Contemplating an apparent paradox in the classic double slit experiment.

[mrspeedybob]

Here is a thought experiment to illustrate the problem...

Suppose you have a light source capable of emitting single photons on command from a computer. these photons travel through a barrier with two parallel slits and then strike a charge coupled device. The computer records each strike and compiles an image.

After a large number of photons have traveled through the experiment the image recorded by the computer will be the interference pattern of the photons wave functions.

Now suppose that the time of each photon emission is compared with the time of its arrival at the CCD. For all locations except for the line equidistant from both slits the travel time will be different for a photon traveling through slit A then one traveling through slit B. Making this comparison is strictly a software function, every physical characteristic of the experiment remains the same but somehow this determination collapses the wave function of each photon and the interference pattern is not produced. So far so good.

Does recording and then immediately destroying the time data without observing it collapse the wave function? If so, how is this different then not recording it?

If it doesn't then what happens if the image and time data are recorded separately and moved to distant locations. If a decision is made to observe or destroy the time data is there some sort of "action-at-a-distance" that affects what will be seen when the image is observed? What if the image is observed before a decision is made about whether to observe or destroy the time data?

 

[questionsyes]

I think it's true to say that in all instances within this setup, there will not be an interference pattern, regardless of any decision to view the data.

The fact that data is available at all indicates a classical interaction. And it is this that collapses the wave function, not your decision to access it.

 

[AlexPeltser]

It's an interesting question and I don't think the answer is so simple.
Suppose we do not record emission time but instead emit photons at predetermined intervals - like 1 second apart - so each photon has plenty of time to arrive. So far we should see interference pattern, right?
Next we connect the detector to a recording device that is able to record each photon's arrival time and position BUT we do not turn it on - meaning that device is not recording arrival time and position. We must still see interference pattern. If we say that we shouldn't see interference pattern in this setup then it is equal to assume that probability wave collapsed because it is somehow detected that there is a device that is able to record such 'dangerous' information, even when device is off. I doubt that probability wave can be affected by a dead device because dead device is equal to no device.
Does turning the recording device on immediately destroy interference pattern? It is doubtful too because the rest of the experiment setup didn't change.
Maybe the answer is that measuring photon's fly time doesn't allow deciphering which slit it went through due to uncertainty principle? Fly time is 'fuzzy' enough to figure the slit.

 

[DrChinese]

Does recording and then immediately destroying the time data without observing it collapse the wave function? If so, how is this different than not recording it?

Welcome to PhysicsForums, mrspeedybob and AlexPeltser!

Actually this is "possible". But the requirements are steep. You must make it impossible, in principle, to discern the which-path information. If you are successful, an interference pattern appears.

Keep in mind that these questions come back to the Heisenberg Uncertainty Principle (HUP). You cannot beat the HUP! I.e. you cannot obtain more reliable information tham is consistent with the HUP. This is true with entangled particles and with individual particles.

 

[Tac-Tics]

Here's my stab at it.

You can't decide which hole the particle moves through based on its travel time.

The position has to be uncertain enough along the vertical axis that you can't tell ought right which hole it went through by looking at its initial trajectory. After its diffracted, it's position is still sufficiently uncertain you can't tell "when" it hits the projector with sufficient precision to measure which hole it went through.

So, in short, fuzzy thing goes in, fuzzy thing comes out, and travel time of fuzzy thing is fuzzy.

 

[Cthugha]

Now suppose that the time of each photon emission is compared with the time of its arrival at the CCD. For all locations except for the line equidistant from both slits the travel time will be different for a photon traveling through slit A then one traveling through slit B. Making this comparison is strictly a software function, every physical characteristic of the experiment remains the same but somehow this determination collapses the wave function of each photon and the interference pattern is not produced. So far so good.

It is not the determination of this total travel time that collapses the travel time. The mere fact that you have a well defined emission time is already enough. Whether you see an interference pattern or not entirely depends on the spatial and temporal coherence properties of your light source. If both slits are inside the coherence volume (coherence length times coherence area) of the light you will see a pattern. Otherwise you will not. However, all photons inside one coherence volume are indistinguishable and the the position of the photon energy also cannot be localized better than to a volume of the order of the coherence volume. In the case of single photons, this finite extent also corresponds to a not precisely defined photon emission time. As a consequence, you will get a smaller coherence volume if you can define the exact photon emission time, resulting in a vanishing interference pattern. Most of these paradoxes with the double slit experiments are results of applying a classical ball-like picture to photons. This can be very misleading.

 

[mrspeedybob]

It is not the determination of this total travel time that collapses the travel time. The mere fact that you have a well defined emission time is already enough. Whether you see an interference pattern or not entirely depends on the spatial and temporal coherence properties of your light source. If both slits are inside the coherence volume (coherence length times coherence area) of the light you will see a pattern. Otherwise you will not. However, all photons inside one coherence volume are indistinguishable and the the position of the photon energy also cannot be localized better than to a volume of the order of the coherence volume. In the case of single photons, this finite extent also corresponds to a not precisely defined photon emission time. As a consequence, you will get a smaller coherence volume if you can define the exact photon emission time, resulting in a vanishing interference pattern. Most of these paradoxes with the double slit experiments are results of applying a classical ball-like picture to photons. This can be very misleading.

Thank you very much. That makes sense.

