Related papers: Quantum theory does not need complex numbers
While complex numbers are essential in mathematics, they are not needed to describe physical experiments, expressed in terms of probabilities, hence real numbers. Physics however aims to explain, rather than describe, experiments through…
Two recent papers (Renou et al., arXiv:2101.10873, and Chen et al., arXiv:2103.08123) have indicated that complex numbers are necessary for quantum theory. This short note is a comment on their result.
Complex numbers play a crucial role in quantum mechanics. However, their necessity remains debated: whether they are fundamental or merely convenient. Recently, it was claimed that quantum mechanics based on real numbers can be…
It is often stated that complex numbers are essential in quantum theory. In this article, the need for complex numbers in quantum theory is motivated using the results of tandem Stern-Gerlach experiments
The usual formulation of quantum theory is rather abstract. In recent work I have shown that we can, nevertheless, obtain quantum theory from five reasonable axioms. Four of these axioms are obviously consistent with both classical…
We show that the presented real-number quantum theories, compatible with the independent source assumption, require the inclusion of a nonlocal map. This means that if the independent source assumption holds, in these models, complex-number…
Quantum theory (QT) has been confirmed by numerous experiments, yet we still cannot fully grasp the meaning of the theory. As a consequence, the quantum world appears to us paradoxical. Here we shed new light on QT by being based on two…
In standard quantum mechanics, complex numbers are used to describe the wavefunction. Although complex numbers have proven sufficient to predict the results of existing experiments, there is no apparent theoretical reason to choose them…
Quantum theory (QT) has been confirmed by numerous experiments, yet we still cannot fully grasp the meaning of the theory. As a consequence, the quantum world appears to us paradoxical. Here we shed new light on QT by having it follow from…
Quantum theory provides an extremely accurate description of fundamental processes in physics. It thus seems likely that the theory is applicable beyond the, mostly microscopic, domain in which it has been tested experimentally. Here we…
Standard quantum theory was formulated with complex-valued Schrodinger equations, wave functions, operators, and Hilbert spaces. Previous work attempted to simulate quantum systems using only real numbers by exploiting an enlarged Hilbert…
The usual formulation of quantum theory is based on rather obscure axioms (employing complex Hilbert spaces, Hermitean operators, and the trace rule for calculating probabilities). In this paper it is shown that quantum theory can be…
Quantum theory makes the most accurate empirical predictions and yet it lacks simple, comprehensible physical principles from which the theory can be uniquely derived. A broad class of probabilistic theories exist which all share some…
Quantum computers take advantage of interfering quantum alternatives in order to handle problems that might be too time consuming with algorithms based on classical logic. Developing quantum computers requires new ways of thinking beyond…
We look at the fundamental use of complex numbers in Quantum Mechanics (QM). A review of some of the most popular reasons given in the literature to support the necessity of the complex formalism, We add some insight by invoking others.…
Recent work by Renou et al. (2021) has led to some controversy concerning the question of whether quantum theory requires complex numbers for its formulation. We promote the view that the main result of that work is best understood not as a…
The complexity of quantum computation remains poorly understood. While physicists attempt to find ways to create quantum computers, we still do not have much evidence one way or the other as to how useful these machines will be. The tools…
The concept of number is fundamental to the formulation of any physical theory. We give a heuristic motivation for the reformulation of Quantum Mechanics in terms of non-standard real numbers called Quantum Real Numbers. The standard axioms…
Wave-particle duality is one of the basic features of quantum mechanics, giving rise to the use of complex numbers in describing states of quantum systems, their dynamics, and interaction. Since the inception of quantum theory, it has been…
We find the minimal number of settings to test quantum theory based on real numbers, assuming separability of the sources, modifying the recent proposal [M.-O. Renou et al., Nature 600, 625 (2021)]. The test needs only three settings for…