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Plane wave representing a particle passing through two slits, resulting in an interference pattern on a screen some distance away from the slits. [1] .

The double-slit experiment is an experiment in quantum mechanics and optics demonstrating the wave-particle duality of electrons , photons , and other fundamental objects in physics. When streams of particles such as electrons or photons pass through two narrow adjacent slits to hit a detector screen on the other side, they don't form clusters based on whether they passed through one slit or the other. Instead, they interfere: simultaneously passing through both slits, and producing a pattern of interference bands on the screen. This phenomenon occurs even if the particles are fired one at a time, showing that the particles demonstrate some wave behavior by interfering with themselves as if they were a wave passing through both slits.

Niels Bohr proposed the idea of wave-particle duality to explain the results of the double-slit experiment. The idea is that all fundamental particles behave in some ways like waves and in other ways like particles, depending on what properties are being observed. These insights led to the development of quantum mechanics and quantum field theory , the current basis behind the Standard Model of particle physics , which is our most accurate understanding of how particles work.

The original double-slit experiment was performed using light/photons around the turn of the nineteenth century by Thomas Young, so the original experiment is often called Young's double-slit experiment. The idea of using particles other than photons in the experiment did not come until after the ideas of de Broglie and the advent of quantum mechanics, when it was proposed that fundamental particles might also behave as waves with characteristic wavelengths depending on their momenta. The single-electron version of the experiment was in fact not performed until 1974. A more recent version of the experiment successfully demonstrating wave-particle duality used buckminsterfullerene or buckyballs , the \(C_{60}\) allotrope of carbon.

Waves vs. Particles

Double-slit experiment with electrons, modeling the double-slit experiment.

To understand why the double-slit experiment is important, it is useful to understand the strong distinctions between wave and particles that make wave-particle duality so intriguing.

Waves describe oscillating values of a physical quantity that obey the wave equation . They are usually described by sums of sine and cosine functions, since any periodic (oscillating) function may be decomposed into a Fourier series . When two waves pass through each other, the resulting wave is the sum of the two original waves. This is called a superposition since the waves are placed ("-position") on top of each other ("super-"). Superposition is one of the most fundamental principles of quantum mechanics. A general quantum system need not be in one state or another but can reside in a superposition of two where there is some probability of measuring the quantum wavefunction in one state or another.

Left: example of superposed waves constructively interfering. Right: superposed waves destructively interfering. [2]

If one wave is \(A(x) = \sin (2x)\) and the other is \(B(x) = \sin (2x)\), then they add together to make \(A + B = 2 \sin (2x)\). The addition of two waves to form a wave of larger amplitude is in general known as constructive interference since the interference results in a larger wave.

If one wave is \(A(x) = \sin (2x)\) and the other is \(B(x) = \sin (2x + \pi)\), then they add together to make \(A + B = 0\) \(\big(\)since \(\sin (2x + \pi) = - \sin (2x)\big).\) This is known as destructive interference in general, when adding two waves results in a wave of smaller amplitude. See the figure above for examples of both constructive and destructive interference.

Two speakers are generating sounds with the same phase, amplitude, and wavelength. The two sound waves can make constructive interference, as above left. Or they can make destructive interference, as above right. If we want to find out the exact position where the two sounds make destructive interference, which of the following do we need to know?

a) the wavelength of the sound waves b) the distances from the two speakers c) the speed of sound generated by the two speakers

This wave behavior is quite unlike the behavior of particles. Classically, particles are objects with a single definite position and a single definite momentum. Particles do not make interference patterns with other particles in detectors whether or not they pass through slits. They only interact by colliding elastically , i.e., via electromagnetic forces at short distances. Before the discovery of quantum mechanics, it was assumed that waves and particles were two distinct models for objects, and that any real physical thing could only be described as a particle or as a wave, but not both.

In the more modern version of the double slit experiment using electrons, electrons with the same momentum are shot from an "electron gun" like the ones inside CRT televisions towards a screen with two slits in it. After each electron goes through one of the slits, it is observed hitting a single point on a detecting screen at an apparently random location. As more and more electrons pass through, one at a time, they form an overall pattern of light and dark interference bands. If each electron was truly just a point particle, then there would only be two clusters of observations: one for the electrons passing through the left slit, and one for the right. However, if electrons are made of waves, they interfere with themselves and pass through both slits simultaneously. Indeed, this is what is observed when the double-slit experiment is performed using electrons. It must therefore be true that the electron is interfering with itself since each electron was only sent through one at a time—there were no other electrons to interfere with it!

When the double-slit experiment is performed using electrons instead of photons, the relevant wavelength is the de Broglie wavelength \(\lambda:\)

\[\lambda = \frac{h}{p},\]

where \(h\) is Planck's constant and \(p\) is the electron's momentum.

Calculate the de Broglie wavelength of an electron moving with velocity \(1.0 \times 10^{7} \text{ m/s}.\)

Usain Bolt, the world champion sprinter, hit a top speed of 27.79 miles per hour at the Olympics. If he has a mass of 94 kg, what was his de Broglie wavelength?

Express your answer as an order of magnitude in units of the Bohr radius \(r_{B} = 5.29 \times 10^{-11} \text{m}\). For instance, if your answer was \(4 \times 10^{-5} r_{B}\), your should give \(-5.\)

Image Credit: Flickr drcliffordchoi.

While the de Broglie relation was postulated for massive matter, the equation applies equally well to light. Given light of a certain wavelength, the momentum and energy of that light can be found using de Broglie's formula. This generalizes the naive formula \(p = m v\), which can't be applied to light since light has no mass and always moves at a constant velocity of \(c\) regardless of wavelength.

The below is reproduced from the Amplitude, Frequency, Wave Number, Phase Shift wiki.

In Young's double-slit experiment, photons corresponding to light of wavelength \(\lambda\) are fired at a barrier with two thin slits separated by a distance \(d,\) as shown in the diagram below. After passing through the slits, they hit a screen at a distance of \(D\) away with \(D \gg d,\) and the point of impact is measured. Remarkably, both the experiment and theory of quantum mechanics predict that the number of photons measured at each point along the screen follows a complicated series of peaks and troughs called an interference pattern as below. The photons must exhibit the wave behavior of a relative phase shift somehow to be responsible for this phenomenon. Below, the condition for which maxima of the interference pattern occur on the screen is derived.

Left: actual experimental two-slit interference pattern of photons, exhibiting many small peaks and troughs. Right: schematic diagram of the experiment as described above. [3]

Since \(D \gg d\), the angle from each of the slits is approximately the same and equal to \(\theta\). If \(y\) is the vertical displacement to an interference peak from the midpoint between the slits, it is therefore true that

\[D\tan \theta \approx D\sin \theta \approx D\theta = y.\]

Furthermore, there is a path difference \(\Delta L\) between the two slits and the interference peak. Light from the lower slit must travel \(\Delta L\) further to reach any particular spot on the screen, as in the diagram below:

Light from the lower slit must travel further to reach the screen at any given point above the midpoint, causing the interference pattern.

The condition for constructive interference is that the path difference \(\Delta L\) is exactly equal to an integer number of wavelengths. The phase shift of light traveling over an integer \(n\) number of wavelengths is exactly \(2\pi n\), which is the same as no phase shift and therefore constructive interference. From the above diagram and basic trigonometry, one can write

\[\Delta L = d\sin \theta \approx d\theta = n\lambda.\]

The first equality is always true; the second is the condition for constructive interference.

Now using \(\theta = \frac{y}{D}\), one can see that the condition for maxima of the interference pattern, corresponding to constructive interference, is

\[n\lambda = \frac{dy}{D},\]

i.e. the maxima occur at the vertical displacements of

\[y = \frac{n\lambda D}{d}.\]

The analogous experimental setup and mathematical modeling using electrons instead of photons is identical except that the de Broglie wavelength of the electrons \(\lambda = \frac{h}{p}\) is used instead of the literal wavelength of light.

• Lookang, . CC-3.0 Licensing . Retrieved from https://commons.wikimedia.org/w/index.php?curid=17014507
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• Published: 18 July 2019

The Young-Feynman controlled double-slit electron interference experiment

• Amir H. Tavabi   ORCID: orcid.org/0000-0003-1551-885X 1 ,
• Chris B. Boothroyd 1 , 2 ,
• Emrah Yücelen 3 ,
• Stefano Frabboni 4 , 5 ,
• Gian Carlo Gazzadi 5 ,
• Rafal E. Dunin-Borkowski   ORCID: orcid.org/0000-0001-8082-0647 1 &
• Giulio Pozzi 1 , 6  

Scientific Reports volume  9 , Article number:  10458 ( 2019 ) Cite this article

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• Quantum optics
• Transmission electron microscopy

The key features of quantum mechanics are vividly illustrated by the Young-Feynman two-slit thought experiment, whose second part discusses the recording of an electron distribution with one of the two slits partially or totally closed by an aperture. Here, we realize the original Feynman proposal in a modern electron microscope equipped with a high brightness gun and two biprisms, with one of the biprisms used as a mask. By exciting the microscope lenses to conjugate the biprism plane with the slit plane, observations are carried out in the Fraunhofer plane with nearly ideal control of the covering of one of the slits. A second, new experiment is also presented, in which interference phenomena due to partial overlap of the slits are observed in the image plane. This condition is obtained by inserting the second biprism between the two slits and the first biprism and by biasing it in order to overlap their images.

