### The quantum world is really strange. It looks like - particle exists in different places at the same time, - a particle can affect anot...

The quantum world is really strange. It looks like

- particle exists in different places at the same time,

- a particle can affect another particle instantly in the distance,

- a particle can exist both as smeared out wave and as a point-like entity in the same place but never at the same time,

- and the presence of the members of the quantum world and their interactions are probabilistic in nature.

Our everyday experience rebels against what the quantum world is. Our experienced world is local, determined, exactly direct, and the cause and effect work in time orderly way. However, the experiments that we are performing in the quantum world cannot lie. Experiments show the quantum world is undeniably strange but real. And not just real, but describable by math in an extremely precise way. We don't understand the physical fundaments of the quantum world, but the math, the quantum mechanics, our abstract model of the quantum world is working precisely.

The most straightforward way to demonstrate the strangeness of the quantum world is the double-slit experiment. As Richard Feynman said (besides that, he safely states that nobody understands quantum physics), the double-slit experiment is enough to demonstrate all the mystery of the quantum world. And a specific setting to demonstrate the double-slit experiment is the Mach-Zehnder interferometer.

Theoretically, the Mach-Zehnder interferometer is able to demonstrate the classical double-slit experiment identically, yet, the equipment and the setup are very different. The Mach-Zehnder interferometer uses two half-transparent mirrors instead of two slits to create quantum behavior. It might be conceptually possible to demonstrate the same phenomena of the quantum interactions what the classical double-slit experiment does by using the Mach-Zehnder interferometer, but there is a profound difference between the two experiments.

The classical double-slit experiment applies the well-understood wave nature of the quantum world utilizing the two slits on the dimension that is comparable to the wavelength of the examined quantum particle.

Using the Mach-Zehnder interferometer in a single-particle quantum experiment applies and demonstrates a completely different quantum phenomenon, the seemingly most mysterious quantum effect, the distance independent self-superposition (self-entanglement). All the mythical mysteries of the quantum world, like the delayed choice experiment, the delayed choice quantum eraser experiment, the interaction-free measurement as Elitzur-Vaidman bomb test or Hardy electron-positron thought experiments are associated with the quantum phenomenon of the distance independent self-superposition. What is that?

Most of the strangeness of the quantum world is originated from its wave nature. The quantum wave, the wave function is a smeared-out entity, and it has a relation to the dimension of its wavelength. The wave function - representing a particle, for example - exists in different places at the same time with well-defined but continuously different values of its parameters. The appearance of the wave function is place-dependent, well, but only interpretable physically as a space-related probability distribution.

However, as it is demonstrated experimentally using the Mach-Zehnder interferometer in a single-particle experiment, a photon takes both paths of the arms in the Mach-Zehnder interferometer when both half-transparent mirrors are present regardless how far the second half-transparent mirror is or when it is placed to its required position before the photon arrives, and takes only one path if the second half-transparent mirror is missing, and over and above, the photon can do this path switch at any time, and instantly before an actual detection is made. Or equivalently, the single photon's probability distribution does not depend on spatial distance in the Mach-Zehnder interferometer. A single photon in the Mach-Zehnder interferometer takes both paths of the arms, do not matter how distantly separated the two paths from each other when we do not check which arm the photon is taking, but the photon can be found only in one arm, takes only one path when we check the presence of the photon before reaching the second half-transparent mirror or if the second transparent mirror is not present by collapsing the photon's wave function by detection, and the photon can switch between this different behavior in any spatial distance instantly. According to the single-particle Mach-Zehnder experiment, a particle demonstrates distance independent superposition with itself. As it is demonstrated in the experiment, that the quantum world bears this phenomenon.

The Mach-Zehnder interferometer setting is profoundly different from the classical double-slit experiment and utilizes fundamentally different phenomena of the quantum world.

The classical double-slit experiment uses the wave nature of the quantum world. In the classical double-slit experiment, the photon takes both slits because of the wave nature of the particle and because the slits are within the distance of the photon's de Broglie wavelength. The photon wave function splits, the photon entangles with itself as it passes through both slits, but in a distance-dependent way. If the two slits are far enough from each other, the interference pattern won't appear.

The single-particle Mach-Zehnder experiment uses the experimentally demonstrated distance independent self-superposition phenomenon. In the Mach-Zehnder experiment, the photon, or more precisely its wave function splits at the first half-transparent mirror, creates two of its self-entangled entities, takes both arms of the equipment regardless what distance the two paths are, and combine again at the rightly placed second half-transparent mirror and activate always the same detector, proving it took both pats at the same time unless the photon is detected anywhere on the paths by not applying or before the second half-transparent mirror by a detector regardless how far from the first half-transparent mirror or how far from the other path are by collapsing its wave function and observing it as a definite particle.

Distance independent self-superposition is profoundly different from the probabilistic presence of a particle. A quantum particle can be present in any place at the same time by its wave function, but the probability of the presence depends on the actual place, and the probability quickly tends to be zero in the distance. The distance independent self-superposition is different because the probability of the wave function does not depend on the distance from where the split was made.

The distance independent self-superposition is the strangest of the strange phenomenon of the quantum world. But is it a real effect? The actual single-particle Mach-Zehnder experiment demonstrates it, but is the experiment interpreted correctly? Without it, the delayed choice paradox, the contactless measurement paradox would not exist either. Without the distance-independent self-superposition might be no exotic physical models needed to understand what the quantum world is. Pilot wave theory, many-world theory, spontaneous wave function collapse theory, desynchronization theory all try to understand what is going on in the quantum world. Neither model is perfect in explanation. Some solutions, like the many world theory, even stranger than what to try to explain.

There are proposals to explain the quantum phenomena as local interactions in previous thoughts using the grid model.

+ The quantum interactions' probabilistic nature might be explainable by high-frequency interrelationships.

- Wave-particle duality might be explainable as a localized interaction of the waves.

- The seemingly non-local, action at the distance effect, the entanglement between different particle entities might be understandable by the synchronized vibrations of the quantum objects.

The quantum phenomena might be understandable by a local theory, by the grid model, except the distance independent self-superposition. All the other quantum phenomena are describable by locally acting interactions.

Any theory is false if it does not correspond even with only one experiment. Is the experiment demonstrating the distance independent self-superposition correct? Does it demonstrate correctly an actually existing quantum effect?

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