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Somewhere in 2006 I did watch DVD set called Down The Rabbit Hole (extension of What the Bleep do We Know!?) and that's when and where my fascination with quantum mechanics begun; slit experiments gave me sleepless nights.  I just could not think of anything else than to what sort of information highway are we living in and not sense it.  Our macro world seems to be so distant to what we observe at micro scale which, in essence, builds up our macro world. Quantum mechanics has many intriguing properties and it takes some open mind or knowledge of mathematics to accept it. One of them is quantum entanglement.

 

Quantum entanglement occurs when particles such as photons, electrons, molecules as large as "buckyballs" (made of sixty carbon atoms and called that way as achitect Buckminster Fuller built buildings of those shape) and even small diamonds interact physically and then become separated; the type of interaction is such that each resulting member of a pair is properly described by the same quantum mechanical description (state), which is indefinite in terms of important factors such as position, momentum, spin, polarization, etc. According to the Copenhagen interpretation of quantum mechanics, their shared state is indefinite until measured. Quantum entanglement is a form of quantum superposition. When a measurement is made and it causes one member of such a pair to take on a definite value (for example, clockwise spin), the other member of this entangled pair will at any subsequent time be found to have taken the appropriately correlated value (for example, counterclockwise spin). Thus, there is a correlation between the results of measurements performed on entangled pairs, and this correlation is observed even though the entangled pair may have been separated by arbitrarily large distances. This behavior is theoretically coherent and has been demonstrated experimentally, and it is accepted by the physics community. However there is some debate about a possible underlying mechanism that enables this correlation to occur even when the separation distance is large. The difference in opinion derives from espousal of various interpretations of quantum mechanics.  I won't get into details here, but will focus on what raised fascination in first place with me - slit experiments (those who have read Many Worlds discussion may wish to skip next few paragraph, but I tried not to repeat myself too much).

 

By now, your probably know that particles are not just dots; they tend to be waves as well and we cal this to be wave-particle duality.  And in Many Worlds discussion I covered that along with historical aspect and then turned to simplest of all slit experiments.  What is slit experiment?  Imagine you have slit and marble gun.  Small pool too (kitchen sink will do it too).  First we need to understand what particles and what waves do.  Waves are easy, we can easily create those on surface of water (thus we get our slit in pool or kitchen sink if you want).  As for particles, we will use marbles.  We wish to see what patern on background we get once push wave or marble (acting here as an particle) through slit.  In short, this is what we get following.

 

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This one is easy.  We shoot marbles through single slit and what do we get on background?  We get pattern which is easy to understand; single band aligned with slit through which marbles have passed.

 

This is is what we would expect and this is what happens in reality when we use matter through single slit.  As said, this one was easy.

 

Can you guess what happens if use double slit?

Let's use now double slit and see what happens then, shall we? If we use double slit we get double pattern on background - we see two bands and this is sort of expected results as well.

 

This results is also expected and nothing to be surprised of. Background bands are alligned with slits and we see kind of one-to-one relationship; if marble passed throug left slit we see background pattern on left band and same goes for right side.

 

OK, what about waves?

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Here we are with our slit sinked in water (pool, kitchen sink, aquarium or something else - it is your call).  Waves are different.  A water wave disturbs the flat surface of a surface by creating regions where the water level is higher than usual and regions where it is lower than usual. The highest part of a wave is called its peak and the lowest part is called its trough. A typical wave involves a periodic succession: peak followed by trough followed by peak, and so forth. 

 

How does this reflect our single slit?

The wave radiates out and with most intensity in line with slit.  This creates single band patern on the background which is very similar to what marble one did before. 

 

At this point it seems as there is nothing unusual about waves when compared to marbles.

 

What about double slit and wave?  And most importantly, what about pattern on the background?  Are going to see two bands?

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If two waves head toward each other when they cross there results an important effect known as interference.  When a peak of one wave and a peak of the other cross, the height of the water is even greater, being the sum of the two peak heights. Similarly, when a trough of one wave and a trough of the other cross, the depression in the water is even deeper, being the sum of the two depressions.

 

And here is the most important combination: when a peak of one wave crosses the trough of another, they tend to cancel each other out, as the peak tries to make the water go up while the trough tries to drag it down.

If the height of one wave's peak equals the depth of the other's trough, there will be perfect cancellation when they cross, so the water at that location will not move at all.