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Introduction.

Recent advances in electron optics, nanotechnology and specimen preparation have resulted in many studies on the experimental realization of the double-slit thought or gedanken experiment, which was described by Feynman as containing all of the mysteries of quantum mechanics 1 , 2 , using single free electrons.

The Young-Feynman experiment consists of three parts. The first part involves the observation of interference fringes in a double slit setup 3 , 4 , 5 , 6 and their build-up using single electrons 7 , 8 . Two beam interference patterns can be observed using a Möllenstedt-Düker electron biprism 9 , 10 , which has proved to be the most versatile method for carrying out interferometry and holography experiments (see, e . g . 11 , 12 , 13 for reviews). The build-up of two beam Fresnel interference fringes using single electrons was first demonstrated using an electron biprism as a wavefront beam splitter 14 , 15 . The second part of the Young-Feynman experiment involves a comparison of electron distributions recorded before and after one of the slits is closed 16 . Its analysis leads to the idea of the probability amplitude. It has been performed in a controlled manner by stopping one of the two beams in the Fraunhofer image of an electron biprism 17 or in the Fresnel image of two slits 8 . The third part of the Young-Feynman experiment, which has subsequently been renamed the which-way (or which-path ) experiment, aims at demonstrating that interference phenomena disappear when the setup is modified to obtain information about which slit the electron passes through. First experiments in this direction have been carried out by preparing nano-slits and depositing a layer of amorphous material using modern nanotechnology tools on one 18 or both 19 of them. Inelastic scattering in the material can be regarded as a dissipative process during the interaction, which is responsible for the localization mechanism 20 , 21 .

Here, we focus on the second part of the Young-Feynman experiment, which refers to the change in the interference pattern when one of the two slits is partially or totally obstructed in a controllable way. It is then possible to observe the transition of the diffraction pattern from the two- to the one-slit configuration, highlighting the wave-particle duality of the electrons. Although conceptually and mathematically simple, at least from the point of view of wave optical analysis 22 , 23 , its experimental realization is a very challenging task that requires advanced technology and instrumentation, as demonstrated by the partial success of former attempts 8 , 17 . After describing the drawbacks of former setups, we show how they can now be overcome by using a modern electron holography microscope that is equipped with two electron biprisms and a high brightness gun and how a new version of the experiment, in which the fringes are observed in the image instead of the Fraunhofer plane, can be realized.

Analysis of Earlier Experiments

We first recall a few basic concepts in electron optics and microscopy. In general, the illumination system comprises an electron source followed by a system of condenser lenses, which demagnify the source, so that partial coherence does not blur the desired interference phenomena. As a result of the small de Broglie wavelength of high energy electrons, a further system of magnifying lenses is necessary so that interference fringe details can be resolved by an electron detector in the final recording plane. This plane can be optically conjugate to the observation plane OP, which can be the specimen plane if a gaussian image is desired, or the Fraunhofer diffraction plane (coincident with the back focal plane of the imaging lens for plane wave illumination) if a diffraction image is desired. The possibility of continuously varying the excitations of the electron lenses also allows planes in the Fresnel region between these two primary planes to be imaged.

In the first experiment in which an electron biprism was used as an interferometry device 17 , a biprism was inserted in the normal specimen plane, where it could be biased in a specimen holder with contacts connected to an external voltage source. Two beam interference fringes could be observed in the observation plane OP, which was situated in the Fresnel region with respect to the biprism, as the standard gaussian image only showed its bare dark shadow. In order to stop one of the two beams passing to the left and right of the biprism, it was necessary to use an aperture A, which was inserted in a region where they were widely separated, corresponding approximately to the back focal plane of the imaging lens ( i . e ., the Fraunhofer plane), as shown in Fig.  1(a) .

Controlled two beam experiment using an electron biprism. ( a ) Schematic diagram. ( b ) Simulated line profile across a Fraunhofer image of the biased electron biprism. ( c ) Corresponding Fresnel diffraction pattern in the observation plane OP. ( d ) Fraunhofer image of the biased electron biprism with an aperture A stopping the left beam. ( e ) Fresnel image of the complementary half-plane, with the fringes in the geometrical shadow region amplified by a factor of 10.

As a result of the features of the electron microscope that was used 17 , in which the aperture A was the selected area aperture, it was necessary to form the diffraction image of the biprism in this plane by working in the “low angle diffraction” mode 24 by weakly exciting the standard objective lens (which then acted as a condenser lens) and using the following lens, the so-called diffraction lens, as an imaging lens. By changing the excitation of this lens, it was also possible to image a Fresnel plane, with the interference fringes in the overlapping region. This was not a real plane, as shown in Fig.  1 (for reasons of clarity), but a virtual plane in the actual experiment.

From the point of view of the interpretation and simulation of the results, it should be noted that not all of the experimental details are included explicitly in the simulations, which are usually referred to the object space with plane wave illumination. As the dimensions of the biprism and the slits are much larger than atomic dimensions, spherical aberration can be neglected and the standard theory of paraxial imaging, which has been described for both light optics 22 , 25 and electron optics 23 , 26 , can be applied. When the process of image formation is described in the object space, propagation from the object to the Fraunhofer plane ( i . e ., the back focal plane of the imaging lens) can be described by a Fourier transform, while that from the back focal plane to the image plane can be described by an inverse Fourier transform. The effect of observing a Fresnel plane is accounted for simply by multiplying the spectrum by a quadratic phase factor 23 , 25 . This approach is also useful for numerical calculations, which make use of Fast Fourier Transforms. Here, Mathematica software 27 was used to perform simulations.

Figure  1(a) illustrates the electron biprism setup that was used by Matteucci and Pozzi 17 . It involved the use of an aperture A to stop one of the two beams passing to the left and right of the biprism in a region where they were widely separated, corresponding approximately to the Fraunhofer plane behind the imaging lens. However, when the Fraunhofer image in this setup (Fig.  1(b) ) is analyzed in detail, a weak system of diffraction fringes is found to be present in addition to the two bright spots that correspond to the two tilted half planes to the left and right of the biased biprism. These diffraction fringes are responsible for a modulation of the diffraction envelope of the corresponding two beam Fresnel interference image in the observation plane OP (Fig.  1(c) ). As a result, even though aperture A in the Fraunhofer plane is able to completely block one of the spots, it fails to remove the faint fringes that originate from the Young diffracted waves at the edges of the biprism and the electrons are therefore not completely stopped (Fig.  1(d) ). Both the simulation shown in Fig.  1(e) and the experiment 17 show faint interference fringes (amplified by a factor of ten in Fig.  1(e) ), primarily in the region of the geometrical shadow, where the intensity is expected to decrease continuously with distance for an opaque half plane 22 . The simulations start from the transmission function of the electron biprism 23 . Its Fourier Transform gives the Fraunhofer diffraction image shown in Fig.  1(b) , while its Fresnel transform (which is obtained by multiplying the Fraunhofer diffraction image by the Fresnel factor) gives the image shown in Fig.  1(c) . If an aperture is inserted in the Fraunhofer plane, then it cuts part of the Fraunhofer image (Fig.  1(d) ) and its effect on the corresponding Fresnel image is shown in Fig.  1(e) . A further drawback of this setup, which was used in previous experiments, was that experimental control over aperture A was not accurate enough to allow part of the diffracted spot to be intercepted, meaning that only open and closed states could be realized.

Figure  2(a) shows the closest previous setup to the original Feynman proposal. This experiment was realized by Bach and co-workers 8 on a dedicated electron optical bench and aimed to intercept electrons passing through one of two slits by using a movable mask M. However, as the mask could not be in the same plane as the slits but had to be placed some distance below them in the Fresnel region, it intercepted not the slits but their image in the mask plane (Fig.  2(b) ). Observations were carried out by recording the Fraunhofer pattern of the slits (Fig.  2(c) ). When the mask edge was exactly below the edge of the right slit (Fig.  2(d) ), i . e ., when all of the corresponding electrons should have been intercepted from the point of view of geometrical optics, a large fraction of them was still found to contribute to the Fraunhofer image, which displayed two beam interference fringes (Fig.  2(e) ). These detrimental effects can be seen both in the experimental images of Bach and co-workers and in simulations reported in the Supplementary Information of their paper 8 . The simulations shown in Fig.  2 were carried out using their experimental parameters and confirm their results. The object transmission function is now that of two slits. The image is propagated to the aperture plane by multiplying the Fraunhofer image (Fig.  2(c) ) by the Fresnel factor, resulting in Fig.  2(b) . By taking into account the effect of the aperture (Fig.  2(d) ), the original Fraunhofer image is modified, as shown in Fig.  2(e) .

