Quantum physics uncertainty relations

The uncertainty relations have played a central role since the field of quantum mechanics has been created. Prior to the existence of this theory, experimentalist knew, from their work, that every concrete measurement would necessarily carry an associated error. Yet, it was generally believed that this error was of no fundamental nature, and that one could, in principle, approach the true value by filtering out from a huge amount of measurements. Errors were part of the experimental process. With the advent of quantum physics, the error of measurements assumes a new, ontological status, rooted in the very heart of the theory. The theory itself would be built on this unavoidable error process. 

The new, more general uncertainty relations (90) were derived in a causal framework assuming that the physical properties of a quantum system are observer-independent, and even more, that they exist before the measurement process occurs. Naturally, because of the unavoidable physical interaction taking place during the measurement process, when the other conjugated observable is to be measured, the quantum system may not remain in the same state. In any case, in the last instance, the precision of a direct concrete measurement for a nonprepared system depends on the relative size between the measurement basic apparatus and the system on which the measurement is being performed. 

In conclusion, the condition of ordinary statistical physics makes the decoherence theory a valuable perspective, as well as an attractive way of deriving classical from quantum physics. The argument that the Markov approximation itself is subtly related to introducing ingredients that are foreign to quantum mechanics [23] cannot convince the advocates of decoherence theory to abandon the certainties of quantum theory for the uncertainties for a search for a new physics. The only possible way of converting a philosophical debate into a scientific issue, as suggested by the results that we have concisely reviewed in this section, is to study the conditions of anomalous statistical mechanics. In the next sections we shall explore with more attention these conditions. 

In his detailed analysis of Dirac s theory [6], de Broglie pointed out that, in spite of his equation being Lorentz invariant and its four-component wave function providing tensorial forms for all physical properties in space-time, it does not have space and time playing full symmetrical roles, in part because the condition of hermiticity for quantum operators is defined in the space domain while time appears only as a parameter. In addition, space-time relativistic symmetry requires that Heisenberg s uncertainty relations. 

Jammer, when he refers to researches in modern physics, presumably means the philosophical difficulties created by quantum physics. Quantum theory was first introduced to explain a number of experimental laws concerning phenomena of thermal radiation and spectroscopy which are inexplicable in terms of classical radiation theory. Eventually it was modified and expanded into its present state. The standard interpretation of the experimental evidence for the quantum theory concludes that in certain circumstances some of the postulated elements such as electrons behave as particles, and in other circumstances they behave as waves. The details of the theory are unimportant to us except in respect of the Heisenburg uncertainty relations . One of these is the well known formula Ap Aq > hl4ir where p and q are the instantaneous co-ordinates of momentum and position of the particle, Ap and Aqi are the interval errors in the measurements of p and q, and h is the Universal Planck s constant. The interpretation of this formula is, therefore, that if one of these co-ordinates is measured with great precision, it is not possible to obtain simultaneously an arbitrarily precise value for the other co-ordinate. The equations of quantum theory cannot, therefore, establish a unique correspondence between precise positions and momenta at one time and at another time nevertheless the theory does enable a probability with which a particle has a specified momentum when it has a given position. Thus quantum theory is said to be not deterministic (i.e, not able to be precisely determined) in its structure but inherently statistical. Nagel [25] points out that this theory refers to micro-states and not macro-states. Thus although quantum... 

This claim is probably related to modern (approximately 100 years old) physics such as Einstein s theory of special relativity and quantum physics, including the Uncertainty Principle. An exact description (picture) of the material or physical world is impossible. Quantum mechanics means that the world is fuzzy at the atomic and molecular level, and there are limits of experimental precision dictated by the Uncertainty Principle. Matter on the atomic level is schizophrenic due to its wave-particle duality. The material world is described by a series of scientific models, all of which are limited and incomplete as descriptions of physical phenomena. 

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