Quantum theory uncertainty principle

PHYSICAL PRINCIPLES OFTHEQUANTUMTHEORY. Werner Heisenberg. Nobel Laureate discusses quantum theory, uncertainty, wave mechanics, work of Dirac, Schroedinger, Compton, Wilson, Einstein, etc. 184pp. 5X x 8)4. 

Whether this concept can stand up under a rigorous psychological analysis has never been discussed, at least in the literature of theoretical physics. It may even be inconsistent with quantum mechanics in that the creation of a finite mass is equivalent to the creation of energy that, by the uncertainty principle, requires a finite time A2 A h. Thus the creation of an electron would require a time of the order 10 20 second. Higher order operations would take more time, and the divergences found in quantum field theory due to infinite series of creation operations would spread over an infinite time, and so be quite unphysical. 

In Science, every concept, question, conclusion, experimental result, method, theory or relationship is always open to reexamination. Molecules do exist Nevertheless, there are serious questions about precise definition. Some of these questions lie at the foundations of modem physics, and some involve states of aggregation or extreme conditions such as intense radiation fields or the region of the continuum. There are some molecular properties that are definable only within limits, for example, the geometrical stmcture of non-rigid molecules, properties consistent with the uncertainty principle, or those limited by the negleet of quantum-field, relativistic or other effects. And there are properties which depend specifically on a state of aggregation, such as superconductivity, ferroelectric (and anti), ferromagnetic (and anti), superfluidity, excitons. polarons, etc. Thus, any molecular definition may need to be extended in a more complex situation. 

To explain this behaviour, physicists appeal to the very foundations of quantum theory. Because of their much reduced freedom to move in space, the particles can be considered to be more and more localised. Then, by Heisenberg s uncertainty principle, the spread in their velocities has to grow. In other words, some particles may have much higher velocities than those allowed by the temperature. A quantum pressure arises at high densities, when the mean distance between electrons becomes comparable with their associated wavelength... 

The uncertainty principle shows that the classical trajectory of a particle, with a precisely determined position and momentum, is really an illusion. It is a very good approximation, however, for macroscopic bodies. Consider a particle with mass I Xg, and position known to an accuracy of 1 pm. Equation 2.41 shows that the uncertainty in momentum is at least 5 x 10 29 kg m s-1, corresponding to a velocity of 5 x 10 JO m s l. This is totally negligible for any practical purpose, and it illustrates that in the macroscopic world, even with very light objects, the uncertainty principle is irrelevant. If we wanted to, we could describe these objects by wave packets and use the quantum theory, but classical mechanics gives essentially the same answer, and is much easier. At the atomic and molecular level, however, especially with electrons, which are very light, we must abandon the idea of a classical trajectory. The statistical predictions provided by Bom s interpretation of the wavefunction are the best that can be obtained. 

In the Quantum picture of the world, each individual event cannot be determined exactly, but has to be described by a wave of probability. There is a kind of polarity between the position and energy of any particle in which they cannot be simultaneously determined. This was not a failing of experimental method but a property of the kinds of mathematical structures that physicists have to use to describe this realm of the world. The famous equation of Quantum theory embodying Heisenberg s Uncertainty Principle is ... 

An important experiment carried out as recently as summer 1982 by the French physicist, Aspect, has unequivocally demonstrated the fact that physicists cannot get round the Uncertainty Principle and simultaneously determine the quantum states of particles, and confirmed that physicists cannot divorce the consciousness of the observer from the events observed. This experiment (in disproving the separabilty of quantum measurements) has confirmed what Einstein, Bohr and Heisenberg were only able to philosophically debate over - that with quantum theory we have to leave behind our naive picture of reality as an intricate clockwork. We are challenged by quantum theory to build new ways in which to picture reality, a physics, moreover, in which consciousness plays a central role, in which the observer is inextricably interwoven in the fabric of reality. 

On a more philosophical or meta-physical level, one may suspect that free will and consciousness may have some quantum mechanical origin rooted in the Heisenberg Uncertainty Principle. Perhaps at some neurological level an electron at a synapse exists in a superposition of two or more states that ultimately results in someone making some sort of decision. Should I run for President, or not Should I get married, or not . Perhaps there are two states with eigenvalues yes or no that asymptotically lead to very different actions. Does quantum theory enter into our decision making process Perhaps the brain itself acts as some sort of quantum computer taking... 