Controlled diffraction experiment with two slits and a mask M in the Fresnel region below the slits. ( a ) Scheme. ( b ) Fresnel image of the two slits in the plane of the mask M. ( c ) Corresponding Fraunhofer image. ( d ) Fresnel image of two slits with the mask M positioned exactly at the edge of the geometrical image of the right slit. ( e ) Corresponding Fraunhofer image.

The Ideal Controlled Beam Interference Experiment in the Fraunhofer Plane

A solution to the previous drawbacks and to the realization of a clear controlled beam interference experiment can be achieved by using an extra lens after the slits to form a magnified image of the slits instead of the Fraunhofer image. If an aperture is placed in such an intermediate image plane, which is conjugate to the object plane of the slits, then the ideal situation can be realized. The aperture acts as a virtual mask in the object plane, which can be used to cover one of the slits precisely, avoiding the detrimental effects that result from its placement in the Fresnel region.

A more detailed set up is shown in Fig.  3 , which shows that the image of the two-slit specimen is focused by the objective lens in the intermediate image plane, where a biprism wire can be used as a very sharp mask. In the back focal plane of the intermediate lens, a Fraunhofer image is formed, followed, along the optical axis, by a gaussian image in the image plane. Both of these planes can be imaged by suitably exciting the remaining imaging lenses of the microscope, which are not shown in Fig.  3 . The electron optical requirements that are necessary for realizing this experiment can now be satisfied, as described below.

Sketch of the experimental setup (left) and of the corresponding ray path (right) for the ideal controlled two beam interference experiment in the Fraunhofer plane. An intermediate image of the two slits is formed by the objective lens in a plane in which a metallic wire, which is completely opaque to the electron beam, can be positioned with high accuracy to modify the electron transmittance through one of the two slits in a controlled way, acting in this way as a very sharp movable mask.. The position of the wire can be checked with the microscope in image mode. By switching the microscope to diffraction mode, it is possible to record the intensity in the Fraunhofer plane, thereby showing the fringe pattern of the Young-Feynman two slit experiment as a function of wire position, i . e ., of the electron path localization.

Figure  4(a,c,e,g) shows experimental Fraunhofer images, which were recorded using a camera at the end of a post-column Gatan imaging filter (GIF) in Lorentz mode, in order to have a sufficiently long camera length to image the interference fringes within the central maximum of the diffraction envelope. It is interesting that the weak single slit diffraction fringes in the perpendicular (vertical) direction are nearly square, as the lengths of the slits are nearly equal to their separation ( e . g . 6 ). Focused images of the slits, which are shown in Fig.  4(b,d,f,h) , were recorded both before and after recording the diffraction images, in order to detect any drift of the biprism. In Fig.  4(b) , the right slit is completely open and a standard two beam interference image is obtained. In Fig.  4(d) , the biprism has been moved in such a way that the right slit is approximately half open, whereas in Fig.  4(f) only a small fraction of the electron beam is allowed to pass through the right slit. In Fig.  4(h) , the right slit is completely blocked, the interference fringes have disappeared completely and only the diffraction image of the open left slit remains.

Two slit controlled electron beam experiment, showing the use of a mask placed in the conjugate plane of the slits to progressively cover the right-hand slit (right) and its effect on the corresponding Fraunhofer diffraction image (left).

The changes in the contrast and shape of the fringes in Fig.  4 can be examined more quantitatively by taking line scans across the central maximum of the diffraction envelope, as shown in Fig.  5 . The decreasing contrast and intensity of the curves corresponds to the decreasing width of the covered slit. The line scans show that the fringe contrast is approximately 0.5 when the slits are both open, presumably because the electron beam illumination was not perfectly coherent. The observed contrast reduction can be simulated by introducing incoherent plane wave illumination with a gaussian distribution over a semi-angle of 2.8 10 −6  rad. Figure  6 shows the result of convoluting the intensities of perfectly coherent images for two one-dimensional slits (with widths of 36 nm and a separation of 496 nm) with this angular distribution for partial coverages of the right slit of 0, 0.5, 0.8 and 1. The agreement with the experimental results is satisfying. Further details are reported in the  Supplementary Information .

Line scans measured across the central maxima in the experimental Fraunhofer patterns shown in Fig.  4 .

Simulated line scans of the Fraunhofer patterns generated assuming incoherent plane wave illumination with a gaussian distribution over a semi-angle of 2.8 10 −6  rad.

A Controlled Beam Interference Experiment in the Image Plane

In the previous section, the electron microscope was essentially used as an electron optical bench, in order to bring the mask (biprism) plane conjugate to the slit plane and to capture the Fraunhofer diffraction image of the slits on the detector. Another intriguing experiment can be realized by recording interference fringes in the plane of the slits ( i . e ., the object plane) instead of in the Fraunhofer plane, as shown in Fig.  7 . As the microscope used in the present study is equipped with two electron biprisms 28 , 29 , the first of which serves as a mask, the second biprism can be used in the same way as in a standard off-axis electron holography setup 11 , in order to overlap wavefunctions passing on its left and right side in the image plane (conjugate to the object plane). We believe that the paradoxical question of which slit the electron is passing through is even more emphasized by this setup, where the two slits are imaged together.

Sketch of the experimental setup for the ideal controlled two beam interference experiment in the image plane. Just as in Fig.  3 , an intermediate image of the two slits is formed by the objective lens in a plane in which a metallic wire (the unbiased first biprism wire, shown in blue), which is opaque to the electron beam, can be positioned with high accuracy and acts as a very sharp movable mask. In this case, it is possible to locally modify the electron transmittance through both slits. A biased biprism (shown in red), which is positioned in a plane above the second intermediate image plane and held at an applied voltage with respect to ground, acts as a wavefront division interferometric device. The resulting tilted wavefronts are overlapped in the observation plane, which is conjugate to the detector plane, by the remaining lenses of the microscope. Interference fringes are observed, except in the shadow of the mask, where electron path localization is achieved by absorption from the first wire.

We carried out experiments at 300 kV (corresponding to a de Broglie electron wavelength of 1.97 pm) using slits of the same width and separation as before, but with a length of 2  μ m. The lower biprism was inserted between the slits, so that it was in the opaque region between them and could not be seen. Figure  8(a) shows the two edges of the lower biprism marked by dashed lines. As it is positioned above the slit image plane, when a bias is applied to it the two half-planes on its left and right sides shift in perpendicular directions, as shown by arrows. When a suitable potential is applied to the lower biprism, the two slits are brought to a partial (Fig.  8(b) ) or nearly total (Fig.  8(c) ) overlap. In the overlap region, interference fringes appear. Partial transparency of the upper biprism at 300 kV results in the presence of interference fringes in the regions that are shadowed by the upper biprism (where one beam is left).

( a ) Controlled electron beam interference experiments in image space recorded using two electron biprisms. The lower biprism, which is located in the dark region between the slits and positioned some distance above the slit image plane, is marked by dashed lines that indicate its edges. The arrows show the displacement of the two halves of the image when a bias is applied to the lower biprism. The upper biprism crosses the slits at an angle and is in a conjugate image plane to them. Partial ( b ) and total ( c ) overlap of the two slits is achieved when the bias applied to the lower biprism is increased, resulting in the formation of two beam interference fringes.

Unfortunately, as the lower biprism is necessarily located in the Fresnel region below the two slits and the upper biprism, diffraction effects due to its sharp edges cannot be avoided. Moreover, selective filtering of the spatial frequencies by the lower biprism is responsible for the presence of ghost images of the edges of the upper biprism 11 , 30 , which can be seen more clearly in a dynamic way in the form of a movie in the  Supplementary Information . Nevertheless, it is possible to identify single image areas where fringes from two slit interference are present and areas with no (or only faint) interference fringes where the slits are blocked by the upper biprism.

Conclusions

We have shown how the second part of the Young-Feynman experiment, which leads to the physical concept of the probability amplitude, can be realized by using a modern electron microscope as a versatile electron optical bench and nanotechnology preparation methods to fabricate slits at the submicron level. Two versions of the experiment have been presented, one of which corresponds closely to the original proposal and is free from artefacts that plagued previous experiments, while the other is realized by using two electron biprisms to overlap the slits in the image plane.

