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At least 883 records · Page 49
All sourcesNASA NTRSDOE OSTI
DOE OSTI2023

Practical benzylation of N,N -substituted ethanolamines related to chemical warfare agents for analysis and detection by Electron Ionization Gas Chromatography-Mass Spectrometry

The benzylation of three, low-molecular weight N,N-disubstituted ethanolamines related to chemical warfare agents (CWAs) to furnish derivatives with improved Gas Chromatography-Mass Spectrometry (GC-MS) profiles is described. Due to their low molecular weight and polar nature, N,N-disubstituted ethanolamines are notoriously difficult to detect by routine GC-MS analyses during Organisation for the Prohibition of Chemical Weapons (OPCW) proficiency tests (PTs), particularly in scenarios when they are present at low levels (~1-10 ppm) amidst more abundant interferences. Our studies revealed that the optimal derivatization conditions involved the treatment of the ethanolamine with benzyl bromide in the presence of an inorganic base (e.g., Na 2 CO 3 ) in dichloromethane at 55 °C for 2 hours. This optimized set of conditions were then successfully applied to the derivatization of N,N-dimethylethanolamine, N,N-diethylethanolamine and N,N-diisopropylethanolamine present separately at 1 and 10 μg/mL concentrations in a glycerol-rich matrix sample featured in the 48 th OPCW PT. The benzylated derivatives of the three ethanolamines possessed retention times long enough to clear the massive glycerol-containing matrix interferences. In conclusion, the protocol herein is introduced as an alternative method for derivatization of these CWA and pharmaceutically important species and should find broad applicability in laboratories where their routine forensic analysis is carried out.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2026

Towards Commercialization of Low-Cost, Crack-Tolerant, Screen-Printable Metallization by Full-Size Module Testing and Field Characterization

This project is motivated by the need to develop a materials engineering solution to reduce solar module degradation caused by cell cracks. The cell-crack-induced power loss is a long-term degradation mechanism and one of the main causes of solar panel field failures. Cell cracks can occur during module fabrication, transportation, installation, and long-term operation due to thermomechanical stressors. Our team’s internal estimation – based on the national weather pattern, frequency of severe weather, and 39- GW asset survey by Heliolytics – reveals that the cell-crack-induced module degradation translates to lost revenues >$17B over an average 5-year period for solar farm owners and to reduced reliability (<25 years panel lifetime) for solar energy consumers. In response to this challenge, the prime recipient offers a metal matrix composite (MMC) silver paste that is tailor-engineered for screen-printing gridlines and busbars, which serve as the electrical contacts on solar cells. We formulate our MMC paste by adding low-cost (∼0.02¢/WDC for research grade), surface-engineered carbon nanotubes to commercially available silver paste. The MMC paste offers a drop-in, cost-effective solution to cell cracks for solar cell and module manufacturers. The main goal of this project was to conduct field-relevant, module-level analysis and qualification of MMC metallization.

14 SOLAR ENERGY↗
DOE OSTI2022

Partially polaron-transformed quantum master equation for exciton and charge transport dynamics

Polaron-transformed quantum master equation (PQME) offers a unified framework to describe the dynamics of quantum systems in both limits of weak and strong couplings to environmental degrees of freedom. Thus, the PQME serves as an efficient method to describe charge and exciton transfer/transport dynamics for a broad range of parameters in condensed or complex environments. However, in some cases, the polaron transformation (PT) being employed in the formulation invokes an over-relaxation of slow modes and results in premature suppression of important coherence terms. A formal framework to address this issue is developed in the present work by employing a partial PT that has smaller weights for low frequency bath modes. In this work, it is shown that a closed form expression of a second order time-local PQME including all the inhomogeneous terms can be derived for a general form of partial PT, although more complicated than that for the full PT. All the expressions needed for numerical calculation are derived in detail. Applications to a model of a two-level system coupled to a bath of harmonic oscillators, with test calculations focused on those due to homogeneous relaxation terms, demonstrate the feasibility and the utility of the present approach.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2023

Testing shell-model interactions at high excitation energy and low spin: Nuclear resonance fluorescence in Ge 74