 

[DevilsAvocado]

Now suppose that the time of each photon emission is compared with the time of its arrival at the CCD. For all locations except for the line equidistant from both slits the travel time will be different for a photon traveling through slit A then one traveling through slit B.

Welcome to PF mrspeedybob! This is a damned good gedanken experiment!

I guess you’ve heard of the http://en.wikipedia.org/wiki/Delayed_choice_quantum_eraser" ? Your experiment is smarter! They use "equipment" at the slits, while you are just using time without any "intrusion". Smart!

Have you seen this DSE with single electrons?

https://www.youtube.com/watch?v=<object width="640" height="505">
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<param name="allowFullScreen" value="true"></param><param name="allowscriptaccess" value="always"></param>
<embed src="http://www.youtube.com/v/FCoiyhC30bc&fs=1&amp;hl=en_US&amp;rel=0&amp;color1=0x402061&amp;color2=0x9461ca" type="application/x-shockwave-flash" allowscriptaccess="always" allowfullscreen="true" width="640" height="505"></embed>
</object>

There is no doubt in my mind that you could easily control the emission according to AlexPeltser suggestion, one every second, and to clock the detection at the screen could not be a problem at all. Then all you have to do is get an atomic clock and start measuring, and wait for the Nobel Prize in Physics!

Honestly, your idea is just beautiful and simple. There is just one problem – when things look to good to be true, it probably is... (i.e. if this really is functional way of cracking this classical "mystery", it would already have been done by one of all these geniuses thinking about QM every day). But you never know... people do win on the lottery...

Now, my "layman rebuttal" (to get you back on Earth again) would be:

To get interference pattern the single photon, or single electron, has to pass BOTH slits! I know it sounds crazy, but this is the way it is. Thus, when you measure the time with your atomic clock, there are only two options:

1) You will get the exactly the same time for all particles.
2) You will get the Nobel Prize in Physics.​

Another way of looking at this, is that the electron doesn’t exist as a particle before measurement, and until that it’s a wave (function), creating interference with itself:

I think...

 

[mrspeedybob]

Welcome to PF mrspeedybobI guess you’ve heard of the http://en.wikipedia.org/wiki/Delayed_choice_quantum_eraser"

I had not heard of that but it is very interesting. A simple modification of this experiment would likely have the same result as my proposed experiment (whatever that is). If the two idler beams were directed at a distant mirror and reflected back such that the travel time was significant and if the beam splitters were replaced with movable mirrors such that the experimenter could decide which detector the idler beams arrived at then it would seem as though information could be sent back in time. While this would violate causality and raise a host of paradoxical issues I don't really see a way around it from a relativistic standpoint.

Light by definition travels at the speed of light. The closer one travels to the speed of light the less time one perceives to pass compared to a stationary observer. Since light travels at the speed of light then a photon (by its own "perception" of time must coexist at all points along it's history from beginning to end. In other words, from it's own perspective a photon arriving from a distant star is an object many light years long which exists for an infinitesimal time.

Since "before" and "after" have no meaning to a photon there is no causality violation if an event at this end affects that end or if an event at that end affects this end. From this perspective it seems perfectly natural that a photon could be used to send information through time in either direction.

Ok, ready for those that know more then me to poke a million holes in my thought process. ;-)

 

[questionsyes]

Since light travels at the speed of light then a photon (by its own "perception" of time must coexist at all points along it's history from beginning to end.

"It" doesn't exist.

 

[DrChinese]

Since "before" and "after" have no meaning to a photon there is no causality violation if an event at this end affects that end or if an event at that end affects this end. From this perspective it seems perfectly natural that a photon could be used to send information through time in either direction.

Ok, ready for those that know more then me to poke a million holes in my thought process. ;-)

By your logic, the signal could be from past to future or future to past. How would you tell which direction?

 

[DevilsAvocado]

Ok, ready for those that know more then me to poke a million holes in my thought process. ;-)

They probably will. questions,yes has already poked one.

My question to questions,yes: Yes the photon as particle doesn’t exist until measurement, but what about the wavefunction? Does it exist?

If not, how do you explain the strong redshift of the http://en.wikipedia.org/wiki/Cosmic_microwave_background_radiation" that was sent out ~13 billion years ago?

 

[unusualname]

I wonder if you were able to measure the travel time precisely enough to distinguish paths then would this make the photon's energy (and hence frequency) uncertain enough to destroy the interference?

This is an interesting problem for certain cosmic scale experiments, where you might like to observe interference via galactic lensing or similar but have to deal with the fact that the distinct paths may differ by many light-days (or worse) and hence "which-path" information is easily available. A novel method of using the energy/time uncertainty principle to "equalise" the path lengths by considering only narrowband signals has been proposed:

http://arxiv.org/abs/0812.3923

They talk about it here, including referees objections to the argument prior to publishing:
http://www.space.com/searchforlife/090820-seti-quantum-astronomy.html

 

[questionsyes]

They probably will. questions,yes has already poked one.

My question to questions,yes: Yes the photon as particle doesn’t exist until measurement, but what about the wavefunction? Does it exist?

If not, how do you explain the strong redshift of the http://en.wikipedia.org/wiki/Cosmic_microwave_background_radiation" that was sent out ~13 billion years ago?

In context of the OP assertion, no.

As an abstract function, yes. And I would argue that this is what was "sent out ~13 billion years ago"