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The polarizers can be considered as introducing which-path information to each beam. This can also be accounted for by considering the light to be a classical wave,  : 91 and also when using circular polarizers and single photons.
In a highly publicized experiment in , researchers claimed to have identified the path each particle had taken without any adverse effects at all on the interference pattern generated by the particles.
However, commentators such as Svensson  have pointed out that there is in fact no conflict between the weak measurements performed in this variant of the double-slit experiment and the Heisenberg uncertainty principle.
Weak measurement followed by post-selection did not allow simultaneous position and momentum measurements for each individual particle, but rather allowed measurement of the average trajectory of the particles that arrived at different positions.
In other words, the experimenters were creating a statistical map of the full trajectory landscape. In , Pfleegor and Mandel demonstrated two-source interference using two separate lasers as light sources.
It was shown experimentally in that in a double-slit system where only one slit was open at any time, interference was nonetheless observed provided the path difference was such that the detected photon could have come from either slit.
In , the double-slit experiment was successfully performed with buckyball molecules each of which comprises 60 carbon atoms.
In , E. Eliel presented an experimental and theoretical study of the optical transmission of a thin metal screen perforated by two subwavelength slits, separated by many optical wavelengths.
The total intensity of the far-field double-slit pattern is shown to be reduced or enhanced as a function of the wavelength of the incident light beam.
In , researchers at the University of Nebraska—Lincoln performed the double-slit experiment with electrons as described by Richard Feynman , using new instruments that allowed control of the transmission of the two slits and the monitoring of single-electron detection events.
In , the double-slit experiment was successfully performed with molecules that each comprised atoms whose total mass was over 10, atomic mass units.
Hydrodynamic analogs have been developed that can recreate various aspects of quantum mechanical systems, including single-particle interference through a double-slit.
The droplet gently sloshes the liquid with every bounce. At the same time, ripples from past bounces affect its course.
The droplet's interaction with its own ripples, which form what is known as a pilot wave , causes it to exhibit behaviors previously thought to be peculiar to elementary particles — including behaviors customarily taken as evidence that elementary particles are spread through space like waves, without any specific location, until they are measured.
Behaviors mimicked via this hydrodynamic pilot-wave system include quantum single particle diffraction,  tunneling, quantized orbits, orbital level splitting, spin, and multimodal statistics.
It is also possible to infer uncertainty relations and exclusion principles. Videos are available illustrating various features of this system.
See the External links. However, more complicated systems that involve two or more particles in superposition are not amenable to such a simple, classically intuitive explanation.
Much of the behaviour of light can be modelled using classical wave theory. The Huygens—Fresnel principle is one such model; it states that each point on a wavefront generates a secondary wavelet, and that the disturbance at any subsequent point can be found by summing the contributions of the individual wavelets at that point.
This summation needs to take into account the phase as well as the amplitude of the individual wavelets. Only the intensity of a light field can be measured—this is proportional to the square of the amplitude.
In the double-slit experiment, the two slits are illuminated by a single laser beam. If the width of the slits is small enough less than the wavelength of the laser light , the slits diffract the light into cylindrical waves.
These two cylindrical wavefronts are superimposed, and the amplitude, and therefore the intensity, at any point in the combined wavefronts depends on both the magnitude and the phase of the two wavefronts.
The difference in phase between the two waves is determined by the difference in the distance travelled by the two waves. If the viewing distance is large compared with the separation of the slits the far field , the phase difference can be found using the geometry shown in the figure below right.
Where d is the distance between the two slits. When the two waves are in phase, i. This effect is known as interference.
The interference fringe maxima occur at angles. The spacing of the fringes at a distance z from the slits is given by.
For example, if two slits are separated by 0. If the width of the slits b is greater than the wavelength, the Fraunhofer diffraction equation gives the intensity of the diffracted light as: .
This is illustrated in the figure above, where the first pattern is the diffraction pattern of a single slit, given by the sinc function in this equation, and the second figure shows the combined intensity of the light diffracted from the two slits, where the cos function represent the fine structure, and the coarser structure represents diffraction by the individual slits as described by the sinc function.
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