wave and particle behaviors of lcd displays for sale

The theoretical sketch of the wave-particle scheme for the single photon is displayed in Fig. 1. A photon is initially prepared in a polarization state \(\left| {{\psi _0}} \right\rangle = {\rm{cos}}\,\alpha \left| {\rm V} \right\rangle + {\rm{sin}}\,\alpha \left| {\rm{H}} \right\rangle\), where \(\left| {\rm V} \right\rangle\) and \(\left| {\rm{H}} \right\rangle\) are the vertical and horizontal polarization states and α is adjustable by a preparation half-wave plate (not shown in the figure). After crossing the preparation part of the setup of Fig. 1 (see Supplementary Notes 1 and 2 and Supplementary Fig. 1 for details), the photon state is

$$\left| {{\psi _{\rm{f}}}} \right\rangle = {\rm{cos}}\,\alpha \left| {{\rm{wave}}} \right\rangle + {\rm{sin}}\,\alpha \left| {{\rm{particle}}} \right\rangle ,$$

$$\begin{array}{*{20}{l}}\\ {\left| {{\rm{wave}}} \right\rangle } = {{e^{i{\phi _1}/2}}\left( {{\rm{cos}}\frac{{{\phi _1}}}{2}\left| 1 \right\rangle - i\,{\rm{sin}}\frac{{{\phi _1}}}{2}\left| 3 \right\rangle } \right),} \hfill \\ {\left| {{\rm{particle}}} \right\rangle } = {\frac{1}{{\sqrt 2 }}\left( {\left| 2 \right\rangle + {e^{i{\phi _2}}}\left| 4 \right\rangle } \right),} \hfill \\ \end{array}$$

operationally represent the capacity \(\left( {\left| {{\rm{wave}}} \right\rangle } \right)\) and incapacity \(\left( {\left| {{\rm{particle}}} \right\rangle } \right)\) of the photon to produce interference\(\left| {{\rm{wave}}} \right\rangle\) state the probability of detecting the photon in the path \(\left| n \right\rangle \,\) (n = 1, 3) depends on the phase ϕ

1: the photon must have traveled along both paths simultaneously (see upper MZI in Fig. 1), revealing its wave behavior. Instead, for the \(\left| {{\rm{particle}}} \right\rangle\) state the probability to detect the photon in the path \(\left| n \right\rangle \,\) (n = 2, 4) is 1/2, regardless of phase ϕ

2: thus, the photon must have crossed only one of the two paths (see lower MZI of Fig. 1), showing its particle behavior. Notice that the scheme is designed in such a way that \(\left| {\rm V} \right\rangle\)

Conceptual figure of the wave-particle toolbox. A single photon is coherently separated in two spatial modes by means of a polarizing beam-splitter (PBS) according to its initial polarization state (in). A half-wave plate (HWP) is placed after the PBS to obtain equal polarizations between the two modes. One mode is injected in a complete Mach-Zehnder interferometer (MZI) with phase ϕ

1, thus exhibiting wave-like behavior. The second mode is injected in a Mach-Zehnder interferometer lacking the second beam-splitter, thus exhibiting particle-like behavior (no dependence on ϕ

To verify the coherent wave-particle superposition as a function of the parameter α, the wave and particle states have to interfere at the detection level. This goal is achieved by exploiting two symmetric beam-splitters where the output paths (modes) are recombined, as illustrated in the detection part of Fig. 1. The probability P

We remark that the terms \({{\cal I}_{\rm{c}}}\), \({{\cal I}_{\rm{s}}}\) in the detection probabilities exclusively stem from the interference between the \(\left| {{\rm{wave}}} \right\rangle\) and \(\left| {{\rm{particle}}} \right\rangle\) components appearing in the generated superposition state \(\left| {{\psi _{\rm{f}}}} \right\rangle\) of Eq. (1). This fact is further evidenced by the appearance, in these interference terms, of the factor \({\cal C} = {\rm{sin}}\,2\alpha\), which is the amount of quantum coherence owned by \(\left| {{\psi _{\rm{f}}}} \right\rangle\) in the basis {\(\left| {{\rm{wave}}} \right\rangle\), \(\left| {{\rm{particle}}} \right\rangle\)} theoretically quantified according to the standard l

1-norm\({{\cal I}_{\rm{c}}}\), \({{\cal I}_{\rm{s}}}\) are always identically zero (independently of phase values) when the final state of the photon is: (i) \(\left| {{\rm{wave}}} \right\rangle\) (α = 0); (ii) \(\left| {{\rm{particle}}} \right\rangle\) (α = π/2); (iii) a classical incoherent mixture \({\rho _{\rm{f}}} = {\rm{co}}{{\rm{s}}^2}\alpha \left| {{\rm{wave}}} \right\rangle \left\langle {{\rm{wave}}} \right| + {\rm{si}}{{\rm{n}}^2}\alpha \left| {{\rm{particle}}} \right\rangle \left\langle {{\rm{particle}}} \right|\) (which can be theoretically produced by the same scheme starting from an initial mixed polarization state of the photon).

