Quantum uncertainty

According to (2.29), dissipation reduces the spread of the harmonic oscillator making it smaller than the quantum uncertainty of the position of the undamped oscillator (de Broglie wavelength). Within exponential accuracy (2.27) agrees with the Caldeira-Leggett formula (2.26), and similar expressions may be obtained for more realistic potentials. 

Two properties, in particular, make Feynman s approach superior to Benioff s (1) it is time independent, and (2) interactions between all logical variables are strictly local. It is also interesting to note that in Feynman s approach, quantum uncertainty (in the computation) resides not in the correctness of the final answer, but, effectively, in the time it takes for the computation to be completed. Peres [peres85] points out that quantum computers may be susceptible to a new kind of error since, in order to actually obtain the result of a computation, there must at some point be a macroscopic measurement of the quantum mechanical system to convert the data stored in the wave function into useful information, any imperfection in the measurement process would lead to an imperfect data readout. Peres overcomes this difficulty by constructing an error-correcting variant of Feynman s model. He also estimates the minimum amount of entropy that must be dissipated at a given noise level and tolerated error rate. 

The local modification of sample wavefunctions due to the proximity of the tip, and consequently the involvement of the Bloch functions outside the energy window Er eV in the tunneling process, has an effect on the limit of the energy resolution of scanning tunneling spectroscopy. This effect is discussed in detail by Ivanchenko and Riseborough (1991). First, if the tunneling current is determined by the bare wavefunctions of the sample and the tip, the process is linear, and there is no effect of quantum uncertainty. The effect of quantum uncertainty is due to the modification or distortion of the sample wavefunction due to the existence of the tip. Here, we present a simple treatment of this problem in terms of the MBA. 

J. P. Vigier, Theoretical implications of time dependent double resonance neutron interferometry, in W. M. Honig, D. W. Kraft, and E. Panarella (Eds.), Quantum Uncertainties, Recent and Future Experiments and Interpretations. Proc. NATO Advanced Research Workshop on Quantum Violations Recent and Future Experiments and Interpretations, (Bridgeport, CT, June 23-27, 1986) ISBN 0-30-642670-6, Plenum, New York, 1987,... 

Thus on the large scale we can effectively apply a deterministic physics, but when we wish to look in detail at the properties of the sub-atomic realm, lying at the root and foundation of our world, we must enter a domain of quantum uncertainties and find the neat ordered picture dissolving into a sea of ever flowing forces that we cannot tie down or set into fixed patterns. 

Those who begin to work upon their consciousness through some kinds of meditative exercises will experience these quantum uncertainties in the field of consciousness in a strong way. 

The brain can no longer be seen as a vast piece of organic clockwork, but as a subtle device amplifying quantum events. If we trace a nerve impulse down to its root, there lies a quantum uncertainty, a sea of probability. So just how is it that this sea of probability can cast up such ordered structures and systems as the conception of a cello concerto or abstract mathematical entities Perhaps here we may glimpse a way in which "spirit" can return into our... 

Figure 1 2 10. The reduced Lifshitz parameter"z" - (ET - EF)/(EA- ET), where (EA- Er) is the full energy band dispersion in the c-axis direction, as a function of the number of holes in the G subband in A1 doped MgB2. The quantum uncertainty in the z value is indicated by the error bars that are given by D (

As the subject of quantum theory has now been broached, it is perhaps opportune to say something about quantum uncertainty at this point. The discovery toward the end of the nineteenth century that the laws of physics were in many cases based on statistics came as a considerable surprise. However, this surprise was nothing compared to the profound sense of shock experienced by the scientific community as a whole when the propositions of quantum theory first became widely known. In fact, the reverberations of this shock are still keenly felt today, and the ongoing debate about what it all means has remained lively and controversial. Feynman even went as far as to admonish us not to keep asking But... 

The criterion (43) differs significantly from the Bohr s criterion [8], 17 1, which ensures a small quantum uncertainty of the angle of electron... 

Both types of event evolve (in the strict etymological sense) from possibility into actuality only with the benefit of hindsight. But there is no reason to believe that quantum uncertainties will automatically penetrate upward into higher-order dynamics - it all depends on which particular higher-order dynamical system one considers. For example, it is a highly predictable outcome of human behavior that... 

We believe that such reconciliation Is not adequate. Moreover, we believe that the thermodynamic behavior of matter is due to quantum uncertainties of the same nature but broader than those associated with wave functions and invoked in the uncertainty principle. 

Many attempts have been made to defuse the A problem. A common strategy is by vague reference to unexplored, but likely, effects of otherwise well-known ideas, such as divine intervention, quantum uncertainty, many-worlds theory, wormholes or the anthropic principle, to account for any apparent theoretical inadequacies. It requires little more than some reassurance on the future vindication of a viable theory that may now appear flawed. We read (Schwarzschild, 1989) ... 

The two complementary types of experimental approaches are analyzed in this section by using the foregoing description of the energy-time properties of the exciting field. This allows us to relax the convenient but unrealistic approximations of pure monochromatic or impulse 5(t) excitations, and to account for the classical as well as for the quantum uncertainties, which are present in any experiment. 

Since chemical systems are irreversible, nonequilibrium systems, they can be labeled "chaotic." Hence, they may be viewed as macroscopic analogues to the quantum uncertainties. Just as in a chaotic system, every component—minor or major—affects the outcome of the change or transformation, every component affects the outcome of the reaction. 

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