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What Does the New Double-Slit Experiment Actually Show?

The views expressed are those of the author and are not necessarily those of Scientific American.

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Quantum mechanics is one of the most successful theories in all of science; at the same time, it’s one of the most challenging to comprehend and one about which a great deal of nonsense has been written. However, a paper from Science, titled "Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer", holds out hope that we might be able to get closer to understanding how nature works on the smallest scales. The authors – Sacha Kocsis, Boris Braverman, Sylvain Ravets, Martin J. Stevens, Richard P. Mirin, L. Krister Shalm, and Aephraim M. Steinberg – have measured both the trajectory and the interference pattern from photons, a difficult feat to say the least, and one with interesting implications. (Scientific American also has a brief article on this experiment, republished from Nature.)

 Left: Schematic of a generic double-slit experiment, showing how the interference pattern is generated. image by Matthew Francis. Right: Simulated double-slit interference pattern, showing the "graininess" due to individual photons striking the detection screen. Image by Matthew Francis.

It’s easy to overstate how complicated quantum mechanics is: after all, it’s one of the most successful theories in the history of science, something that wouldn’t be possible without some level of comprehension. In many ways, though, the most difficult experiment to understand is one of the simplest: the so-called "double-slit" experiment, in which the experimenter shines a light on a barrier with two narrow openings in it, and study the interference pattern it produces on a screen.

Light famously has two natures: it is wave-like, interfering in the same way that water ripples cross each other; it is also particle-like, carrying its energy in discrete bundles known as photons. If the experiment is sufficiently sensitive, the interference pattern appears grainy, where an individual photon appears on the screen, as you can see in the simulated projection pattern shown. In other words, single photons travel as though they are interfering with other photons, but is itself indivisible. Matter also has this dual character; interference of electrons and atoms has been observed experimentally. All of this is backed up by years of work.

The major difficulty with quantum mechanics is its interpretation. The standard Copenhagen interpretation (named in honor of the home city of Niels Bohr, who first formulated it) takes a simple stance: the reason why photons sometimes seem like particles and sometimes like waves is that our experiments dictate what we see. In this view, photons are products of our experiments without independent reality, so if we’re bothered by seemingly contradictory notions of wave and particle properties, it’s because we’re expecting something unreasonable of the universe.

The Copenhagen interpretation was extremely unsatisfying to several prominent physicists of the day (Einstein was the most famous dissenter, of course), and indeed to many working in the field now. Over the years, other scientists have proposed many alternative interpretations, some of which are more viable than others; many fail the Occam’s razor test by providing no empirical difference from the Copenhagen interpretation, yet are harder to work with.

Quantum Mechanics Without the Bohr(ing) Stuff

Left: Physicist Erwin Schrödinger in 1933, exhibiting the fashion taste scientists could get away with even then.

Quantum mechanics is notorious for tangling people’s minds up. Part of the problem lies in the complicated mathematical formulation: in a typical American physics curriculum, a serious study of quantum mechanics shows up in the third or fourth year and has a large number of prerequisites in both the physics and math departments. Famous physicists such as Richard Feynman have gone so far as to say that nobody actually understands quantum mechanics, and a lot of professors when they teach the subject will reassure their students that it works, even if the interpretation eludes them.

Many (perhaps even most) physicists treat the whole theory as a black box, something that provides very good predictions, but that will lead to madness if you try to figure out why it works the way it does. However, it’s worth our while to go over the structure of quantum mechanics to see why the latest experiment is potentially very important.

The central equation of quantum mechanics is a wave equation, known as the Schrödinger equation (named for its discoverer, Erwin Schrödinger, known for the infamous cat). As with any other mathematical equation relating to physics, you put in different parameters to characterize a particular physical situation and solve it; in this case solutions are known as wave functions. A given wave function represents the state of a system, which may be one or more photons, electrons, atoms, or any number of other entities. The state itself describes the probability that a system has a particular position, momentum, spin, etc.

Outside of quantum mechanics, statistics and probabilities are usually most useful when describing large numbers of things: what is the likelihood that a particular hand in poker turns up, or how many people will vote for a candidate for president based on demographic information. A single person votes in a given way with no uncertainty (the year 2000 presidential election aside), so the statistics you see in poll data are based on a large population. The wave function assigns statistical information to a individual system: what the possible outcomes of a measurement will be, even if the experiment is performed on a single photon.

