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Physics: Wave–Particle Duality


Wave-particle duality is the ability of particles such as atoms, photons, and electrons to behave under some conditions like waves and under others like particles. The objects we call “particles” are actually neither waves nor particles but something else that the human mind is not capable of visualizing. Wave-particle duality has been observed in many experiments and is described by the mathematical laws of quantum mechanics.

Theoretically, duality is a property not only of atomic or subatomic particles but also of larger objects such as footballs, people, and planets. However, duality is harder to observe for larger objects and has not yet been measured for any object bigger than a molecule.

Historical Background and Scientific Foundations

In 1675, English physicist Isaac Newton (1642–1727) published an essay titled Hypothesis of Light to defend the theory that light consists of tiny particles. “Are not,” he asked rhetorically, “the Rays of Light very small Bodies emitted from shining substances?” He proposed that these tiny objects or corpuscles obeyed his three laws of motion, just like any other material objects. By proposing various attractive and repulsive forces, he could account for many facts of optics, such as the properties of lenses.

However, a rival school of thought held that light is really a kind of wave. Dutch scientist Christiaan Huygens (1629–1695) argued that light is a series of pulses in an ethereal or subtle medium. Huygens and others used the wave theory to explain reflection, refraction (bending of light in transparent media), and other properties of light.

Debate over the rival theories raged for over a century, yet the tide slowly turned in favor of the wave theory. In 1801 Thomas Young (1773–1829) discovered that light displays interference, a wave property that can also be seen in a basin of still water. Letting a drop fall anywhere on the surface of the water will cause waves to spread and to reflect from the sides of the basin. The waves reflected from different parts of the basin can be seen to pass through each other; moreover, wherever two peaks or valleys meet for a moment, they form a higher peak or a deeper valley, and where a peak and a valley of equal height pass through each other, they cancel out. Addition of peaks or valleys is called positive interference, while canceling of peaks and valleys is called negative interference.

By the mid 1800s, the wave theory of light had become so successful at explaining optics that it had triumphed. In 1864, Scottish physicist James Clerk Maxwell (1831–1879) showed that light can be described as an electromagnetic wave—that is, a time-varying electric field paired with a time-varying magnetic field, each generating the other as the two move forward. The nature of light seemed, to most scientists, a closed question. Light was clearly a wave.

In 1887, however, German physicist Heinrich Hertz (1857–1894) observed a phenomenon that would, in time, radically change the apparently invincible wave theory. This phenomenon was the photoelectric effect. In 1905, German-American physicist Albert Einstein (1879–1955) announced that the photoelectric effect can be explained by assuming that light consists of particles, which he called “photons.” Yet all the evidence for light's wavelike nature remained, and Einstein did not deny it. How could light be both a wave and a particle, spread out in space but also (somehow) localized to a single point in space? It seemed a bizarre claim, like saying that something could be a musical sound and a bullet at the same time. Yet experiments showed that this was the case. Despite its seeming contradiction to the human experience of the every day world, wave-particle duality is a fact.

Einstein's work established wave-particle duality only for light, and it was not fully accepted by the physics community for years. Other physicists, including Neils Bohr (1885–1962) and Louis de Broglie (1892–1987), took the theory of wave-particle duality farther. Bohr applied Einstein's work to the spectra emitted by atoms, and in 1924 de Broglie predicted that all particles, not just photons, should display wave-particle duality. In particular, if de Broglie was right, electrons could be made to interfere with each other just like photons. By passing electrons through rows of atoms in a nickel crystal, physicists Clinton Davisson (1881–1958) and Lester Germer (1896–1971) proved in 1927 that de Broglie was indeed correct: Interference patterns can be created using electrons. Einstein had shown that waves are particles: Now it had been shown that particles are also waves.


The photoelectric effect occurs when light is shone on certain metals and, as a result, electrons fly off the surface of the metal. According to the wave theory of light, this occurs because light waves impart energy to the electrons, knocking them out of the metal much as ocean waves crashing on a rocky beach might fling rocks into the air. Bigger waves can throw rocks farther, so more intense (brighter) light should, similarly, produce electrons with more energy.

But the photoelectric effect doesn't work this way. For a given color (wavelength) of light, the maximum electron energy is the same for bright light or dim light. When the light is made more intense, more electrons are knocked out of the metal, but they do not have higher maximum energy. The only way to produce electrons with higher energy is to use light with a shorter wavelength (bluer light).

In 1905, German-American physicist Albert Einstein (1879–1955) showed that the photoelectric effect can be explained by assuming that light consists of tiny particles called photons. Each photon carries a fixed quantity (or “quantum”) of energy and can deliver that energy to a single electron. The maximum energy of the kicked-out electrons is therefore limited by the energy in each photon, not by how many photons are arriving (the intensity or brightness of the light). And the energy in each photon is determined by the wavelength of the light.

