According to the quantum theory, the position and velocity of any particle is uncertain, so it may happen that the particle just finds itself somewhere other than where it was. Could it be that all the particles in my body “decide” to be on the other side of the wall and I go through the wall then?

It’s not that simple — more precisely, the degree of inaccuracy in determining the position and together with speed (momentum) is equal to a very small number (Planck’s constant). If the value of the Planck constant was in the order of hundreds of J.s, then we would take going through a wall almost for granted, but because the value of the Planck constant is 1E-34 (very very small), the “strange” behavior of particles (going through a wall, appearing in unexpected places) is limited only by the microworld — that is, electrons. The whole microworld is controlled by probability, and even in the world of electrons, it is not usual for an electron to “go” through a wall but the probability that this will happen is not negligible. And because there is a huge number of electrons, we can observe similar events. Even in our world, the probability that we will not go through the wall is not 100%, but 99.99… (there will certainly be more nines than the letters in this answer after the decimal point), but there are not enough of us in the world for it and life on Earth is not long enough for humankind to experience something similar.

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