The experiments that are reported here were carried out in an FEI Titan 60–300 transmission electron microscope equipped with a high brightness electron gun, a Lorentz lens, a Gatan imaging filter (GIF), a 2048 × 2048 pixel charge-coupled device camera and two rotatable electron biprisms after the specimen plane. The microscope was operated primarily at an accelerating voltage of 60 kV (corresponding to a de Broglie electron wavelength of 4.87 pm) because the biprism wire was not completely opaque to 300 kV electrons. The lens excitations were chosen so that the upper biprism was in the first conjugate intermediate image plane. It could then be carefully aligned and displaced to obscure one of the slits either partially or totally, thanks to its very sharp edge when compared with the roughness of standard apertures.

The slits were designed so that they could be covered completely by the shadow of the upper electron biprism. They were fabricated using focused ion beam milling in a dual beam workstation (FEI Strata DB 235 M) on a commercial silicon nitride membrane window with a 200- μ m-thick Si frame and a 100  μ m × 100  μ m square window that comprised a bilayer of 200 nm of silicon nitride and a further 100-nm-thick Au film. In order to open the slits, a 9 pA Ga ion beam with a nominal spot size of 10 nm was scanned over two 30 nm × 480 nm boxes that were spaced 500 nm apart for 4 s for each box. As a result of the dimensions of the slits and the angular deflections that are involved, the lenses can be considered to be ideal and their geometrical and chromatic aberrations can be considered to be negligible.

Note added during review

In the final stage of the review process, we became aware of a recently published paper by Harada et al . 31 on interference experiments with asymmetric double slits, which were aimed at categorisation of the electrons. As their experiments were carried out using a 1.2 MV field emission electron microscope, the biprisms that were used as slits were not completely opaque to the electrons, as required in the experiments reported in the present work, in which the required opacity was achieved only at a very low accelerating potential of 60 kV.

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Acknowledgements

This project has received funding from the European Union’s Horizon 2020 research and innovation programme under grant agreement No. 823717-ESTEEM3.

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G.P. and S.F. conceived the idea; G.C.G. fabricated the double slit specimens; A.H.T., C.B.B., E.Y. and R.E.D.-B. discussed and performed the experiments; all of the authors discussed the results and contributed to the text of the manuscript.

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Tavabi, A.H., Boothroyd, C.B., Yücelen, E. et al. The Young-Feynman controlled double-slit electron interference experiment. Sci Rep 9 , 10458 (2019). https://doi.org/10.1038/s41598-019-43323-2

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The double-slit experiment: Is light a wave or a particle?

The double-slit experiment is universally weird.

How does the double-slit experiment work?

Interference patterns from waves, particle patterns, double-slit experiment: quantum mechanics, history of the double-slit experiment, additional resources.

The double-slit experiment is one of the most famous experiments in physics and definitely one of the weirdest. It demonstrates that matter and energy (such as light) can exhibit both wave and particle characteristics — known as the particle-wave duality of matter — depending on the scenario, according to the scientific communication site Interesting Engineering .

According to the University of Sussex , American physicist Richard Feynman referred to this paradox as the central mystery of quantum mechanics. 

We know the quantum world is strange, but the two-slit experiment takes things to a whole new level. The experiment has perplexed scientists for over 200 years, ever since the first version was first performed by British scientist Thomas Young in 1801.

Related: 10 mind-boggling things you should know about quantum physics  

Christian Huygens was the first to describe light as traveling in waves whilst Isaac Newton thought light was composed of tiny particles according to Las Cumbres Observatory . But who is right? British polymath Thomas Young designed the double-slit experiment to put these theories to the test. 

To appreciate the truly bizarre nature of the double-split experiment we first need to understand how waves and particles act when passing through two slits. 

When Young first carried out the double-split experiment in 1801 he found that light behaved like a wave. 

Firstly, if we were to shine a light on a wall with two parallel slits — and for the sake of simplicity, let's say this light has only one wavelength. 

As the light passes through the slits, each, in turn, becomes almost like a new source of light. On the far side of the divider, the light from each slit diffracts and overlaps with the light from the other slit, interfering with each other. 

According to Stony Brook University , any wave can create an interference pattern, whether it be a sound wave, light wave or waves across a body of water. When a wave crest hits a wave trough they cancel each other out — known as destructive interference — and appear as a dark band. When a crest hits a crest they amplify each other — known as constructive interference — and appear as a bright band. The combination of dark and bright bands is known as an interference pattern and can be seen on the sensor screen opposite the slits. 

This interference pattern was the evidence Young needed to determine that light was a wave and not a particle as Newton had suggested. 

But that is not the whole story. Light is a little more complicated than that, and to see how strange it really is we also need to understand what pattern a particle would make on a sensor field. 

If you were to carry out the same experiment and fire grains of sand or other particles through the slits, you would end up with a different pattern on the sensor screen. Each particle would go through a slit end up in a line in roughly the same place (with a little bit of spread depending on the angle the particle passed through the slit).  

Clearly, waves and particles produce a very different pattern, so it should be easy to distinguish between the two right? Well, this is where the double-slit experiment gets a little strange when we try and carry out the same experiment but with tiny particles of light called photons. Enter the realm of quantum mechanics. 

The smallest constituent of light is subatomic particles called photons. By using photons instead of grains of sand we can carry out the double-slit experiment on an atomic scale. 

If you block off one of the slits, so it is just a single-slit experiment, and fire photons through to the sensor screen, the photons will appear as pinprick points on the sensor screen, mimicking the particle patterns produced by sand in the previous example. From this evidence, we could suggest that photons are particles. 

Now, this is where things start to get weird. 

If you unblock the slit and fire photons through both slits, you start to see something very similar to the interference pattern produced by waves in the light example. The photons appear to have gone through the pair of slits acting like waves. 

But what if you launch photons one by one, leaving enough time between them that they don't have a chance of interfering with each other, will they behave like particles or waves? 

At first, the photons appear on the sensor screen in a random scattered manner, but as you fire more and more of them, an interference pattern begins to emerge. Each photon by itself appears to be contributing to the overall wave-like behavior that manifests as an interference pattern on the screen — even though they were launched one at a time so that no interference between them was possible.

It's almost as though each photon is "aware" that there are two slits available. How? Does it split into two and then rejoin after the slit and then hit the sensor? To investigate this, scientists set up a detector that can tell which slit the photon passes through. 

Again, we fire photons one at a time at the slits, as we did in the previous example. The detector finds that about 50% of the photons have passed through the top slit and about 50% through the bottom, and confirms that each photon goes through one slit or the other. Nothing too unusual there. 

But when we look at the sensor screen on this experiment, a different pattern emerges. 

This pattern matches the one we saw when we fired particles through the slits. It appears that monitoring the photons triggers them to switch from the interference pattern produced by waves to that produced by particles. 

If the detection of photons through the slits is apparently affecting the pattern on the sensor screen, what happens if we leave the detector in place but switch it off? (Shh, don't tell the photons we're no longer spying on them!) 

This is where things get really, really weird. 

Same slits, same photons, same detector, just turned off. Will we see the same particle-like pattern? 

No. The particles again make a wave-like interference pattern on the sensor screen. 

The atoms appear to act like waves when you're not watching them, but as particles when you are. How? Well, if you can answer that, a Nobel Prize is waiting for you. 

In the 1930s, scientists proposed that human consciousness might affect quantum mechanics. Mathematician John Von Neumann first postulated this in 1932 in his book " The Mathematical Foundations of Quantum Mechanics ." In the 1960s, theoretical physicist, Eugene Wigner conceived a thought experiment called Wigner's friend — a paradox in quantum physics that describes the states of two people, one conducting the experiment and the observer of the first person, according to science magazine Popular Mechanics . The idea that the consciousness of a person carrying out the experiment can affect the result is knowns as the Von Neumann–Wigner interpretation.

Though a spiritual explanation for quantum mechanic behavior is still believed by a few individuals, including author and alternative medicine advocate Deepak Chopra , a majority of the science community has long disregarded it. 

As for a more plausible theory, scientists are stumped. 

Furthermore —and perhaps even more astonishingly — if you set up the double-slit experiment to detect which slit the photon went through after the photon has already hit the sensor screen, you still end up with a particle-type pattern on the sensor screen, even though the photon hadn't yet been detected when it hit the screen. This result suggests that detecting a photon in the future affects the pattern produced by the photon on the sensor screen in the past. This experiment is known as the quantum eraser experiment and is explained in more detail in this informative video from Fermilab . 

We still don't fully understand how exactly the particle-wave duality of matter works, which is why it is regarded as one of the greatest mysteries of quantum mechanics. 

The first version of the double-slit experiment was carried out in 1801 by British polymath Thomas Young, according to the American Physical Society (APS). His experiment demonstrated the interference of light waves and provided evidence that light was a wave, not a particle. 

Young also used data from his experiments to calculate the wavelengths of different colors of light and came very close to modern values.

Despite his convincing experiment that light was a wave, those who did not want to accept that Isaac Newton could have been wrong about something criticized Young. (Newton had proposed the corpuscular theory, which posited that light was composed of a stream of tiny particles he called corpuscles.) 