One aspect is uncertainty. All experiments have uncertainty attached to them, simply because no equipment is perfect. Where quantum mechanics differs is by saying that even with perfect equipment, there will be a fundamental limit to how well a measurement can be performed. That uncertainty is directly connected to the wave-like character of matter and light: if you have a water wave traveling across the ocean, what is the precise position of the wave? How fast is it moving?

The answer isn’t so clear, simply because the wave takes up a finite amount of space and may overlap with other waves in such a way that separating out which wave is which is too hard; also, different parts of the wave may be moving at different rates. Therefore, the position and momentum are best described by an average and a spread of values around that average, which carries the name uncertainty – not in the sense of doubt but in the sense of indeterminacy. There is an inherent limit to our ability to describe these physical quantities, with no need for soul-searching on the part of scientists.

The Heisenberg uncertainty principle tells us what the minimum uncertainty for quantum waves must be: the smaller the uncertainty in position, the larger the uncertainty in momentum – and vice versa. Returning to the double-slit experiment, the wavelength (the size of the wave, in other words) depends on momentum, so the entire interference pattern is in effect a measurement of momentum.

However, that means determination of which slit the photon passed through – which is a measurement of position – has an increased uncertainty. Although the graininess of the interference pattern indicates where an individual photon lands, determining what path it took to get to that spot is not generally possible.

So What Does It All Mean, Anyway?

Enter the experiment by Kocsis et al.: by reducing the resolution of the measurements, the experimenters increased the uncertainty in the momentum, allowing a better chance at determining the trajectories of an ensemble of photons. The Heisenberg uncertainty principle still stands, in other words, and is an essential part of this experiment (whatever some headlines may say).

The difficulty of this measurement should not be overstated! After all, quantum mechanics has been around for nearly 100 years and based on the controversies surrounding the Copenhagen interpretation, had it been easy, surely someone would have attempted it by now.

The experiment involves producing individual photons from a quantum dot and measuring their momentum indirectly through the polarization of each photon. Because polarization is correlated with momentum, but not exactly the same quantity, measurement of one doesn’t strongly affect the other, preserving the state of the system fairly well. The final position of the photon is measured using a charge-coupled device (CCD), similar to what you find in ordinary digital cameras or telescope imaging devices.

By repeating the experiment for a large number of individual photons and moving the apparatus to measure polarization at various points along the trajectories, the researchers were able to reconstruct the paths not of the individual photons but of the complete ensemble of all photons – yet due to the statistical nature of quantum mechanics, information about the individual photons within the system can still be inferred.

One possible interpretation of the experiment is in line with the pilot wave model, formulated by Louis de Broglie with later additions by David Bohm. In this view, the wave function describes a statistical distribution that says what physical properties the point-like particle is likely to have – while the particles themselves may follow precise trajectories, even if those are very difficult to track. This certainly is consistent with what we see in detectors, although one might ask whether the pilot waves themselves can ever be directly observed – and if they can’t, whether they can be said to be "real".

Obviously a detailed discussion of that idea is too much for one post, so I won’t try. However, if the complete trajectory of a photon can be observed in some way and its interference pattern still exists, it indicates that indeed a view of quantum physics consistent with a realists’ perspective is possible (the kicking of rocks being completely optional).

Has the Copenhagen interpretation fallen? Has the pilot wave interpretation been vindicated? The cautious scientific answer must be "not yet". After all, there is nothing in this experiment that isn’t completely compatible with the mathematical predictions of quantum mechanics, so any valid interpretation – including the Copenhagen interpretation – will describe its results.

However, measurements such as this make it harder to say smugly that photons don’t follow any particular trajectory and that it’s unreasonable to expect them to. I for one look forward to more experiments along these lines.

Acknowledgments: Thanks to Arthur Kosowsky and Nuria Royo for resources and comments on earlier drafts of this post.

About the author: Matthew Francis is visiting professor of physics at Randolph-Macon College, freelance science writer, and seeker of weirdness throughout the cosmos. He blogs at Galileo’s Pendulum and tweets at @DrMRFrancis; his opinions are his own.

The views expressed are those of the author and are not necessarily those of Scientific American.


