Abstract Also physics has its impossibility statements. We compare them with the mathematical impossibility theorems and look into the history of one of them: the impossibility of building a perpetual motion machine. We also consider impossibilities in twentieth-century physics, in particular in quantum mechanics. For example, Heisenberg’s uncertainty relations imply that it is impossible to measure both the place and momentum of a particle accurately. We also discuss von Neumann’s controversial proof that it is impossible to obtain a deterministic version of quantum mechanics by introducing hidden variables.
Abstract Also physics has its impossibility statements. We compare them with the mathematical impossibility theorems and look into the history of one of them: the impossibility of building a perpetual motion machine. We also consider impossibilities in twentieth-century physics, in particular in quantum mechanics. For example, Heisenberg’s uncertainty relations imply that it is impossible to measure both the place and momentum of a particle accurately. We also discuss von Neumann’s controversial proof that it is impossible to obtain a deterministic version of quantum mechanics by introducing hidden variables.
It is shown that, although correct mathematically, the celebrated 1932 theorem of von Neumann which is often interpreted as proving the impossibility of the existence of "hidden variables" in Quantum Mechanics, is in fact based on an assumption which is physically not reasonable. Apart from that, the alleged conclusion of von Neumann proving the impossibility of the existence of "hidden variables" was already set aside in 1952 by the counterexample of the possibility of a physical theory, such as given by what is usually called the "Bohmian Mechanics". Similar arguments apply to other two well known mathematical theorems, namely, of Gleason, and of Kochen and Specker, which have often been seen as equally proving the impossibility of the existence of "hidden variables" in Quantum Mechanics.
Abstract As Heisenberg began to promulgate his version of the new quantum philosophy as the ‘Copenhagen spirit’, John von Neumann undertook to purge quantum mechanics of its defects and make it comprehensible to Göttingen’s prince of mathematics, David Hilbert. The result is familiar to any student of physical science. Von Neumann separated the continuous, deterministic, and reversible evolution of the wavefunction from its discontinuous, indeterministic, and irreversible ‘collapse’ in an act of measurement. He saw no reason why the first process should not continue all the way up the chain to the observer’s conscious mind, where the second process occurs. Bohr had little to say about von Neumann’s theory, other than it was ‘wrongly put’. Von Neumann also closed the door that Born had left ajar. Causality could not be restored to the quantum domain by supposing the existence of ‘hidden variables’, as these, according to his reasoning, were mathematically impossible.
Since the publication of Heisenberg’s paper1 on the “anschaulichen Inhalt” of quantum mechanics, discussions of the fundamental limitations on the accuracy of physical measurements have been much in the foreground. According to Heisenberg, the quantum mechanics implies that it is impossible to measure simultaneous values of a coordinate and its conjugate momentum with unlimited precision. Instead, if Δp be the estimated error or uncertainty in a momentum and Δq that in the associated coordinate one must have the inequality,
ΔpΔq>2πh
(1)
This inequality has come to be known quite generally as Heisenberg’s uncertainty relation.
Forty years after the advent of quantum mechanics the problem of hidden variables, that is, the possibility of imbedding quantum theory into a classical theory, remains a controversial and obscure subject. Whereas to most physicists the possibility of a classical reinterpretation of quantum mechanics remains remote and perhaps irrelevant to current problems, a minority have kept the issue alive throughout this period. (See Freistadt [5] for a review of the problem and a comprehensive bibliography up to 1957.) As far as results are concerned there are on the one hand purported proofs of the non-existence of hidden variables, most notably von Neumann’s proof, and on the other, various attempts to introduce hidden variables such as de Broglie [4] and Bohm [1] and [2]. One of the difficulties in evaluating these contradictory results is that no exact mathematical criterion is given to enable one to judge the degree of success of these proposals. These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
Abstract We will first define what is meant by “hidden variables”. Then, we will review theorems proving the impossibility of theories introducing such variables in a naive way. Next, we will outline the de Broglie-Bohm theory and show that it is not refuted by those theorems. To do that, we will explain how “measurements” work in that theory, using the examples of spin measurements and of momentum measurements. Those measurements do not reveal pre-existing properties of the quantum particle but are the result of interactions between that particle and the measuring apparatus. And this is why the de Broglie-Bohm theory is not refuted by the theorems on the impossibility of hidden variables. We will also explain the relationship between the no “hidden variables” theorems and nonlocality, with and without introducing Bell’s inequalities.
Abstract: Quantum mechanics, to the broader public, is often introduced through its seemingly paradoxical and counterintuitive principles-most famously the uncertainty principle, the principle of complementarity, and the no-cloning theorem. These ideas have long symbolized the “impossibility features” of the quantum world, setting it apart from the deterministic and predictable framework of classical physics. For decades, such principles fuelled intense debates among both physicists and philosophers, centering on how one should properly interpret the nature of quantum reality. However, as the twentieth century drew to a close, a remarkable shift began to unfold. Rather than treating these peculiar features merely as philosophical curiosities or obstacles to understanding, physicists started exploring whether these very strangenesses of quantum mechanics could be harnessed as resources for practical use. What emerged from this vision was an entirely new scientific discipline-quantum information theory and its technological counterpart, quantum computation. This new field reimagines the counterintuitive traits of quantum systems as powerful tools for accomplishing tasks fundamentally impossible within the classical paradigm. Out of this rethinking arose foundational protocols such as quantum cryptography, offering unprecedented levels of secure communication; quantum dense coding, enabling the transmission of more information using fewer resources; quantum teleportation, allowing the transfer of quantum states across distance without physically moving the particles themselves; and quantum algorithms, capable of solving certain computational problems at speeds unattainable by any classical machine. In this way, what was once regarded primarily as a domain of abstract puzzles and interpretational controversies has transformed into a vibrant, application-oriented science-laying the groundwork for the future of information, computation, and technology itself. Keywords: EPR paradox, Bell’s theorem, Entanglement, Quantum teleportation