How does it take a diffraction pattern to appear?
suppose a light with intensity as equal as passing a photon per second.
Classical physics tells us a diffraction pattern appears as fast as the light reaches a screen but quantum physics tells that if the intensity of light is very low as a photon per second, the diffraction pattern takes many times because we must wait lots of seconds for lots of photons to reach a detector(suppose we put ,say, a photon detector instead of the screen )
Is there any experiment to measure the time of pattern appearance?
"Is there any experiment to measure the time of pattern appearance?"
I think the integration time depends on (1) the intensity of the light source used and (2) on the desired signal/noise ratio for the experiment. So it depends on the specifics of each experiment.
But you are correct, the interference takes place even at the single photon level. Only a "hard" measurement on a camera or detector collapses the inteference pattern to a particular position.
You may find these articles interesting:
Observing the Average Trajectories of Single Photons in a Two-Slit Interferometer http://doi.org/10.1126/science.1202218
A double-slit 'which-way' experiment on the complementarity–uncertainty debate http://doi.org/10.1088/1367-2630/9/8/287
Mojtaba Shahbazi
In double slit diffraction, the electromagnetic radiation is polarized into conical diffraction (CD) as shown in Fig.3 in “The Double Slit Experiment Re-Explained” at:
https://www.researchgate.net/publication/307122920_The_Double_Slit_Experiment_Re-Explained
The CD which is the Circular Magnetic Field (CMF) enter both slits, interacted to form the patches, the time it takes to perform this is instantly.
To better understand this, you better asks yourself, what is the Photon?
Historically, Einstein introduced quanta to knock electron from atom when he solved the photoelectric effect in 1905, it was opposed by most scientists, till he was rescued by Compton in 1923, who claimed electromagnetic radiation contain quantum (photon), with momentum p=hv/c, but this important formula is found to be derived from Einstein mass energy equivalent with Planck's radiation formula, and his claim is proved to be untrue, and the formula of momentum used by Compton can't remove electron from atom, because it's a formula for particle with mass, meaning photon doesn’t exist, this is tackled in:
"Compton was Greatly Mistaken Using the Quantum"
Researchgate:
https://www.researchgate.net/publication/322835620_Compton_was_Greatly_Mistaken_Using_the_Quantum
Since this is the backbone of quantum mechanics, then the question is how did this state occurred? It’s thought there were three historical mistakes which allowed such fault to happened.
When Orstead discovered the relation between magnetism and electricity in 1820, the first mistake occurred when Ampere presented his formula based on electric components, although it was correct mathematically, but since dynamical activities occurred between magnetism due to the production of magnetic field, then a dynamic solution exist, we presented this in “The Magnetic Interaction”
https://www.researchgate.net/publication/215870160_The_Magnetic_Interaction
To understand the micro-world, you need to better understand the electromagnetic radiation, how the electric and magnetic fields integrated to form electromagnetic radiation, this was not been solved by Maxwell, although scientists thought he solved what been developed by QE, which was the second mistake, this is resolved through the Flip-Flop mechanism in “The Electromagnetic Radiation Mechanism”
https://www.researchgate.net/publication/266143373_The_Electromagnetic_Radiation_Mechanism
The radiation energy, it’s relation with Planck constant, condition to start radiation are given in “Electromagnetic Radiation Energy and Planck’ Constant”
https://www.researchgate.net/publication/271703848_Electromagnetic_Radiation_Energy_and_Planck'_Constant
As Planck’s formula gives us the radiation energy, there is a magnetic force embedded in radiation, Einstein and his contemporary scientists couldn’t get it, instead of looking for the formula, he invoked photon, that was the third mistake, the force is named the Radiation Magnetic Force (FmR) given by Eq. (24), in: “The Photoelectric Effects: Radiation Based With Atomic Model”
https://www.researchgate.net/publication/274509898_The_Photoelectric_Effects-Radiation_Based_With_Atomic_Model
When the above magnetic force formula FM=B1 B2 r^2 c, is known, and above electromagnetic radiation is known and the above Eq. (24) is known, then the Compton effect is solved as suggested by the Indian scientist Raman a century ago, as the reproduction of secondary electromagnetic radiation, as given in: “The Compton Effect Re-Visited”
https://www.researchgate.net/publication/299347018_The_Compton_Effect_Re-Visited
While the Double Slit Experiment which Richard Feynman said it’s impossible to be solved classically, it’s solved in: “The Double Slit Experiment Re-Explained”
https://www.researchgate.net/publication/307122920_The_Double_Slit_Experiment_Re-Explained
The last experiment for wave particle duality is the electron Diffraction, we solve this in: “Electron Diffraction Re-Explained (The Intense Magnetic Field Interaction with Crystals)”
https://www.researchgate.net/publication/308947884_Electron_Diffraction_Re-Explained_The_Intense_Magnetic_Fields_Interactions_within_Crystals
From all these electromagnetic radiation consists from wave, the interaction of two CD or the CMF is what constitute the patches.
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