 

As consequence, this cancellation vs peak effects will cause stripes across background.  Correct, we will see multiple bands on the background - this is the nature of wave.  We say that bright lines are interference pattern caused by sums of peaks or troughs.

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OK, so let's see what we know now.  When matter is pushed through the slits we see background paterns corrensponding slits. If marbles go through the slits they will most likely land directly behind the slit, but if they come in at a slight angle, they will land slightly to the sides. The resulting pattern is a map of the likelihood of a bullet landing at each point.

 

This is nothing unusual and this is all ok.  For now, keep in mind that all matter or particle like objects act like that.  One would expect particles like electrons, photons, protons or any other to act the same, right?  We'll come to that soon.

With waves we get interference pattern of many bands on background. 

 

You probably heard that light (photons) acts as both particle and waves; indeed, you can see the same with flashlight or lights used by cars.

 

Again, this in nothing unusual and expected.  This is easy to comprehand as we get to see these effects in real life thus nothing weird yet.  Yet.

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So where is the weird stuff?  Where is quantum magic?  Well, it started many years ago.  While above has been affected for photons, in 1924 Louis de Broglie introduced something called matter wave. In 1926, Erwin Schrodinger published an equation describing how this matter wave should evolve - the matter wave equivalent of Maxwell’s equations - and used it to derive the energy spectrum of hydrogen. That same year Max Born published his now-standard interpretation that the square of the amplitude of the matter wave gives the probability to find the particle at a given place. This interpretation was in contrast to De Broglie's own interpretation, in which the wave corresponds to the physical motion of a localized particle.  In 1927, Davisson and Germer decided to test the whole thing.  A double-slit experiment was not performed with anything other than light (photons) until 1961, when Clauss Jönsson of the University of Tübingen performed it with electrons.  In 2002, Jönsson's double-slit experiment was voted "the most beautiful experiment" by readers of Physics World.  Now let's see why.

 

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In 1927, Clinton Davisson and Lester Germer fired a beam of electrons at a piece of nickel crystal; this experiment is equivalent to firing a beam of electrons at a barrier with two slits.

 

When you shoot electrons through single slit you get single band pattern on the background.

 

This is expected and we have seen this for both particles and waves to be the case.  Again, there is nothing unusual about this.

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Classical physics predicts that electrons fired at a barrier with two slits will produce two bright stripes on a detector. Quantum physics predicts, and experiments confirm, that electrons will produce an interference pattern, showing that they embody wavelike features.

 

So, back in 1927 it has been shown that the beam of particulate electrons must, unexpectedly, be some kind of wave.  The world of physics would never be the same after that.

 

And the story then started to unfold...

 

Originally, whole beam of electrons has been fired so scientists suspected this is how interference happened and suggested interference would go away if electrons would be fired one at the time.  We can tune the gun so that it fires fewer and fewer electrons every second; in fact, we can tune it all the way down so that it fires, say, only one electron every ten seconds. In 1974, technology became able to perform the experiment by releasing a single electron at a time. Again, the interference patterns showed up. But when a detector is placed at the slit, the interference once again disappears. The experiment was again performed in 1989 by a Japanese team that was able to use much more refined equipment. With enough patience, we can run this experiment over a long period of time and record the impact position of each individual electron that passes through the slits.  Surprisingly, we can very same effect.  Hm...

 

Now, think for a moment what this really means.  We see that individual, particulate electrons, moving to the background independently, separately, one by one, build up the interference pattern characteristic of waves.  Think of single electron going through double slit - what is necessary to happen to get interference pattern?  It needs to behave like wave and that means it would need to pass through both slits and create intereference pattern against itself. What!?  Same electron passing through both slits?  At the same time?  Yes!  But wait, it get's even stranger.

 

Once you settle down and accept the fact that this can only happen if same electron passes through both slits, next logical move is to try to observe this.

 

Can we detect same electron passing through both slits?  Can we place measuring device that will inform us about this outcome?

 

The answer is yes.  And the result of such test is even more shocking!

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When slits are observed to be seen how electron goes through suddenly background pattern changes from wave-like to particle-like one.  If you shut down monitoring, it changes back to wave one.  Switch monitoring back on, it turns to particle one.


You perform the exact same experiment, but only add a simple measurement at an earlier phase, and the result of the experiment changes drastically.

