Visualizing Quantum Interference
By Doug Sweetser | August 16th 2011 02:22 AM | 17 comments | Print | E-mail | Track Comments

Trying to be a semi-pro amateur physicist (yes I accept special relativity is right!). I _had_ my own effort to unify gravity with other forces in...

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Quantum interference is really, really, really well-supported by data, data, data. Visualizing quantum interference is a blank slate. This may be a root source of frustration with any world view based on quantum mechanics. More of our brains are devoted to visualization than any other process. Given a diet of equations and stories, the visual section of our brains in the back of the skull must sit idle. "Idleness is the devil's workshop."

In this blog, John Wheeler's delayed choice thought experiment will be explained. The idea briefly is to ask if a single photon goes down a specific path or if the solitary photon goes down two paths so it can interfere with itself. In 2006, the thought experiment was made real by Alain Aspect and his collaborators. The paper provides the simple equations I was able to use to make quaternion animations of the process. The reader will be able to see animations of quantum interference for the first time.
click or skip this reading of the blog
Here is a sketch of John Wheeler's nightmare:

The intensity of the source is adjusted so that it emits one photon at a time. The photon comes to a beam splitter. The solitary photon can either stay down, or turn and go to the up path or perhaps the silent solitary one decides to go on both paths as part of a plan to create an interference pattern (photons are devilishly clever). At the detector box, the experimentalist makes a choice: see if the photon took the down path, or the up path, or both paths as would be needed to see an interference pattern. The decision about what type of measurement to do is delayed until after the photon has passed by the beam splitter (technically, a spacelike separation is required). Wheeler argued that the odd logic of quantum mechanics demands such schizophrenic behavior.
Side bar: The single photon red herring
Intensity has never been an issue in quantum mechanics since the day Einstein explained the photo electric effect. People will nod along with the statement that intensity is not relevant to quantum processes. The consequence of the statement is that lowering the intensity to one photon a day does not change an effect except to slow the rate the experimentalist collects data. Water molecules hold hands using hydrogen bonds, so water waves are changed by intensity. Photons are isolationists, whether as solitary skaters in this experiment, or if sent as a swarm of a billion a second. The photons never hold hands or work together. Looking at a quantum effect one photon at a time is a red herring. People love their herrings and  will defend their right to focus on the fish. I intend to swim on by.
Wheeler's thought experiment was made real by Alain Aspect and his collaborators. The paper was fun to read and reread. I think the experimentalists got it right. Here is the entire abstract:
ABSTRACT: The quantum "mystery which cannot go away" (in Feynman's words) of wave-particle duality is illustrated in a striking way by Wheeler's delayed-choice Gedanken Experiment. In this experiment, the configuration of a two-path interferometer is chosen after a single-photon pulse has entered it: either the interferometer is closed (i.e. the two paths are recombined) and the interference is observed, or the interferometer remains open and the path followed by the photon is measured. We report an almost ideal realization of that Gedanken Experiment, where the light pulses are true single photons, allowing unambiguous which-way measurements, and the interferometer, which has two spatially separated paths, produces high visibility interference. The choice between measuring either the 'open' or 'closed' configuration is made by a quantum random number generator, and is space-like separated -- in the relativistic sense -- from the entering of the photon into the interferometer. Measurements in the closed configuration show interference with a visibility of 94%, while measurements in the open configuration allow us to determine the followed path with an error probability lower than 1%.

With the information provided so far, I don't think this story can make sense. People defend the idea that this story must be accepted as is, after all it is supported by the following data from the paper:

This situation reminds me of something I learned about illusion in the film "The Prestige". That was a great film by the way, one that has to be watched two or three times before you get it. An illusion has three parts:
1. The Pledge
2. The Turn
3. The Prestige
The Pledge starts out the story with something ordinary. Members of the audience are invited on stage to prove to themselves the items are everyday, that knots are secure, that everything is as it seams. The Turn is when things disappear that should not be able to vanish. The audience is confused, nervous that something may have gone wrong. The work for the illusionist happens at the third step: the Prestige, when the missing thing is brought back, completely unharmed.
In quantum mechanics today, I feel we must live with the Turn. People who study and know some of the vital experiments in quantum oddness like the delayed choice experiment will tell you that is the way, accept that you cannot understand. A small circle of fringe folks will holler about their own approach, one which shows no understanding of the Pledge or Turn of quantum mechanics. A real illusionist would know exactly where the answer was placed. I put the answer in plain English, but surrounded it with words that would make the reader focus on a different subject. It was in the illustration, but let me now supply some detail:
I mentioned the source was coherent, but only in the context of intensity. The math of the source is treated as ordinary, even if it isn't.