The experimental single-photon toolbox, realizing the proposed scheme of Fig. 1, is displayed in Fig. 2 (see Methods for more details). The implemented layout presents the advantage of being interferometrically stable, thus not requiring active phase stabilization between the modes. Figure 3 shows the experimental results for the measured single-photon probabilities P

n. For α = 0, the photon is vertically polarized and entirely reflected from the PBS to travel along path 1, then split at BS1 into two paths, both leading to the same BS3 which allows these two paths to interfere with each other before detection. The photon detection probability at each detector Dn (n = 1, 2, 3, 4) depends on the phase shift ϕ

1: \({P_1}\left( {\alpha = 0} \right) = {P_2}\left( {\alpha = 0} \right) = \frac{1}{2}{\rm{co}}{{\rm{s}}^2}\frac{{{\phi _1}}}{2}\), \({P_3}\left( {\alpha = 0} \right) = {P_4}\left( {\alpha = 0} \right) = \frac{1}{2}{\rm{si}}{{\rm{n}}^2}\frac{{{\phi _1}}}{2}\), as expected from Eqs. (3) and (4). After many such runs an interference pattern emerges, exhibiting the wave-like nature of the photon. Differently, if initially α = π/2, the photon is horizontally polarized and, as a whole, transmitted by the PBS to path 2, then split at BS2 into two paths (leading, respectively, to BS4 and BS5) which do not interfere anywhere. Hence, the phase shift ϕ

2 plays no role on the photon detection probability and each detector has an equal chance to click: \({P_1}\left( {\alpha = \frac{\pi }{2}} \right) = {P_2}\left( {\alpha = \frac{\pi }{2}} \right) = {P_3}\left( {\alpha = \frac{\pi }{2}} \right) = {P_4}\left( {\alpha = \frac{\pi }{2}} \right) = \frac{1}{4}\), as predicted by Eqs. (3) and (4), showing particle-like behavior without any interference pattern. Interestingly, for 0 < α < π/2, the photon simultaneously behaves like wave and particle. The coherent continuous morphing transition from wave to particle behavior as α varies from 0 to π/2 is clearly seen from Fig. 4a and contrasted with the morphing observed for a mixed incoherent wave-particle state ρ

2 = 0, the coherence of the generated state is also directly quantified by measuring the expectation value of an observable \(\sigma _x^{1234}\), defined in the four-dimensional basis of the photon paths \(\left\{ {\left| 1 \right\rangle ,\left| 2 \right\rangle ,\left| 3 \right\rangle ,\left| 4 \right\rangle } \right\}\) of the preparation part of the setup as a Pauli matrix σ

x between modes (1, 2) and between modes (3, 4). It is then possible to straightforwardly show that \(\left\langle {\sigma _x^{1234}} \right\rangle = {\rm{Tr}}\left( {\sigma _x^{1234}{\rho _{\rm{f}}}} \right) = 0\) for any incoherent state ρ

f, while \(\sqrt 2 \left\langle {\sigma _x^{1234}} \right\rangle = {\rm{sin}}\,2\alpha = {\cal C}\) for an arbitrary state of the form \(\left| {{\psi _{\rm{f}}}} \right\rangle\) defined in Eq. (1). Insertion of beam-splitters BS4 and BS5 in the detection part of the setup (corresponding to β = 22.5° in the output wave-plate of Fig. 2) rotates the initial basis \(\left\{ {\left| 1 \right\rangle ,\left| 2 \right\rangle ,\left| 3 \right\rangle ,\left| 4 \right\rangle } \right\}\) generating a measurement basis of eigenstates of \(\sigma _x^{1234}\), whose expectation value is thus obtained in terms of the detection probabilities as \(\left\langle {\sigma _x^{1234}} \right\rangle = {P_1} - {P_2} + {P_3} - {P_4}\) (see Supplementary Note 2). As shown in Fig. 4c, d, the observed behavior of \(\sqrt 2 \left\langle {\sigma _x^{1234}} \right\rangle\) as a function of α confirms the theoretical predictions for both coherent \(\left| {{\psi _{\rm{f}}}} \right\rangle\) (Fig. 4c) and mixed (incoherent) ρ

f wave-particle states (the latter being obtained in the experiment by adding a relative time delay in the interferometer paths larger than the photon coherence time to lose quantum interference, Fig. 4d).

Experimental setup for wave-particle states. a Overview of the apparatus for the generation of single-photon wave-particle superposition. An heralded single-photon is prepared in an arbitrary linear polarization state through a half-wave plate rotated at an angle α/2 and injected into the wave-particle toolbox. b Overview of the apparatus for the generation of a two-photon wave-particle entangled state. Each photon of a polarization entangled state is injected into an independent wave-particle toolbox to prepare the output state. c Actual implemented wave-particle toolbox, reproducing the action of the scheme shown in Fig. 1. Top subpanel: top view of the scheme, where red and purple lines represent optical paths lying in two vertical planes. Bottom subpanel: 3-d scheme of the apparatus. The interferometer is composed of beam-displacing prisms (BDP), half-wave plates (HWP), and liquid crystal devices (LC), the latter changing the phases ϕ

2. The output modes are finally separated by means of a polarizing beam-splitter (PBS). The scheme corresponds to the presence of BS4 and BS5 in Fig. 1 for β = 22.5°, while setting β = 0 equals to the absence of BS4 and BS5. The same color code for the optical elements (reported in the figure legend) is employed for the top view and for the 3-d view of the apparatus. d Picture of the experimental apparatus. The green frame highlights the wave-particle toolbox

1, for different values of α. a Wave behavior (α = 0). b Particle behavior (α = π/2). c Coherent wave-particle superposition (α = π/4). d Incoherent mixture of wave and particle behaviors (α = π/4). Points: experimental data. Dashed curves: best-fit of the experimental data. Color legend: orange (P1), green (P2), purple (P3), blue (P

1 and of the angle α. Points: experimental data. Surfaces: theoretical expectations. In all plots, error bars are standard deviation due to the Poissonian statistics of single-photon counting

4). In a black triangles highlighted the position for wave behavior (α = 0), black circle for particle behavior (α = π/2) and black diamonds highlight the position for coherent wave-particle superposition behavior (α = π/4). c Coherence measure \(\sqrt 2 \left\langle {\sigma _x^{1234}} \right\rangle\) as a function of α in the coherent case and d for an incoherent mixture (the latter showing no dependence on α). Points: experimental data. Solid curves: theoretical expectations. Error bars are standard deviations due to the Poissonian statistics of single-photon counting