The famous uncertainty principle is a typical example of a concept, well known to classical physics, which entered into the vocabulary of laymen and philosophers and created an aura around quantum theory, now widely believed to describe a mysterious netherworld that defies comprehension. The philosophical fall-out has been enormous, to the point where quantum theory is dragged into debates on free will, cosmology and determinism even into theological discourse. 

The realization that both matter and radiation interact as waves led Werner Heisenberg to the conclusion in 1927 that the act of observation and measurement requires the interaction of one wave with another, resulting in an inherent uncertainty in the location and momentum of particles. This inability to measure phenomena at the subatomic level is known as the Heisenberg uncertainty principle, and it applies to the location and momentum of electrons in an atom. A discussion of the principle and Heisenberg s other contributions to quantum theory is located here http //www.aip.org/historv/heisenberg/. 

Most of modern physics and chemistry is bast d on three fundamental ideas first, matter is made of atoms and molecules, very small and very numerous second, it is impossible in principle to observe details of atomic and molecular motions below a certain scale of smallness and third, heat is mechanical motion of the atoms and molecules, on such a small scale that it cannot be completely observed. The first and third of these ideas are products of the last century, but the second, the uncertainty principle, the most characteristic result of the quantum theory, has arisen since 1000. By combining these three principles, we have the theoretical foundation for studying the branches of physics dealing with matter and chemical problems. 

It was pointed out by Dirac [230] that the contradiction between relativity and the aether is resolved within quantum theory, since the velocity of a quantum aether becomes subject to uncertainty relations. For a particular state at a certain point in space-time, the velocity is no longer well defined, but follows a probability distribution. A perfect vacuum state, in accordance with special relativity, could then have a wave function that equalizes the velocity of the aether in all directions. The passage from classical to quantum theory affects the interpretation of symmetry relationships. As an example, the Is state of the hydrogen atom is centrosymmetric only in quantum, but not in classical theory. A related redefinition of quantum symmetry provides the means of reconciling the disturbance of Lorentz symmetry in space-time, produced by the existence of an aether with the principle of relativity. 

In order to make the theory useful it is necessary to know the constant of proportionality, which is calculated in such a way as to give the classical limit of the number of quantum states. This matter is dealt with in standard books on statistical mechanics [26]. The result is that for a system with n degrees of freedom, i.e. n position coordinates q and n momentum coordinates p, the number of states in the infinitesimal volume element rfq rfp is equal to rfq rfp//i", where n is Planck s constant. The association of a phase space volume /i with each quantum state can be thought of as a consequence of the uncertainty principle, which limits the precision with which a phase point can be specified in a quantum mechanical system. 

Quantum theory dictates that the measurement of certain pairs of properties of particles, including position and momentum are limited by the Heisenberg uncertainty principle first advanced by German physicist Werner Heisenberg (1901-1976). In essence, although it is possible to measure either position or momentum the pair can not be measured simultaneously. The more exact the determination of position, the more uncertain becomes the measurement of momentum. 

Although the uncertainty principle is not relevant to the measurement of momentum of large objects, it places severe constraints on measurements of momentum of subatomic particles. Accordingly, quantum theory places a limitation on the experimental measurement of momentum. The more accuracy required in the determination of position, the less the accuracy possible with regard to the determination of momentum. For example, in attempting to make an accurate determination of the position of an electron it is necessary to bombard the electron with photons. In doing so the collisions between the photons and the electron alter the momentum of the electron and therefore introduce uncertainty in the measurement of the momentum of the electron. 

We must acknowledge that our information about the location of a particle is limited, and that it is statistical in nature. So not only are we restricted by the uncertainty principle as to what we can measure, but we must also come to grips with the fact that fundamental properties of quantum systems are unknowable, except in a statistical sense. If this notion troubles you, you are in good company. Many of the best minds of the 20th century, notably Einstein, never became comfortable with this central conclusion of the quantum theory. 

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