if you move a detector around before a detection event occurs and while the particle is in flight. We have answered repeatedly, NO, it does not matter. Exactly what is there to ponder?

Finally: we really hope you are not attempting to push a personal argument here. We are discussing established physics. Your speculation is actually not allowed (see the FAQ). And it is beginning to look like that. I would urge you to get to the point more quickly. You will note that diggnforgold is confused the progress, which is not a good sign. There are more folks reading this than just a handful. This discussion should benefit others too.

 

[DrChinese]

Where is the original thread? I would like to know the particulars of the new take on the double slits experiment!

Sadly, this is the original thread.

And as an FYI: despite the title, there is no *new* version of the double slit experiment being discussed here.

 

[Nugatory]

The fact of switching the source on/off is completely independent from the probabilities eventually observed at each detector. Regardless of how diabolical the operator decides to behave the probabilities after sufficiently long run will tend to be the same as if there were no operator and the source was just controlled by a timer which switches the source on every two hours and then off 10 minutes after switching on?

Before we go on, I have to back up some.

When you said "we have been observing a photon registered by one of the detectors consistently every 2 hours plus-minus 10 minutes" I read that as saying that the expectation value for the number of photons detected during the twenty minutes around the two-hour mark is one: sometimes we get zero in that twenty minute period, often we get one, occasionally we get two or more, over enough trials it averages out to one. That's consistent with a source that is switched on ten minutes before the hour every two hours and left to run for twenty minutes.

If you had some other probability distribution in mind, you'll have to describe very clearly exactly how it is produced. Be clear about what it means to emit a photon every twenty minutes: It means that the source is illuminating the detector with a very dim light for twenty minutes, during the time that the detector is illuminated there is some probability of a photon being detected at the detector, and the expectation value of the number of detections across the twenty minutes that the detector is illuminated is one.

 

[DrChinese]

...

If you had some other probability distribution in mind, you'll have to describe very clearly exactly how it is produced. Be clear about what it means to emit a photon every twenty minutes: It means that the source is illuminating the detector with a very dim light for twenty minutes, during the time that the detector is illuminated there is some probability of a photon being detected at the detector, and the expectation value of the number of detections across the twenty minutes that the detector is illuminated is one.

Well said. The other issue is that since OP won't disclose where he is going, we don't know if any of this matters or not. So far, I haven't seen a hint of an actual question, at least one that hasn't already been answered multiple times.

 

[universecode]

That's consistent with a source that is switched on ten minutes before the hour every two hours and left to run for twenty minutes.

Thanks, I actually made a small correction after that post to make sure it reads better and you should understand it now as a source that is switched on right on the hour every two hours and left to run for 10 minutes with 1 photon expectation emitted within this 10 minute interval. Presumably a typical distribution of photon emissions within this 10 minute interval would be Poisson, but I suppose in such setup it is not relevant for our eventual probabilities observed by the detectors.

Here is a repeat of the correction:

Let me also make a small correction. Previously I said:
"... we have been observing a photon registered by one of the detectors consistently every 2 hours plus-minus 10 minutes..."

I am correcting that to the following:
"... we have been observing a photon registered by one of the detectors consistently within 10 minute interval past every 2 hours ..."
i.e., we receive a photon within 10 minutes past 1.00am, then a photon within 10 minutes past 3.00 am and so on.

Does this change anything we have already confirmed?

If not, then is it safe to assume that after sufficiently long run required to build appropriate statistics to estimate probabilities (which is what we do in both cases of having detectors in one or the other sets of locations) we can be certain that this is what actually happens i.e., the source is predictable in a sense that it does emit a photon within 10 minute interval past every two hours?

 

[universecode]

I guess I need to make another small correction:

the source is predictable in a sense that it does emit a photon within 10 minute interval past every two hours?

It should be:
"... the source is predictable in a sense that on average it does emit one photon within 10 minute interval past every two hours?"

 

[DrChinese]

I guess I need to make another small correction:

...

"... the source is predictable in a sense that on average it does emit one photon within 10 minute interval past every two hours?"

OK, great, now what is the setup? Until we know more, we won't know if the details will make a difference or not.

 

[Nugatory]

Now, may I confirm something that I think will be very useful for anyone who might decide to read this so they can clearly understand what's going here.

The fact of switching the source on/off is completely independent from the probabilities eventually observed at each detector. Regardless of how diabolical the operator decides to behave the probabilities after sufficiently long run will tend to be the same as if there were no operator and the source was just controlled by a timer which switches the source on every two hours and then off 10 minutes after switching on?

Ok, now that we're done with the long sidebar about how the source behaves (every two hours it's turned on; during the time that it's on it illuminates the detctor with light at intensity such that the expectation value is that only one detection event will occur) then... In general, the above is wrong.

