As we know, spin one particles can occupy the same place and spin one-half particles cannot. Why is this difference, where is it come fr...
As we know, spin one particles can occupy the same place and spin one-half particles cannot. Why is this difference, where is it come from? It is Pauli's postulate, which says that no spin one-half particles can be in the same place at the same time in the same quantum state. What is the physical reality behind this?
Are the spin-one particles really can be at the same time in the same place in the same quantum state? Or it is really just an illusion, the illusion of the interchangeability of these particles? Maybe they cannot occupy the exact same place at the same time, but because they are interchangeable, we cannot differentiate between them. They can be packed in a tight place, quantum tightly which we may see that they are in the same place.
We see the spin one particles like a photon as waves. The energy that they are representing is related only to the frequency of them (multiplied with the Planck constant) but not of the amplitude of the wave. However, every wave has its amplitude. If they really can be in the same place at the same time that would not see that the amplitude of the wave is changing?
Let suppose now that the spin one particles cannot be packed in the same place only can be packed in quantum tightly place. Because they are the same, and they are interchangeable, the swap operation does not change the quantum state, we cannot differentiate between them, so as we can see from outside, they can be in the same place. How about the spin one-half particles? We know originally that they cannot be in the same place at the same time, or as should we say more scientifically, they cannot be in the same quantum state in the same place at the same time. But we saw this already in the case of the spin-one particles. Actually, the spin-half particles can be packed even more tightly. Because they have two different spin states, two of them can be packed in the same place at the same time because the two different spin states are different quantum states.
So as may be, the spin-half particles can be packed even tighter than the spin-one particles. Why then the spin-half particles can build up the matter, which occupies space? Because of two reasons. One reason is that they can build up structures, structures that are stationary in place. For example, the electron can create a stationary structure around the nucleus. It is necessary for the spin one-half particles to be capable of building stable structures to occupy space, but it is not enough. The second reason that the spin one-half particles can occupy space is that the interchange of them, acting a swap operation on them is distinctive, does not create the same quantum state as it creates the same in the case of the spin-one particles. Because of the interchange, the swap operation creates different quantum states, when two structures built by spin half particles are getting closer and try to occupy the same place, to go through on each other, it is necessary that the interchange, the swap operation takes action between them. However, because this operation creates different quantum states, the swap cannot take place, the swap cannot create the same thing as the original. For example, if an electron, which creates a structure, tries to pass through on a space, which places occupied by another electron, which creates the same structure, to pass through the swap operation needs to take action. But the swap action creates different quantum states of the electrons, not the original states, the swap cannot create the same quantum states, the pass-through cannot happen, the electrons cannot exchange they place. The Pauli's principle prevails.
What kind of internal structure of the particles has to have to the swap operation has this phenomenon? It was discussed in the thought of "The structure of the photon and the electron" before.
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