The above single-photon scheme constitutes the basic toolbox which can be extended to create a wave-particle entangled state of two photons, as shown in Fig. 2b. Initially, a two-photon polarization maximally entangled state \({\left| \Psi \right\rangle _{{\rm{AB}}}} = \frac{1}{{\sqrt 2 }}\left( {\left| {{\rm VV}} \right\rangle + \left| {{\rm{HH}}} \right\rangle } \right)\) is prepared (the procedure works in general for arbitrary weights, see Supplementary Note 3). Each photon is then sent to one of two identical wave-particle toolboxes which provide the final state

$${\left| \Phi \right\rangle _{{\rm{AB}}}} = \frac{1}{{\sqrt 2 }}\left( {\left| {{\rm{wave}}} \right\rangle \left| {{\rm{wave}"}} \right\rangle + \left| {{\rm{particle}}} \right\rangle \left| {{\rm{particle}"}} \right\rangle } \right),$$

where the single-photon states \(\left| {{\rm{wave}}} \right\rangle\), \(\left| {{\rm{particle}}} \right\rangle\), \(\left| {{\rm{wave}"}} \right\rangle\), \(\left| {{\rm{particle}"}} \right\rangle\) are defined in Eq. (2), with parameters and paths related to the corresponding wave-particle toolbox. Using the standard concurrenceC to quantify the amount of entanglement of this state in the two-photon wave-particle basis, one immediately finds C = 1. The generated state \({\left| \Phi \right\rangle _{{\rm{AB}}}}\) is thus a wave-particle maximally entangled state (Bell state) of two photons in separated locations.

The output two-photon state is measured after the two toolboxes. The results are shown in Fig. 5. Coincidences between the four outputs of each toolbox are measured by varying ϕ

1 and \(\phi _1^{\prime}\). The first set of measurements (Fig. 5a–d) is performed by setting the angles of the output wave-plates (see Fig. 2c) at {β = 0, β′ = 0}, corresponding to removing both BS4 and BS5 in Fig. 1 (absence of interference between single-photon wave and particle states). In this case, detectors placed at outputs (1, 3) and (1′, 3′) reveal wave-like behavior, while detectors placed at outputs (2, 4) and (2′, 4′) evidence a particle-like one. As expected, the two-photon probabilities \({P_{n{n^{\prime}}}}\) for the particle detectors remain unchanged while varying ϕ

1 and \(\phi _1^{\prime}\), whereas the \({P_{nn"}}\) for the wave detectors show interference fringes. Moreover, no contribution of crossed wave-particle coincidences \({P_{nn"}}\) is obtained, due to the form of the entangled state. The second set of measurements (Fig. 5e–h) is performed by setting the angles of the output wave-plates at {β = 22.5°, β′ = 22.5°}, corresponding to the presence of BS4 and BS5 in Fig. 1 (the presence of interference between single-photon wave and particle states). We now observe nonzero contributions across all the probabilities depending on the specific settings of phases ϕ

1 and \(\phi _1^{\prime}\). The presence of entanglement in the wave-particle behavior is also assessed by measuring the quantity \({\cal E} = {P_{22"}} - {P_{21"}}\) as a function of ϕ

1, with fixed \(\phi _1^{\prime} = {\phi _2} = \phi _2^{\prime} = 0\). According to the general expressions of the coincidence probabilities (see Supplementary Note 3), \({\cal E}\) is proportional to the concurrence C and identically zero (independently of phase values) if and only if the wave-particle two-photon state is separable (e.g., \(\left| {{\rm{wave}}} \right\rangle\) ⊗ \(\left| {{\rm{wave}"}} \right\rangle\) or a maximal mixture of two-photon wave and particle states). For \(\left| \Phi \right\rangle\)

AB of Eq. (5) the theoretical prediction is \({\cal E} = \left( {1{\rm{/}}4} \right){\rm{co}}{{\rm{s}}^{\rm{2}}}\left( {{\phi _1}{\rm{/}}2} \right)\), which is confirmed by the results reported in Fig. 5i, j (within the reduction due to visibility). A further test of the generated wave-particle entanglement is finally performed by the direct measure of the expectation values \(\left\langle {\cal W} \right\rangle = {\rm{Tr}}\left( {{\cal W}\rho } \right)\) of a suitable entanglement witness

z Pauli matrix between modes (1, 2) and between modes (3, 4). The measurement basis of \(\sigma _z^{1234}\) is that of the initial paths \(\left\{ {\left| 1 \right\rangle ,\left| 2 \right\rangle ,\left| 3 \right\rangle ,\left| 4 \right\rangle } \right\}\) exiting the preparation part of the single-photon toolbox. It is possible to show that \({\rm{Tr}}\left( {{\cal W}{\rho _{\rm{s}}}} \right) \ge 0\) for any two-photon separable state ρ

e is entangled in the photons wave-particle behavior (see Supplementary Note 3). The expectation values of \({\cal W}\) measured in the experiment in terms of the 16 coincidence probabilities P

1 = 0, \(\phi _1^\prime\) = π). These observations altogether prove the existence of quantum correlations between wave and particle states of two photons in the entangled state \(\left| \Phi \right\rangle\)

Generation of wave-particle entangled superposition with a two-photon state. Measurements of the output coincidence probabilities \({P_{nn"}}\) to detect one photon in output mode n of the first toolbox and one in the output mode n′ of the second toolbox, with different phases ϕ

1 = π and \(\phi _1^{\prime} = \pi\). White bars: theoretical predictions. Colored bars: experimental data. Orange bars: \({P_{n{n^{\prime}}}}\) contributions for detectors Dn and \({{\rm{D}}_{n"}}\) linked to wave-like behavior for both photons (in the absence of BS4 and BS5). Cyan bars: \({P_{nn"}}\) contributions for detectors Dn and \({{\rm{D}}_{n"}}\) linked to particle-like behavior for both photons (in the absence of BS4 and BS5). Magenta bars: \({P_{nn"}}\) contributions for detectors Dn and \({{\rm{D}}_{n"}}\) linked to wave-like behavior for one photon and particle-like behavior for the other one (in absence of BS4 and BS5). Darker regions in colored bars correspond to 1 σ error interval, due to the Poissonian statistics of two-photon coincidences. i, j, Quantitative verification of wave-particle entanglement. i, \({P_{22"}}\) (blue) and \({P_{21"}}\) (green) and j, \({\cal E} = {P_{22"}} - {P_{21"}}\), as a function of ϕ