The distribution of detections at the detector most certainly does depend on when the detector is switched on and off. Only if the diabolical operator diabolically chooses to switch the source on and off in exactly the same way as the timer would there be no difference.

(I have to point out that the times and distances we're dealing with here are classical; this one light-hour scenario is like using a very dim light on Earth to illuminate a detector on Saturn. When you scale the times and distances down, you will find that there are limits on what the operator can do and how quickly he can turn the source on and off).

 

[universecode]

Ok, now that we're done with the long sidebar about how the source behaves (every two hours it's turned on; during the time that it's on it illuminates the detctor with light at intensity such that the expectation value is that only one detection event will occur) then... In general, the above is wrong.

The distribution of detections at the detector most certainly does depend on when the detector is switched on and off. Only if the diabolical operator diabolically chooses to switch the source on and off in exactly the same way as the timer would there be no difference.

Thanks, I need to think about what you said...

(I have to point out that the times and distances we're dealing with here are classical; this one light-hour scenario is like using a very dim light on Earth to illuminate a detector on Saturn. When you scale the times and distances down, you will find that there are limits on what the operator can do and how quickly he can turn the source on and off).

I think this is fine by me - the objective is to test a unified behavior of both quantum and classical theories. Hence we must be observing quantum effects on classical time and distance scales.

 

[universecode]

Ok, now that we're done with the long sidebar about how the source behaves (every two hours it's turned on; during the time that it's on it illuminates the detctor with light at intensity such that the expectation value is that only one detection event will occur) then... In general, the above is wrong.

The distribution of detections at the detector most certainly does depend on when the detector is switched on and off. Only if the diabolical operator diabolically chooses to switch the source on and off in exactly the same way as the timer would there be no difference.

I though about this and so far I am failing to see how the probability distribution of photon emissions would make a difference on the expected probability of photon detections at the detectors if nothing changed with regards to the source/detectors locations or anything around them.
Of course if you meant the form of the distribution of detections with respect to time then yes - the form will depend on it but the expected value will converge to the same one regardless.

 

[DrChinese]

I though about this and so far I am failing to see how the probability distribution of photon emissions would make a difference on the expected probability of photon detections at the detectors if nothing changed with regards to the source/detectors locations or anything around them.
Of course if you meant the form of the distribution of detections with respect to time then yes - the form will depend on it but the expected value will converge to the same one regardless.

The average could be arbitrarily close to 1 photon, but that also means sometimes you get 0, 2, 3, etc. photons instead. There would be a fairly high standard deviation. I don't know if this is relevant to your secret example or not.

On the other hand, it is *possible* to create a photon source that will deliver 1 photon to a specific target detector with a very high degree of certainty. This involves turning off the source once 1 photon is delivered, much as Nugatory said. There are a few other caveats too. You would occasionally get 0 or 2, but far less likely. On the other hand, this technique generally would not work for multiple targets.

 

[Nugatory]

I though about this and so far I am failing to see how the probability distribution of photon emissions would make a difference on the expected probability of photon detections at the detectors if nothing changed with regards to the source/detectors locations or anything around them.
Of course if you meant the form of the distribution of detections with respect to time then yes - the form will depend on it but the expected value will converge to the same one regardless.

I don't understand what you're saying here. Several points of confusion:

First you say "I am failing to see how the probability distribution of photon emissions would make a difference on the expected probability of photon detections at the detectors if nothing changed with regards to the source/detectors locations or anything around them". Then in the very next sentence you explain how that happens: "of course the distribution of detections with respect to time [will change]".

Second, you're still speaking in terms of "photon emission". But the source cannot be made to emit photons in a controlled way; as I explained a few posts back, it's just a very dim light illuminating the detectors when it's on. If you want anything more interesting than that, you have to specify exactly how and when you're turning the source on and off to get that more interesting distribution.

Third, you say "the form [of the probability distribution] will depend on it but the expected value will converge to the same one regardless". That's confusing in several ways:
-The expected value doesn't "converge", it's something that we calculate directly by integrating the PDF across a particular time interval. When we do a large number of measurements, our results will approach the expected value - that's what makes it "expected".
-Different PDFs can produce the same expected value across a particular time interval, but that doesn't make them the same PDF, and we can distinguish them experimentally by measuring across other time intervals. Five minutes of high intensity followed by five minutes of low intensity has the same expectation value as ten minutes of moderate intensity over a ten minute period, but will produce very different results if we sample across five minutes instead.

 

[universecode]

Apologies for delay, I am back to this again.

I don't understand what you're saying here. Several points of confusion:
First you say "I am failing to see how the probability distribution of photon emissions would make a difference on the expected probability of photon detections at the detectors if nothing changed with regards to the source/detectors locations or anything around them". Then in the very next sentence you explain how that happens: "of course the distribution of detections with respect to time [will change]".

