DParlevliet

Of course I agree with Huygens. But as referenced above, Huygens calculated his principle with a medium (ether) in which every point becomes a source of a spherical wave. Later on it was proven that no ether exist. But if a QM wave acts exactly according Huygens principle, then also in vacuum every point acts as a source of a spherical wave. Why? that was the question of this topic.

The interference is caused by difference in path length between both waves, which cause difference in phase. The result you see in the interference formula above.

I don't think so. Otherwise the diffraction would depend on the roughness of the edge. When you make is very smooth, there will be hardly diffraction. Also only a small part of the wave, at the slit edges, does diffract while the main part in the middle would pass without diffraction. According Huygens principle and calculation (and light reacts in that way) the whole surface of the slit diffracts, not only the edges.

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Several Wiki: "In 1678, Huygens[1] proposed that every point to which a luminous disturbance reaches becomes a source of a spherical wave" "According to the wave theory of light proposed by Christiaan Huygens, light travelled in the form of longitudinal waves via an omnipresent, perfectly elastic medium having zero density, called aether" QM: "Huygens' principle can be seen as a consequence of the isotropy of space—all directions in space are equal. Any disturbance created in a sufficiently small region of isotropic space (or in an isotropic medium) propagates from that region in all radial directions. The waves created by this disturbance, in turn, create disturbances in other regions, and so on. The superposition of all the waves results in the observed pattern of wave propagation" "Einstein himself noted that his own model which replaced these theories could itself be thought of as an aether, as it implied that the empty space between objects had its own physical properties" So Huygens certainly calculated his principle on the existance of a medium. Even the QM explanation implies some medium. In all cases not a classical medium of matter is ment, like the earlier ether.

What do I assume? I fill in the standard formula of interference.

So it is calculated with a medium. But when it was proven that there was no medium, the way he prooved and calculated it is wrong. Of course the outcome is still right, but now it is only a description, not an explanation. For classical waves with a medium Huygens principle is still right and calculated right (an interference pattern from sferical; radiating particles)

So at a minimum the cosine is -1, and then the difference between a1 and a2 determines if A is zero or not. The more a1 and a2 differs between the two phases, the higher A will be. So the cosine shape of the interference is always the same, But the hight of this cosine depends on the difference of amplitude between two phases.

Huygens is calculated on spherical radiating particles of the medium. But QM waves are no supposed to have a medium.

Phase is fixed function of the geometric of the experiment (distance between slits and detector). The peak and minimum (cosine = +1 or -1) are visible in the cosine shaped interference pattern on the detector.

That is what I wanted to know. What is the formula which predict this? On what physical effect is that based?

Cosine gives only the shape, depending on the position on the detector. Suppose the detector position where the phase difference is 450 degree (2.5 period) then Cosine = -1 and if a1=a2 then A=0. So no propability to absorb photons. If a1 and a2 differ at that position, A gets a value above zero, so some propability.

Formula of E-M waves does not predict diffraction Feynman is a method of calculation, based on the assumption of diffraction. It does not explain why. EM-waves has no medium

Because in the formula above only a1 and a2 has influence on A

How does Quantum mechanics explain diffraction? If light goes throught a single slit it is diffracted, the waves bent in the slit. In classical waves this is caused by the carrier, which consists of particles which radiate spherical. But a EM-wave has no carrier. So why does the wave bends in exactly the same way as classical waves?

It is partial cancellation of the wave, not the photon. The quadrature of the wave is the propability that the photon is absorbed at that prosition. If both waves cancel each other fully this propability is zero (no photons detected). If they cancel partial the propabity becomes higher (some photons detected).

That at the black lines no photons arrive, because both waves cancel each other. 1: that is the principle of the double slit, it introduces different lentgh path so a phase/time shift. For instance with 2.5 period shift between both waves, they cancel each other. 2.5 period = 2,5E-15 s (~green). 2: if the amplitude is differs in 2,5E-15 s change, there is no full cancel anymore.

Now another result of the double-slit. Suppose the distance between the slits is one kilometre, Then there will be interference too. Full interference is only possible when the waves through both slits have the same amplitude. So the amplitude of (one) photon wave is equal at both slits, at a kilometre distance.... My first or second sentence? Let's say the base frequency of the fourier

The photon-wave through one slit interferes with its copy through the other slit, but with a phase = time shift. So if the original photon-wave amplitude changes with time, you will see that in the interference. Yes, the same frequency.

So the place where it can end up (or not) tells you something about the wave. The location depends on the wavelength because of the phase shift between tho waves, and the amplitude of both waves. See the German Wiki formula of the sum of two waves: If the amplitude of both waves differ (a1, a2) the interference will be different. If phase difference is 180 degree, cos = -1, A = 0 if a1=a2. Then there never a photon will end up. If they differ from each other (like when the amplitude is not constant with time/phase) A will have some value, so some propability of photon absorption.

Photons are not fundamentally quantised. They have both waves or particle proporties. This shows in the double slit, so therefore this experiment is always used in QM explanations. But why, and how they interact, nobody knows. How it acts in the double slit with the particle, is a mystery. That is the Copenhagen interpretation, who also forbids to think about it. It is what the experiment shows and thats all. If you can make a formula that's enough. There is another minority view of Boglie-Bohm, who states that particle and wave are connected and are physicly real. In this explanation the particle goes throught one slit but is pushed by the two interfering waves to where it will be detected.

How do you get constructive interference.when there is only one wave from one slit?

But there are parts of the detector where the photon is never localized. These are the places where two waves from both slits arrive which cancel each other fully. That is only possible if they have opposite sign (180 degree phase shit) and equal amplitude. If not then the cancelling is not complete.

That is the question of this topic. Is it really constant amplitude (of one photon), also a kilometre ahead of the photon? For instance the wave of a mass particle I showed before (#13) does not have constant amplitude, but is short. Because the consequence is: the quadruple of the modulus of this wave is the probability. So a constant amplitude would mean that the probability of absorption of the photon right after emitting is these same near the emitting atom is a kilometre ahead. Now I think it: the Born rule (propability is the quadruple of the wave) is for matter particles. Is that also for photons?

See my earlier image of the wave with 5 periods. Let us discus only on the length of the wave. If the wave had infinite periods then interference will be the dashed sine: full interference on all distances of the middle of the detector. Black lines will occur at 0.5, 1.5, 2.5, ... periods phase shift between the waves through slit 1 and slit 2. But suppose the wave has only 5 periods, what happens after the phase shift between both is 5 periods and larger? Then both (short) waves don't see each other anymore, so they cannot interfere. At the detector position of 5.5 period phase shift first wave 1 arrives while there is no yet wave 2, and only after wave 1 has passed wave 2 arrives. So there will be light of cause, because there are waves, so propability of absorption, but there will be no interence pattern anymore. I don't say that the interference pattern looks the same as the wave, but you can calculate it (more of less)