According to APS, Young wrote in response to one of the critics, "Much as I venerate the name of Newton, I am not therefore obliged to believe that he was infallible."

Since the development of quantum mechanics, physicists now acknowledge light to be both a particle and a wave. 

Explore the double-slit experiment in more detail with this article from the University of Cambridge, which includes images of electron patterns in a double-slit experiment. Discover the true nature of light with Canon Science Lab . Read about fragments of energy that are not waves or particles — but could be the fundamental building blocks of the universe — in this article from The Conversation . Dive deeper into the two-slit experiment in this article published in the journal Nature . 

Bibliography

Grangier, Philippe, Gerard Roger, and Alain Aspect. " Experimental evidence for a photon anticorrelation effect on a beam splitter: a new light on single-photon interferences. " EPL (Europhysics Letters) 1.4 (1986): 173.

Thorn, J. J., et al. "Observing the quantum behavior of light in an undergraduate laboratory. " American Journal of Physics 72.9 (2004): 1210-1219.

Ghose, Partha. " The central mystery of quantum mechanics. " arXiv preprint arXiv:0906.0898 (2009).

Aharonov, Yakir, et al. " Finally making sense of the double-slit experiment. " Proceedings of the National Academy of Sciences 114.25 (2017): 6480-6485.

Peng, Hui. " Observations of Cross-Double-Slit Experiments. " International Journal of Physics 8.2 (2020): 39-41. 

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The Double Slit Experiment for Electrons

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Together with the double slit experiment for photons the corresponding experiment for electrons represents one of the most celebrated and famous experiments in physics. Its fame is due more to the conceptual problems it creates rather than its contribution to understanding quantum physics. The observation of wavelike diffraction of electrons and their definite particlelike behavior in other circumstances has remained a conceptual mystery in quantum physics until this day. The basic experimental setup shown in Fig. 8.1 is simple enough. A stream of focused electrons from a hot cathode impinges on a plate with two narrow slits separated a small distance apart. The electrons transmitted through the slits are observed to form a typical diffraction pattern on the screen behind the slit plate. If the intensity of the electron source is reduced to the point when only one electron at a time is reaching the screen, it produces a pointlike spot located somewhere on the screen, not necessarily just below the slits. This behavior is certainly in accord with classical concepts of the electron as a particle, with the electron passing through one of the two slits. In the process it is deflected by some angle and finally hitting the screen at some localized point. The deflection has no classical explanation. But there are worse things to come.

She went on, “Would you tell me please which way I ought to go from here?” “That depends a good deal on where you want to get to,” said the Cat “I don’t much care where—” said Alice. “Then it doesn’t matter which way you go,” said the Cat “—as long as I get somewhere,” Alice added as an explanation. “Oh, you are sure to do that,” said the Cat, “if you walk long enough.” Lewis Carroll Alice in Wonderland

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Wessel-Berg, T. (2001). The Double Slit Experiment for Electrons. In: Electromagnetic and Quantum Measurements. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-1603-3_8

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• Quantum mechanics
• Research update

Do atoms going through a double slit ‘know’ if they are being observed?

Does a massive quantum particle – such as an atom – in a double-slit experiment behave differently depending on when it is observed? John Wheeler’s famous “delayed choice” Gedankenexperiment asked this question in 1978, and the answer has now been experimentally realized with massive particles for the first time. The result demonstrates that it does not make sense to decide whether a massive particle can be described by its wave or particle behaviour until a measurement has been made. The techniques used could have practical applications for future physics research, and perhaps for information theory.

In the famous double-slit experiment, single particles, such as photons, pass one at a time through a screen containing two slits. If either path is monitored, a photon seemingly passes through one slit or the other, and no interference will be seen. Conversely, if neither is checked, a photon will appear to have passed through both slits simultaneously before interfering with itself, acting like a wave. In 1978 American theoretical physicist John Wheeler proposed a series of thought experiments wherein he wondered whether a particle apparently going through a slit could be considered to have a well-defined trajectory, in which it passes through one slit or both. In the experiments, the decision to observe the photons is made only after they have been emitted, thereby testing the possible effects of the observer.

For example, what happens if the decision to open or close one of the slits is made after the particle has committed to pass through one slit or both? If an interference pattern is still seen when the second slit is opened, this would force us either to conclude that our decision to measure the particle’s path affects its past decision about which path to take, or to abandon the classical concept that a particle’s position is defined independent of our measurement.

Photon first

While Wheeler conceived of this purely as a thought experiment, experimental advances allowed Alain Aspect and colleagues at the Institut d’Optique, Ecole Normale Supérieure de Cachan and the National Centre for Scientific Research, all in France, to actually perform it in 2007 with single photons, using beamsplitters in place of the slits envisage by Wheeler. By inserting or removing a second beamsplitter randomly, the researchers could either recombine the two paths or leave them separate, making it impossible for an observer to know which path a photon had taken. They showed that if the second beamsplitter was inserted, even after the photon would have passed the first, an interference pattern was created.

The wave–particle duality of quantum mechanics dictates that all quantum objects, massive or otherwise, can behave as either waves or particles. Now, Andrew Truscott and colleagues at Australian National University carried out Wheeler’s experiment using atoms deflected by laser pulses in place of photons deflected by mirrors and beamsplitters. The helium atoms, released one by one from an optical dipole trap, fell under gravity until they were hit by a laser pulse, which deflected them into an equal superposition of two momentum states travelling in different directions with an adjustable phase difference. This was the first “beamsplitter”. The researchers then decide whether to apply a second laser pulse to recombine the two states and create mixed states – one formed by adding the two waves and one formed by subtracting them – by using a quantum random-number generator. When applied, this final laser pulse made it impossible to tell which of the two paths the photon had travelled along. The team ran the experiment repeatedly, varying the phase difference between the paths.

Double pulse

Truscott’s team found that when the second laser pulse was not applied, the probability of the atom being detected in each of the momentum states was 0.5, regardless of the phase lag between the two. However, application of the second pulse produced a distinct sine-wave interference pattern. When the waves were perfectly in phase on arrival at the beamsplitter, they interfered constructively, always entering the state formed by adding them. When the waves were in antiphase, however, they interfered destructively and were always found in the state formed by subtracting them. This means that accepting our classical intuition about particles travelling well-defined paths would indeed force us into accepting backward causation. “I can’t prove that isn’t what occurs,” says Truscott, “But 99.999% of physicists would say that the measurement – i.e. whether the beamsplitter is in or out – brings the observable into reality, and at that point the particle decides whether to be a wave or a particle.”

Indeed, the results of both Truscott and Aspect’s experiments shows that a particle’s wave or particle nature is most likely undefined until a measurement is made. The other less likely option would be that of backward causation – that the particle somehow has information from the future – but this involves sending a message faster than light, which is forbidden by the rules of relativity.

Aspect is impressed. “It’s very, very nice work,” he says, “Of course, in this kind of thing there is no more real surprise, but it’s a beautiful achievement.” He adds that, beyond curiosity, the technology developed may have practical applications. “The fact that you can master single atoms with this degree of accuracy may be useful in quantum information,” he says.

The research is published in Nature Physics .

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Does an electron pass through both slits in the double-slit experiment?

The double-slit experiment can be regarded as a demonstration that light and matter can display characteristics of both classically defined waves and particles. It also displays the fundamentally probabilistic nature of quantum mechanical phenomena.

In a double-slit experiment using an electron beam an interference pattern is formed after experimenters record a large amount of electron detections.

I have seen this answer by "anna v" which states an electron never travels through both slits only one slit per electron and the pattern formed is only a statistical probability distribution for the entire accumulation.

But assuming in an experiment in which electrons travel one after the other and each electron travels only through one slit then how could the pattern on the screen be different from the one when we close one slit interchangeably and send electrons only through one slit at a time. ( Actual experiments have shown patterns are different indeed)

I think an electron through double-slit as a superposition of probabilities of spatial distribution. Like this picture below:

But according to anna v picture that come to my mind is below (several electrons illustrated):

So I have two related questions:

Is the so-called wave nature of particles only a mathematical model or is there some physical nature (properties) to the probabilistic wave that passes through the double slit?

Is stating whether the electron passes through both slits or it only passes through one slit just a personal opinion/interpretation that cannot be proven or disproven by observations?