With their complex low-spin structure, the germanium isotopes have accrued a large number of experimental data which challenge nuclear models. The structure of the 74 Ge isotope is investigated here with nuclear resonance fluorescence as part of an extensive campaign of experimental tests of the shell model in the germanium isotopic chain using a number of complementary techniques. Levels were excited with 3.10 – 5.44 MeV photon beams provided by the High Intensity Gamma-Ray Source at TUNL. Many new levels were identified and their spins, parities, branching ratios, and associated scattering cross section values were determined. Large-scale shell-model calculations, which include jj44b and JUN45 effective interactions developed to describe nuclei in this mass region, predict the new data satisfactorily. Herein this study extends the validation of these two interactions, which are candidates for computation of matrix elements to be used in the interpretation of neutrinoless double-β decay experiments in 76 Ge, into the low-spin, high excitation energy domain.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2022

Validation of Power Distribution Models using Load Flow Analysis in an ADMS Environment

Electric utilities are facing the need for better monitoring, analysis, and control of their distribution systems. An accurate mathematical model is a key to both the development of cutting-edge, scalable model-based algorithms and the assessment of emerging technologies such as distributed energy resources (DER) for grid planning and operation. However, the constantly evolving nature of power distribution systems poses challenges to maintaining accurate models. In this paper, we propose a novel load flow based approach to validate power distribution models. Networked equipment models described according to the Common Information Model (CIM) standard and a measurement model are used to formulate the distribution load flow problem. First, a system admittance matrix (Ybus) is derived from device-level CIM parameters. Next, the operational parameters (dynamic Ybus and nodal injections) are extracted from the measurement model using sensor configuration and equipment state. An iterative power flow method is then used to compute nodal voltages and branch flows that are compared against the measurement data to find any inconsistencies in the networked equipment model. This approach is implemented within GridAPPS-D, an open-source standards-based platform for advanced distribution management system (ADMS) application development, and demonstrated on the IEEE 13-bus, 123-bus, and 8500-node test feeders.

Common information model, model validation, power ↗
DOE OSTI2021

Tractable Learning in Underexcited Power Grids

Estimating the structure of physical flow networks, such as power grids, is critical to secure delivery of energy. This article discusses statistical structure estimation in power grids in the “underexcited” regime, where a subset of internal nodes has zero injection fluctuations. Prior estimation algorithms based on nodal voltages fail for such grids as the voltage covariance matrix is not invertible. Here, we propose a novel topology learning algorithm for learning underexcited general networks. Our algorithm uses physics-informed conservation laws to first identify the zero-injection buses and their neighbors, and then estimates the remaining edges in the grid. We prove the asymptotic correctness of our algorithm for grids with nonadjacent internal zero-injection nodes. More important, we theoretically analyze our algorithm’s efficacy under noisy measurements, and determine bounds on maximum noise under which asymptotically correct recovery is guaranteed. Our approach is validated through simulations with voltage samples generated on test distribution grids with real injection data and nonlinear power flow models.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Forced Oscillation Source Location of Bulk Power Systems Using Synchrosqueezing Wavelet Transform

Forced oscillation source location (FOSL) plays a significant role in mitigating forced oscillations (FOs), which threaten the power system stability. Here, this paper proposes a data-driven approach for FOSL in power systems using synchrosqueezing wavelet transform (SWT). The proposed approach conducts SWT on the measured system responses to obtain the SWT matrix. Then, the SWT-based dissipating energy flow (DEF) model in time-frequency domain and dissipating energy spectrum (DES) model in frequency domain are derived from the traditional DEF model. Further, the characteristics of SWT-based DEF and DES are revealed by referring to the traditional DEF, and the FOSL criteria of the SWT-based DEF and DES can be hereby obtained. Using the obtained FOSL criteria, the FO source can be located from the measured responses. The performance of the proposed FOSL method is evaluated by simulation data of the WECC 179-bus test system and field-measurement PMU data of the ISO New England. The results confirm the accuracy and efficiency of the proposed method in the FOSL.

