# SPACE QUANTIZATION AND ENTANGLEMENT

1.4 SPACE QUANTIZATION AND ENTANGLEMENT

1.4.1 Background and actual interpretation

Apparently with the accreditation of idea that spin is a quantum property, and using a new mathematical formalism (operators), quantum mechanic solved the interpretation of Stern Gerlach experiment. But, the oddity of situation appear when using the same silver beam, the magnet is rotated with a certain angle. The results are the same indifferent of the angle of magnet rotation. This is a quite complicate and without meaning situation for quantum interpretation. Of course there is nothing special about the direction z, i.e. there is nothing to distinguish the z direction from any other direction in space. And this situation is only the beginning....

Suppose we put a second identical Stern Gerlach (SG) instrument and the fascicle pass from one instrument to the second one and we make a series of measurement as indicate in fig 1.7

Figure 1.7 Successive SG measurements

In figure 1.7, by plus or minus sign we indicate the orientation of fascicle at escape from SG device, relative to the external magnetic field.

In the first case, when both magnetic-fields are similarly-oriented after z axis, with north and south poles parallels, and we eliminate so called magnetic down fascicle, we observe that the magnetic up fascicle remain unmodified. So the magnetic-up atoms are still magnetic-up after a second measurement. Suppose that again a second magnetic-field setup is positioned such that only spin-up atoms enter it, but the second setup and detector are rotated by 90 degrees so the inhomogeneity is on the x axis. After first instrument we obtain a split on the z direction and we eliminate one fascicle (magnets down). If only the spin up fascicle enter in the second SG x axis orientated, we obtain again a separation in 2 fascicle. The same things are happened if we orientate de second SG after y direction.

Let’s complicate a little bit the situations. With the first SG in the direction z we obtain a first split and we block spin down fascicle. In the second SG orientation is after x axis and we obtain again a split of fascicle. We block again spin down component and we pass the spin up fascicle again through a SG orientated on the z axis. And surprise … the fascicle is again splits in two components.

Being incapable to explain succession of SG experiments, quantum mechanic define new concepts (entanglement and correlation) and new philosophical interpretation.  According to quantum mechanics when the two filters have the same orientation, the correlation is zero. When the two filters have opposite orientations, the correlation is 100%. When the two filters have perpendicular orientations, the correlation is 50%. It turns out that the correlation goes smoothly from zero to 100% as the relative orientation goes from 0° to 180°. It remains to atribute even a  decisional power  or right ov vote for these particles and the menu is complet.

In the same time a new theorem (Bell’s theorem ) was formulated in order to have a theoretical support for this entanglement. We will not discuss here these theorem which is supposed to be after some scientists the most important theorem from science (not from physics!!!), because these theorem does not exist, and is based on a wrong interpretation of SG experiments.

The quantum interpretation of succession of SG experiments starts form idea that ,,measurement of one physical observable can make a previously-measured different observable probabilistic again”. So a measurements change the variable from deterministic to probabilistic, and an entirely interpretation of physical phenomenon is made, actually on this basis. Of course we can ask rhetorically if the measurements change the variable (and the universe), what does measurement means?

The quantum explanations are unsustainable because as we have seen in case of a succession of two SG devices with only magnet up atoms, the second measurement doesn’t make probabilistic the result, and starting from a magnet up atom we obtain finally magnet up. If we put a third SG device and we measure again the up fascicle we will see that again the measurement is not probabilistic, but contrary, deterministic.

1.4.2 Proposed classical interpretation

It was shown at classical Stern Gerlach measurement that inhomogeneous magnetic field split the fascicle of atoms or particle in two beams according to orientation of atomic magnetic moment relative to direction of external field.

Also it was presented that the atomic magnetic moment executes a precession in x-y plane, and acceleration after z axes when direction of inhomogeneity toward z axes direction. In this movement of precession there is an equal probability that atomic moment are orientated toward positive x direction or negative x direction, and similarly after y axis. Statistical speaking there is an equal probability that an atomic moment is orientated toward positive x direction or negative x direction. Also due to the continuous precession movement there is equilibrium between number of magnetic moment orientated in positive x direction and number of magnetic moment orientated in x negative direction.

Having this image of spin comportment in inhomogenous magnetic fields we can explain clearly what’s happened when we change the direction of external inhomogeneous magnetic field.

Through moment up we understand atomic moments which are up orientated, with a certain angle related to the direction of inhomogeneous magnetic field and consequently are deviated upwards on the screen. For moment down the situation is opposite.

Let’s suppose we block from a first experiment the down fascicle, and we introduce the up fascicle in a secondary SG device orientated after z axis (2 successive SG instruments with identically set-up). After escape from the first inhomogeneous magnetic field, when enter in the secondary inhomogeneous field in the same direction, the magnetic moments continue their precession around z axis and we don’t have a split in the second SG device. The acceleration of fascicle is made again in the up direction due to the secondary SG device.

We repeat the experiment, but we change the direction of magnet in the second SG in the x direction. From the first instrument we block the down fascicle and only up fascicle is introduced in the second SG device. In the first SG device, the atomic magnetic moments execute a precession in the x-y plane, around z direction (the thick line in the picture), so at entrance in the second SG there is an equal probability to have an orientation of magnetic moments toward positive or negative direction of x axis (fig 1.8).When we change the magnetic field inhomogenity (second SG device) in x direction, all magnetic moments will change start to precess around x direction or in a z-y plane. The probability of existence of magnetic moments orientated toward positive or negative x direction is equal.

Due to the acceleration in x direction magnetic moments orientated toward positive x direction are accelerated up and magnetic moments orientated in negative x direction are considered down and move down on the photographic plate. It is very clear why from one fascicle up orientated in z direction we obtained in other direction two fascicle up and down orientated.

The same thing is happened if we change the second SG orientation toward y direction; a split of spin up fascicle is obtained due to the precession of magnetic moment around y axis.

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Fig .1.8 Change in precession direction when the direction of magnetic filed is changed in successive SG device

Let’s analyze the last experiment presented in the fig. 1.7 In the first SG a fascicle is split in spin up and spin down. The spin down is blocked, and spin up is again spitted in a spin down spin up due to a second SG orientated in x direction. Again spin up is selected and introduced in a third SG orientated in z direction and, amazing .. the fascicle is split down again. Of course in this condition anyone asks what does it represent quantization in a specific direction if in reality we don’t have this fact? Classical physics can solve this apparent ,,paradox” of ,,quantum mechanic” very simple. After first SG instrument the up fascicle will execute a precession in positive z direction, in x-y plane. So due to that, in x direction we have a secondary split in x direction in the second SG. At escape from the second SG, and when we block the down fascicle, the up spin fascicle is directed to positive x, and executes a precession in z-y plane. Consequently in the third SG the fascicle will be again separated in two fascicles, because at entrance in the third SG there is an equal probability of magnetic moments to be directed to positive or negative z direction

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