Modern Cultural Connections

However counterintuitive (differing from normal perceptions and assumptions), the wave nature of light was well-established experimentally. It is, therefore, a human limitation that we cannot accurately describe the exact nature of light, but must instead characterize it in terms such as particles and waves, a situation which further forces us to accept that light has characteristics of both a particles and waves, no matter how hard this situation might be to picture in the mind's eye.


The classic proof that particles have wave properties is the two-slit interference experiment. In this experiment, a barrier is set up with two slits cut in it so that particles shot towards the barrier might pass through either slit. On the far side of the barrier, arriving particles are counted by photographic film or some other method. An interference pattern is observed at the detector, stripes where particles are more (and less) likely to arrive. The areas of likeliest arrival are regions of positive interference between waves (particles) passing out of the slits.

Strangely, electrons, photons, and other particles not only interfere with each other when passing through an interferometer, but with themselves. That is, even when particles are shot at the barrier one at a time, the interference pattern built up on the far side over many trials is exactly the same as if they were fired in showers. This leads to the conclusion that each single particle passes, wavelike, through both slits at the same time—even though, if a detector is placed in either or both slits, the particle is always found to have chosen only one path or the other. At the same time, this act of detection destroys the interference pattern: It is as if trying to catch the particle in the act of being a wave forces it to stop being a wave. As Bohr put it, the types of properties—particle or wave—that we can attribute to a quantum system depend on the type of observation we choose to make of that system. For example, measuring the location of a particle collapses its wavelike properties.

It should be remembered that wave-particle duality is not an effect that appears only in experimental setups. All particles and waves, everywhere and at all times, possess wave-particle duality.

The impact of wave-particle duality on physics, on technology via physics, and on society via technology has been profound. In 2007, physicist Alain Aspect (1947–) described wave-particle duality as “the main ingredient of the first quantum revolution,” that is, that burst of new physics knowledge in the early twentieth century that led eventually to the transistor, the laser, and the other microelectronic devices that have made our information-dependent society possible.

Scientists continue to test wave-particle duality. For example, the de Broglie quantum theory asserts that even large objects like people and cars have wave-particle duality; however, to state a claim theoretically is not the same as experimentally proving it. Scientists have therefore sought to detect the wave-particle duality of larger and larger particles by forcing them to produce

interference patterns just like photons or electrons. As of 2007, the largest particle whose wave-particle duality had been observed in the laboratory was the C 60 F 48 molecule, 60 carbon atoms combined with 48 fluorine atoms (atomic weight 1,632).

In philosophy and theology, wave-particle duality has diminished the persuasiveness of what are sometimes called Either-Or arguments—arguments that rely on the common-sense assumption that a thing cannot have two natures at once or be in two places at once. Other influences by wave-particle duality on society are mostly indirect, mediated by the growth of information technologies. Quantum cryptography, quantum computing, and the engineering of nanometer-scale transistors are all technologies depending on acceptance and use of the nature of wave-particle duality.

Primary Source Connection

Something is counterintuitive if it is different from what everyday experience or common sense suggests. Wave-particle duality is a part of the often counterintuitive quantum world and its increasingly broad application. It forces scientists into sometimes philosophically uncomfortable arguments in which acceptance of experimental results is paramount, and the inability to articulate or comprehend the exact state of nature provides insight on the limitations of human thought and perception.

In a heralded 1996 article, “Weirdness Makes Sense,” published in the New York Times, Timothy Ferris (1944–), a professor emeritus of journalism at the University of California at Berkeley, wrote of the paradoxes of the quantum world. In the excerpt published below he articulated the difficulties in reconciling the quantum theory with the logic and language of everyday experience.


If the next Einstein were born today, what might he or she be doing in the year 2022, having reached the age, 26, at which Einstein formulated the theory of relativity?

My suggestion would be—solving the problem of quantum weirdness. The term is scientific slang. It stands for a conundrum, more properly known as the “quantum observership” or “quantum measurement” problem, that has defied some of our century's strongest minds.

Quantum physics is a famously strange realm where matter, energy and knowledge are spooned out in indivisible units, the quanta—as if the world were a pub where you could quaff a pint of beer, or no beer, but never a half pint. In quantum physics we have learned to accept such unlikelihoods as “quantum leaps,” in which particles vanish from one place and reappear in another—instantly. (Raymond Chiao of the University of California at Berkeley has recently measured photons, the carriers of light, quantum-leaping at velocities that would amount to twice the speed of light if they crossed the intervening space, which they don't.) But quantum physics itself is not the problem. It remains a highly successful branch of science that promises to cruise with flying colors through the centennial, in 2000, of Max Planck's discovery of the quantum principle. Weirdness arises when we try to reconcile some of the oddities of the quantum world with the dictates of common sense.