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2024

Process Intensification for Nanostructure Aluminum Extrusions

A new technology called Shear Assisted Processing and Extrusion (ShAPE™), pioneered at the Pacific Northwest National Laboratory (PNNL), has the potential to revolutionize the US extrusion industry. Maturation of the ShAPE™ process would create a new cross cutting US manufacturing technology that advances three key the objectives within AMO; namely, nanomaterials processing, process intensification, and materials for extreme and harsh environments. PNNL and SCM Metals Products, Inc. (SCM), a division of Kymera International, will collaborate to mature the ShAPE™ extrusion process beyond TRL 3 to increase the likelihood of its adoption by industry. PNNL’s custom (one-of-a-kind in the world) ShAPE™ machine will be used to extrude round rods of high strength aluminum alloy feedstock powder provided by SCM. As proof-of-concept, PNNL has previously extruded 5 mm diameter rods with SCM aluminum alloy powder AL-12.4TM. This project aims to scale up the process to a diameter of 25 mm while retaining the excellent mechanical properties achieved for the 5 mm diameter rods. The degree of process intensification with ShAPE™ will also be estimated. The primary objectives of this project are as follows. 1) Fabricate 25 mm diameter nanostructured extrusions in bulk, directly from AL-12.4TM aluminum alloy powder without the need for canning, degassing, compaction, and other intermediate steps typical of powder metallurgy extrusion. 2) Achieve a microstructure with an ultrafine grained (UFG <1 µm) aluminum matrix having refined and homogenously distributed nanoscale second phases. 3) Show that the ram force can be significantly reduced compared to conventional powder metallurgy extrusion of the same material and estimate the extent of process intensification that may be possible with ShAPE™. 4) Demonstrate improved high-temperature mechanical properties compared to conventional extrusion of the same material. The following tasks will be undertaken to achieve these objectives. PNNL will develop the die set and process parameters necessary to fabricate Al-12.4TM extrusions with a 25 mm diameter. Microstructural analysis will be performed by PNNL while mechanical testing will be conducted by SCM. With information learned from the process development and characterization, PNNL will perform an estimate of the degree of process intensification that may be possible with ShAPE™.

42 ENGINEERING↗
DOE OSTI2024

Accuracy optimized neural networks do not effectively model optic flow tuning in brain area MSTd

Accuracy-optimized convolutional neural networks (CNNs) have emerged as highly effective models at predicting neural responses in brain areas along the primate ventral stream, but it is largely unknown whether they effectively model neurons in the complementary primate dorsal stream. We explored how well CNNs model the optic flow tuning properties of neurons in dorsal area MSTd and we compared our results with the Non-Negative Matrix Factorization (NNMF) model, which successfully models many tuning properties of MSTd neurons. To better understand the role of computational properties in the NNMF model that give rise to optic flow tuning that resembles that of MSTd neurons, we created additional CNN model variants that implement key NNMF constraints – non-negative weights and sparse coding of optic flow. While the CNNs and NNMF models both accurately estimate the observer's self-motion from purely translational or rotational optic flow, NNMF and the CNNs with nonnegative weights yield substantially less accurate estimates than the other CNNs when tested on more complex optic flow that combines observer translation and rotation. Despite its poor accuracy, NNMF gives rise to tuning properties that align more closely with those observed in primate MSTd than any of the accuracy-optimized CNNs. This work offers a step toward a deeper understanding of the computational properties and constraints that describe the optic flow tuning of primate area MSTd.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

Development of Additive Manufacturing for Ceramic Matrix Composite Vanes

This report discusses the development of additive manufacturing for polymer-derived ceramic materials to create novel cooled gas turbine airfoils made from ceramics. Gas turbine engines have extremely high temperatures in the hot section of the engine that exceed the melting point of nickel superalloy materials that the engine is made from. Advanced cooling technologies have been developed over decades for metallic parts. Ceramic materials have higher temperature capabilities than superalloys, but are difficult to shape in the complex designs used in modern turbines. Several thrusts were investigated during the project, including development of higher material strength resins, improvement of ultraviolet (UV) photopolymerization and post-processing techniques to increase survivability of ceramic parts, thermomechanical modeling of novel ceramic airfoil designs for higher cooling effectiveness, and experimental validation of the modeling and manufacturing in a turbine vane test facility at nondimensional conditions that are relevant to modern gas turbines. Some major findings of the work include a significant increase in ceramic survivability during pyrolysis (a high temperature process that converts the organic material to a ceramic) by adjusting the composition ratios of the resins, as well as a tolulene soak after printing to remove unreacted polymer material. Thermomechanical optimization of the internal cooling structure indicated that a high density pin fin array would enable an 80% increase in overall cooling effectiveness relative to a baseline geometry, which was later verified during experimental testing in a high speed linear cascade. Ceramic vanes were tested at Mach numbers of up to 0.9 which is relevant to modern gas turbines. High temperature capability of the ceramic vanes was not tested in this work.