1 for \(\phi _1^{\prime} = 0\) and {β = 22.5°, β′ = 22.5°}. Error bars are standard deviations due to the Poissonian statistics of two-photon coincidences. Dashed curves: best-fit of the experimental data

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The type of home-focused indoor air-monitoring devices we evaluated for this guide offer less information by comparison, as they typically measure only the local airborne particle levels and sometimes volatile organic compounds—gases like the vapors from paint, cleaners, and glue. They rarely measure carbon monoxide and radon, two potentially deadly gases. Many smoke detectors also detect carbon monoxide; see our guide to smoke alarms for more about them. The EPA has a guide to radon, including state-by-state resources for knowing whether your region is at risk and how to get your home tested. And whether you have measured proof or just a hunch that your indoor air quality is poor, there are simple, consistently effective ways to clear the air as much as possible: Run an air purifier or upgrade your HVAC filters to capture fine airborne particles, and open your windows on nice days to vent any volatile organic compounds.

For 2022, we have added a recommendation for a CO2 (carbon dioxide) monitor. Researchers at the University of Colorado in Boulder found that CO2 levels could be used as a proxy for coronavirus risk in crowded public indoor spaces because we exhale both CO2 and, if we’re sick, viruses in the same breath. And even absent the virus, both public spaces and homes can accumulate high levels of CO2 from everyday activities—not just breathing, but from using gas stoves and water heaters. We contacted a researcher to talk about using CO2 monitors for air quality measurements, and together we came up with a product recommendation, as well as some advice on how to interpret and react to its information when monitoring CO2 at home.

The EPA’s free AirNow app is easily searchable, delivers air quality readings in almost every corner of the US, and lets you know in advance of upcoming air quality problems.

We recommend using the AirNow app as your first step because outdoor conditions usually cause any indoor air quality issues you may experience. Although AirNow isn’t the only app of its kind, we found in our research that many other air quality apps simply repackage the data that the EPA stations gather, often without adding much clarity, new information, or interface improvements. Compared with AirNow, some apps make it harder to pinpoint your location, whereas others use a less complete network of monitoring stations to gather the data. AirNow offers you the simplest way to get the info and interpret what it means. And—unlike other apps we tested—it doesn’t bombard you with ads the whole time.

The concentration of carbon dioxide (CO2) in indoor spaces is usually higher than in natural outdoor air, and it can rise to levels that impair cognitive function. The main reasons are the combustion of natural gas and of simply exhaling CO2. If you’d like to know how much CO2 is in your home’s or office’s air, the Aranet 4 is our pick. Its measurements are easy to read onscreen, as are its alerts when the level is getting too high. Its app also sends alerts, works with both iOS and Android, and adds seven-day trend monitoring to help you identify patterns of high CO2. And, helping to offset the cost, the high-quality sensor should last for up to seven years.

This device sits on a desk or table and presents indoor air quality readings of particulates, but we’re concerned about its VOC measures and its long-term durability.

We understand that many people reading this guide really do want to take indoor measurements, and for that we suggest the Temtop M10 Air Quality Monitor—with caveats. A lot of the air quality monitors we’ve considered over more than two years of research for this guide have too many credible reports of faulty sensors and connectivity problems for us to strongly recommend them. The M10 is distinguished by its simplicity, though, with a bright display showing particulate measurements (that we confirmed to be accurate), a tiny size, and a lack of Wi-Fi connectivity (a good thing in this case). It’s also affordable enough for you to keep your expectations relatively low—and there’s good reason for you to approach it that way. As with other inexpensive air quality monitors, its VOC measurement is dubious, and some buyers have reported that their M10 arrived damaged or failed within a few weeks.

Quantum objects are notoriously shifty. Take the photon, for example. The quantum of light can act as a particle one moment, following a well-defined path like a tiny projectile, and a wave the next, overlapping with its ilk to produce interference patterns, much like a ripple on the water.

Wave–particle duality is a key feature of quantum mechanics, one not easily understood in the intuitive terms of everyday experience. But the dual nature of quantum entities gets stranger still. New experiments demonstrate that photons not only switch from wave to particle and back again but can actually harbor both wave and particle tendencies at the same time. In fact, a photon can run through a complex optical apparatus and disappear for good into a detector without having decided on an identity—assuming a wave or particle nature only after it has been destroyed.

Physicists have shown in recent years that a photon "chooses" whether to act as a wave or a particle only when forced. If, for instance, a photon is steered by a beam splitter (a kind of fork in the optical road) onto one of two paths, each leading to a photon detector, the photon will appear at one or the other detector with equal probability. In other words, the photon simply chooses one of the routes and follows it to the end, like a marble rolling through a tube. But if the split paths recombine before the detectors, allowing the contents of the two channels to interfere like waves flowing around a pillar to meet on the other side, the photon demonstrates wavelike interference effects, having essentially traversed both paths at once. In other words, measure a photon like a particle, and it behaves like a particle. Measure a photon like a wave, and it acts like one.

One might suspect that photons simply assume one of two behaviors—wave or particle—beforehand, or when they hit the beam splitter. But a 2007 "delayed choice" experiment ruled out that possibility. Physicists using an interferometer, an experimental device that includes the beam splitter, toggled between combining the paths and leaving them separate. But they made the choice only after the photon had passed through the beam splitter. The photons still demonstrated interference effects when recombined, even though (in a simpler world, at least), the particles should already have been forced to decide which path to take.

