Hidden variables

This technique is derived from a method developed by electrical engineers to facilitate the analysis of electrical networks. It has been applied to process operator studies by Beishon (1967). The method describes the process to be controlled in terms of "manually controlled" variables, "displayed" variables and "hidden" variables which can be deduced from those displayed or from... 

Signal-flow graphs are particularly useful in two respects. First, they make the process designer examine in considerable detail the dynamic structure and fimctioning of the process. Second, the nature of the interface between person and machine can be seen more clearly. The variables that are displayed in a system are, of course, available for study, but workers frequently respond to derivative functions of variables or "hidden" variables that must be deduced. Given that the process variables to be displayed will influence the worker s control strategy and that the number of deductions to be made will affect the mental workload involved, a process designer can select the type and amoimt of process information which will enhance performance of the task. 

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 shows that for any local hidden variable theory, this expectation value must satisfy the following inequality. 

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. 

Achinstein, P. [1968] Concepts of Science, Baltimore University Press, Baltimore. Bell, J. S. [1966] On the Problem of Hidden Variables in Quantum Mechanics , Reviews of Modern Physics, 38, p. 447. 

However, in Maxwell s days everyone assumed that there had to be a mechanical underpinning for the theory of EM. Many researchers worked on very detailed hidden variable theories for the EM field, in an attempt to prove that the laws of EM were in fact a theorem in NM, just like Kepler s laws are a theorem in NM. No one noticed that it was impossible to do this, since Maxwell s equations are not Galilei invariant and Newton s laws are. That includes Lorentz who discovered around 1900 that the Maxwell equations are invariant under another transformation that now bears his name. 

Similarly, after 70 years of successful application of QM, it is clear that the wave function does not describe the properties of something else. There is no Ether, there are no hidden variables. The effect on the wave function of every interaction between QM systems is described by the Schrbdinger equation. The wave function does not describe something unknown and eluding(14, IS), that is sometimes a wave and sometime a particle. 

The wave function is an irreducible entity completely defined by the Schrbdinger equation and this should be the cote of the message conveyed to students. It is not useful to introduce any hidden variables, not even Feynman paths. The wave function is an element of a well defined state space, which is neither a classical particle, nor a classical field. Its nature is fully and accurately defined by studying how it evolves and interacts and this is the only way that it can be completely and correctly understood. The evolution and interaction is accurately described by the Schrbdinger equation or the Heisenberg equation or the Feynman propagator or any other representation of the dynamical equation. 

Often, the correlation is not good, and we need to search for the hidden variable that we have not yet discovered. But when we find a good correlation, it could prove useful in the reverse search for other untried compounds that may have higher or lower camphor smell, even if we do not understand the mechanism of how it works. There is always the hope that, if we know which parameters are important to smell, we may generate one or more hypotheses on the nature of camphor smell this would be followed by predictions and experiments that could lead us to future understanding. 

When we are truly clueless, we can nevertheless rely on intuition to propose an ad hoc set of structural and related property parameters for the correlation. We may be lucky and find the hidden variable by chance, and we may be inspired. An example is the topological index, which describes how carbon atoms are connected together, and was proposed in the hope that it would correlate a large range of molecular properties. 

Discover and add one or more hidden variables that have a strong influence on the value of y. 

So the boiling points of this data set can be attributed much more to the number of chlorine atoms than to the dipole moment, with very little influence from the number of fluorine atoms. We are now using three parameters to explain 15 data points, for 15 - 3 = 12 degrees of freedom, and we have a standard error of 11.4 " C. If we want a standard deviation of less than 1 "C, then this is not good enough, and we would have to dig deeper for more hidden variables. 

In spite of stubborn efforts to reduce it to a statistical probability distribution over states of hidden variables D. Bohm, Phys, Rev. 85, 166 and 180 (1952) F.J. Belinfante, A Survey of Hidden-Variables Theories (Pergamon, Oxford 1973) E. Nelson, Quantum Fluctuations (Princeton University Press, Princeton, NY 1985) J.S. Bell, Speakable and Unspeakable in Quantum Mechanics (Cambridge University Press, Cambridge 1987). 

M. Flato, C. Piron, J. Grea, D. Sternheimer, and J. P. Vigier, Are Bell s inequalities concerning hidden variables really conclusive Helv. Phys. Acta 48(2), 219-225 (1975). 

J. P. Vigier, Three recent experiments to test experimentally realizable predictions of the hidden variables theory, C. R. Acad. Sci., Ser. B (Sciences Physiques) 279(1), I 4 (1974). 

A. The Least-Arbitrariness Principle The Necessary Hidden Variables... 

The physicists tried to solve this profound problem by the principle of least arbitrariness or a fortiori [2c]. This principle means the optimum relation among the introduced hidden variables, which are necessary to description of the phenomena. (This maxim is well known and accepted in the scientific community as (Occam s razor.)... 

Lorentz, Fitz-Gerald, and others were able to formally explain the lack of changing in interference fringes [1] using a hidden variable that is essentially the quotient of the theoretical and the measured results. This method, combined with the least-arbitrariness principle, obtained the optimal hidden parameter, which was satisfied by the experiment. The operator of the optimal hidden... 

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... 

The final coup de grace against any alternative to the orthodox formulation was supposed to be delivered by John von Neumann (1932) with mathematical proof that dispersion-free states2 and hidden variables are impossible in quantum mechanics. He concluded [29] that ... 

The idea of hidden variables is fairly common in chemical models such as the kinetic gas model. This theory is formulated in terms of molecular momenta that remain hidden, and evaluated against measurements of macroscopic properties such as pressure, temperature and volume. Electronic motion is the hidden variable in the analysis of electrical conduction. The firm belief that hidden variables were mathematically forbidden in quantum systems was used for a long time to discredit Bohm s ideas. Without joining the debate it can be stated that this proof has finally been falsified. 

Which way does it take the material system through the system Again, this is not a question that can be answered by abstract QM. Yet, hidden variable model can give an answer, but this is not the issue here. 

This inequality must be satisfied for a local hidden variable theory to apply to the singlet system of two particles with spin. A test for locality on the basis of the measurement of four sets of correlations becomes possible in terms of the inequalities. 

The idea of action at a distance was resisted both by Newton, and by Einstein [42] who called it "spooky", but it has now been demonstrated experimentally [43, 44] that local realistic theory cannot account for correlations between measurements performed at well separated sites. The conclusion is that quantum theory permits hidden variables and is non-local. This conclusion is at variance with relativity, but, as pointed out by Bohm [34], the nonlocality of quantum theory only applies to complex wave functions and does not imply that the quantum potential can be used to transmit signals faster than light. 

In some cases, surface-active agents can reduce significantly the rate of mass transfer. The relationships involved are complex and poorly understood. Since only trace quantities may be sufficient to exert a marked influence, surface-active contamination must always be considered as a possible hidden variable in these systems. 

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. 

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