A thesis of this book is that quantum mechanics could have started to be a biquaternion quantum theory with any loss of generality; on the contrary, resulting from its starting a more complete formulation: a general quantum theory. In Chapters 2 and 3 the author develops some standard and old arguments of quantum mechanics, often transfering a direct matrix method into the direct formulation by biquaternions just to confirm his thesis that standard quantum mechanics could have been, from its starting, a biquaternion calculus. To this regard he considers how biquaternions allow quantization and how some basic problems of the traditional quantum mechanics, as the harmonic oscillator or the hydrogen atom, may be reobtained following directly the use of a biquaternion algebra. In this manner a thesis of the book becomes to be that all the standard quantum mechanics was and is a biquaternion calculus. All the quantum physical quantities become biquaternions. If only so, this book could have expressed some interest only from an hystorical perspective. Instead, in the following Chapters 4 and 5, the biquaternion formulation of quantum mechanics reveals all its extraordinary interest. It is shown that by biquaternions the usual quantum mechanics becomes a good general quantum theory where it is found that quantum states are biquaternions, that Dirac’s and Schrödinger’s equations may be reconsidered by biquaternion quantum states, still that some quantum physical quantities, missed in the traditional formulation of quantum mechanics, now appear to give also support with regard to the solution of basic problems of the old quantum mechanics. A new perspective is given, as esample, to correlation and non locality of EPR systems and hidden variables, as well as, for the first time, a good solution is evidenced for the basic problem that remained unsolved in the standard formulation of quantum mechanics: the problem of the wave function reduction and of the quantum measurements. The Author has written a very simple book for any kind of reader but for the first time he has also given a strong elimination of the traditional manner to intend the mathematical apparatus, the symbolic and numerical structures that usually support the physical theories. He has given the first and fundamental advise that a general physical theory as the biquaternion quantum theory enters necessarily into a new manner to conceive the algebraic structure, arranged by algebra and subalgebra. Having fixed in this new manner, this correspondence existing berween numbers and physical reality, between algebra-subalgebra and physical processes, he has given a completely new explanation of such physical and biological reality.
E. Conte: the author is a theoretical phycist. He teachs Quantum Biology. Director of the center for studies on Radioactivity (CSRR – Bari) he is author of over 120 – research papers and some advanced monographs on theoretical and nuclear physics.