In contradiction to a number of other authors (sample ref below), Gerrit Coddens, at France’s prestigious Ecole Poytechnique, asserts that:

2.2 Preliminary caveat: Spinors do not build a vector space

As we will see, spinors in $SU(2)$ do not build a vector space but a curved manifold. This is almost never clearly spelled out. A consequence of this is that physicists believe that the linearity of the Dirac equation (and the Schrödinger equation) implies the superposition principle in QM, which is wrong because the spinors are not building a vector space. In this respect Cartan stated that physicists are using spinors like vectors. This confusion plays a major rôle in one of the meanest paradoxes of QM, viz. the double-slit experiment.

…in his recent preprint submitted to the HAL archives in March 2021: “The geometrical meaning of spinors as a key to make sense of quantum mechanics. 2021. ffhal-03175981” available through https://hal.archives-ouvertes.fr/hal-03175981/document (where the download button refers to it, confusingly, as Spinors and Dirac 4.pdf) . The same view has been developed via an earlier and perhaps better-known paper “Spinors for everyone” (accessible in browsers) and his seductively-titled book published in 2015 From Spinors To Quantum Mechanics.

Authors stating that spinors do form a vector space include Jean Hladik’s crystal clear “Spinors in Physics” Springer 1999 (p. 24), as well as the standard https://en.wikipedia.org/wiki/Spinor .

While attracted to Coddens’s stated promise to: " provide the reader with a perfect intuitive insight about what is going on behind the scenes of the spinor algebra" and also to "make sense of QM" I am loathe to spend time on what may be a mathematical statement at variance to conventional definitions.

My question is therefore “Do spinors in general form a vector space, or do they do so only in restricted cases?”

In contradiction to a number of other authors (sample ref below), Gerrit Coddens, at France’s prestigious Ecole Poytechnique, asserts that:

2.2 Preliminary caveat: Spinors do not build a vector space

As we will see, spinors in $SU(2)$ do not build a vector space but a curved manifold. This is almost never clearly spelled out. A consequence of this is that physicists believe that the linearity of the Dirac equation (and the Schrödinger equation) implies the superposition principle in QM, which is wrong because the spinors are not building a vector space. In this respect Cartan stated that physicists are using spinors like vectors. This confusion plays a major rôle in one of the meanest paradoxes of QM, viz. the double-slit experiment.

…in his recent preprint submitted to the HAL archives in March 2021: “The geometrical meaning of spinors as a key to make sense of quantum mechanics. 2021. ffhal-03175981” available through https://hal.archives-ouvertes.fr/hal-03175981 (where the download button refers to it, confusingly, as Spinors and Dirac 4.pdf) . The same view has been developed via an earlier and perhaps better-known paper “Spinors for everyone” (accessible in browsers) and his seductively-titled book published in 2015 From Spinors To Quantum Mechanics.

Authors stating that spinors do form a vector space include Jean Hladik’s crystal clear “Spinors in Physics” Springer 1999 (p. 24), as well as the standard https://en.wikipedia.org/wiki/Spinor .

While attracted to Coddens’s stated promise to: " provide the reader with a perfect intuitive insight about what is going on behind the scenes of the spinor algebra" and also to "make sense of QM" I am loathe to spend time on what may be a mathematical statement at variance to conventional definitions.

My question is therefore “Do spinors in general form a vector space, or do they do so only in restricted cases?”

In contradiction to a number of other authors (sample ref below), Gerrit Coddens, at France’s prestigious Ecole Poytechnique, asserts that:

2.2 Preliminary caveat: Spinors do not build a vector space

As we will see, spinors in SU(2) do not build a vector space but a curved manifold. This is almost never clearly spelled out. A consequence of this is that physicists believe that the linearity of the Dirac equation (and the Schrödinger equation) implies the superposition principle in QM, which is wrong because the spinors are not building a vector space. In this respect Cartan stated that physicists are using spinors like vectors. This confusion plays a major rôle in one of the meanest paradoxes of QM, viz. the double-slit experiment.

…in his recent preprint submitted to the HAL archives in March 2021: “The geometrical meaning of spinors as a key to make sense of quantum mechanics. 2021. ffhal-03175981” available through https://hal.archives-ouvertes.fr/hal-03175981/document (where the download button refers to it, confusingly, as Spinors and Dirac 4.pdf) . The same view has been developed via an earlier and perhaps better-known paper “Spinors for everyone” (accessible in browsers) and his seductively-titled book published in 2015 From Spinors To Quantum Mechanics.

Authors stating that spinors do form a vector space include Jean Hladik’s crystal clear “Spinors in Physics” Springer 1999 (p. 24), as well as the standard https://en.wikipedia.org/wiki/Spinor .

While attracted to Coddens’s stated promise to: " provide the reader with a perfect intuitive insight about what is going on behind the scenes of the spinor algebra" and also to "make sense of QM" I am loathe to spend time on what may be a mathematical statement at variance to conventional definitions.

My question is therefore “Do spinors in general form a vector space, or do they do so only in restricted cases?”

In contradiction to a number of other authors (sample ref below), Gerrit Coddens, at France’s prestigious Ecole Poytechnique, asserts that:

2.2 Preliminary caveat: Spinors do not build a vector space

As we will see, spinors in $SU(2)$ do not build a vector space but a curved manifold. This is almost never clearly spelled out. A consequence of this is that physicists believe that the linearity of the Dirac equation (and the Schrödinger equation) implies the superposition principle in QM, which is wrong because the spinors are not building a vector space. In this respect Cartan stated that physicists are using spinors like vectors. This confusion plays a major rôle in one of the meanest paradoxes of QM, viz. the double-slit experiment.

…in his recent preprint submitted to the HAL archives in March 2021: “The geometrical meaning of spinors as a key to make sense of quantum mechanics. 2021. ffhal-03175981” available through https://hal.archives-ouvertes.fr/hal-03175981/document (where the download button refers to it, confusingly, as Spinors and Dirac 4.pdf) . The same view has been developed via an earlier and perhaps better-known paper “Spinors for everyone” (accessible in browsers) and his seductively-titled book published in 2015 From Spinors To Quantum Mechanics.

Authors stating that spinors do form a vector space include Jean Hladik’s crystal clear “Spinors in Physics” Springer 1999 (p. 24), as well as the standard https://en.wikipedia.org/wiki/Spinor .

While attracted to Coddens’s stated promise to: " provide the reader with a perfect intuitive insight about what is going on behind the scenes of the spinor algebra" and also to "make sense of QM" I am loathe to spend time on what may be a mathematical statement at variance to conventional definitions.

My question is therefore “Do spinors in general form a vector space, or do they do so only in restricted cases?”