The up/down path detector is another herring, albeit more tempting given the name of the thought experiment. No matter what the source is, we can detect if it went on one path or another after a beam splitter. That is not a mystery. What needs to be understood is the interference for a non-interacting particle of a coherent source.

The source is so not random. Write out the wave function that would account for both ports, the complete picture:
$\psi = (cos(\omega t), sin(\omega t), 0, 0) \quad eq.~1$
Take the norm in order to calculate the probabilities of being in port 1 or 2:
\begin{align*}|\psi|^2 = \psi^* \psi &= (cos(\omega t), -sin(\omega t), 0, 0)(cos(\omega t), sin(\omega t), 0, 0) \\ &= (cos^2(\omega t) + sin^2(\omega t), 0, 0, 0) \\&= (1, 0, 0, 0) \quad eq.~2 \end{align*}
This is unity as it must be. Observers, sitting as they do at the spatial center of their own Universe (0, 0, 0), get probabilities of seeing an event from the source by taking the norm.

Let's use the quaternion animation software to look at the amplitude of the wave function as is, equation 1, even though no one can see it.

The animation has the symmetry U(1), a unit circle in the complex plane of Right-Left+time.

The animation reveals a problem with the visualization. When the phase shift is introduced, it will all be in the x direction. That shift will be darn near impossible to notice. To aid visualization, take the shift in x, and also create a corresponding shift in y. This spreads out what is happening along x.

$\phi = (cos(\omega t + \Delta), sin(\omega t + \Delta), k \Delta, 0) \, \textrm{with} \, \Delta: 0 \to 10 \pi \quad eq. ~3$
Two walls collide. Is it possible to follow one value of the phase? Again we are not being physical because individual photons cannot be marked in red, but the software can do the job:

Why are there so many points in this animation? Because every point in spacetime can be mapped to this unit circle.

Label the two paths A and B.  A is never shifted, B is shifted anywhere from phi = 0 to 10 pi.  The data in figure 3 of the paper involves 4 calculations:

A* B - interference (3a)
B* A - interference (3a)
$\\(cos(\omega t), -sin(\omega t), 0, 0)(cos(\omega t + \Delta), sin(\omega t + \Delta), 0, 0) \\= (cos(\omega t) cos(\omega t + \Delta) + sin(\omega t) sin(\omega t + \Delta), \\cos(\omega t)sin(\omega t + \Delta) - sin(\omega t) cos(\omega t + \Delta), 0, 0) \\ \\(cos(\omega t + \Delta), -sin(\omega t + \Delta), 0, 0)(cos(\omega t), sin(\omega t), 0, 0) \\= (cos(\omega t) cos(\omega t + \Delta) + sin(\omega t) sin(\omega t + \Delta), \\ cos(\omega t + \Delta) sin(\omega t) - sin(\omega t + \Delta) cos(\omega t), 0, 0) \quad eq. ~4-5$

A* A - no interference (3b)
B* B - no interference (3b)

$\\(cos(\omega t), -sin(\omega t), 0, 0)(cos(\omega t), sin(\omega t), 0, 0) \\= (cos^2(\omega t) + sin(\omega t)^2, 0, 0, 0) \\= (1, 0, 0, 0)$

$\\(cos(\omega t + \Delta), -sin(\omega t + \Delta), 0, 0)(cos(\omega t + \Delta), sin(\omega t + \Delta), 0, 0) \\= (cos^2(\omega t + \Delta) + sin(\omega t + \Delta)^2, 0, 0, 0) \\= (1, 0, 0, 0)$
We can see the lack of ambiguity for the no interference case.  The first two are going to be more complicated.  For a fixed value of phi and omega = 1, vary t and plot:

"Animations of equations 4&5 with additional shift"

This is what quantum interference can look like: the combination of three complex plane images: a straight line, a circle, and something sinusoidal. No wonder this is tricky!
(one technical detail: for the way my software is designed, I had to swap the roles of x and y, as you can tell since the circle is now in the ty plane instead of the tx plane. A bigger and smoother version of this animation is available).