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By observing, we are changing the experiment!  To see the electron you must do something to it - for instance, you shine light on it, that is, bounce photons off it. Now, on everyday scales photons act as negligible little probes that bounce off trees, paintings, and people with essentially no effect on the state of motion of these comparatively large material bodies. But electrons are little wisps of matter. Regardless of how gingerly you carry out your determination of the slit through which it passed, photons that bounce off the electron necessarily affect its subsequent motion. And this change in motion changes the results of above experiment.  If you disturb the experiment just enough to determine the slit through which each electron passes, experiments show that the results change from that of wave like and become like marble (particle) one. The quantum world ensures that once it has been established that each electron has gone through either the left slit or the right slit, the interference between the two slits disappears.  You way wonder if number of slits plays any role here and the answer is - it does not, as see on following picture.

 

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If we keep the spacing between slits the same, then there is no change in the location of the maxima, no matter how many slits the laser beam passes through. Thus an analysis of the location of the maxima for 2 slits applies to any number of slits. Also note that the single slit pattern acts as an envelope for the multiple slit patterns.

 

Feynman proclaimed that each electron that makes it through to the background actually goes through both slits. It sounds crazy, but hang on - things get even more wilder.  Feynman argued that in traveling from the source to a given point on background each individual electron actually traverses every possible trajectory simultaneously; a few of the trajectories are illustrated below.


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It goes in a nice orderly way through the left slit. It simultaneously also goes in a nice orderly way through the right slit. It heads toward the left slit, but suddenly changes course and heads through the right. It meanders back and forth, finally passing through the left slit. It goes on a long journey to distant galaxy before turning back and passing through the left slit on its way to the screen. And on and on it goes - the electron, according to Feynman, simultaneously "sniffs" out every possible path connecting its starting location with its final destination. Feynman showed that he could assign a number to each of these paths in such a way that their combined average yields exactly the same result for the probability calculated using the wave-function approach. And so, from Feynman's perspective, no probability wave needs to be associated with the electron. Instead, we have to imagine something equally if not more bizarre. The probability that the electron - always viewed as a particle through and through - arrives at any chosen point on the screen is built up from the combined effect of every possible way of getting there. This is known as Feynman's "sum-over-paths" approach to quantum mechanics. 

 

Still, how can one electron simultaneously take different paths - and no less than an infinite number of them?  The result of calculations using Feynman's approach agree with those of the wave function method, which agree with experiments. You must allow nature to dictate what is and what is not sensible. As Feynman once wrote, "[Quantum mechanics] describes nature as absurd from the point of view of common sense. And it fully agrees with experiment. So I hope you can accept nature as She is - absurd."  Fair enough, but let's leave now these discussions and get back to slit experiment - more precisly to its extension.

 

Individual photons directed at tilted glass have an option of being reflected or going through.  They can’t do both because they can’t be divided, or so we are told.  Yet some experiments seem to imply that they sometimes take both paths unless a detector is in place.  Let's enhance previous experiment with something called beam splitter (for example, half-silvered mirror).  To make it easier, we will use photon to explain this, but keep in mind that this applied to all particles.  Beam splitter reflects half of the light that hits it while allowing the other half to pass through.  In practice, we call these "which-way interferometer experiments".  In essence, what beam splitter does is to split initial single light beam in two, the left beam and the right beam, similar to what happens to a light beam that impinges on the two slits in the double-slit setup.

 

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Using judiciously placed fully reflecting mirrors, as in figure above, the two beams are brought back together further downstream at the location of the detector. Treating the light as a wave, as in the description by Maxwell, we expect - and, indeed, we find - an interference pattern on background. When detector D1 registers a hit, it is said that "the photon took the lower arm" of the interferometer and similarly for D2 and the upper arm. This is the interferometer analogue of putting two up-close detectors after the 2 slits in the 2-slit experiment.  When a single photon hits the beam splitter, classical intuition says that it will either pass through or will be reflected. Classical reasoning doesn't even allow a hint of any kind of interference, since there is nothing to interfere: all we have are single, individual, particulate photons passing from source to detector, one by one, some going left, some going right. But when the experiment is done, the individual photons recorded over time, do yield an interference pattern.  According to quantum physics, the reason is that each detected photon could have gotten to the detector by the left route or by going via the right route. If you use other beam splitters to put the two beams back together you can get an interference pattern, not unlike the one depicted in the double slit experiment.   The beam goes both ways, but one path is longer and so when they come back together, they interfere with each other.