36 MATERIALS SCIENCE↗
DOE OSTI2021

An initial exploration of Bayesian model calibration for estimating the composition of rocks and soils on Mars

The Mars Curiosity rover carries an instrument, ChemCam, designed to measure the composition of surface rocks and soil using laser-induced breakdown spectroscopy (LIBS). The measured spectra from this instrument must be analyzed to identify the component elements in the target sample, as well as their relative proportions. This process, which we call disaggregation, is complicated by so-called matrix effects, which describe nonlinear changes in the relative heights of emission lines as an unknown function of composition due to atomic interactions within the LIBS plasma. In this work, we explore the use of the plasma physics code ATOMIC, developed at Los Alamos National Laboratory, for the disaggregation task. ATOMIC has recently been used to model LIBS spectra and can robustly reproduce matrix effects from first principles. The ability of ATOMIC to predict LIBS spectra presents an exciting opportunity to perform disaggregation in a manner not yet tried in the LIBS community, namely via Bayesian model calibration. However, using it directly to solve our inverse problem is computationally intractable due to the large parameter space and the computation time required to produce a single output. Therefore, we also explore the use of emulators as a fast solution for this analysis. We discuss a proof of concept Gaussian process emulator for disaggregating two-element compounds of sodium and copper. The training and test datasets were simulated with ATOMIC using a Latin hypercube design. After testing the performance of the emulator, we successfully recover the composition of 25 test spectra with Bayesian model calibration.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2021

Seeded Stage III glass dissolution behavior of a statistically designed glass matrix

The glass dissolution rate of some glasses accelerates after prolonged time spent at a slow, residual glass dissolution rate. This phenomenon is referred to as Stage III behavior. Here, the acceleration in glass dissolution rate linked to Stage III behavior is significant and may be the most impactful to long-term performance of glass in a repository. This work is aimed at understanding the effect of glass composition on Stage III behavior to add a level of technical defensibility to glass disposal. To this end, a set of twenty-four glass compositions were statistically designed, where eight glass components (SiO 2 , B 2 O 3 , Al 2 O 3 , CaO, Na 2 O, SnO 2 , ZrO 2 , and Others) have been independently varied in order to study the individual effects of each. These glasses have been subjected to static dissolution tests at 90 °C in deionized water and then seeded with zeolite Na-P2 28 days into the testing to induce Stage III behavior. The response of the glasses to the zeolite seeds fell into four primary types: 1) no response to seeds; 2) an immediate linear sustained acceleration in the rate; 3) an immediate linear acceleration in the rate followed by a decrease; and, 4) a progressive acceleration in the rate that is concurrent with the addition of the seeds. The main glass components observed to influence these behaviors were CaO, Al 2 O 3 , B 2 O 3 , and ZrO 2 , where: 1) CaO influenced which glasses showed a Stage III response to seeds (high CaO: Types 2, 3, and 4) or did not respond to seeds (low CaO: Type 1), 2) Al 2 O 3 and B 2 O 3 influenced which glasses showed a sustainable Stage III response (high Al 2 O 3 : Types 2 and 4) versus transitory response (low Al 2 O 3 and high B 2 O 3 : Type 3), and 3) ZrO 2 concentration influenced whether glasses showed a linear (high ZrO 2 : Type 2) versus progressive (low ZrO 2 : Type 4) response to seeds.

36 MATERIALS SCIENCE↗
DOE OSTI2023

Benchmark between antenna code TOPICA, RAPLICASOL and Petra-M for the ICRH ITER antenna

ITER will be equipped with three plasma heating systems: neutral beam (NB), electron cyclotron (EC), and ion cy-clotron resonance heating (ICRH). The latter consists of two identical ICRH antennas to deliver 20 MW to the plasma (baseline, upgradable to 40 MW). ICRH will play a crucial role in the ignition and sustainment of burning plasmas in ITER. A high fidelity and robust modeling effort to understand the interaction of the IC waves with the scrape-off-layer (SOL) plasma is a very important aspect. Among the main important research topics, we have the assessment of the antenna loading for different plasma scenarios, the role of the lower hybrid resonance in front of the antenna and how to include it in our models, and the RF sheath boundary conditions to evaluate the antenna impurity generation. In this work, we tackle the first of these by reporting on ICRF simulations employing the Petra-M code, which is an electromagnetic simulation tool for modeling RF wave propagation based on MFEM [http://mfem.org] for the ITER ICRH antenna. Moreover, a benchmark between the well tested antenna codes TOPICA, RAPLI-CASOL, which is based on COMSOL [www.comsol.com], and the Petra-M code is also presented. In conclusion, S- and Z-matrices and wave electric field are compared showing an excellent agreement among these codes.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2021