I am not going to market these images as trivial to understand as that would mock any earlier efforts to have a visual interpretation of quantum interference. Instead I can point out why these images are a challenge. Time is a scalar, space is a vector. In quantum mechanics, the scalar is not a dull, monotonically increasing function. Instead, time toys with space, but mapping it back into the same space, thus hiding its hand. I needed to take what was only happening between time and one dimension of space and use another dimension to get a better handle on what was happening.

"What does one plus equal?" That is good English, math gibberish. "Did the photon go on the up or the down path?" While the question is perfect English, its is a poorly formed question for quantum interference. Poorly formed questions can never be answered. "Was there a photon at this location and at this time?" is a well-formed question. If you know exactly when a photon is seen, then a second prior to being detected you can make a statement about where it was, no matter what detector was used. Say the beam splitter was 2 light seconds away from the detector. Then there is a 50-50 chance the photon was at the half-way point of the up or the down path. If the down detector saw the photon, then the photon was at the half-way point in the down path. Notice I said both time and space locations. The photon was not in some arbitrary place along the down path a light second before detection.

What can be said if the interference detector was used? If the interference saw the maximal constructive interference, then one light second before detection, the photon was a the half-way point between either up or down. If the interference was at the maximal destructive point, then there was definitely no photon at the halfway point in either branch. For interference value between these two extremes, it sets the odds on a photon being at the halfway point a light second before being detected.

The coherent source is exceptionally well organized. It is the exquisite organization of the source that one sees in the interference pattern. Let messengers from the neat source house of particles travel down two paths of different lengths, and the resulting pattern looks like interference. The emissaries have no need to interact with each other, the proverbial bump into each other.

From my perspective, the height of absurdity in theoretical physics today are those trying to work without time. No doubt they think the delayed choice experiment is on their side. The event of the beam splitting and the choosing the type of detector is spacelike separated (a feat that was technically a great challenge to accomplish). A physics illusionist would point out that spacelike separation is a calculation done on two events in spacetime.

The results look rational, the visual part of my brain is happy.

Doug

Snarky puzzle: Supersymmetry has superpartners to build super friends between particles that take different amounts of time to jog around a circle. Animate this:
$A=(cos(t), 2 sin(t/2), 3 sin(t), 4 sin(2 t))/\sqrt{30}$
Notice how the tx takes  4 pi to get back to go, ty needs 2pi, and tz zips around in pi radians.If you like a three-way as much as I do (in theory at least), please discuss.

Google+ hangout: 11:00-11:45pm Eastern time, Tuesday-Friday. http://gplus.to/sweetser

This could be an efficient way to exchange a few ideas. If you have a question or two, hangout.
Bet against the Higgs being found,

If Mr. Sweetser does not get angry. (Google plus do not let me enter)
In my opinion there is a possible explanation, but little strange!
....For each photon emitted 'another photon is released by the "target"!!

It 'possible that, is the target, to emit the second photon?.
I think so, because Newton has written a law "F12 = -F21". If this law is valid also for photons ...
Then, for each emitted photon, there is an 'other moving by the opposite direction !
And, is this second photon, I think, to be detected at the destination,together with the first one,
for a total of "two" photons .
Into my idea, the "Kinetic Energy" of a photon move very fast ( Brachistochrone problem ) but "Potential Energy" is faster, because connected to " separation of bodies" as Gravitational Force.

So at the final destination, is the " Potential Energy" connected to F12, to stimulate the second one (-F21).
Yes..., we see the presence of "two" photons, one connected to F12 and the second connected to -F21.

