arXiv subjects

Ulf Klein

Publications and source records attributed to Ulf Klein.

8 recordsLinked to original sources

arXiv2023

Quantizing Galilean spacetime: a reconstruction of Maxwell's equations in empty space

As was recently shown, non-relativistic quantum theory can be derived by means of a projection method from a continuum of classical solutions for (massive) particles. In this paper we show that Maxwell's equations in empty space can be derived using the same method. In this case the starting point is a continuum of solutions of equations of motion for massless particles describing the structure of Galilean space-time. As a result of the projection, the space-time structure itself is changed by the appearance of a new fundamental constant $c$ with the dimension of a velocity. This maximum velocity $c$, derived here for massless particles, is analogous to the accuracy limit $\hbar$ derived earlier for massive particles. The projection method can thus be interpreted as a generalized quantization. We suspect that all fundamental fields can be traced back to continuous sets of particle trajectories, and that in this sense the particle concept is more fundamental than the field concept.

quant-ph↗

arXiv2022

A reconstruction of quantum theory for nonspinning particles

Within the framework of the individuality interpretation of quantum theory (QT), the basic equations of QT cannot be derived from the basic equations of classical mechanics (CM). The unbridgeable gap between CM and QT is given by the fact that a certain system which is described in CM by a finite number of degrees of freedom requires an infinite number in QT. The standard quantization method, which is conceptually closely linked to the individuality interpretation, is limited to finding structural similarities between observables and operators. The fundamental question \emph{why} one must move from a finite number to an infinite number of degrees of freedom, remains unanswered. This gap can only be closed if probabilistic aspects are already taken into account in the classical area. This may be done by taking the uncertainty in initial conditions into account. In this probabilistic version of mechanics (PM), a system is mathematically described as an ensemble, with an infinite number of degrees of freedom, thus bridging the gap mentioned above. This step then enables the reconstruction of QT, in particular the derivation of the Schr\"odinger equation, from PM. This work is the third in a series of works in which this program is carried out. The method used here differs from the previous one and allows a better understanding of the structural differences between classical physics and QT. The derivation of the Schr\"odinger equation essentially takes place in two steps: a projection from phase space to configuration space and a linearization. Some contradictions of the individuality interpretation are analyzed and eliminated from the point of view of the ensemble interpretation.

quant-ph↗

arXiv2022

A reconstruction of quantum theory for spinning particles

As part of a probabilistic reconstruction of quantum theory (QT), we show that spin is not a purely quantum mechanical phenomenon, as has long been assumed. Rather, this phenomenon occurs before the transition to QT takes place, namely in the area of the quasi-classical (here better quasi-quantum) theory. This borderland between classical physics and QT can be reached within the framework of our reconstruction by the replacement $p \rightarrow M (q, t)$, where $p$ is the momentum variable of the particle and $M(q, t)$ is the momentum field in configuration space. The occurrence of spin, and its special value $1/2$ , is a consequence of the fact that $M(q,t)$ must have exactly three independent components $M_{k}(q,t)$ for a single particle because of the three-dimensionality of space. In the Schr\"odinger equation for a "particle with spin zero", the momentum field is usually represented as a gradient of a single function $S$. This implies dependencies between the components $M_{k}(q,t)$ for which no explanation exists. In reality, $M(q,t)$ needs to be represented by three functions, two of which are rotational degrees of freedom. The latter are responsible for the existence of spin. All massive structureless particles in nature must therefore be spin-one-half particles, simply because they have to be described by $4$ real fields, one of which has the physical meaning of a probability density, while the other three are required to represent the momentum field in three-dimensional space. We derive the Pauli-Schr\"odinger equation, the correct value $g=2$ of the gyromagnetic ratio, the classical limit of the Pauli-Schr\"odinger equation, and clarify some other open questions in the borderland between classical physics and QT.

quant-ph↗

arXiv2020

From probabilistic mechanics to quantum theory

We show that quantum theory (QT) is a substructure of classical probabilistic physics. The central quantity of the classical theory is Hamilton's function, which determines canonical equations, a corresponding flow, and a Liouville equation for a probability density. We extend this theory in two respects: (1) The same structure is defined for arbitrary observables. Thus we have all of the above entities generated not only by Hamilton's function but by every observable. (2) We introduce for each observable a phase space function representing the classical action. This is a redundant quantity in a classical context but indispensable for the transition to QT. The basic equations of the resulting theory take a "quantum-like" form, which allows for a simple derivation of QT by means of a projection to configuration space reported previously [Quantum Stud.:Math. Found. (2018) 5:219-227]. We obtain the most important relations of QT, namely the form of operators, Schrödinger's equation, eigenvalue equations, commutation relations, expectation values, and Born's rule. Implications for the interpretation of QT are discussed, as well as an alternative projection method allowing for a derivation of spin.