 

slit16.jpgHowever, if you turn the light down so only one photon at a time goes through you still see the same effect, implying the photons go both ways.   If you leave the single-photon-at-a-time beam on long enough, the outcome will be a well defined interference pattern. So far so good.  What if we place a detector along each path this particle could go through?  What if we place detector for each route just after beam splitter?  Well, by now you already know the answer - we recored one path and intereference disappears.


Is there any clever way to expand these tests?  Becuase at the moment it seems as we if we do not look everything is possible, but the moment we observe most statisticaly likehood realized itself.  It sounds a bit like a black magic - surely, there has to be more than this?  There are some very sophisticated delayed choice experiments involving beam splitters.  These are super fast detectors that can be switched into the photon beam after it goes through the splitter. In other words, spit a photon at the splitter, calculate when it reaches it (about 1 nanosecond per foot of travel) and then switch the detector into the path behind the splitter. The idea is to try to trick the photon into "thinking" there is no detector so it is ok to split, then turning on the detector at the last moment and try to catch the photon doing something it is not supposed to do, breaking laws along the way.  If it arrived at a detector in the reflected path and was also seen by the detector behind the splitter, some law has been broken and the mystery solved - figure out a new law. You do this randomly. If the photon goes both ways, it can be caught by the detectors.  These were suggested in 1980s by John Wheeler.

 

We begin with the same experiment as in previous example. We do have small modification though; we attach a new photon detector next to the beam splitter. If the new detector is switched off we are back in the original experimental setup and the photons generate an interference pattern.  If the new detector is switched on it tells us which path each photon traveled: if it detects a photon, then the photon took that path; if it fails to detect a photon, then the photon took the other path. Such "which-path" information, as it's called, compels the photon to act like a particle, so the wavelike interference pattern is no longer generated.  So far so good.

 

Here is what Wheeler suggested (thought experiment) in 1978. Move the new photon detector far downstream along one of the two pathways. In principle, the pathways can be as long as you like, so the new detector can be a considerable distance away from the beam splitter. Again, if this new photon detector is switched off, we are in the usual situation and the photons fill out an interference pattern on the screen. If it is switched on, it provides which-path information and thus precludes the existence of an interference pattern.

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Strange thing here is the fact that the "which-path" measurement takes place long after the photon had to "decide" at the beam splitter whether to act as a wave and travel both paths or to act as a particle and travel only one. When the photon is passing through the beam splitter, it can't "know" whether the new detector is switched on or off-as a matter of fact, the experiment can be arranged so that the on/off switch on the detector is set after the photon has passed the splitter. To be prepared for the possibility that the detector is off, the photon's quantum wave had better split and travel both paths, so that an amalgam of the two can produce the observed interference pattern. But if the new detector turns out to have been on - or if it was switched on after the photon fully cleared the splitter - it would seem to present the photon with an identity crisis: on passing through the splitter, it had already committed itself to its wavelike character by traveling both paths, but now, sometime after making this choice, it "realizes" that it needs to come down squarely on the side of being a particle that travels one and only one path.  Somehow, though, the photons always get it right.  Whenever the detector is on-again, even if the choice to turn it on is delayed until long after a given photon has passed through the beam splitter - the photon acts fully like a particle.

 

In a response to the argument that at short distances interactions at the screen with slits in it might be compromised by "knowledge" of events that occur at the location of the detector screen, Wheeler is reported to have come up with a more elaborate thought experiment. Wheeler suggests that one may imagine a more extraordinary scenario wherein the scale of the experiment is magnified to astronomical dimensions: a photon has originated from a star or even a distant galaxy, and its path is bent by an intervening galaxy, black hole, or other massive object, so that it could arrive at a detector on earth by either of two different paths.  Something as following picture shows.

 

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What should really strike you is that photons could have been traveling for many billions of years. Their decision to go one way around the galaxy, like a particle, or both ways, like a wave, would seem to have been made long before the detector, any of us, or even the Earth existed. Still, some billions of years later, the detector was built, installed along one of the paths the photons take to reach Earth and switched on. And these recent acts somehow ensure that the photons under consideration act like particles. They act as though they have been traveling along precisely one path or the other on their long journey to Earth. But if, after a few minutes, we turn off the detector, the photons that subsequently reach the photographic plate start to build up an interference pattern, indicating that for billions of years they have been traveling in tandem with their ghostly partners, taking opposite paths around the galaxy.  This new moment, with time component being more in foreground, I will use later in some other post when discussing nature of time.  Wheeler thought experiment has been experimentally confirmed in 2007 by Alain Aspect.

