We must be careful in the case of the spin notion: it has been supposed that the are two kinds of spin but there is no prove, in fact With the spin hypothesis it was supposed an additional half quantum number, but without discussion about the interaction. I think there is a missing point to clarify. Can we really consider the classical interaction between the electron and the proton and another one giving the spin? It is a dark aspect of the quantum mechanics. I have recently published “The spin and the angular momentum” in which I suppose that the first quantum state involve the three directions of the space. Indeed, there is no reason that the interaction between the electron and the proton involve just the two directions of a plane.
According to this approach the first quantum state give one-half magneton de Bohr corresponding to one-half quantum h of action and one-half quantum of action giving a linear contribution to the motion. The other states are the result of additional quantum.
Finally, there is no spin but just one interaction between the electron and the proton.
The so called spin has little to do with electron and nucleus. This is a matter of geometry, and the properties which are assumed for solids. As far as we can measure, all solids, including elementary particles, can rotate in space, with respect to any frame. Rotation is a geometric feature, which is well known in Mathematics, but badly treated in cartesian geometry, and Newton's physics. The representation of a rotation, in the 3 dimensional space, by an element of the group SO(3) is incorrect, in particular its representation by a vector of the 3 dimensional space (the common way to represent a rotational speed). It is convenient, but not faithful. The right representation requires the use of Clifford algebra, and the same happens in Relativity with 4 dimensions. Then one can work without this childish "spin number". Scalars belong to the Clifford algebra and their groups.
Hi,
I have developed a theory " The Daon Theory" which gives a very precise description of the electrons behaviour within the atom. Also the electron itself is explained. You will find all this in my profile (and much more, if you are interested).
Have fun,
JES
Dear Jean-Claude,
For an experimentalist the rotation is a phenomenon that we observe for different objects. As far as know we cannot observe such a phenomenon with the electron. On the other hand, with magnetism we observe half-quantum numbers an observation to explain. The mathematics is not physics, you have to use understandable language by many people if you wish to be followed, it is not the case with Clifford algebra.
Can you say something about an interaction involving the three directions of the space?
Dear Xavier,
When discussing rotation, we have to find a way to represent a rotational motion. We are used to the vectorial representations, and indeed the derivative of the matrix of a rotation leads (by multiplication with the inverse) to an antisymmetric matrix which can be represented by 3 scalars, or a vector. And it happens that this vector is also the axis of rotation, and the eigen vector of the rotational motion. So everything is good, except that this representation is not faithful : you have 2 different physical rotations which can be represented this way, whence the use of a scalar to distinguish the 2. But, with just a bit of mathematics, with Clifford algebra you get the whole.
When doing experiments, physicists accept new electronic devices, why is it difficult to accept new mathematical devices ? (they are old anyway...)
Electric charges are properties of elementary particles and the value of the charge is related to the symmetry of the platform on which the particle resides. This platform is a quaternionic separable Hilbert space and the symmetry depends on the version of the quaternionic number system that the Hilbert space applies to specify the inner products of vector pairs. The Cartesian coordinate system that sequences the elements of the selected version determines the symmetry. A polar coordinate system determines the spin of the particle. The polar coordinate system can focus on the polar angle or on the azimuth. The azimuth range is 2π radians, and the polar angle range is π radians. This selects between integer spin and half integer spin. The ranges can be walked up or down.
See
DOI: 10.13140/RG.2.2.35002.75202
Dear Hans van Leunen,
The experimentalists expect a more comprehensive language in which the hypothesis use can be understand. We must avoid discussion of mathematicians.
Regards,
Xavier
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