Therefore, in twistor theory, the most fundamental object are twistors instead of spacetime points. Twistor theory was created with the idea of treating real coordinates of spacetime points as composed quantities of more general complex objects called twistors. Even when possible, that it is in the form of quantum field theory, many questions arise: entanglement, the measurement problem, the collapse of wave functions/state vector reduction and the quantum gravity issue. That coordinates of spacetime are real numbers is just an hypothesis of our mathematical models, despite the fact it is well supported by experiments! The main difficulty is a consistent formulation of special relativistic quantum theory. But this is again a restricted option determined by experiments. That is, complex numbers describe oscillations interpreted as probability waves! By the other hand, relativity implies that spacetime points is a real four dimensional (in general D-dimensional) vectors. The probability amplitudes are the complex numbers. Quantum Mechanics(QM) is baed on complex structure of Hilbert space of physical states (both of finite or infinite dimensions!). Roger Penrose formulated twistor theory in the hope of making complex geometry and not the real geometry the fundamental arena of geometric theoretical physics, and a better way to understand quantum mechanics. I want to use new TeX packages, and that is not easy here, to simplify things, and to write better things I wish to tell the world. TSOR is ending and from its ashes will arise another project.
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