What I meant here is that the form of PDF of arrivals at each detector can be any and depends on the properties of the source and its PDF of emissions but the expected value of the PDF of arrivals at each detector will not change as long as locations of the source and the detectors have not changed.

Second, you're still speaking in terms of "photon emission". But the source cannot be made to emit photons in a controlled way; as I explained a few posts back, it's just a very dim light illuminating the detectors when it's on. If you want anything more interesting than that, you have to specify exactly how and when you're turning the source on and off to get that more interesting distribution.

Sure, the source cannot be controlled precisely but I think we have already established that it is possible to have a source that has some PDF of emissions with 1 expected emission during the 10 minute interval after being switched on.

Third, you say "the form [of the probability distribution] will depend on it but the expected value will converge to the same one regardless". That's confusing in several ways:
-The expected value doesn't "converge", it's something that we calculate directly by integrating the PDF across a particular time interval. When we do a large number of measurements, our results will approach the expected value - that's what makes it "expected".
-Different PDFs can produce the same expected value across a particular time interval, but that doesn't make them the same PDF, and we can distinguish them experimentally by measuring across other time intervals. Five minutes of high intensity followed by five minutes of low intensity has the same expectation value as ten minutes of moderate intensity over a ten minute period, but will produce very different results if we sample across five minutes instead.

Sure, all that is correct. By "converging" I meant that during the experiment the number of arrivals at each detector divided by the number of times the source is switched on (since it is switched on every two hours it will be total running time in hours divided by 2) will converge to some value which is the expected value of the PDF of arrivals for a particular detector or the probability of arrival at each detector.

So, to re-iterate what we have been talking about here are some statements:
1. We are in a patch of our universe extremely remote from anything and all around is just vacuum of space.

2. We have a source which is switched on every two hours by a precise timer and switched off 10 minutes after. The source has some PDF of emissions within that 10 minute interval with expected value 1.

3. We have detectors located at various distances from the source but they are all around 1 to 1.2 light-hours away from the source, let call the set of such locations as L1

4. We run experiment for a sufficient period of time to observe probabilities of arrival at each detector in L1, let's call them P1

5. We move detectors to another location L2 but still having them between 1 and 1.2 light-hours away from the source, and run the experiment again to observe new set of probabilities P2

6. We know that there is an expected one photon emission within 10 minute interval past every two hours and since detectors are located 1-1.2 light-hours away we can assume that each photon "travels" for at least 1 hour but not more than 1.2 hours before it reaches a detector.

7. What I would like to know is, given our setup, what existing QM theories would predict with regards to probabilities of arrivals observed at the detectors if during 1 hour after 10 minutes past every two hours (i.e. after the source being on for 10 minutes) we move detectors from L1 (where probabilities of arrival are P1) to L2 (where probabilities of arrival are P2). Then 0.2 hours later we move detectors back to L1 and they stay there waiting for the next time the source is turned on/off.
The timing of detector moves is controlled by second timer which is initially synchronised with the timer controlling the source.

In my understanding, if outcome is created at the measurement, all theories should predict that probabilities will be P2 because when each of our photons reaches the detectors they will be at L2 (even though at time of emission detectors were at L1) and we know that at L2 probabilities are P2.

Is this correct and this is what QM would predict?
I understand relativity may have something to say about this too, can someone explain what effect might be observed here?

 

[DrChinese]

7. What I would like to know is, given our setup, what existing QM theories would predict with regards to probabilities of arrivals observed at the detectors if during 1 hour after 10 minutes past every two hours (i.e. after the source being on for 10 minutes) we move detectors from L1 (where probabilities of arrival are P1) to L2 (where probabilities of arrival are P2). Then 0.2 hours later we move detectors back to L1 and they stay there waiting for the next time the source is turned on/off.
The timing of detector moves is controlled by second timer which is initially synchronised with the timer controlling the source.

In my understanding, if outcome is created at the measurement, all theories should predict that probabilities will be P2 because when each of our photons reaches the detectors they will be at L2 (even though at time of emission detectors were at L1) and we know that at L2 probabilities are P2.

Is this correct and this is what QM would predict?

In your purely hypothetical situation in which all other variables are held constant and the only change is movement from L1 to L2 or back, the probability will be P2 because the detectors are at L2 when the detection event (or non-event) occurs. Relativity is not really a factor here regardless of the speed at which you move the detector. It's a "just in time" effect.

 

[universecode]

In your purely hypothetical situation in which all other variables are held constant and the only change is movement from L1 to L2 or back, the probability will be P2 because the detectors are at L2 when the detection event (or non-event) occurs. Relativity is not really a factor here regardless of the speed at which you move the detector. It's a "just in time" effect.

Thanks, well, if what you are saying is correct i.e., all known theories predict P2 this is an example of where my theory predicts different result that it would be P1 without contradicting anything already shown to be correct, as far as I know thus far.