quant-ph↗

arXiv2018

From Koopman-von Neumann Theory to Quantum Theory

Koopman and von Neumann (KvN) extended the Liouville equation by introducing a phase space function $S^{(K)}(q,p,t)$ whose physical meaning is unknown. We show that a different $S(q,p,t)$, with well-defined physical meaning, may be introduced without destroying the attractive "quantum-like" mathematical features of the KvN theory. This new $S(q,p,t)$ is the classical action expressed in phase space coordinates. It defines a mapping between observables and operators which preserves the Lie bracket structure. The new evolution equation reduces to Schrödinger's equation if functions on phase space are reduced to functions on configuration space. This new kind of "quantization" does not only establish a correspondence between observables and operators, but provides in addition a derivation of quantum operators and evolution equations from corresponding classical entities. It is performed by replacing $\frac{\partial}{\partial p}$ by $0$ and $p$ by $\frac{\hbar}{\imath} \frac{\partial}{\partial q}$, thus providing an explanation for the common quantization rules.

quant-ph↗

arXiv2012

Is the individuality interpretation of quantum theory wrong ?

We analyze the question whether or not quantum theory should be used to describe single particles. Our final result is that a rational basis for such an 'individuality interpretation' does not exist. A critical examination of three principles, supporting the individuality interpretation, leads to the result that no one of these principles seems to be realized in nature. The well-known controversy characterized by the names of Einstein (EPR), Bohr and Bell is analyzed. EPR proved 'predictive incompleteness' of quantum theory, which implies that no individuality interpretation exists. Contrary to the common opinion, Bell's proof of 'metaphysical completeness' does not invalidate EPR's proof because two crucially different meanings of 'completeness' are involved. The failure to distinguish between these two meanings is closely related to a fundamentally deterministic world view, which dominated the thinking of the 19th century and determines our thinking even today.

quant-ph↗

arXiv2005

ARACNE: An Algorithm for the Reconstruction of Gene Regulatory Networks in a Mammalian Cellular Context

Background: Elucidating gene regulatory networks is crucial for understanding normal cell physiology and complex pathologic phenotypes. Existing computational methods for the genome-wide ``reverse engineering'' of such networks have been successful only for lower eukaryotes with simple genomes. Here we present ARACNE, a novel algorithm, using microarray expression profiles, specifically designed to scale up to the complexity of regulatory networks in mammalian cells, yet general enough to address a wider range of network deconvolution problems. This method uses an information theoretic approach to eliminate the majority of indirect interactions inferred by co-expression methods. Results: We prove that ARACNE reconstructs the network exactly (asymptotically) if the effect of loops in the network topology is negligible, and we show that the algorithm works well in practice, even in the presence of numerous loops and complex topologies. We assess ARACNE's ability to reconstruct transcriptional regulatory networks using both a realistic synthetic dataset and a microarray dataset from human B cells. On synthetic datasets ARACNE achieves very low error rates and outperforms established methods, such as Relevance Networks and Bayesian Networks. Application to the deconvolution of genetic networks in human B cells demonstrates ARACNE's ability to infer validated transcriptional targets of the c MYC proto-oncogene. We also study the effects of mis estimation of mutual information on network reconstruction, and show that algorithms based on mutual information ranking are more resilient to estimation errors.

q-bio.MN↗

arXiv2000

Has the FFLO state been observed in the organic superconductor $κ-$(BEDT-TTF$)_2$Cu(NCS$)_2$ ?

We compare the theoretical anisotropic upper critical field $H_{C}(Θ,T)$ of a quasi-two-dimensional d-wave superconductor with recent $H_{c2}$ data for the layered organic superconductor $κ-(BEDT-TTF)_2Cu(NCS)_2$. We find agreement both with regard to the angular and the temperature dependence of $H_{C}$. This supports the suggestion that the Fulde-Ferrell-Larkin-Ovchinnikov state (FFLO state) exists in this material for exactly plane-parallel orientation of the magnetic field. Indications of precursor states, occurring for small deviations from the plane-parallel field direction, are also pointed out and further measurements for confirming the existence of the FFLO state are proposed.

cond-mat.supr-con↗