Identifying Entangled Physics Relationships Through Sparse Matrix Decomposition to Inform Plasma Fusion Design

We report a sustainable burn platform through inertial confinement fusion (ICF) has been an ongoing challenge for over 50 years. Mitigating engineering limitations and improving the current design involves an understanding of the complex coupling of physical processes. While sophisticated simulation codes are used to model ICF implosions, these tools contain necessary numerical approximation but miss physical processes that limit predictive capability. Identification of relationships between controllable design inputs to ICF experiments and measurable outcomes (e.g., neutron yield, neutron velocity, areal density) from performed experiments can help guide the future design of experiments and development of simulation codes, to potentially improve the accuracy of the computational models used to simulate ICF experiments. We use sparse matrix decomposition methods to identify clusters of a few related design variables. Sparse principal component analysis (SPCA) identifies groupings that are related to the physical origin of the variables (laser, hohlraum, and capsule). A variable importance analysis finds that in addition to variables highly correlated with neutron yield, such as picket power and laser energy, variables that represent a dramatic change of the ICF design, such as number of pulse steps, are also very important. The obtained sparse components are then used to train a random forest (RF) regression surrogate for predicting total yield. The RF performance on the training and testing data compares with the performance of the RF trained using all the design variables considered. This work is intended to inform design changes in future ICF experiments by augmenting the expert intuition and simulation results.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

Scintillation Hydro-Gel for Isotopic Neutron (SHINE): Eco-Friendly Quantum Dot Neutron Detectors

The development of new neutron detectors to replace helium-3 (3He) detectors is imperative due to a worldwide shortage of 3He following the draw down in nuclear weapons production since the end of the Cold War. The United States Department of Homeland Security would like to deploy monitors for the detection of neutron emissions from shipping containers housing illicit nuclear material; however, this effort has been put on hold until new replacements for 3He detectors can be developed. Scintillation Hydro-Gel for isotopic Neutron Emitters (SHINE) is a unique, first of its kind, 6Li-loaded quantum dot gel scintillator developed at INL. By incorporating 6Li with quantum dots in a gel matrix, SHINE displays the best properties of liquid and solid scintillators without their disadvantages such as continuous filtering to keep liquids free of contaminates, slow throughput of containers, higher base component costs, ‘dead’ voids in solid scintillators, and a high loading of 6Li without compromising on light transparency. Additionally, SHINE is completely eco-friendly, a breakthrough in high-efficiency detection systems. SHINE is a unique combination of 6LiCl, a highly water-soluble compound, and InP/ZnS core/shell quantum dots, which are poured into a gel-form using cross-linking polymers. In this presentation, SHINE has been successfully tested for neutron detection and shows promise as both a replacement for current 3He neutron detectors as well as potential use in handheld, compact neutron detection units and antineutrino detection.

36 MATERIALS SCIENCE↗
DOE OSTI2025

Develop a new integrated macro→micro←nano (MMN) multiscale modeling framework to optimize high strength aluminum alloys and processes for vehicle light-weighting​