The history of that effort is littered with the bleached bones of mighty thinkers. Einstein pondered its paradoxes for decades and got next to nowhere. Niels Bohr didn't get much further. David Bohm, John Stewart Bell and Hugh Everett 3d labored mightily at it, and may someday be revered as pioneers, but all three went to their graves with little more than obscurity to reward their efforts. Quantum weirdness is so weird that just discussing it stands the normal rules of exposition on their heads: to understand it is to become not enlightened but confused. As the physicist John Archibald Wheeler says, “The quantum is the greatest mystery we've got.”

Some scientists dismiss quantum weirdness as a mere brain teaser. But it was a brain teaser that started Einstein on the road to relativity, when at age 16 he wondered what he would see if he observed an electromagnetic field while traveling at the velocity of light. Superconductivity was once a brain teaser. So were the mathematical oddities that led to digital computers. With recent improvements in technology, physicists are actually conducting the thought experiments that Einstein and Bohr could only imagine, and their efforts have already led to intriguing technological breakthroughs—a new kind of laser in Germany, a demonstration of quantum cryptography in England and the promise of powerful microscopes, miniature particle colliders and computers fast enough to break any code. Where such diamonds are strewn on the surface, it's reasonable to wonder what lies deeper down.

The essence of quantum weirdness can be summed up in the statement that quantum systems—typically, photons and electrons, things smaller than an atom—exhibit “nonlocal” behavior. In all previous scientific investigations, nature acts locally. For a cause here to produce an effect over there, an intervening mechanism must link the two. Such a mechanism is “local” in that you can identify it here and now; the waves that make a skiff bob in its moorings can be traced to a passing ship. If no waves or other mechanisms could be found connecting the ship to the skiff, we would have nonlocal behavior, which seems as inexplicable as if a car were to continue accelerating down the road after losing its drive shaft.

Newton worried that his theory of gravitation was non-local, since he never found a mechanism that could propagate gravitational force across space. Einstein cleared that up with the general theory of relativity, which revealed that gravitation results from the curvature of space. Changes in a gravitational field are conveyed, at the velocity of light, by ripples in space itself. As Einstein also found, neither this nor any other causal mechanism can work at faster than light speed. Yet quantum systems evidently behave in such a way that a cause here produces an effect over there instantaneously, with no discernable causal mechanism between the two points, and with insufficient time for such a mechanism, working at light speed, to have carried the news from one place to the other. Einstein regarded nonlocality as absurd. He called it “spooky action at a distance.”

Quantum nonlocality first reared its weird head with Werner Heisenberg's uncertainty principle. Heisenberg discovered that certain kinds of information about quantum systems can be obtained only at the cost of forsaking other kinds of information. You can ascertain exactly where a particle is (its position) or exactly where it is going (its momentum), but not both. The more precisely you pinpoint its position, the less you can know about its momentum, and vice versa. It is as if you were handed an autographed baseball in a lightless room and told you could take but a single flash photograph of it. The photo might show the signature on the ball, or it might show the manufacturer's emblem embossed on the opposite side, or part of the signature and part of the emblem. But you could not learn everything about both the autograph and the emblem from a single photo. Bohr called these complementary aspects of the system. In real life, you could take the baseball out into the sunlight and examine it fully. But with quantum systems, what you see is all you get.

The central tenet of complementarity resides in the “wave-particle duality.” Subatomic particles act like either waves or particles, depending on how they are examined. But common sense says they cannot be both at once, since waves and particles behave very differently. A wave is all over the place; a particle is in one place only.

The distinction is demonstrated by a simple test that the physicist Richard Feynman called “the experiment with the two holes.” To run the experiment, punch two small holes in a sheet of steel, fire a stream of photons or other quanta at the sheet and record what comes through, using a detector of some sort on the far side of the steel sheet. (The detector can be something as simple as a sheet of photographic film.) When both holes are open, the detector records an interference pattern—the signature of interacting waves. Drop two stones in a pond and an interference pattern appears where the waves intersect. Wave peaks reinforce each other where they coincide, as do valleys, and where a wave peak intersects with a valley, the two cancel each other out. In the two-holes experiment, the interference pattern appears even if you send only a single photon through the apparatus: the photon finds its way through both holes and interferes with itself. Close one hole, however, and the photon's wavelike behavior disappears. Now it acts like a bullet: either it emerges from the single open hole to register a point impact on the detector, or it misses the hole and hits the steel sheet, and nothing comes through.

The weird thing is that the photon does this—responds to whether one or both holes are open—instantly, even if you wait until the last moment, just before it reaches the steel sheet, before deciding to close one hole or leave both open. It is as if the particle (or wave, whichever you prefer) were everywhere at once, feeling out the entire setup and responding to it instantaneously, everywhere.