The emitted photon move with a very efficient "cycloid" kinetic , but near the target...
a second photon is emitted, faster than light ( sorry ), as an answer to the first one ( F12) because
of "Potential transfering".
Actually Gravitational Force is not yet known " how much fast is " , I am correct ?
Now I ask , my idea Is possible ?
Sorry for the English.

Giacomo:
This sounds like physics babbling to me. Pairs of photons are created all the time, travelling in opposite ways, so that energy and momentum can be conserved. That would happen at the source. The source is design so that photons are travelling out in one direction only. The other photon would either be absorbed by the walls or reflected by them, then head out in the same direction as the first. If there is only one doorway out, there is only one doorway out. The detectors have a known efficiency for detecting single photons, which is what is going on in this experiment. The human eye can detect a single photon too pretty efficiently, way to go evolution. Sorry, but I see no value in the two photon model.
So my idea can be called " two photons model" ?
Is this a kind of " big praise" ?
I only wrote 18 lines , with my bad English....
Thank You Mr Sweetser. Really, i appreciate.
But ,what i explain in those 18 lines is a "new" model or "old" one?
It is very important to me.
Thank You , Thank You very much.
I will send my "extensive version" , when ready.
Maybe the larger version will change Your judgement.

Giacomo-

you are considering a paradigm that was abandoned when aether was abandoned, since aether is the potentiation of space by gravitation and was the ancient conception for cycle-generation. the preplatonic philosophers were interested in this same two source event and this plays out in Berkeley's idealism, Leibnizian monadology, etc - precisely because they believed firmly in the primacy of aether and core essences. many of the problems of this are philosophical in framing and seemed insoluble (metaphysical), eventually the influence of mathematicians (vienna circle, analytic tradition, etc) helped swing things back into empiricism and experimental primacy. this makes the observor into God, and his POV the sole "source". two-source or two-photon phenomena do not seem to be provable and hence entanglement is framed upon a different sort of thought experiment than the old "gravity first" account. it is framed with getting around the UV catastrophe, quantification of packets,... etc

Good luck with your work. What is often babble in physics turns out to be conversation in philosophy. Hence two hundred years of idealists.

Sorry Mr. "Euanthes", but Mr. Sweetser is right.

Even our galaxy is still "bubbling". So now, I believe "Somebody Up There Likes Me."

http://www.nytimes.com/2010/11/10/science/space/10galaxy.html

http://arxiv.org/PS_cache/arxiv/pdf/1005/1005.5480v3.pdf

My theory is closer to reality than I thought.
It 's the universe itself to produce bubbles, bubbles of photons in pairs.
I will continue and adjust my ideas.
Thank You, Mr. Sweetser. You helped me.
PS . Mr "Euanthes" , my name is really Giacomo ...

Doug-

great article, btw. it is fascinating how much of academic papers thrive on this exact sort of magician's play. it is a conceptual art but it's results so far can't be taken too lightly. afterall, if the demonstrations are accurate depictions of indeterminateness, then we needn't wonder where the magic really is.

I've been trying to figure this one out. First, I have to better understand the experiment. CIG Theory (www.CIGTheory.com) offers a solution to the normal "Young's Double Slit". Essentailly, the particle starts as a particle, then becomes heavenly spatial, and can go through both slits (therefore interference) . When the spatial version of the phton goes through one slit, there is nothing to interfere with, and so only the particle collapse is apparent (i.e. the wavefront did not have any other wavefront to interferre with). As for delayed choice, I have to understand it better. But, perhaps : when the "particle" leaves the source, it becomes spatial in accordance with CIG, then part of the spatial manifestation gets: 1) absorbed and re-emmited (either through or reflected), continuing as a "whole" through one or the other path (up or down), or 2) maintains its spatial self, partly reflected/partly emmitted, to carry onward and interferre with itself. In either case, once the "particle photon" leaves the source, it becomes spatial.

See www.CIGTheory for better (though still confusing) details. Dark Matter and Dark Energy are also explained using the same concept.

Thanks Doug Sweetser for a delightful evening.
Thank you Giacomo for insight into the Two Photon Model, for Two Photons are better than one!