Bending tests provide a means to study plane strain fracture performance of 6000 series aluminum alloys. Metrics from bending tests have been correlated with self-pierce riveting (SPR) performance of a high strength AA6111 automotive aluminum alloy in previous works. Using the ORNL HPC resources, this project developed an innovative macro→micro←nano (MMN) multiscale microstructure-based finite element (FE) code to further understanding of the relationship between microstructure and fracture properties of high-strength 6000-series alloys. This work started with microstructural characterization in both mesoscale and nanoscale and bending performance characterization of AA6111 HS2-T6 alloy at Ford, the MMN framework was applied to this alloy to simulate 3-point VDA bending. From the results of the macro-modeling of 3-point VDA bending, the critical region of fracture was identified, and the region geometry was used to construct the micro-model. The fracture criterion of micron-scale precipitates and aluminum matrix which contains submicron and nano particles (AL-SMP-NP) in the micro-model was calibrated and validated by comparing simulated and measured bending results. With the AL-SMP-NP fracture strain obtained, the fracture strain of Al-matrix containing nano particles (ALNP) will similarly be determined by a submicron scale-model using an edge-constrained FE modeling approach developed by Hu et al. With the ALNP fracture strain obtained, the fracture strain of Al-matrix containing no particles will similarly be determined by a nano scale-model using an edge-constrained FE modeling approach. After the MMN framework is built and fracture criterion calibrated, nano-model FE simulations with virtual microstructures was performed to obtain a reduced order model (ROM) of the fracture criterion of the ALNP as a function of volume fraction, size, and distribution of the nanoparticle. This nano→submicron→micro modeling part allows exploration of the influence of different material nanostructures from different process conditions on the bending properties within the multiscale bending simulation framework and the ROM of material bendability as a function of nanoparticle size and shape was established. This obtained reduced order model (ROM) could help guide the design and selection of materials to improve existing SPR process models that could replace trial-and-error rivet/die selection and help to design new rivet/die combinations capable of robustly joining new higher strength 6000 5 series alloys in automotive body structures. This would enable lightweighting of Ford vehicles leading to greater fuel efficiency and reduce manufacturing time and energy.

36 MATERIALS SCIENCE↗
DOE OSTI2020

Cask RT-100 Type B(U) Self-Certification for DOT 7A, Type A Nuclear Waste Transportation - 20098

The purpose of this Type A certification is to diversify the use of the RT-100 cask by allowing the end user to transport either Type A or Type B radioactive waste in accordance with the handling procedures for each waste category. The project's scope included the development of a matrix that contains all applicable requirements for a Type A package from the Code of Federal Regulations (CFR), Title 49 for the Department of Transportation (DOT) with a justification for each requirement. Moreover, the scope included the writing of conditions and restrictions list for the transportation of Type A nuclear waste, the writing of a compliance statement, and the design and fabrication of a Type A placard to be permanently placed on the RT-100 cask. Type A packages are self-certified by the end user using one of three methods as permitted by 49 CFR 173.461, either by performance of tests with prototypes or samples of the specimens representing the packaging, or reference to a previous satisfactory demonstration of compliance of a sufficiently similar nature, or calculations or reasoned evaluation using reliable and conservative procedures and parameters. Since the RT-100 cask was licensed by the Nuclear Regulatory Commission (NRC) as a Type B cask, Robatel relied on the method of reference to a previous satisfactory demonstration of compliance of a sufficiently similar nature for Type A certification. This method was determined to be acceptable, since Type B packages are evaluated for more demanding transport conditions than those required for Type A packages. This paper presents Robatel's process for certifying the RT-100 cask for Type A shipments, an overview of the DOT regulations related to Type A packages, and the documents that were generated for the end user. This paper is concluded with a discussion on the advantages of having the option to transport both Type A and Type B nuclear waste, and possible future projects to further improve the operation of the cask when making Type A shipments. (authors)

12 MANAGEMENT OF RADIOACTIVE AND NON-RADIOACTIVE W↗
DOE OSTI2024

A retrospective review of von Neumann’s analysis of hidden variables in quantum mechanics

This article reviews the history of J. von Neumann’s analysis of hidden variables in quantum mechanics and the subsequent analysis by others. In his book The Mathematical Foundations of Quantum Mechanics , published in 1932, von Neumann performed an analysis of the consequences of introducing hidden parameters (hidden variables) into quantum mechanics. He arrived at two principal conclusions: first, hidden variables cannot be incorporated into the existing theory of quantum mechanics without major modifications, and second, if they did exist, the theory would have already failed in situations where it has been successfully applied. This analysis has been taken as an “incorrect proof” against the existence of hidden variables, possibly due to a mistranslation of the German word prufen . von Neumann’s so-called proof isn’t even wrong as such a proof does not exist, but it is an examination of the limitations imposed by internal consistency of the Hilbert space formulation of the theory. One of the earliest attempts to eliminate uncertainty, by D. Bohm, requires a major modification of quantum mechanics (observables are not represented by Hermitian operators), which supports von Neumann’s first principal conclusion. However, testing the Bohm theory requires constructing a physically impossible initial state. As such, the theory has no experimental consequences, so W. Pauli referred to it as an “uncashable check”. As there are no observable consequences, the Bohm theory is possibly a counterexample to von Neumann’s second conclusion that hidden variables in particular would have already led to a failure of the theory.

density matrix↗