Edit: Evidence supporting simultaneous two (path) position:

Using a Mach-Zehnder Interferometer to Illustrate Feynman's Sum Over Histories Approach to Quantum Mechanics

One particle on two paths: Quantum physics is right by Vienna University of Technology

Double-slits with single atoms: Selective laser excitation of beams of individual rubidium atoms by Andrew Murray, professor of atomic physics, University of Manchester, UK

• quantum-mechanics
• interference
• double-slit-experiment
• wave-particle-duality

• 1 $\begingroup$ There simply is no "electron" without an electron being detected. An electron is not a thing that has an existence independent of emission and absorption processes. That's the great lesson of quantum mechanics... which is being taught poorly. $\endgroup$ –  FlatterMann Commented Jun 9, 2023 at 19:08
• 1 $\begingroup$ No it passes thru one slit ... the EM field that guides it goes thru both. $\endgroup$ –  PhysicsDave Commented Jun 10, 2023 at 0:40
• $\begingroup$ @FlatterMann I think the mainstream physics POV is that things like particles exist even between the measurements. It is true what you said that we cannot determine the existence of such things outside of measurements or interactions. But as Einstein, they do not like to think the moon is not there when you don't look at it. So the standard is to take measurements as indicators of the real thing (measurement is derived from the real physical thing), not the measurement/interaction itself as the only real thing. $\endgroup$ –  Duke William Commented Jun 10, 2023 at 4:59
• 1 $\begingroup$ As a general comment: physics is not what the majority believes. It is a collection of facts about nature and their rational explanation. Nowhere in that rational explanation do particles show up. What does show up is exactly what you were told in high school: irreversible energy transfers. Does energy in a system get lost if you don't look at it? Of course not. Does that mean that it is localized in some speck of dust? Of course not. It's that trivially false "logical" step that creates particles in your mind and only in your mind. $\endgroup$ –  FlatterMann Commented Jun 10, 2023 at 14:13
• $\begingroup$ Interesting wiki/Dirac note on QFT: “Therefore, even in a perfect vacuum, there remains an oscillating electromagnetic field having zero-point energy. It is this quantum fluctuation of electromagnetic fields in the vacuum that "stimulates" the spontaneous emission of radiation by electrons in atoms. $\endgroup$ –  PhysicsDave Commented Jun 10, 2023 at 16:18

5 Answers 5

In general, a different pattern of slits in a single particle interference experiment will result in a different pattern of fringes at the end of the experiment. Consider a point P on the screen that is lit when there is one slit and is dark when there are two slits. If there was one slit an electron might be detected at P, but with two slits the electron won't be detected at P. And if you subject the region after the slit to an electric or magnetic field in general that will change the pattern of fringes. That's not a matter on which physicists disagree, but there is disagreement on what is happening in reality to produce that outcome, or whether such an account is required.

If somebody doesn't have an account of what is happening in the experiment, then they have no account of what is happening in the experiment. So then how could they say whether the experiment has been conducted correctly? If there is no account of what's happening in the experiment, then what is the standard by which the correctness of the setup is judged and what is the explanation for why you adjust the experiment in a particular way to improve it? So we can and should discard the idea that it's acceptable to have no explanation of what's happening in the experiment.

What is the explanation?

The only idea that I think actually works goes like this. The pattern changes if you introduce a second slit, so there must be something coming through the second slit that prevents the electron from arriving at P and that thing is blocked by substances that block electrons, i.e. - the material of the screen. Whatever the thing is that's coming through the second slit it will be affected by magnets and electric fields, just as an electron would be. So it's something that acts like an electron except that we don't detect it. This electron can only be blocked by a portion of a screen or a detector if it interacts with it, but we don't see the result of that interaction, so it must be interacting with an screen or detector that we don't see. That "invisible" screen or detector must have been put there by somebody, so there are "invisible" people too and it must have been manufactured by a factory and so on. There are entire universes full of "invisible" stuff that only interacts with the universe we see around us in such a way that we can exclude other explanations under some limited conditions in labs. And that is what quantum mechanics implies about the world too. This way of looking at quantum mechanics is often called the Everett interpretation, but nobody has proposed another account of what's happening in single particle interference or other quantum mechanical experiments. For more details see "The Fabric of Reality" by David Deutsch and

https://arxiv.org/abs/1111.2189

https://arxiv.org/abs/quant-ph/0104033

There are other theories whose advocates claim to be able to explain what's happening, such as collapse theories:

https://arxiv.org/abs/1910.00050

that say other versions of the electron are eliminated by some physical process.

One problem with such theories is that saying they have admitted in substance that the electron exists in multiple versions so what are they gaining by adding collapse? There are other criticisms too:

https://arxiv.org/abs/1407.4746

https://arxiv.org/abs/2205.00568

There are other proposed explanations like the pilot wave theory:

https://arxiv.org/abs/2205.13701

which has also been criticised:

https://arxiv.org/abs/quant-ph/0403094

There are other variants too, but there's not much point in listing them all and I guess I've linked enough material above for you to make your own decision.

• $\begingroup$ You don't need invisible electrons to explain the change in the pattern. A different geometry of the barrier represents a different charge distribution (the electrons and nuclei in the barrier). A different charge distribution means that the electron would experience a different EM force, hence its trajectory would be different. $\endgroup$ –  Andrei Commented Jun 9, 2023 at 7:02
• $\begingroup$ A photon is a particular kind of state of the EM field. Saying the field guides the photon seems to imply there is a clear separation between the field and the photon, which is false. That state of the EM field has to go through both slits to produce the interference pattern, so the photon goes through both slits. The electron too is a state of a quantum field that is affected by the slit as a result of interacting with it. $\endgroup$ –  alanf Commented Jun 9, 2023 at 7:57
• $\begingroup$ @Andrei A charge distribution is a classical property formed by many electrons (and other charge carrying quanta). It is not something that comes "before" quanta. It is an effect caused by quanta. The same is true for "electromagnetic forces". They are phenomena of the many-quantum system. $\endgroup$ –  FlatterMann Commented Jun 9, 2023 at 19:10
• $\begingroup$ @alanf A photon is not a state of the em field. A photon is the irreversible energy transfer between a source and the em field or the em field and an absorber. In the theory it is the physical result AFTER the application of the Born rule. The only "thing" with state in quantum theory is the ensemble of the system and that is not even a thing. The ensemble is an abstract that we write down on paper to calculate the probability estimate for the actual frequentist observations. Physically quanta are irreversible energy exchanges. In the theory they are indices into probability distributions. $\endgroup$ –  FlatterMann Commented Jun 9, 2023 at 19:16
• $\begingroup$ @FlatterMann, and how is the fact that charge distribution is a "classical property formed by many electrons" supposed to invalidate my point? A barrier with two slits has a different charge distribution (or if you want, the molecular orbitals associated with the barrier) than a barrier with one slit. So, the incoming electrons would be scattered in a different way. No mystery about that. $\endgroup$ –  Andrei Commented Jun 12, 2023 at 7:21

This question is difficult to give a proper answer. The correct course of action is to identify the unequivocal current best theory and the thing they are meant to explain, and so then the mathematical description is exactly the physical reality. i.e. the wavefunction of the single electron in an empty universe is exactly the physical electron itself. Needless to say, this is somewhat interpretation dependent and also hotly debated.

In the double slit experiment, electrons and photons essentially behave the same way, so we can just state it as a general thing for all quantum particles. What we can really conclude from the experiments are that

The excitation in quantum fields get detected like particles but moves like waves.

It is necessary to have some wave parts, because the only way for the isolated single excitations, one-by-one passing through the slits and having interference patterns emerge, the whole "one electron/photon at a time", requires that the wave parts pass through both slits at once. Plenty of people insist that this wave part is not the single electron/photon, but they will not likely disagree that there is this wave part that passes through both. It thus comes down to whether one chooses to include the wave part with the particle part or not. Lots of arguing, very little sense.

There is this little book on some philosophical foundations of quantum theory, and in it, the author covered the fact that you could choose between "the particle passed through slit A AND slit B" and "the particle passed through slit A OR slit B", because as long as you are consistent, these two alternatives are both allowed by quantum theory. I am still searching for the book, though.

Instead, the better argument to have, is to consider that we really ought to stop using the wave-particle concept. Instead, what we have are quantum fields, and what we consider to be waves or particles, are really just excitations on these quantum fields. In that sense, both the wave aspects and the particle aspects come together, and we would sidestep all of these silly arguments.

It is actually rather bad to not include some interpretations business when answering this question. The de Broglie Bohm Pilot Wave Interpretation is rather illuminating here, because if you work out the actual trajectories of a hidden particle riding along the guiding wave, the wave part goes through both slits and causes the interference pattern, but the particle only ever passes through one slit. It is then a very curious thing that the trajectories are separated by the symmetry centre line. That is, it is only after quite a lot of work into Pilot Waves, did we discover that a particle that passes through the bottom slit, will appear on the bottom half of the screen, and never on the top half, and vice versa. It is obvious upon hindsight that such things can occur, but otherwise completely non-trivial.

Alas, that is completely interpretation dependent, and bringing it up is not an endorsement of Pilot Wave Interpretation. It is just fun to consider that there are such interesting things.