Bohr explained the wave-particle duality by declaring that subatomic systems don't have either of their complementary states until they are observed. This view came to be known as the “Copenhagen” interpretation of quantum mechanics, named for the city where Bohr and his colleagues set up shop. It might be summarized as “Don't ask, don't tell.” Are photons particles or waves? Don't ask! They are neither—or they are both. Their complementary states are only resolved, one way or the other, by their being observed.

In 1935 the Austrian physicist Erwin Schrodinger challenged Bohr's view of the role of observation in quantum systems by proposing a famous thought experiment, known ever since as “Schrodinger's cat.” An unfortunate cat is placed in a sealed box with a quantum device that has a 50–50 chance of going to a particular state within, say, one hour. If the state is not achieved, nothing happens. If it is achieved, it explodes a cyanide capsule and kills the cat. At the end of the hour, but before we open the box, what has happened? If we accept the Copenhagen assertion that the system has no state until it is observed, we have to believe that the cat, until observed, remains in a “superposed” state of both dead and alive. If you object that the cat itself made the observation, then let's leave the cat out of it, run the experiment with an empty box, then clear the laboratory except for a graduate student who opens the box and will be killed if the cyanide has been released. As we stand outside the closed lab door, we reflect that according to Bohr the cyanide has been neither released nor unreleased until the student opens the box. The student's own observation, and not the prior state of the cyanide canister, will decide whether he lives or dies. Does anybody believe that the world really works this way?

To further highlight the weirdness of the Copenhagen view, Einstein and two of his Princeton colleagues constructed the E.P.R. (Einstein-Podolsky-Rosen) thought experiment. Let an atom spit out two particles, which then fly apart for an enormous distance. The physics equations tell us that the two particles must have opposite spin: if one is “spin up,” the other must be “spin down.” But according to the Copenhagenians, the particles have no spin state at all until observed. So now we observe one particle and find, say, that it is spin up. We have thus “resolved” the spin state of a particle that allegedly had no such state until we made the observation. But that means that the other particle, millions of miles away, suddenly “became” spin down. How did it know that its state was now supposed to be spin down?

Logic would seem to dictate that the particles actually had spin states all along. Einstein took that position, postulating that some underlying, causal agency must carry the spin. In other words, the spin state is not decided at the moment of observation after all, as Bohr claimed, but was in the particles to start with. But there is no evidence that any such mechanism exists. Theories like Einstein's are therefore known as “hidden variables” interpretations, since they propose the existence of something hidden in the quantum systems.

Since the Copenhagen view rejected hidden variables, the question remained at an impasse for decades. Which interpretation a given physicist preferred mainly depended on which seemed less repugnant, the hidden variables theory or spooky action at a distance.

Then the Irish physicist John Stewart Bell thought up an experiment that would decide whether hidden variables exist, as Einstein believed. The experiment, which involved obtaining the statistics of large numbers of photon interactions, was not technologically feasible when he proposed it in 1964. But in the 1970's Bell's experiment was performed, first by John Clauser and Stuart J. Freedman at Berkeley and later by Alain Aspect and his colleagues at the University of Paris. The verdict was clear: there are no hidden variables of the sort Einstein envisioned. Quantum physics really does exhibit nonlocality.

Some scientists reacted with a shrug of the shoulders. Quantum physics is simply like that, they asserted, and if it doesn't fit our notions of common sense, too bad. But quantum weirdness remains disturbing insofar as we wish to reconcile quantum theory with the logic and language of the wider world—something that Bohr himself held to be a fundamental imperative of the scientific enterprise. And as Feynman noted, quantum weirdness “is impossible, absolutely impossible to explain in any classical way. …”

Timothy Ferris

ferris, timothy. “weirdness makes sense” new york times (september 29, 1996).

See Also Physics: Heisenberg Uncertainty Principle; Physics: Maxwell's Equations, Light and the Electromagnetic Spectrum; Physics: Optics; Physics: QED Gauge Theory and Renormalization; Physics: The Quantum Hypothesis.



Achinstein, Peter. Particles and Waves. New York: Oxford University Press, 1991.

de Broglie, Louis. Physics and Microphysics. Wakefield, MA: Pantheon Books, 1955.

de Broglie, Louis. The Revolution in Physics: A Non-Mathematical Survey of Quanta. New York: Noonday Press 1960.


Arndt, Markus, et al. “Wave-particle Duality of C60 Molecules.” Nature 401 (1999): 680–682.

DeKieviet, Maarten, and Joerg Schmiedmayer. “Atom Waves in Passing.” Nature 437 (2005):1102.

Dowling, Jonathan P. “To Compute or Not to Compute?” Nature 439 (2006): 919–920.

Ferris, Timothy. “Weirdness Makes Sense.” New York Times (September 29, 1996).

Rae, Alastair I. “Waves, Particles, and Fullerenes.” Nature 401 (1999): 651–653.

Larry Gilman

Paul Davies

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Physics: Wave–Particle Duality

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