Hello Douglas:

I do put your work in the "small circle of fringe folks" that despite their sincerity and conviction, don't understand the basics. Here is a quote from p14-15 of the 48 page pdf:
Pertinent Components
I. There is but One Particle and that I term a GODROP (Thing One).
II. All else is part thereof and this I term GODDROPLETS (Things Two).
III. Knowing Sir Newton's three Laws of Motion and this theory of Gravity.
iV. To Sir Newton's three Laws is added the following Fourth Law of Spontaneous Motion (of course it's not spontaneous - it's just the name):
My prediction is that no one will join your quest to find the GODROP or GODDROPLETS. I am putting the 3 comments count on your comments in this thread.
Good Evening Mr. Sweetser and thank you again for your site,

I was pleasantly suprised to see the small excerpt from my theory. The posted comments had the effect of informing me that I need elaborate on the intention of the reference to "Godroplet" and "Godrop". The Fourth Law of Motion was formulated simply to offer a reasonable synthesis (equivalence or "equating gravity to") of the motion of gravity to all the other "spontaneous" forms of motion. For instance, radiation and half lives, or a bubble under the ocean, or even Chemistry. I saw that there was a lacking of "no motion" to "motion" in Newtons Laws. Therefore, after intense thought, I added this new law to the existing three. The concept of the "Godroplets" was simply to consolidate all the existing matter into one concept. The "Godroplets" is not to be found, as it already exists in the form of any part or parcel of matter (e.g. Neutron, proton, electron, muon, planet, star, asteroid, etc.). Within the fourth law of motion, one can see a reduction of the forces, and therefore the number of particles, needed to obtain a consolidation, or synthesis, of the Standard Model (obviously the Standard Model works as is). It reduces the number of particles to one (either the smallest or a clump of them) and offers a Law of Motion common to all. So, a "Godroplet" is any part of the whole (Godrop). The Godroplet was not meant to be searched for, nor found, as it already exists as any of the known particles (or subparticles) and/or gathering of them (i.e. the pencil at my desk). It was an attempt to simplify the Standard Model, and all known forces. I do not see any difference between motions of say, Gravity and Radiation. Or, a bubble rising from the ocean and the motion in fire. Or between all of them. That is why the charge equation is so parallel to the equation for gravity.

The hard part, was trying to figure out the "WHY" of motion. Ultimately, I settled on the desire to attain TIME EQUILIBRIUM as the cause for all motion.

As far as this quantum topic is concerned, I'm still working on Delayed Choice. I will try to write more later (delay).

Thanks , Doug

This site attracts a lot of crackpots. t,

Should the reference to crackpot be directed at me, or, in defense of others if the comment is directed at them, please note that any existence wherein we wake up to find ourselves spiraling through the cosmos, descending into an unknown future, from an ambiguous past, makes us all crackpots. To accept this as reality is akin to saying, "Yeah, I'm crazy", while to deny it, puts us in the insane asylum, as their is no other reality offered to my knowledege. Read CIGTheory in its entirety and attempt a thorough understanding of it. The theory is experimentally verifiable, and I have requested other experts in their field to focus on this verification. I have not heard back. As for your comment, we have all cracked the pot some time ago. The pot is very fragile for us all. Read CIGTheory today! Enjoy the "FUN SECTION" as well. Thanks for your complete understanding......DOUG

This is Mr. Lipp's third comment on this article, so any further ones will be deleted.
Doug a nice article as usual. I actually have a topic I would be really interested in your views on that being Quantum Discord. It appeals to my sensabilities because it appears to be like a halfway house between QM and GR but you know the beast the devils in the details. There seems to be some tentative positive results but many are skeptical ... care to cast your thoughts out into the arena.