Comments 20 Comments

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  1. 1. jtdwyer 7:16 pm 06/7/2011

    Very nice review.

    However, it states:
    "The authors… have measured both the trajectory and the interference pattern from photons."

    The linked SA article (from Nature) states that the experiment allowed a the researchers to "to make a very rough estimate of each photon’s momentum". By repeating the single photon experiment they were able to "work out the average" momentum at each detector. By moving the crystal "progressively further away from the slits" they were able to trace the _average_ trajectories of the photons.

    By my reading, the ‘average very roughly estimated momentum’ and ‘average trajectory’ should not be
    described as ‘measurements’, inferring a level of precision not really achieved by the experiment.

    Still, I agree that this is an exciting result.

    As a casual reader, it has occurred to me that the the pilot wave concept implies that particles are propagated by separate wave energy. I suspect there may be a direct relationship between kinetic emission/propagation wave energy and potential particle mass energy, implying that particle and the wave are perhaps oscillating manifestations of a single entity (with frequencies varying by particle type). Do you know if this idea has been previously considered?

    Link to this
  2. 2. koantum 9:38 pm 06/7/2011

    The following should clarified what has actually been achieved by this measurement:

    Link to this
  3. 3. jtdwyer 11:08 pm 06/7/2011

    Thanks for the reference – damned copy & paste gremlins!'s_experiment_new_revised-79666
    Still, that didn’t lead to the intended article – there seem to be some navigation issues. I suggest first:
    – search for "Young’s experiment"
    – click on the link "Young’s experiment, new revised"
    Tedious, but worthwhile.

    You’re right – "Must I insist that a consolidated plot of (approximately) locally observed average momenta is one thing, and a plot of strictly unobservable Bohmian trajectories is quite another?" puts it so succinctly!

    I suppose it would be nice to find a freely available preprint version of the research report, but I’ve had no luck…

    Link to this
  4. 4. jtdwyer 11:11 pm 06/7/2011

    They got me! Note the single apostrophes…
    - search for "Young’s experiment"
    - click on the link "Young’s experiment, new revised"

    Link to this
  5. 5. PWarnell 2:16 am 06/8/2011

    I find this as a very thoughtful and careful review of what I consider an important experiment. It’s fair when you say the jury will still remain out on this for a while. However as the Copenhagen interpretation (standard QM) long resisted the reality of non localness as being simply an artefact of its formalism, as not being real in being experimentally identifiable, and now having this added, it would not be unwarranted to suggest that the normal and prevailing positivist position is on shaky ground, as it now needing vigorous defence, instead of the other way around.
    That being with this additional result it has the deBroglie-Bohm perpective further pass the duck test. That is as James Whitcomb Riley first reminded in such regard, "when I see a bird that walks like a duck and swims like a duck and quacks like a duck, I call that bird a duck” Moreover it drives home what John Stewart Bell had to say in 1982, in pointing out how theory if not considered properly has our choices to dictate how nature should, be instead of the other way around.

    “But in 1952 I saw the impossible done. It was in a paper by David Bohm (5). ……. But why then had Born not told me of this `pilot wave’? If only to point out what was wrong with it? Why did von Neumann not consider it? More extraordinarily, why did people go on producing “impossibility” proofs, after 1952, and as recently as 1978? . When Pauli, Rosenberg and Heinsenberg, could produce no more devastating criticism of Bohm’s version than to brand it as “metaphysical” and “idealogical”. Why is the pilot wave picture ignored in text books? Should it not be taught, not as the only way, but as an antidote to the prevailing complacency? To show us that vagueness, subjectivity, and indeterminism, are not forced on us by experimental facts, but by deliberate theoretical choice?”

    -John Stewart Bell, “On The Impossibility of The Pilot Wave”, CERN, Geneva, Ref.Th.3315-CERN (1982)

    Link to this
  6. 6. matthewfrancis 8:18 am 06/8/2011

    Thanks for the comments, everyone. I actually considered using that John Bell quote — like many physicists who think about this stuff, I’m a Bell fan. He thought more clearly about this subject than most of us.