• $\begingroup$ I'm confused how traversing one or two slits is a matter of personal preference? If we don't try to see which slit is traversed, we see an interference pattern that indicates both slits were traversed. This isn't possible if only one slit is traversed? $\endgroup$ –  just a phase Commented Jun 9, 2023 at 23:34
• $\begingroup$ @justaphase The physics is the same: if you perform an observation of which slit is traversed, the interference pattern goes away. But when the interference pattern is there, there is a choice of whether to say "it passed through slit A AND slit B" or "it passed through slit A OR slit B". As long as you are internally consistent, it would work out. Reality is often horrible like that. $\endgroup$ –  naturallyInconsistent Commented Jun 11, 2023 at 0:23
• $\begingroup$ an interference pattern requires AND though...OR would have no interference? Interference requires both components, so OR would be insufficient? $\endgroup$ –  just a phase Commented Jun 11, 2023 at 17:17
• $\begingroup$ @justaphase I just told you that someone worked out the maths and proved that OR is also able to get the interference. $\endgroup$ –  naturallyInconsistent Commented Jun 11, 2023 at 21:37
• $\begingroup$ @naturallyInconsistent provide a citation to said maths...your answer does not appear rigorous, and anyone can claim that a rigorous justification for their claims exists somewhere in the literature...for example...maybe reveal the title of the "little book" you mentioned? $\endgroup$ –  just a phase Commented Jun 11, 2023 at 23:39

A helpful fact that few physicists will disagree with is that the wavefunction of the electron certainly goes through both slits. Also, personally I think that describing the whole wavefunction of the electron sufficiently describes that electron.

The origional and simplest model of QM models the electron as follows:

When the electron is not being measured, a "wavefunction" (which moves similarly to a wave) propagates in space. This wave can interfere with itself just like how a wave of water can split into smaller waves and interfere with itself. When the electron is measured, the probability of finding the electron is proportional with how high that wave is at the point in space that wave is located at.

Because the wave is associated with probability of seeing the electron at a specific spot, it's not as if the wave-itself can be seen. Furthermore, because the electron is not seen when it is traveling (since measuring it would stop this wave from existing), we cannot make statements easily about what is happening when it is traveling.

Ultimately though, there is a lot of good conceptual intuition that the electron is going through "Both" slits, simply because it behaves in a way that is different than if it had simply went through either one or the other.

• $\begingroup$ So wave-particle duality is the most reasonable approximation according to the standard interpretation of QM? The particle part comes in because when we measure, measurement is in the form of a particle, wave part comes in because its position derives from wave-like properties. $\endgroup$ –  Duke William Commented Jun 15, 2023 at 6:52
• 1 $\begingroup$ Personally I'm not a big fan of "wave-particle duality" as a concept. I think it just makes things less clear. You are correct though that the position of the particle, when not observed behaves wavelike. When it is observed, it picks a spot and only begins to act like a wave when you stop observing it. The wavelike behavior can happen for any degree of freedom the particle can have, and is not limited to its position. For example, it's "spin-orientation" or which path it takes, or what energy it is in are all things that can act wavelike when not observed. $\endgroup$ –  Steven Sagona Commented Jun 15, 2023 at 19:33

"But assuming in an experiment in which electrons travel one after the other and each electron travels only through one slit then how could the pattern on the screen be different from the one when we close one slit interchangeably and send electrons only through one slit at a time. (Actual experiments have shown patterns are different indeed)"

Even if we do not understand the details, we know that the reason for the observed pattern is the electromagnetic interaction between the electrons and the barrier. We also know that the forces acting on the electron depend on the distribution of charges (the electrons and nuclei in the barrier). So, it is to be expected that if the charge distribution changes (by adding/removing a slit) the EM force acting on the electron changes as well, leading to a different pattern. I see nothing remarkable/unexpected about that.

Of course, in order to get a detailed understanding one needs to actually simulate the electron/barrier interaction. Unfortunately, due to the large number of charges involved, such a calculation is not possible at this time.

"Is the so-called wave nature of particles only a mathematical model or is there some physical nature (properties) to the probabilistic wave that passes through the double slit?"

I think it is only a mathematical model, otherwise, the collapse of the wave to one point would imply faster than light effects which are unlikely.

"Is stating whether the electron passes through both slits or it only passes through one slit just a personal opinion/interpretation that cannot be proven or disproven by observations?"

Same as above, we have good evidence that nature is local, therefore any explanation that requires non-local effects is unlikely.

• $\begingroup$ Comments have been moved to chat ; please do not continue the discussion here. Before posting a comment below this one, please review the purposes of comments . Comments that do not request clarification or suggest improvements usually belong as an answer , on Physics Meta , or in Physics Chat . Comments continuing discussion may be removed. $\endgroup$ –  Buzz ♦ Commented Jun 9, 2023 at 16:57

This is a long comment about what is an electron as far as particle physics goes.

Here is a bubble chamber photograph of an electron track:

Bubble chamber photograph of an electron knocked out of a hydrogen atom

The curly line was produced by an electron that was struck by one of twelve passing beam $K^-$ particles in a liquid hydrogen bubble chamber. It curves in an applied magnetic field and loses energy rapidly, spiraling inward

We have called them elementary particles , because they act like particles , no wave nature is seen within the accuracy of the dots where the particle ionizes (very low energy transfer) the hydrogen atoms and bubbles form in the super-cooled liquid hydrogen, so a picture can be taken. The bubble dots are dimensions of microns.

There is no personal opinion about the size of elementary particles, because the quantum field theory which has been well verified with the particle data , the standard model, axiomatically assumes that elementary particles like the electron are point particles, and that is where mainstream particle physics is now.

• $\begingroup$ Comments have been moved to chat ; please do not continue the discussion here. Before posting a comment below this one, please review the purposes of comments . Comments that do not request clarification or suggest improvements usually belong as an answer , on Physics Meta , or in Physics Chat . Comments continuing discussion may be removed. $\endgroup$ –  Buzz ♦ Commented Jun 12, 2023 at 20:14

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• Quantum Physics

Double-slit experiment and watching the electrons

• Thread starter forcefield
• Start date Dec 9, 2013
• Tags Double-slit Double-slit experiment Electrons Experiment
• Dec 9, 2013

A PF Molecule

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A PF Mountain

If there is no interaction between your probing light and the electrons, you can get no information and the interference persists. If there is an interaction, the interference will not be present.  

• Dec 10, 2013
• Dec 11, 2013

Mentz114 said: If there is an interaction, the interference will not be present.

naima said: So you see that here photons always interact but the result is not a yes/no interference

• Dec 12, 2013

I found the calculation in an old book of L Tarassov (1980) Surprisingly i did not see it in another book nor online.  

• Dec 13, 2013

forcefield said: Also I'd like to know if this experiment has been done with strong light source of long wavelength and what was the result ?

Both Mentz114 and Naima's explanations are compatible. Mentz114 explains in "photon-by-photon" and "electron-by-electron" terms. If photon interacts with electron; coherence between the two slits is lost and interference is lost...on the other hand if the photon does not interact, the interference persists. Clearly, on average, this is a situation where there is partial coherence - which Naima outlines in more explicit terms. Claude.  

I do not believe that this is the correct way to see what happens. We have not a mixture of interacting electrons and of not interacting ones. |a|² is not the probability of an interaction giving the which-path information: We would have P(x) = |a|² (|L(x)|² + |R(x)|²) + |b|² |L(x) + R(x)|² This is not the formula tarasov gives. We have a source of photons between the slits. Remember that when the right slit is closed electrons pass through the left slit , then |b|² is the probability that the right photon receptor clicks. Giving you a wrong which-path information. You may have interference with always interacting electrons and photons but giving you an unreliable information.  

I am confused. P(x) = |a|² (|L(x)|² + |R(x)|²) + |b|² |L(x) + R(x)|² = (|a|²+ |b|²) (|L(x)|² + |R(x)|²) + |b|² (L(x)R*(x) + L*(x)R(x)) As |a|² + |b|² = 1 we get something like Tarasov formula. Can we say that an unreliable information interaction is just like no interaction in this case?  

I think (hope?) that there exist experiments in which low energy photons have been used to detect "which-slit" information. I'd love to read the papers. I'd even more love to see a similar experiment using massive projectiles through the slits - buckyballs perhaps - in conjunction with RF detection of the path information. I am wondering whether such methods would yield BOTH a proportion of interference patterns and "one-slit" patterns, depending upon the nature and magnitude of the individual detections. I would be fascinated if the results varied depending upon the frequency used, especially if the results shifted rapidly from one state to another as the frequency is swept.  

EskWIRED said: I'd even more love to see a similar experiment using massive projectiles through the slits - buckyballs perhaps - in conjunction with RF detection of the path information. I am wondering whether such methods would yield BOTH a proportion of interference patterns and "one-slit" patterns, depending upon the nature and magnitude of the individual detections.

