Hidden variables, existence

Bell s Theorem In a celebrated 1935 paper, Einstein, Podolsky and Rosen (EPR) [ein35] argued that quantum mechanics provides an essentially incomplete description of reality unless hidden variables exist. 

Since quantum mechanics allows us to predict, with certainty, the component of the second spin by measuring the same spin component of the first (and remotely positioned) particle - and to do so without in any way disturbing that second particle - BPR s first two assumptions attribute an element of physical reality to the value of any spin component of either particle i.e. the spin components must be determinate. On the other hand, assuming that the particles cannot communicate information any faster than at the speed of light, the only way to stay consistent with BPR s third postulate is to assume the existence of hidden variables. 

Bell s result, made all the more remarkable for the very few assumptions he makes to derive it, rather dramatically asserts that cither EPR s three premises are wrong or quantum mechanics is incorrect. However, recent experiments by A.spect, et.al. ([aspect82a], [aspect82b]). On and Mandel [01188], and others have shown, virtually conclusively, that nature satisfies the quantum mechanical prediction (equation 12.54) and not Bell s inequality (equation 12.55), thus strongly denying the possibility of local hidden variables. We are thus left with what is arguably one of the deepest mysteries in the foundations of physics the existence of a profoundly nonclassical correlation between spatially-far separated systems, or nonscparability. 

The second major section will focus on those special centers of minerals thought to be of importance to their catalytic activity, with an emphasis on the known and possible effects of electronic excitation on the population and mode of action of these centers. Metastable states constitute a hidden variable in defective solids, a non-negligible one for non-stoichiometric ones. With regard to concepts of mineral catalysis, the only systems for which extensive spectroscopic information on mineral catalytic centers has been definitively coupled to the mechanism of a well understood surface chemical reaction is exchange on binary oxides. Existing data for the... 

Thus, the wavelength-frequency relation (2.1) implies the Compton-effect formula (2.10). The best we can do is to describe the phenomena constituting the wave-particle duality. There is no widely accepted explanation in terms of everyday experience and common sense. Feynman referred to the experiment with two holes as the central mystery of quantum mechanics. It should be mentioned that a number of models have been proposed over the years to rationalize these quantum mysteries. Bohm proposed that there might exist hidden variables whieh would make the behavior of each photon deterministic, i.e., particle-like. Everett and Wheeler proposed the many worlds interpretation of quantum mechanics in which each random event causes the splitting of the entire universe into disconnected parallel universes in whieh eaeh possibility becomes the reality. 

According to the viewpoint of local realism, the recurring correlations in the Bohm experiment can be attributed to the existence of hidden variables which determine the spin state in every possible direction. It is as if each particle carried a little code book containing all this detailed information, a situation something like the left-hand drawing in Fig. 16.4. It must be concluded—so far—that both local realism and the quantum-mechanical picture of the world are separately capable of giving consistent accounts of the EPR and Bohm experiments. In what follows, we will refer to the two competing worldviews as local realism (LR) and quantum mechanics ("QM). By QM we will understand the conventional formulation of the theory, complete as it stands, without hidden variables or other auxilliary constructs. 

The preceding formalism of SU(2) phase states can be used in a number of problems of quantum physics. As an illustrative example of great importance, consider the so-called Einstein-Podolsky-Rosen (EPR) paradox [73] (see also discussions in Refs. 14, 15, 74, and 75). The EPR paradox touches on the conceptual problems of reality and locality and existence of hidden variables in quantum physics as well as the more technological aspects of quantum cryptography [34]. 

Finally, there is a precautionary rule Kinetics should always be measured in two different reactors to identify any hidden variables or parameters. In addition to experimenting in a perfect bioreactor, one should also evaluate a trial in the pilot plant. This testing has another purpose as well, which might be called kinetic similarity (Moser, 1978b) (as exists, e.g., between DCSTRs and CPFRs). Real biological processes are so complex that altered flow... 

Getting answers from experiments is often difficult, time consuming, and the results hardly unequivocal. So-called hidden variables which exist in nature do not manifest themselves in simulations. Moreover, changing only one parameter at a time is easy in simulations, but not in real materials. One example should suffice here to lower the density in an experiment one increases the temperature of the material. However, then the energetics changes too, heating has pumped more energy into the material. There is hardly a procedure for the separation of the two effects. 

Resistive nodes In this first category of power continuous nodes the power continuity is hidden, as the power entering the resistive ports is converted into thermal power and not explicitly represented by a thermal port, such that energy seems to be dissipated, but careful use of concepts shows that only free energy can be dissipated and that the use of power as a flow of free energy corresponds to an implicit assumption, viz., that the temperature at the thermal port is constant or its fluctuations are slow with respect to the fluctuations of interest, such that the temperature can be considered constant. For a resistive node a semi-positive definite scalar potential function ( entropy production function or dissipation function ) of the independent variables exists that generates its constitutive relations. A resistive node has at least one port. Its node label is R. A modulated resistive node has node label MR. A resistive node or resistor is sometimes called a dissipative node or dissipator. 

Obviously, for any CPL formula p with propositional variables in pi,..., p , if p is satisfiable, then t p) pi/ opi,...,p / o p ]) (l,..., 1) = 1 for some assignment of values to hidden variables. An interesting question is whether there exists any method, in accordance with PRC, that allows to eliminate hidden variables in such a way that polynomials distinct to the constant polynomial 0 reduces to the constant polynomial 1. For some paraconsistent logics that we have explored, this seems to be impossible, but we also do not have a definite negative result (the possibility of polynomial conditions, see last paragraph of... 

The standard Maxwell equations are the exact linearization by change of variables (not by truncation) of a set of nonlinear equations referring to the scalars <[), 0. The fact that this change is not completely invertible produces a hidden nonlinearity, thanks to which the linearity of the Maxwell equations is compatible with the existence of topological constants of motion that are nonlinear in A 1 and F[IV. 

Clustering can be viewed as a density estimation problem. The basic premise used in such an estimation is that in addition to the observed variables (i.e., descriptors) for each compound there exists an unobserved variable indicating the cluster membership. The observed variables are assumed to arrive from a mixture model, and the mixture labels (cluster identifiers) are hidden. The task is to find parameters associated with the mixture model that maximize the likelihood of the observed variables given the model. The probability distribution specified by each cluster can take any form. Although mixture model methods have found little use in chemical applications to date, they are mentioned here for completeness and because they are obvious candidates for use in the future. 

The principal value of spreadsheets, other than their universal acceptance and use over the past decade, is the ability to display efficiently and use individual estimates of costs and benefits for each period over the life of the project, reflecting anticipated variability rather than a uniform average value or an approximate mathematical series. This will be discussed as each discounted cash flow method is presented. The principal disadvantage of a spreadsheet is that computational errors are hidden, even though an audit tool exists. However, the problem of quality assurance is not a new one, and the engineer must always be alert to the prevention and elimination of errors. 

No combinational loop exists in the circuit, which guarantees both that there is no hidden state holding variable outside the designated registers, and that the combinational signals always stabilize, for all values of the stabilized inputs and registers. 

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