Now, two research groups have implemented an even more bizarre version of the delayed choice experiment. In two studies in the November 2 issue of Science, a team based in France and a group in England each reported using a quantum switch to toggle the experimental device. Except in this experiment, the switch was not flipped—thus forcing the photon to act like a wave or like a particle—until the physicists had identified the photon in one of the detectors.

By changing the settings on the device, both teams could not only force the experimental photon to behave as a particle or as a wave, but could explore intermediate states as well. "We can continuously morph the behavior of the test photon from wavelike to particlelike behavior," says Sébastien Tanzilli, a study co-author and a quantum optical physicist with the National Center for Scientific Research in Paris who is based at the University of Nice Sophia Antipolis. "Between the two extremes, we have states that come with reduced interference. So we have a superposition of wave and particle."

The key to both experiments is the use of a quantum switch in the apparatus, which allows the interferometer to hover in a superposition of measuring wave or particle behavior. "In these traditional delayed choice experiments, somewhere in your apparatus you have a big, classical binary switch," says Peter Shadbolt, a co-author of the other study and a PhD student in quantum physics at the University of Bristol in England. "It has "wave" written on one side and "particle" written on the other side. What we do is replace that classical switch with a qubit, a quantum bit, which is a second photon in our experiment."

The quantum switch determines the nature of the apparatus—whether the two optical paths recombined to form a closed interferometer, which measures wavelike properties, or remained separate to form an open interferometer, which detects discrete particles. But in both cases, whether the interferometer was open or closed—and whether the photon zipped through the apparatus like a particle or a wave, respectively—was not determined until the physicists measured a second photon. The first photon"s fate was linked to the state of the second photon via the phenomenon of quantum entanglement, through which quantum objects share correlated properties.

In the Bristol group"s experiment, the state of the second photon determines whether the interferometer is open, closed or a superposition of both, which in turn determines the wave or particle identity of the first photon. "In our case that choice is more of a quantum choice," Shadbolt says. "Without this kind of approach, you wouldn"t be able to see this morphing between wave and particle."

The device built by Tanzilli"s group functions similarly—the interferometer is closed for vertically polarized photons (which therefore act as waves) and open for horizontally polarized photons (which behave as particles). Having sent a test photon through the apparatus, the researchers measured an entangled partner photon 20 nanoseconds later to determine the test photon"s polarization, and hence on which side of the wave–particle divide it fell.

Because of the design of the experiment and the nature of entanglement, the test photon"s wave or particle nature was not determined until the second photon was measured—in other words, until 20 nanoseconds after the fact. "The test photon makes its life in the interferometer and is detected, which means it is destroyed," Tanzilli says. "Afterward we determine its behavior." That order of operations takes the concept of delayed choice to the extreme. "It means that space and time seem to not play any role in this affair," Tanzilli adds.

Quantum information researcher Seth Lloyd of the Massachusetts Institute of Technology dubbed the phenomenon "quantum procrastination," or "proquastination" in a commentary for Science accompanying the two research papers. "In the presence of quantum entanglement (in which outcomes of measurements are tied together)," he wrote, "it is possible to hold off making a decision, even if events seem to have already made one."

The new experiments add another wrinkle to the warped world of quantum mechanics, where a photon can be seemingly whatever it wants, whenever it wants. "Feynman called it the one true mystery of quantum mechanics," Shadbolt says of wave–particle duality. "It"s deeply, deeply strange. Quantum mechanics is deeply weird, completely without classical analogue, and we just have to accept it as such."

Light is well known to exhibit both wave-like and particle-like properties, as imaged here in this ... [+]2015 photograph. What"s less well appreciated is that matter particles also exhibit those wave-like properties. Even something as massive as a human being should have wave properties as well, although measuring them will be difficult.Fabrizio Carbone/EPFL (2015)

“Is it a wave or is it a particle?” Never has such a simple question had such a complicated answer as in the quantum realm. The answer, perhaps frighteningly, depends on how you ask the question. Pass a beam of light through two slits, and it acts like a wave. Fire that same beam of light into a conducting plate of metal, and it acts like a particle. Under appropriate conditions, we can measure either wave-like or particle-like behavior for photons — the fundamental quantum of light — confirming the dual, and very weird, nature of reality.

This dual nature of reality isn’t just restricted to light, either, but has been observed to apply to all quantum particles: electrons, protons, neutrons, even significantly large collections of atoms. In fact, if we can define it, we can quantify just how “wave-like” a particle or set of particles is. Even an entire human being, under the right conditions, can act like a quantum wave. (Although, good luck with measuring that.) Here’s the science behind what that all means.

This illustration, of light passing through a dispersive prism and separating into clearly defined ... [+]colors, is what happens when many medium-to-high energy photons strike a crystal. If we struck this prism with a single photon and space were discrete, the crystal could only possibly move a discrete, finite number of spatial steps, but only a single photon would either reflect or transmit.Wikimedia Commons user Spigget

The debate over whether light behaves as a wave or a particle goes all the way back to the 17th century, when two titanic figures in physics history took opposite sides on the issue. On the one hand, Isaac Newton put forth a “corpuscular” theory of light, where it behaved the same way that particles did: moving in straight lines (rays) and refracting, reflecting, and carrying momentum just as any other kind of material would. Newton was able to predict many phenomena this way, and could explain how white light was composed of many other colors.

On the other hand, Christiaan Huygens favored the wave theory of light, noting features like interference and diffraction, which are inherently wave-like. Huygens’ work on waves couldn’t explain some of the phenomena that Newton’s corpuscular theory could, and vice versa. Things started to get more interesting in the early 1800s, however, as novel experiments began to truly reveal the ways in which light was intrinsically wave-like.

The wave-like properties of light, originally hypothesized by Christiaan Huygens, became even better ... [+]understood thanks to Thomas Young"s two-slit experiments, where constructive and destructive interference effects showed themselves dramatically.Thomas Young, 1801

If you take a tank filled with water and create waves in it, and then set up a barrier with two “slits” that allow the waves on one side to pass through to the other, you’ll notice that the ripples interfere with one another. At some locations, the ripples will add up, creating larger magnitude ripples than a single wave alone would permit. At other locations, the ripples cancel one another out, leaving the water perfectly flat even as the ripples go by. This combination of an interference pattern — with alternating regions of constructive (additive) and destructive (subtractive) interference — is a hallmark of wave behavior.