 

Has our turning the detector on or off in the 21st century had an effect on the motion of photons some billions of years earlier? No one tends to believe that. It is not that the photon, billions of ago, decided to go one way around the galaxy or the other, or both. Instead, as quantum physics teaches us, for billions of years it has been in the quantum norm - a hybrid of the possibilities.  If we insert photon detectors along the two pathways light takes, then our story of the past will include a description of which path each photon took.  If we don't insert the photon detectors, our story of the past will be different; without the photon detectors we can't recount anything about which path the photons took.  Both stories are valid - they just describe different situations.

 

But we are no yet done with slit experiments.  Human nature is such that drives us towards new experiments in endless search for the answers.  By doing so, scientists ask themselves, if you can't change something that has already happened, can you do the next best thing and erase its impact on the present? The answer is - yes.  This sort of experiment is called quantum eraser and it was first suggested in 1982 by Marlan Scully and Kai Druhl.

 

A simple version of the quantum eraser experiment makes use of the double-slit setup with following modification. A tagging device is placed in front of each slit; it marks any passing photon so that when the photon is examined later, you can tell through which slit it passed. Roughly, the process relies on using a device that allows a photon to pass freely through a slit but forces its spin axis to point in a particular direction. If the devices in front of the left and right slits manipulate the photon spins in specific but distinct ways, then a more refined detector background that not only registers a dot at the photon's impact location, but also keeps a record of the photon's spin orientation, will reveal through which slit a given photon passed on its way to the detector.  As before, we should know the outcome; when we tag photons in a way that we know through which slit they have passed interference pattern is gone.

 

Now, what if, just before the photon hits the background, you eliminate the possibility of determining through which slit it passed by erasing the mark imprinted by the tagging device? When the tagging devices are turned on, we imagine that the photon obediently acts as a particle, passing through the left slit or the right slit. If somehow, just before it hits the background, we erase the which-slit mark it is carrying, it seems too late to allow an interference pattern to form. For interference, we need the photon to act like a wave so it must pass through both slits.  And since it appears that in this case it would pass through one - did we finally tricked the nature?  At this point, you can't not to think of Scully and Druhl as genius couple. Raymond Chiao, Paul Kwiat and Aephraim Steinberg carried out the mission of testing this in 1992.  Setup was close to what is shows below, with a new erasure device inserted just in front of background. Eraser ensures that regardless of whether a photon from the left slit or the right slit enters, its spin is manipulated to point in one and the same fixed direction. That means that any subsequent examination of its spin would yields no information about which slit it passed through and so the which-path mark has been erased.

 

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In above left picture we see that which-path information spoils the interference pattern.  In above right picture setup device that erases the mark on the photons is inserted just in front of background. Remarkably, the photons detected on background after this erasure do produce an interference pattern. Because the which-path information is eliminated, the interference pattern reappears.  As in the delayed choice experiment, in principle this kind of erasure could occur billions of years after the influence it is thwarting, in effect undoing the past, even undoing the ancient past.  How are we to make sense of this?  Well, the core truth is still the same; if we can trace path back we kill interference as only single path realizes itself.  On the other hand, if we have no clue from where it came we see sum of all possibilities shows through wave function of possibilities by particle position and these create interference. The difference now is, that, we have setup where we first clear out interference (as we have detectors in front of the slit) thus our wave is killed and we have single path (we establish which-path scenario).  We can say that wave is blurred and and just one path is brought to the focus.  But if we remove which-path information, if we remove the tag, like a pair of glasses, it compensates for the blurring, brings both waves back into sharp focus and allows them once again to combine into an interference pattern. It's as if after the tagging devices accomplish their task, the interference pattern disappears from view but patiently lies in wait for someone or something to resuscitate it.

 

Sort of quantum eraser (but not really as the one described above) you can do yourself with some instructions found here.  Again, this is not the end of the story as finale lies just ahead and challenges conventional notions of space and time even further.  This experiment, called the delayed-choice quantum eraser, was also proposed by Scully and Druhl.

