Precision fundamental limitations

For a light source of a specific power, there is a fundamental limit to the precision to which the intensity can be determined within a specific period. This is termed the shot-noise limit. If n photons are accumulated, the variance is /n and the signal-to-noise ratio (S/N) is fnln. Any additional noise source (due to the amphfier, interference or detector imperfections) will degrade this value. Theoretically, shot-noise in coherently squeezed light can be slightly lower than this limit, but ultimately only by a factor of 1/ 2. 

Werner Heisenberg, who was also involved in the development of the quantum mechanical model for the atom, discovered a very important principle in 1927 that helps us to understand the meaning of orbitals—the Heisenberg uncertainty principle. Heisenberg s mathematical analysis led him to a surprising conclusion There is a fundamental limitation to just how precisely we can know both the position and the momentum of a particle at a given time. Stated mathematically, the uncertainty principle is... 

At last, we can resolve the paradox between de Broglie waves and classical orbits, which started our discussion of indeterminacy. The indeterminacy principle places a fundamental limit on the precision with which the position and momentum of a particle can be known simultaneously. It has profound significance for how we think about the motion of particles. According to classical physics, the position and momentum are fully known simultaneously indeed, we must know both to describe the classical trajectory of a particle. The indeterminacy principle forces us to abandon the classical concepts of trajectory and orbit. The most detailed information we can possibly know is the statistical spread in position and momentum allowed by the indeterminacy principle. In quantum mechanics, we think not about particle trajectories, but rather about the probability distribution for finding the particle at a specific location. 

Heisenberg uncertainty principle a principle stating that there is a fundamental limitation to how precisely we can know both the position and the momentum of a particle at a given time. 

As with any laboratory instrument, there are fundamental limitations to the accuracy of the information given by spectrophotometers. Even though the absorbance reading may appear quite precise especially with digital and/or computer display - how do we know it is telling the truth ... 

Heat of vaporization the energy required to vaporize one mole of a liquid at a pressure of one atmosphere. (16.10) Heating curve a plot of temperature versus time for a substance where energy is added at a constant rate. (16.10) Heisenberg uncertainty principle a principle stating that there is a fundamental limitation to how precisely both the position and momentum of a particle can be known at a given time. (12.5)... 

The German physicist Werner Heisenberg ( FIGURE 6.14) proposed that the dual nature of matter places a fundamental limitation on how precisely we can know both the location and... 

The German physicist Werner Heisenberg ( Figure 6.15) proposed that the dual nature of matter places a fundamental limitation on how precisely we can know both the location and the momentum of an object at a given instant. The limitation becomes important only when we deal with matter at the subatomic level (that is, with masses as small as that of an electron). Heisenberg s principle is called the uncertainty principle. When appHed to the electrons in an atom, this principle states that it is impossible for us to know simultaneously both the exact momentum of the electron and its exact location in space. 

One way to overcome the fundamental limitation of the porous coatings is to use an extraction time much less than the equilibrium time so that the total amount of analytes accumulated onto the fiber is substantially below the saturation value. When performing such experiments, is it critical to precisely control extraction times and convection conditions to ensure that they are constant or can be compensated for. One way of eliminating the need for compensation of convection is to normalize agitation conditions. 

As the number of analyte molecules used in an analysis approaches the single molecule level, the relative uncertainty in the number of molecules present becomes huge. Molecular shot noise is the term that we have given to this fundamental uncertainty in a chemical measurement. It is an irreducible and fundamental limitation of chemical analysis at the single molecule limit only by analyzing a large sample can we obtain precise information that is characteristic of the composition of the sample. 

The ability to measure simultaneously the isotopes of two different elements with high precision has never been a particular challenge in mass spectrometry. The challenge has always been to ensure the accuracy of the mass bias transfer. Hence a fundamental limitation of the traditional mass bias correction models is their... 

The above example illustrates that the idea of uncertainty cannot be ignored at the atomic level. Certainly, if the velocity were known to lower precision, say, to one part in ten, the corresponding minimum uncertainty in the position would be lower. But the uncertainty principle states mathematically that as one goes up, the other goes down, and neither can be zero for simultaneous determinations. The uncertainty principle does not address a maximum uncertainty, so the actual uncertainty can be (and usually is) larger. But some measurements have a fundamental limit to how exactly they can be determined simultaneously with other observables. 

There has always been a strong belief in the potential of technology to overcome human limitations with regard to, for example, force, speed, precision, perception and cognition. This belief has made automation a preferred solution to many human factors problems. In a seminal analysis of the use of automation to replace humans, Lisanne Bainbridge pointed out some of the fundamental limitations in a delightful paper published in 1983 entitled Ironies of automation, Automatica, 19, 775-79. 

While density functional methods have proven to be remarkably useful for predicting a variety of molecular properties, and are certainly computationally efficient, there are a number of fundamental limitations upon the accuracy of existing functionals which preclude application to wide clas.ses of chemical problems. The most serious deficiency is in the computation of dispersion (van der Waals) interactions, which are not even qualitatively reproduced by any current functional. More generally, DFT calculations cannot yet be systematically improved if higher precision is desired, unlike wavefunction-based methods. For example, the B3LYP functional yields an average error of 2 kcal mol for atomization energies of the G2 data base (a set of small molecules for which accurate experimental data exist) whereas the CBS-ANO method, ... 

Electrochemistry is a large and important area of physical chemistry. It is, however, difficult to define precisely the limits of this area, not amply on account of its size but because of its influence in so many areas in chemistry as well as in biology and physics. Many concepts, accepted universally now as fundamental to chemistry, originated in electrochemistry. On the other hand it is now realized that future developments in many fields, and we may at random quote such widely differing ones as corrosion prevention, power supply and biochemistry and cellular biology, are dependent in no small way upon the exploitation of electrochemical principles. 

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