Bell’s Theorem: Form and Information in the Quantum Theory

Anton Zeilinger

Guang-Liang Li

Bell’s inequality is derived by resorting to a hidden-variable theory devised for resolving the Einstein-Bohr debate on the conceptual foundations of quantum mechanics. The legitimacy of quantum superposition for describing the physical world is the essence of the debate. Einstein argued against the legitimacy of quantum superposition. Testing Bell’s inequality by experiment with the experimental result explained by Bell’s theorem opened the door to so-called quantum information technologies. In quantum information theory, “quantum bit” (or “qubit” for short) in a form of quantum superposition is supposed to carry quantum information. Although most physicists believe that Einstein’s vision of the physical world contradicts the experimental result of testing Bell’s inequality, actually neither the experimental result nor Bell’s theorem is relevant to Einstein’s viewpoint. In the present paper, a new principle, the general principle of measurements, is proved as a mathematical theorem. Based on this principle, the experiment for testing Bell’s inequality and so-called experimental evidence for physically realizable “qubit” are scrutinized. The findings are as follows. The experimental result of testing Bell’s inequality and the measurement outcomes of experiments involving “qubit” are all erroneously explained. Bell’s inequality failed to capture the essence of the Einstein-Bohr debate, and Bell’s theorem is irrelevant to Einstein’s vision of the physical world. Quantum mechanics can be completed by using disjunction (“or”) as the logical relation between the orthonormal vectors that span an arbitrarily given Hilbert space without resorting to any hidden-variable theory, while the mathematical setting will remain essentially unchanged. All kinds of “qubit” violate the general principle of measurements and can only describe imaginary objects that do not exist in the physical world. The findings inevitably lead to a very regrettable conclusion: Quantum information has no physical carers and all quantum information technologies are not physically realizable.

Menas C. Kafatos

Jiří Souček

The standard Bell’s theorem states that quantum mechanics (QM) cannot be locally realistic. Here we prove the strong Bell’s theorem which states that QM cannot be realistic. In the proof we use the Mermin’s form of the Bell’s theorem. Our result solves the old dilemma: non-locality or non-realism. Then we discuss the consequences of the strong Bell’s theorem, e.g. that no Bell non-locality of QM exists and that quantum theory is local and non-realistic.

Emilio Santos

André Allan Méthot

The strongest attack against quantum mechanics came in 1935 in the form of a paper by Einstein, Podolsky and Rosen. It was argued that the theory of quantum mechanics could not be called a complete theory of Nature, for every element of reality is not represented in the formalism as such. The authors then put forth a proposition: we must search for a theory where, upon knowing everything about the system, including possible hidden variables, one could make precise predictions concerning elements of reality. This project was ultimatly doomed in 1964 with the work of Bell Bell, who showed that the most general local hidden variable theory could not reproduce correlations that arise in quantum mechanics. There exist mainly three forms of no-go theorems for local hidden variable theories. Although almost every physicist knows the consequences of these no-go theorems, not every physicist is aware of the distinctions between the three or even their exact definitions. Thus we will discuss here the three principal forms of no-go theorems for local hidden variable theories of Nature. We will define Bell theorems, Bell theorems without inequalities and pseudo-telepathy. A discussion of the similarities and differences will follow. 1