That same wave-like pattern shows up for light, as first noted by Thomas Young in a series of experiments performed over 200 years ago. In subsequent years, scientists began to uncover some of the more counterintuitive wave properties of light, such as an experiment where monochromatic light shines around a sphere, creating not only a wave-like pattern on the outside of the sphere, but a central peak in the middle of the shadow as well.The results of an experiment, showcased using laser light around a spherical object, with the actual ... [+]optical data. Note the extraordinary validation of Fresnel"s wave theory of light prediction: that a bright, central spot would appear in the shadow cast by the sphere, verifying the "absurd" prediction of the wave theory of light. The original experiment was performed by Francois Arago.Thomas Bauer at Wellesley

Later in the 1800s, Maxwell’s theory of electromagnetism allowed us to derive a form of charge-free radiation: an electromagnetic wave that travels at the speed of light. At last, the light wave had a mathematical footing where it was simply a consequence of electricity and magnetism, an inevitable result of a self-consistent theory. It was by thinking about these very light waves that Einstein was able to devise and establish the special theory of relativity. The wave nature of light was a fundamental reality of the Universe.

Those developments and realizations, when synthesized together, led to arguably the most mind-bending demonstration of quantum “weirdness” of all.Double slit experiments performed with light produce interference patterns, as they do for any wave ... [+]you can imagine. The properties of different light colors is understood to be due to the differing wavelengths of monochromatic light of various colors. Redder colors have longer wavelengths, lower energies, and more spread-out interference patterns; bluer colors have shorter wavelengths, higher energies, and more closely bunched maxima and minima in the interference pattern.Technical Services Group (TSG) at MIT’s Department of Physics

If you take a photon and fire it at a barrier that has two slits in it, you can measure where that photon strikes a screen a significant distance away on the other side. If you start adding up these photons, one-at-a-time, you’ll start to see a pattern emerge: an interference pattern. The same pattern that emerged when we had a continuous beam of light — where we assumed that many different photons were all interfering with one another — emerges when we shoot photons one-at-a-time through this apparatus. Somehow, the individual photons are interfering with themselves.

Normally, conversations proceed around this experiment by talking about the various experimental setups you can make to attempt to measure (or not measure) which slit the photon goes through, destroying or maintaining the interference pattern in the process. That discussion is a vital part of exploring the nature of the dual nature of quanta, as they behave as both waves and particles depending on how you interact with them. But we can do something else that’s equally fascinating: replace the photons in the experiment with massive particles of matter.Electrons exhibit wave properties just as well as photons do, and can be used to construct images or ... [+]probe particle sizes just as well as light can. (And in some cases, they can even do a superior job.) This wave-like nature extends to all matter particles, even composite particles and, in theory, macroscopic ones.Thierry Dugnolle

Your initial thought might go something along the lines of, “okay, well photons can act as both waves and particles, but that’s because photons are massless quanta of radiation. They have a wavelength, which explains the wave-like behavior, but they also have a certain amount of energy that they carry, which explains the particle-like behavior.” And therefore, you might expect, that these matter particles would always act like particles, since they have mass, they carry energy, and, well, they’re literally defined as particles!

But in the early 1920s, physicist Louis de Broglie had a different idea. For photons, he noted,each quantum has an energy and a momentum, which are related to Planck"s constant, the speed of light, and the frequency and wavelength of each photon. Each quantum of matter also has an energy and a momentum, and also experiences the same values of Planck’s constant and the speed of light. By rearranging terms in the exact same way as they’d be written down for photons, de Broglie was able to define a wavelength for both photons and matter particles: the wavelength is simply Planck’s constant divided by the particle’s momentum.When electrons are fired at a target, they will diffract off at an angle. Measuring the electrons" ... [+]momenta enables us to determine whether their behavior is wave-like or particle-like, and the 1927 Davisson-Germer experiment was the first experimental confirmation of de Broglie"s "matter wave" theory.Roshan220195 / Wikimedia Commons

Mathematical definitions are nice, of course, but the real test of physical ideas always comes from experiments and observations: you have to compare your predictions with actual tests of the Universe itself. In 1927, Clinton Davisson and Lester Germer fired electrons at a target that produced diffraction for photons, and the same diffraction pattern resulted. Contemporaneously. George Paget fired electrons at thin metal foils, also producing diffraction patterns. Somehow, the electrons themselves, definitively matter particles, were also behaving as waves.

Subsequent experiments have revealed this wave-like behavior for many different forms of matter, including forms that are significantly more complicated than the point-like electron. Composite particles, like protons and neutrons, display this wave-like behavior as well. Neutral atoms, which can be cooled down to nanokelvin temperatures, have demonstrated de Broglie wavelengths that are larger than a micron: some ten thousand times larger than the atom itself. Even molecules with as many as 2000 atoms have been demonstrated to display wave-like properties.In 2019. scientists achieved a quantum superposition of the largest molecule ever: one with over ... [+]2000 individual atoms and a total mass of more than 25,000 atomic mass units. Here, the delocalization of the massive molecules used in the experiment is illustrated.© Yaakov Fein, Universität Wien

Under most circumstances, the momentum of a typical particle (or system of particles) is sufficiently large that the effective wavelength associated with it is far too small to measure. A dust particle moving at just 1 millimeter per second has a wavelength that’s around 10-21 meters: about 100 times smaller than the smallest scales humanity’s ever probed at the Large Hadron Collider.