 

Setup for this test is similar to the one seen before with addition of down-converters, one per each pathway. Down-converters are devices that take one photon as input and produce two photons as output, each with half the energy ("downconverted") of the original. One of the two photons (called the signal photon) is directed along the path that the original would have followed toward the detector screen. The other photon produced by the down-converter (called the idler photon) is sent in a different direction altogether.  On each run of the experiment, we can determine which path a signal photon takes to the screen by observing which down-converter splits out the idler-photon partner. And once again, the ability to glean which path information about the signal photons -even though it is totally indirect, since we are not interacting with any signal photons at all - has the effect of preventing an interference pattern from forming. This can be easily be shown on following picture.

 

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OK, so far this gives us the same picture as before - we do know path and there is no interference seen.  What is so special about this setup?  Here it comes - what if we manipulate the experiment so as to make it impossible to determine from which down-converter a given idler photon emerged? What if, that is, we erase the which-path information embodied by the idler photons? At that point some strange happens; even though we've done nothing directly to the signal photons, by erasing the which-path information carried by their idler partners we can recover an interference pattern from the signal photons. Confused?  Not to be worried... this is indeed a bit trickier.  I'm using reference here by Brian Greene here in his Fabric of Cosmos where he gave fairly easy to follow description of this matter.  Take a look at picture below which embodies all the essential ideas.

 

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The setup in above picture differs from previous one with regard to how we detect the idler photons after they've been emitted. Originally, we detected them straight out, and so we could immediately determine from which down-converter each was produced - that is, which path a given signal photon took. In the new experiment, each idler photon is sent through a maze, which compromises our ability to make such a determination. For example, imagine that an idler photon is emitted from the down-converter labeled "L". Rather than immediately entering a detector, this photon is sent to a beam splitter (labeled "a"), and so has a 50 percent chance of heading onward along the path labeled "A," and a 50 percent chance of heading onward along the path labeled "B". Should it head along path A, it will enter a photon detector (labeled "1"), and its arrival will be duly recorded.  But should the idler photon head along path B, it will be subject to yet further shenanigans. It will be directed to another beam splitter (labeled "c") and so will have a 50 percent chance of heading onward along path E to the detector labeled "2", and a 50 percent chance of heading onward along path F to the detector labeled "3".  The exact same reasoning, when applied to an idler photon emitted from the other down-converter, labeled "R", tells us that if the idler heads along path D it will be recorded by detector 4, but if it heads along path C it will be detected by either detector 3 or detector 2, depending on the path it follows after passing through beam splitter b.

 

Easy to follow, right?  But why did we complicate this in the first place?  Notice that if an idler photon is detected by detector 1, we learn that the corresponding signal photon took the left path, since there IS no way for an idler that was emitted from down-converter R to find its way to this detector. Similarly, if an idler photon is detected by detector 4, we learn that its signal photon partner took the right path. But if an idler photon winds up in detector 2, we have no idea which path its signal photon partner took, since there is an equal chance that it was emitted by down-converter L and followed path B-E, or that it was emitted by down-converter R and followed path C-E. Similarly, if an idler is detected by detector 3, it could have been emitted by down-converter L and have traveled path B-F, or by down-converter R and traveled path C-F. Thus, for signal photons whose idlers are detected by detector 1 or 4, we have which-path information, but for those whose idlers are detected by detector 2 or 3, the which-path information is erased. And now, does this erasure of some of the which-path information - even though we've done nothing directly to the signal photons - mean interference effects are recovered?

 

Indeed it does - but only for those signal photons whose idlers wind up in either detector 2 or detector 3. Namely, the totality of impact positions of the signal photons on the screen will look like the data in picture above showing not the slightest hint of an inteference pattern, as is characteristic of photons that have traveled one path or the other. But if we focus on a subset of the data points - for example, those signal photons whose idlers entered detector 2 - then that subset of points will fill out an interference pattern.  These signal photons, whose idlers happened, by chance, not to provide any which-path information act as though they've traveled both paths!  If we were to hook up the equipment so that the screen displays a red dot for the position of each slgnal photon whose idler was detected by detector 2, and a green dot for all others, someone who is color-blind would see no interference pattern, but everyone else would see that the red dots were arranged with bright and dark bands - an interference pattern. The same holds true with detector 3 in place of detector 2. But there would be no such interference pattern if we single out signal photons whose idlers wind up in detector 1 or detector 4, since these are the idlers that yield which-path information about their partners.  Needless to say, this has been confirmed in practice with real experiment.

