The purpose of this short post is to provide a very brief presentation of Quantum Theory.

In quantum theory, particles are waves of various shapes. You cannot directly observe the waves, only some of their properties. Each property is well defined only for some of the possible shapes. There is no shape for which the properties "position" and "momentum" are simultaneously well defined (Heisenberg's principle). When you observe a property, you find the wave in a shape corresponding to that property (like magic!), without regard of its previous shape. Entanglement: n particles are a single wave in a space with n x 3 dimensions, they don't have individual shapes.

In classical physics, particles are points moving on well-defined trajectories. This picture turned out to be an approximation:

**Short:**In quantum theory, particles are waves of various shapes. You cannot directly observe the waves, only some of their properties. Each property is well defined only for some of the possible shapes. There is no shape for which the properties "position" and "momentum" are simultaneously well defined (Heisenberg's principle). When you observe a property, you find the wave in a shape corresponding to that property (like magic!), without regard of its previous shape. Entanglement: n particles are a single wave in a space with n x 3 dimensions, they don't have individual shapes.

**Details:**In classical physics, particles are points moving on well-defined trajectories. This picture turned out to be an approximation:

**a particle is in fact a wave**(although there is no waving medium for this wave). We know it is a wave, because it interferes, it can be diffracted, its allowed states in an atom are those corresponding to an integral number of wavelengths, and it is governed by a wave equation. As a wave, it has no definite trajectory, and insisting in discussing in terms of position and momentum as for point particles leads to problems.But

**you can't observe the wave directly, only classical properties**, like position or momentum. Each property you observe is well defined only for a particular set of possible shapes of the wave. When you observe its position, the wave appears to be concentrated at a point, but it has an undefined momentum. Conversely, the possible shapes that have well defined momentum have no well defined position – they are spread in all the space. Similar things happen when you want to observe any other classical property.The first strangest thing about quanta is that

**when you look at them, they take precisely one of those shapes corresponding to the property you observe**, without regard of their previously known shape. If further you try to observe another property, which is not well defined for the previously observed shape, you will find the new kind of shape, allowed by the new property. Knowing its shape before an observation, you can not predict which of the allowed shapes you obtain, but only the probability for each allowed shape.The second strangest thing is the

**entanglement**. When dealing with more particles, say*n*, they are not described by individual waves, but by a single wave on a space obtained by multiplying the usual three-dimensional space with itself*n*times. This means that after two particles interact, they have no individual shape, but a common shape on this space with 6 dimensions. We can still observe one of the particles, and obtain a particular 3-dimensional shape for it, but if we try to observe both particles, the shape of one is dependent on the shape of the other. The strangest part is that**their shapes are correlated even if the particles are separated by very large distances**.