    I do agree that individual trajectories are not being measured — and even in a pilot wave picture that kind of measurement is probably never going to be possible. (I could have stated this more clearly in the 3rd paragraph from the end — I did make it sound like the trajectory of an *individual* photon can be determined, and that’s not quite my intention!) The experiment is constructing a kind of view of trajectories from the *ensemble* of photons, which may indeed let us *think* of photons following a specific trajectory, even if we aren’t able to determine the path of a particular photon. Does that make sense?

    Link to this
  7. 7. jacobs2k 11:39 am 06/8/2011

    Quite a remarkable article. The most lucid I’ve seen summarizing the recent work with a sound historical perspective. Many thanks.

    On a somewhat whimsical note… the pilot wave notion always strikes me as something akin to a Platonic Ideal — a useful and maybe necessary construct with no direct perception possible. Or, closer to my working world of semantics, a description of class characteristics that only approximates the specifics of any individual of that class.

    Link to this
  8. 8. jtdwyer 2:09 pm 06/8/2011

    It seems that these exciting results may indicate that each photon does actually follow a specific deterministic trajectory, but we cannot derive sufficient information to precisely determine what each photon’s trajectory will be – if that makes sense.

    While the idea of a separate wave function guiding a localized particle may best fit the data, I’m bothered by what I consider to be the unphysicality of this arrangement.

    It seems to me that the experiment indicates that it is a wave function that determines the eventual position of the eventually detected particles – no more, no less. That particles are eventually detected does not prove that discrete localized particles ever passed through a slit, only that a wave function passed through a slit and eventually produced the detection of a particle. Without sufficient foundation, perhaps I’m misunderstanding something?

    BTW, I found an interesting reference in wikipedia:
    Couder et al, (2010), "Walking droplets: a form of wave-particle duality at macroscopic level?",

    Link to this
  9. 9. Wayne Williamson 5:52 pm 06/8/2011

    Does anyone know if the double slit experiment has been performed with many different materials and temperatures using the exact same slit width & height & thickness and same placement of the detector? Just wondering if the slit material properties change the resulting interference…ie. is the photon interacting with the matter(fields) of the guides….

    Link to this
  10. 10. Torbjörn Larsson, OM 5:53 pm 06/8/2011

    I agree with the commenters that notice that this is a nice review. And I have to pitch in with Francis hoping for more experiments rejecting non-realistic theories.

    My only nitpick would be to mention pilot wave theory at anything beyond a useful pathway model as it fails Bell test experiments. A more useful pathway model would be Feynman’s path integrals

    [Pilot wave has hidden variables, Bell test experiments say there are none; the reason for the conflict being that pilot wave is non-local (non-relativistic).

    Path integrals incorporate special relativity.]

    Link to this
  11. 11. Torbjörn Larsson, OM 6:12 pm 06/8/2011

    @ jtdwyer:

    "it has occurred to me that the the pilot wave concept implies that particles are propagated by separate wave energy."

    As I just noted to you on the previous article on this, it is the quantum field that embodies the energy and other particle characteristics. As an intro to field energy, you may want to study Wikipedia’s article on the Poynting vector for the EM field.

    @ PWarnell:

    "However as the Copenhagen interpretation (standard QM) long resisted the reality of non localness … the … positivist position is on shaky ground, as it now needing vigorous defence, instead of the other way around."

    You are shaking some ideological spear to non-existing demons.

    All other physics obey special relativity so it shouldn’t be controversial that quantum mechanics does too. Indeed it is shown that it can be so extended (relativistic Schroedinger’s equation) and embraced (quantum field theory, incorporating it explicitly).

    Further, Bell test experiments are informative on hidden variables precisely only when special relativity is fully embraced. Lastly, photon timing from high-z supernova events shows that Lorentz invariance extends well into the Planck regime; the relativistic turtle stacks all the way down.

    "Indeterminism" comes out of contrafactual determinism, trying to place realism on not yet existing observables instead of on the actual object, the wave function.

    "To show us that vagueness, subjectivity, and indeterminism, are not forced on us by experimental facts, but by deliberate theoretical choice?"

    Now you are trying to impute facts where there are none. Neither experiment nor theoretical choice have yet forced us to abandon relativity/locality/objectivity/realism.

    On the other hand, embracing something like the pilot wave theory would do that precisely that, as I mentioned in an earlier comment. (Objectivity and realism would be dropped by construing what not is consistent with physics at large, even if pilot wave theory is realist in isolation.) So why do you support that?