A PF Electron

try frensel lens  

• Dec 14, 2013

I found another easy experiment. photons pass through two slits. a polarizer stands behind each slit. When the polarizers are parallel (sin² = 0) there is no which-path information and fringes are well seen. we can rotate one of the polarizer. fringes progressively disappear. Here photons allways pass and interact through the polarizers. So fringes are not a question of yes/no interaction. read this  

• Dec 15, 2013

naima said: So fringes are not a question of yes/no interaction.

• Dec 16, 2013

forcefield said: I'm not convinced in the case of this thread where we are sending electrons through the slits.

Cthugha said: By using a double slit and a reasonably narrow photon or electron source you prepare a scenario with reasonably well defined relative phases. The question of whether you see fringes at the detection screen or not depends on whether this phase gets messed up along the way. The extreme cases of no phase distortion and complete phase randomization correspond to perfect and no fringes, but there are always ways to distort the phase just a bit or inside a narrow range of values which just gives you reduced fringe visibility (and of course little which-way information).

naima said: Suppose that the screen is shuttered when photons are not detected by the detectors near the screen. we will have a pattern due to the only electrons that are observed. they all interacted with photons. Now let the photons wavelength greater than the distance between the slits. we cannot see details smaller than that distance. so we have no which path information. In this case all electrons interacted but we have interference.

Did feynman say something about watching the electrons?  

forcefield said: Does that mean that if you prepare the electrons with complete phase randomization, you get no interference ?

naima said: Did feynman say something about watching the electrons?

Sorry I did not see it. Feynman says: "when we make the wavelength longer than the distance between our holes, we see a big fuzzy flash when the light is scattered by the electrons. We can no longer tell which hole the electron went through! We just know it went somewhere! And it is just with light of this color that we find that the jolts given to the electron are small enough so that P′12 begins to look like P12—that we begin to get some interference effect." That is what i said. You have the answer to your question. When wavelength increases interaction are still there but you cannot see through which slit the electron passes. You begin to see interference . the "a" and "b" are functions of wavelength. it would be interesting to know the function.  

• Dec 17, 2013

So whether we have interference is not just about whether we interact with the electrons. Also it is not about whether we know the path taken by the electron. Can you say that it is about whether we change the wave into a particle before final detection ?  

It is about how light interact with photons and about what we can learn about paths Feynman tells you to calculate. I think that it is a good advice. Words are not enough to understand QM One needs hilbert spaces operators and so on.  

• Dec 18, 2013

i delete this post. formulas were wrong  

• Dec 20, 2013

When there is a goog lightning, electrons are always detected so we need two 2-dimensional Hilbert spaces. H1 has a |L> and |B> basis. One vector for each slit the electron passes through. Suppose that there is a photon detector near each slit i call these detectors 1 and 2. I need another hilbert space H2 with basis |1> and |2> |1> correspond to a photon seen near the left slit and |2> near the other. The set electron + photon is in the tensor product H = [itex]H1 \otimes H2. A basis of this 4 dimensional space is |L>|1>, |R>|1>, |L>|2>, |R>|2> A generic vector in H is a|L>|1>+b |R>|1>+c|L>|2>+d |R>|2> If the vector is normalized, this corresponds to an amplitude «a*» that the electron passes through left slit and seen near it, an amplitude «*b*» that it passes through the right slit but is seen near the other one and so on. As the setup is symmetric we have a = d and b = c. So the state is (a|L>+b |R>)|1> + (a|L>+b |R>)|2> When we measure where the photon is seen (|1> or |2>) the state vector collapses on (a|L>+b |R>)|1> or on (a|L>+b |R>)|2> with equal probabilities. As these vectors are orthonormal, the probalility that the electron hits the screen at a given point is |aL(x)+b R(x)|² + |aL(x)+b R(x)|² So the visibility of fringes depends on the values of a and b in the statistical mixture. If the light is low we have to extend H2 with two vectors |L>[3> and |R>|3> where |3> corresponds to a no-click on the detectors. This looks like a POVM. The values of a and b depend on the wavelength of the photon. I do not know what are a(wl) and b(wl) We have a(0) = 1, b(0) = 0 (no interference). If di is the distance between the slits we have no information when wl = di, so i suppose that a(di) = b(di) What about them when wl > di*? do they remain equal*? I found that the disappearance of the fringes is due to the recoil of the electron but i found no formula with the limit wl = di.  

naima said: i found no formula with the limit wl = di.

• Dec 22, 2013

I used the ² "little 2 " (under escape) for sqarring in my posts, they appear now as unrecognized character. Could anyone repair this bug? As i was looking for how "b" depends on the wl wavelength, i found that [itex] \frac {|a| - |b|}{|a| + |b|}[/itex] has a name It is Visibility. look here when |b| = 0 V = 1 so fringes are well seen. when V = 0 you cannot see the fringes. The V(wl) function is not so simple that i thought. you can find it by googling "loss of coherence tan" or "Fringe Visibility and Which-Way Information: An Inequality" I thought that the Visibility was null when wl = d. Feynman wrote "So now, when we make the wavelength longer than the distance between our holes, we see a big fuzzy flash when the light is scattered by the electrons. We can no longer tell which hole the electron went through!" Formulas seem to say something else. Do you understand this?  

• Dec 25, 2013

Merry Christmas, I found three links with (he same formula of fringes Visibility: jump to p 12 jump to p 5 look at fig 7 It gives the curve of the electron fringes visibility as a function of the light wavelength.+ It is surprising that fringes disappear then reappear and so on.  

• Dec 27, 2013

There is a problem with the third link (the one with fig 7). When i click it the pdf is loading but i cannot read it. if you have the same problem: save it on your desk quit the forum and read it from your computer. Please tell me if you succeed. It is worthwhile It is the best paper i found about watching the double slit. it was written by Daniel Walls who worked with Glauber (Nobel prize). the Visibility(u) is [itex]\frac{3}{2}(\frac{sin u}{u}+\frac{cos u}{u^2}-\frac{sin u}{u^3})[/itex] you can verify that lim u-> 0 is = 1 You can find the complete derivation of this formula by googling "decoherence from spontaneous emission ole steuermagel and harry paul" if the same problem occurs save it also!  

A PF Asteroid

Here is an alternative link to the Tan & Walls paper (the 3rd link in post #28): http://www.physics.arizona.edu/~cronin/Research/Lab/some%20decoherence%20refs/LossOfCoherenceInInterf.pdf  

Do you know if S M TAN is Shina Tan? He looks very young.  

naima said: Do you know if S M TAN is Shina Tan?

• Dec 28, 2013

thank you. There is a 3/2 factor in the visibility formula. From which identity does it come?  

• Jan 7, 2014

We begin with an integral from zero to pi of a function of the angle [itex]\theta[/itex]. Using x = cos ([itex]\theta[/itex].) visibility of the fringes becomes [itex]A\int_{-1}^1 (1+x^2) e^{i u x} dx[/itex]. Integrating it twice by parts we get [itex]4A [\frac{sin u}{u}+\frac{cos u}{u^2}-\frac{sin u}{u^3}] [/itex]. "u" being the distance of slits divided by the wavelength of the photon when it decreases to zero the limit of visibility must be 1. We need so a normalization factor and the good formula is [itex]3/2 [\frac{sin u}{u}+\frac{cos u}{u^2}-\frac{sin u}{u^3}] [/itex]. We can compute the visibility when u = 1. It is when we watch the electrons with light having for wavelength the distance between the slits. We have V(1) = 3/2 cos(1) = 0.8 So the visibility is still very good!  

Related to Double-slit experiment and watching the electrons

1. what is the double-slit experiment.

The double-slit experiment is a classic experiment in quantum physics that demonstrates the wave-particle duality of light and matter. It involves passing a beam of particles, such as electrons, through a barrier with two narrow slits and observing the resulting pattern on a screen behind the barrier.

2. How does the double-slit experiment demonstrate wave-particle duality?

The double-slit experiment shows that particles can exhibit both wave-like and particle-like behavior. When the particles pass through the slits, they create an interference pattern on the screen, similar to what would be expected if waves were passing through the slits. This suggests that particles have wave-like properties, such as diffraction and interference.

3. What happens when we watch the electrons in the double-slit experiment?

When we observe the electrons in the double-slit experiment, the interference pattern disappears and the electrons behave like particles, creating two distinct bands on the screen. This is known as the observer effect, where the act of observation affects the behavior of the particles being observed.

4. Why do the electrons behave differently when we watch them in the double-slit experiment?

The behavior of the electrons changes when we observe them because the act of measurement or observation causes the wave function of the particles to collapse. This means that the particles are forced to behave like particles, rather than waves, and the interference pattern disappears.

5. What implications does the double-slit experiment have for our understanding of reality?

The double-slit experiment challenges our traditional understanding of reality and raises questions about the nature of particles and the role of observation in shaping reality. It suggests that particles can exist in multiple states at once and that our observation or measurement can influence their behavior. This has significant implications for our understanding of the universe and the fundamental laws of physics.

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