For an adult human being moving at the same speed, our wavelength is a minuscule 10-32 meters, or just a few hundred times larger than the Planck scale: the length scale at which physics ceases to make sense. Yet even with an enormous, macroscopic mass — and some 1028 atoms making up a full-grown human — the quantum wavelength associated with a fully formed human is large enough to have physical meaning. In fact, for most real particles, only two things determine your wavelength:

Matter waves, at least in theory, can be used to amplify or impede certain signals, which could bear ... [+]fruit for a number of interesting applications, including the potential for rendering certain objects effectively invisible. This is one potential approach towards a real-life cloaking device.G. Uhlmann, U. of Washington

In general, that means there are two things you can do to coax matter particles into behaving as waves. One is that you can reduce the mass of the particles to as small a value as possible, as lower-mass particles will have larger de Broglie wavelengths, and hence larger-scale (and easier to observe) quantum behaviors. But another thing you can do is reduce the speed of the particles you’re dealing with. Slower speeds, which are achieved at lower temperatures, translate into smaller values of momentum, which means larger de Broglie wavelengths and, again, larger-scale quantum behaviors.

This property of matter opens up a fascinating new area of feasible technology: atomic optics. Whereas most of the imaging we conduct is strictly done with optics — i.e., light — we can use slow-moving atomic beams to observe nanoscale structures without disrupting them in the ways that high-energy photons would. As of 2020, there is an entire sub-field of condensed matter physics devoted to ultracold atoms and the study and application of their wave behavior.The 2009 invention of the quantum gas microscope enabled the 2015 measurement of fermionic atoms in ... [+]a quantum lattice, which could lead to breakthroughs in superconductivity and other practical applications.L.W. Cheuk et al., Phys. Rev. Lett. 114, 193001 (2015)

There are many pursuits in science that seem so esoteric that most of us have a hard time envisioning how they’d ever become useful. In today’s world, many fundamental endeavors — for new highs in particle energies; for new depths in astrophysics; for new lows in temperature — seem like purely intellectual exercises. And yet, many technological breakthroughs that we take for granted today were unforeseeable by those who laid the scientific foundations.

Heinrich Hertz, who created and sent radio waves for the first time, thought he was merely confirming Maxwell’s electromagnetic theory. Einstein never imagined that relativity could enable GPS systems. The founders of quantum mechanics never considered advances in computation or the invention of the transistor. But today, we’re absolutely certain that the closer we get to absolute zero, the more the entire field of atomic optics and nano-optics will advance. Perhaps, someday, we’ll even be able to measure quantum effects for entire human beings. Before you volunteer, though, you might be happier to put a cryogenically frozen human to the test instead!

Just what is the true nature of light? Is it a wave or perhaps a flow of extremely small particles? These questions have long puzzled scientists. Let"s travel through history as we study the matter.

Around 1700, Newton concluded that light was a group of particles (corpuscular theory). Around the same time, there were other scholars who thought that light might instead be a wave (wave theory). Light travels in a straight line, and therefore it was only natural for Newton to think of it as extremely small particles that are emitted by a light source and reflected by objects. The corpuscular theory, however, cannot explain wave-like light phenomena such as diffraction and interference. On the other hand, the wave theory cannot clarify why photons fly out of metal that is exposed to light (the phenomenon is called the photoelectric effect, which was discovered at the end of the 19th century). In this manner, the great physicists have continued to debate and demonstrate the true nature of light over the centuries.

Known for his Law of Universal Gravitation, English physicist Sir Isaac Newton (1643 to 1727) realized that light had frequency-like properties when he used a prism to split sunlight into its component colors. Nevertheless, he thought that light was a particle because the periphery of the shadows it created was extremely sharp and clear.

The wave theory, which maintains that light is a wave, was proposed around the same time as Newton"s theory. In 1665, Italian physicist Francesco Maria Grimaldi (1618 to 1663) discovered the phenomenon of light diffraction and pointed out that it resembles the behavior of waves. Then, in 1678, Dutch physicist Christian Huygens (1629 to 1695) established the wave theory of light and announced the Huygens" principle.

Some 100 years after the time of Newton, French physicist Augustin-Jean Fresnel (1788 to 1827) asserted that light waves have an extremely short wavelength and mathematically proved light interference. In 1815, he devised physical laws for light reflection and refraction, as well. He also hypothesized that space is filled with a medium known as ether because waves need something that can transmit them. In 1817, English physicist Thomas Young (1773 to 1829) calculated light"s wavelength from an interference pattern, thereby not only figuring out that the wavelength is 1 μm ( 1 μm = one millionth of a meter ) or less, but also having a handle on the truth that light is a transverse wave. At that point, the particle theory of light fell out of favor and was replaced by the wave theory.

The next theory was provided by the brilliant Scottish physicist James Clerk Maxwell (1831 to 1879). In 1864, he predicted the existence of electromagnetic waves, the existence of which had not been confirmed before that time, and out of his prediction came the concept of light being a wave, or more specifically, a type of electromagnetic wave. Until that time, the magnetic field produced by magnets and electric currents and the electric field generated between two parallel metal plates connected to a charged capacitor were considered to be unrelated to one another. Maxwell changed this thinking when, in 1861, he presented Maxwell"s equations: four equations for electromagnetic theory that shows magnetic fields and electric fields are inextricably linked. This led to the introduction of the concept of electromagnetic waves other than visible light into light research, which had previously focused only on visible light.

The term electromagnetic wave tends to bring to mind the waves emitted from cellular telephones, but electromagnetic waves are actually waves produced by electricity and magnetism. Electromagnetic waves always occur wherever electricity is flowing or radio waves are flying about. Maxwell"s equations, which clearly revealed the existence of such electromagnetic waves, were announced in 1861, becoming the most fundamental law of electromagnetics. These equations are not easy to understand, but let"s take an in-depth look because they concern the true nature of light.

Maxwell"s four equations have become the most fundamental law in electromagnetics. The first equation formulates Faraday"s Law of Electromagnetic Induction, which states that changing magnetic fields generate electrical fields, producing electrical current.