 

So, in summary, by including down-converters that have the potential to provide which-path information, we lose the interference pattern. And without interference, we would naturally conclude that each photon went along either the left path or the right path. But we now learn that this would be a hasty conclusion. By carefully eliminating the potential which-path information carried by some of the idlers, we can coax the data to yield up an interference pattern, indicating that some of the photons actually took both paths. There is another point which has been mentioned briefly in previous examples of experiments.  The three additional beam splitters and the four idler-photon detectors can be on the other side of the laboratory or even on the other side of the universe, since nothing depended at all on whether they receive a given idler photon before or after its signal photon partner has hit the background. Imagine, then, that these devices are all far away, some ten light-years away or whatever, and think about what this entails.  Future measurements do not change anything at all about things that took place in your experiment today; the future measurements do not in any way change the data you collected today. But the future measurements do influence the kinds of details you can invoke when you subsequently describe what happened today.

 

There are many ongoing discussions on these tests and what far reaching consequences there might be based on outcomes we have witnessed.  One which took me by surprise, as I was not aware things have got some much they they are, is the concept of quantum radar. Quantum radar is a hypothetical remote-sensing method based on quantum entanglement. One possible implementation of such technology has been developed and patented by defense contractor Lockheed Martin. It intends to create a radar system which provides a better resolution and higher detail than classical radar can provide. The technology is hoped to work by using photon entanglement to allow several entangled photons to function as if a shorter wavelength was used to allow detection of small details while having an overall longer group wavelength that allows long distance transmission. According to a recent and controversial (but not yet known to have been disapproved) theory, any such remote-sensing device (including, but not limited to Lockheed Martin's planned implementation of technology), using quantum (photon) entanglement, may be able to extract meaningful information from specific regions of hyperspace. A hypothetical research paper on the subject suggests that photon-entanglement, combined with interferometry, can possibly be used to remote-sense distant quantum properties of past, present or even future hypersurfaces of spacetime. The paper is based on exploiting causal and relativistic loopholes supposedly found in the 1999 realization of the Delayed Choice Quantum Eraser experiment by Yoon-Ho Kim, R. Yu, S.P. Kulik, Y.H. Shih, designed by Marlan O. Scully. Crazy, isn't it?  A really good site discussion all these and more can be found here (Hungarian).

 

But how do we stand with as much as sane explanation of what is going on today?  How should we perceive our reality then?  Beofre getting there I have to state something obvious: quantum mechanical framework and laws sounds strange and describe reality at level far away from what we perceive on daily basis.  And indeed, and the world we perceive at our level, are all composite structures.  However, these composite structures are made of elementary particles or structures (elementary for now that is) which follow different laws and in doing so are responsible for everything around us and at the end us too. Double slit experiment was carried out in early 20th century.  Same experiment with "buckyballs" was made by very end of 20th century (1999).  And all these along with what has been shown above comes from a single phenomena - particle/wave duality. 

 

wave_particle.gif

 

The fact that particle matter behaves as wave caught by surprise everyone, but it is accepted now though in daily life our interactions are not as near as wave like thus we keep ignoring this important fact.  Still, waves are getting today more and more attention (for example, Fabrizio Logiurato at Trento University encourages his students to search wave structures using Google Earth to explore wave dynamics - you check following paper for some details and cool pictures).  Werner Heisenberg, in 1926, formulated so called uncertainty principle.  In short, it states there are limits to measure same properties or certain data at the same time.  Heisenberg stated that if you multiply the uncertainty in position of any particle with the uncertainty in momentum (which is its speed times its mass) the result can't be smaller than Planck constant.  Reverse engineered and translated to simple English, that means that the more precisely we measure the speed the less precisely we know exact location and the vice versa.  Planck constant is small - 6.626068 × 10-34 m2 kg / s. Being small, it has small effect on macro objects.  Going down in size, to realms of electrons, things do change quite a bit.  It is calculated that if you measure position of an electron to precision of roughly a size of an atom, then we can't know speed more precisely than about plus or minus 1000km/s. That's not precise at all and that's exactly from where uncertainty comes from.  It might not be best in the world symmetry to think about, but whenever I think of this principle I get to remember problems I have when taking photos of moving objects.  If they are very fast and my shutter speed is slow, I get blurred motion.  If my shutter speed is fast, I get sharp picture, but whoever observes that photo is left unaware whether object has been in motion or not. Not being able to determine certain aspects of data allows different eventualities to pop up which might sound strange given that science tend to keep things defined at smallest scales. Quantum mechanics thus leads us to new model of determins, one where laws of nature determine the probabilities of various futures and pasts rather than future and past with certainty.  The calculated probabilities determine most expected outcome of experiments.  So, if you shoot electron through double slit there is chance this electron is also found in some distant galaxy, but its probability determines that we will find at the background at the end.  As they say, nothing is 100% sure as if something would be definite in location then it would have infinite uncertainty in momentum. While it feels strange to us to be it that way, this has been tested and proved many times in practice and there is hardly anything that hasn't been tested so many times as quantum mechanics predictions.