I had not heard of quantum discord, but was able to find the 2001 paper that may have started the subject. Looks like the paper has been cited 202 times. I don't read enough of the literature to know how "good" that is.  Here is the abstract:
Two classically identical expressions for the mutual information generally differ when the two systems involved are quantum. We investigate this difference -- quantum discord -- and show that it can be used as a criterion for the classicality of the correlations. We also show that quantum discord can be used for describing the selection of the preferred, effectively classical, pointer states.
A brief scan of the paper does not ring bells in my head (or perhaps I should just say, "I don't get it yet"). To me, what defines a classical system is if the operators that make up the expression are all scalar or all 3-vector. Since no one else says that, let me write out Newton's second law:

$\left(0,\vec{F}\right)=\left(\sqrt{\frac{G \hbar }{c^5}}\frac{\partial }{\partial t},\vec{0}\right)\left(\sqrt{\frac{G}{\hbar c}}m,\vec{0}\right)\left(0,\frac{1}{c}\frac{\partial \vec{R}}{\partial t}\right)=\left(0,\frac{G}{c^4}\left(m \frac{\partial^2\vec{R}}{\partial t^2}+\frac{\partial \vec{R}}{\partial t}\frac{\partial m}{\partial t}\right)\right)$

See all those zeroes? That is the sign of a completely classical law, no more, no less. Everything that goes in is pure scalar or pure 3-vector, not both. Here is Schrödinger (plus a phase everyone ignores), with complex valued operators:

$(1,\frac{\hbar}{2 m c} \vec{\nabla})\left( \sqrt{ \frac{G \hbar}{c^5}} \frac{\partial}{\partial t}, \sqrt{ \frac{G \hbar}{c^3}} \vec{\nabla}\right)^* \psi = (\sqrt{ \frac{G }{\hbar c^5}} V, \sqrt{ \frac{G }{\hbar c^3}} \vec{P}) \psi$

Multiply this out, and the scalar equation is a dimensionless form of the Schrödinger equation. This is not completely relativistic because of that leading scalar being the constant 1.

For me what changes in the classical to quantum expressions is going from reals or imaginaries to reals and imaginaries.

Okay my mathematics doesn't go to your level which is why I am asking your opinion :-)
I know what they mean at a world view (entropy) level but the mathematic level is where I wonder if it is even possible.

So let me dumb this down to what I am trying to understand:
Here is a slideshow I am trying to understand (http://qols.ph.ic.ac.uk/qi_ims/slides/slides_2010_08_10.pdf)

And the experimental results:
http://www.physorg.com/news/2011-08-quantum-entanglement.html
http://www.physorg.com/news/2011-08-entanglement-macroscopic-dissipation...

I was the same as you I hadn't heard of this stuff at all and I am trying to work out what it all means.

It would require a HUGE amount of work to understand those slides which are not meant for a general audience :-)

Here is my guess at what-it-all-means. Take for example Bell's inequality. Here is the experimental setup: a source emits 2 electrons. Those electrons have spin. One goes and measures the spin at 2 different, separated detectors. If both detectors point the same exact way, both observers make exactly the same measurement. Nature is consistent, a good thing.

Now put one of the detectors at 90 degrees to the other. One will detect the electron, the other will not. This is explained by quantum mechanics. It can also be explained by classical physics.

Correlations come into play when the detectors are at an angle to each other between 0 and 90 degrees. Sometimes they will both be seen, or not, or at only one detector. The experimenters collect much data.

Classical physics can explain the majority of the correlation of the measurements between the two detectors. There is however more correlation than a classical theory can account for. Quantum theory exactly accounts for the data seen.

I think the quantum discord folks are finding a technical way to quantify the difference between the classical correlation and the quantum one. They may be saying, look, the math here matches a quantum discord equation, ergo we have a system that is showing off its underlying quantum behavior.

Sorry late in getting back to you Doug been busy. Thanks for that explaination I am learning stuff on multiple fronts :-)

This all started from the paper (http://arxiv.org/PS_cache/arxiv/pdf/1102/1102.0016v2.pdf) the twin paradox experiment done with entangled partciles. It implies that QM version of time is quite different from SR/GR version of time.

I think I get it now what the QM people are doing is saying GR/SR is subordinate to QM rather than QM fitting into GR/SR framework as Einstein/Hawkings would want :-)

I think I get Quantum Discord now in that light it's some measure of the difference in time predictions.