The second equation is called the Ampere-Maxwell Law. It adds to Ampere"s Law, which states an electric current flowing over a wire produces a magnetic field around itself, and another law that says a changing magnetic field also gives rise to a property similar to an electric current (a displacement current), and this too creates a magnetic field around itself. The term displacement current actually is a crucial point.

The fourth equation is Gauss"s Law of magnetic field, stating a magnetic field has no source (magnetic monopole) equivalent to that of an electric charge.

If you take two parallel metal plates (electrodes) and connect one to the positive pole and the other to the negative pole of a battery, you will create a capacitor. Direct-current (DC) electricity will simply collect between the two metal plates, and no current will flow between them. However, if you connect alternating current (AC) that changes drastically, electric current will start to flow along the two electrodes. Electric current is a flow of electrons, but between these two electrodes there is nothing but space, and thus electrons do not flow.

Maxell wondered what this could mean. Then it came to him that applying an AC voltage to the electrodes generates a changing electric field in the space between them, and this changing electric field acts as a changing electric current. This electric current is what we mean when we use the term displacement current.

A most unexpected conclusion can be drawn from the idea of a displacement current. In short, electromagnetic waves can exist. This also led to the discovery that in space there are not only objects that we can see with our eyes, but also intangible fields that we cannot see. The existence of fields was revealed for the first time. Solving Maxwell"s equations reveals the wave equation, and the solution for that equation results in a wave system in which electric fields and magnetic fields give rise to each other while traveling through space.

The form of electromagnetic waves was expressed in a mathematical formula. Magnetic fields and electric fields are inextricably linked, and there is also an entity called an electromagnetic field that is solely responsible for bringing them into existence.

Now let"s take a look at a capacitor. Applying AC voltage between two metal electrodes produces a changing electric field in space, and this electric field in turn creates a displacement current, causing an electric current to flow between the electrodes. At the same time, the displacement current produces a changing magnetic field around itself according to the second of Maxwell"s equations (Ampere-Maxwell Law).

The resulting magnetic field creates an electric field around itself according to the first of Maxwell"s equations (Faraday"s Law of Electromagnetic Induction). Based on the fact that a changing electric field creates a magnetic field in this manner, electromagnetic waves-in which an electric field and magnetic field alternately appear-are created in the space between the two electrodes and travel into their surroundings. Antennas that emit electromagnetic waves are created by harnessing this principle.

Maxwell calculated the speed of travel for the waves, i.e. electromagnetic waves, revealed by his mathematical formulas. He said speed was simply one over the square root of the electric permittivity in vacuum times the magnetic permeability in vacuum. When he assigned "9 x 109/4π for the electric permittivity in vacuum" and "4π x 10-7 for the magnetic permeability in vacuum," both of which were known values at the time, his calculation yielded 2.998 x 108 m/sec. This exactly matched the previously discovered speed of light. This led Maxwell to confidently state that light is a type of electromagnetic wave.

The theory of light being a particle completely vanished until the end of the 19th century when Albert Einstein revived it. Now that the dual nature of light as "both a particle and a wave" has been proved, its essential theory was further evolved from electromagnetics into quantum mechanics. Einstein believed light is a particle (photon) and the flow of photons is a wave. The main point of Einstein"s light quantum theory is that light"s energy is related to its oscillation frequency. He maintained that photons have energy equal to "Planck"s constant times oscillation frequency," and this photon energy is the height of the oscillation frequency while the intensity of light is the quantity of photons. The various properties of light, which is a type of electromagnetic wave, are due to the behavior of extremely small particles called photons that are invisible to the naked eye.

The German physicist Albert Einstein (1879 to 1955), famous for his theories of relativity, conducted research on the photoelectric effect, in which electrons fly out of a metal surface exposed to light. The strange thing about the photoelectric effect is the energy of the electrons (photoelectrons) that fly out of the metal does not change whether the light is weak or strong. (If light were a wave, strong light should cause photoelectrons to fly out with great power.) Another puzzling matter is how photoelectrons multiply when strong light is applied. Einstein explained the photoelectric effect by saying that "light itself is a particle," and for this he received the Nobel Prize in Physics.

The light particle conceived by Einstein is called a photon. The main point of his light quantum theory is the idea that light"s energy is related to its oscillation frequency (known as frequency in the case of radio waves). Oscillation frequency is equal to the speed of light divided by its wavelength. Photons have energy equal to their oscillation frequency times Planck"s constant. Einstein speculated that when electrons within matter collide with photons, the former takes the latter"s energy and flies out, and that the higher the oscillation frequency of the photons that strike, the greater the electron energy that will come flying out.

In short, he was saying that light is a flow of photons, the energy of these photons is the height of their oscillation frequency, and the intensity of the light is the quantity of its photons.

Einstein proved his theory by proving that the Planck"s constant he derived based on his experiments on the photoelectric effect exactly matched the constant 6.6260755 x 10-34 (Planck"s constant) that German physicist Max Planck (1858 to 1947) obtained in 1900 through his research on electromagnetic waves. This too pointed to an intimate relationship between the properties and oscillation frequency of light as a wave and the properties and momentum (energy) of light as a particle, or in other words, the dual nature of light as both a particle and a wave.

French theoretical physicist Louis de Broglie (1892 to 1987) furthered such research on the wave nature of particles by proving that there are particles (electrons, protons and neutrons) besides photons that have the properties of a wave. According to de Broglie, all particles traveling at speeds near that of light adopt the properties and wavelength of a wave in addition to the properties and momentum of a particle. He also derived the relationship "wavelength x momentum = Planck"s constant."

From another perspective, one could say that the essence of the dual nature of light as both a particle and a wave could already be found in Planck"s constant. The evolution of this idea is contributing to diverse scientific and technological advances, including the development of electron microscopes.

For the case of the top, we would find some mark on its rim. Its angular position would be the angular position of that mark around the rim, where we use the axis of rotation of the top as the axis around which the angles are measured.