 

Feynman in 1940s had insight, as mentioned earlier, and stated that particles takes all possible paths from point A to point B.  He formulated a mathematical expression - called sum over histories - reflecting this idea.  It is exactly this process, taking all paths, that causes interference we see in double slit experiment.  In Feynman's model a quantum particle samples every path connecting A and B, collecting a number called a phase for each path.  That phase represents the position in the cycle of a wave.  When you add together these waves for all paths you get so called probability amplitude for given particle. Its square then gives the correct probability that the particle will reach point B.  Amazing!  Though number of paths may be infinite making you believe this is impossible to calculate, the nature of wave is such that many of those cancel each other.  Further, Feynman theory and model allows us to determine probable outcomes of not just particle, but rather system.  Feynman showed, for a general system, the probability of any observation that could have led to the observed one is constructed from all the possible histories that might have led there (this from where term sum over histories comes from).

 

Closely related is something called measurement problem.   The measurement problem in quantum mechanics is the unresolved problem of how (or if) wave function collapse occurs. The inability to observe this process directly has given rise to different interpretations of quantum mechanics, and poses a key set of questions that each interpretation must answer. The wavefunction in quantum mechanics evolves according to the Schrödinger equation into a linear superposition of different states, but actual measurements always find the physical system in a definite state. Any future evolution is based on the state the system was discovered to be in when the measurement was made, meaning that the measurement "did something" to the process under examination. Whatever that "something" may be does not appear to be explained by the basic theory.  If observers and their measuring apparatus are themselves described by a deterministic wave function, why can we not predict precise results for measurements, but only probabilities?  Or based on experiments above, what causes no interference when we try to determine path of particle?

 

There is no doubt, as anything else, this continues to be one of the topics beings look into by scientists around the world.  While I lack details (but I suspect this reflects work publices later), in summer 2011 Nature brought news about international team of researchers, led by University of Toronto physicist Aephraim Steinberg of the Center for Quantum Information and Quantum Control, has found a way to apply a modern measurement technique to the historic two-slit interferometer experiment. With this new experiment (BBC version here), the researchers have succeeded for the first time in experimentally reconstructing full trajectories which provide a description of how light particles move through the two slits and form an interference pattern. Their technique builds on a new theory of weak measurement that was developed by Yakir Aharonov's group at Tel Aviv University. Howard Wiseman proposed that it might be possible to measure the direction a photon (particle of light) was moving, conditioned upon where the photon is found. By combining information about the photon's direction at many different points, one could construct its entire flow pattern ie. the trajectories it takes to a screen. The original double-slit experiment played a central role in the early development of quantum mechanics, leading directly to Bohr's formulation of the principle of complementarity. Complementarity states that observing particle-like or wave-like behavior in the double-slit experiment depends on the type of measurement made: the system cannot behave as both a particle and wave simultaneously. Steinberg's recent experiment suggests this doesn't have to be the case: the system can behave as both.  This shows that long-neglected questions about the different types of measurement possible in quantum mechanics can finally be addressed in the lab, and weak measurements, such as used in this experiment, may prove crucial in studying all sorts of new phenomena.  So, after many decades of believing we can't know what photon does when it passes through interferometer - this has changed too, adding further excitement to this whole story and future test along with possible outcomes.  And it may bring also quantum enntanglement back to focus too explaining non-locality of quantum world, wave reality and what mechanism makes world visible real to us so real.

 

 

Credits: Brian Greene, Stephen Hawking, Leonard Mlodinow, E.R. Huggins, Wikipedia, Science magazine, Sacha Kocsis, Sylvain Ravets, Boris Braverman, Krister Shalm, Aephraim M. Steinberg