    Link to this
  12. 12. Neil Bee 7:21 pm 06/8/2011

    This is fascinating, and shows the power of weak measurements to show <I>collective</i> properties of photons. However, I came up with a way that might enable treating a single photon like an ensemble, and thus learning more about its polarization state than standard theory says is possible. It involves sending the same photon repeatedly through the same half-wave plate (reverses rotational sign of the photon’s circular components) and building up angular momentum in the plate. (Corrector plate restores photon before each reentry.)
    See .
    I had trouble with image file, am working on that but not hard to imagine from verbal.

    Link to this
  13. 13. matthewfrancis 8:38 am 06/9/2011

    A couple of details from the original Science article: the "slits" are actually a beam splitter rather than a solid barrier with two openings (as in the classic Young interference experiment like we always do in introductory physics class). Also, the *particular* polarization measurement depends on the optical properties of the material, but that’s not a weakness of the design, in this physicists’ opinion at least — it’s a necessity for taking this kind of measurement.

    Link to this
  14. 14. matthewfrancis 8:47 am 06/9/2011

    Bell’s theorem doesn’t rule out all "hidden variables" models, just certain types — including the type Einstein preferred, for what it’s worth. Similarly, the famous experiments by Alain Aspect and colleagues rule out some types of hidden variable models. The Bohmian type of pilot wave model is known as a "nonlocal" hidden variables model, and so far is not ruled out by experiment or by Bell’s theorem.

    I agree with you that a path-integral formulation is an improvement over a simple wave function. Actually, you don’t need special relativity for path integrals — Feynman originally developed path integrals in the non-relativistic context, though they don’t offer any particular computational advantage for most applications. I teach a tiny bit of the path integral formulation when I teach non-relativistic quantum mechanics to my students (senior-level undergraduates).

    Link to this
  15. 15. waltond 11:57 am 06/9/2011

    There are two things I don’t understand:

    1) The wavelength of the light is known, therefore the momentum is known; so why does it have to be measured?

    2) The single photons have to go through both slits; so, establishing the trajectory of a photon is meaningless.

    I’m not sure the paper proves anything.

    Link to this
  16. 16. mmfiore 2:58 pm 06/9/2011

    That was a very good review. I enjoyed it immensely. Now more than ever I need to say. As an alternative to Quantum Theory there is a new theory that describes and
    explains the mysteries of physical reality. While not disrespecting the value of Quantum Mechanics as a tool to explain the role of quanta in our universe. This theory states that there is also a classical explanation for the paradoxes such as EPR and the Wave-Particle Duality. The Theory is called the Theory of Super Relativity and is located at:
    This theory is a philosophical attempt to reconnect the physical universe to realism and deterministic concepts. It explains the mysterious.

    Link to this
  17. 17. matthewfrancis 5:14 pm 06/9/2011

    The wavelength of light is known to a certain limit — there will always be some uncertainty in that, even for lasers or quantum dots, which are close to be monochromatic. But even more than that, the wavelength is related to the magnitude of the momentum, but momentum also has a direction. Determining the momentum in total involves both the magnitude and the direction. Does that clarify the situation a bit?

    Link to this
  18. 18. waltond 3:34 pm 06/11/2011

    reply to matthewfrancis:

    It is easier to consider the equivalent classical double slit, to which this is equivalent. The photon is a wave packet some of which goes through one slit, and the rest through the other, leading to interference. Thus the trajectory of the photon, or the transverse component of its momentum is meaningless.

    Link to this
  19. 19. srlenzotti 1:02 am 06/11/2012

    question… whether coming from a flashlight or any other form of light source, the light is not coming from the same point of origin. Example: a light is not a single source, it has size that extends passed a single point of origin- reflecting its light off the medium that surrounds the flint, gas, or the burning substance that creates light. Wouldn’t this create different angles from which the light comes from therefore creating a distinguished shading which would resemble the “2 slit experiment”‘s results?

    Link to this
  20. 20. 12:45 pm 02/21/2013

    And what if it’s all wrong interpreted?

    Is it about dual state of the matter, interference, or collision with the interiors surfaces and the corners of the wall thickness???
    Think about!!!

    I’ve make a short movie explain this, hope you find it useful:

    Link to this

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