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Perceptions of Physical Reality - 9 |
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by Dr. Raj Vatsya |
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Quantum Theories – Interpretations
Although the metaphysical element underlies all basic physical theories and interpretations are required for their basic understanding as well as to relate them with the observations, in classical mechanics there was little room to address observations that were considered anomalous. On the other hand, quantum mechanics has tried and continues to try to come to terms with many such observations, some of which are discussed in the article, “Perceptions of physical reality – 8,” referred to here as [8 ]. Interpretations of quantum mechanics were developed to address the pertaining issues. Copenhagen Interpretation
In quantum mechanics, state of a physical system is represented by its wavefunction, which can be expressed as a superposition of many “pure states.” Outcome of a single measurement shows the system in one of the pure states. The Copenhagen interpretation, due mainly to Bohr and Heisenberg, was the first attempt to understand this state of affairs, which “explains” it by assuming that the wavefunction “collapses” into a definite state by an act of observation. This “explanation” means that
The cat phenomenon resembles the double slit experiment with one slit open: Radioactive material is bulk material as is the source in the double slit system; in both cases the radiation of the entity is a bulk stochastic, semi-classical, random process; and the entity is captured by the triggering mechanism just as by the detector. Thus, in case of the cat consider the wavefunction of the entity after its radiation. Bohr argued that as a particle is registered by the triggering mechanism, the Geiger counter, the wavefunction has collapsed as in case of the double slit observation. Based on this argument, Bohr did not consider the cat phenomenon a paradox. Pilot Waves
Since the trajectory a “particle” follows is not known, the “particle trajectories” are the hidden variables in this formulation. For this reason, Bohm’s formulation is considered a hidden variable theory. There are other hidden variable theories not considered here. It is anticipated that the hidden variables of such theories will become known in a better theory than quantum mechanics, but given the nature of observations it is also thought that there may never be such a theory. Some consider hidden variable theories justified. Many Worlds
Around 1957, Everett introduced the concept of relative states to eliminate the concept of wavefunction collapse, which was developed into what is commonly known as the many worlds interpretation, and developed further into many histories, and even many minds interpretations. This interpretation has enjoyed more popularity than the others at times, including the Copenhagen, although not always.
In Figure 2, to the left the cat is both alive and dead before it is observed. The middle shows the effect of an observation when the cat branches off in two branches: Gauge Description of Anomalies
Formulation of quantum mechanics based on the action gauge principle in terms of gauge transformations of the Weyl geometry was described in [7]. The founding assumption of the Weyl geometry is that the length of a vector at B transported along a trajectory from A to B is in general, different from that at A, with lengths at two points related by a gauge transformation, termed the natural or essential gauge. In addition, a measure of length, a gauge, can be assigned to the points, which is called the assigned gauge. Understanding of the quantum anomalies discussed in [8] as well as the double slit phenomenon, is described below in some detail referring specifically to each one of them on the background of this formulation. The description is based on the properties of the physical trajectories discussed in [7]. Double Slit Phenomenon Consider the double slit arrangement of Figure 3 below, which is the same as Figure 1 of [7]:
In Figure 3, S is the source, A and B are the slits in the screen S
First consider the case when the slits A and B are physically equivalent and thus the assigned gauges there are equal. Since A and B in this configuration are the end points of a single, non-monotonic, trajectory ASB with equal assigned gauges, the assigned gauges there become ineffective and thus, can be set equal to one as everywhere else.
For low energy, i.e., low frequency photons, the transferred momentum is small causing a small shift of C, for which there are still many correlated trajectories constituting composite non-monotonic physical trajectories AC”B, where C” represents the terminal point of the trajectory in a small neighborhood of AC, AC’ on O. This applies to the configuration for all locations of C including X. This causes the density pattern to shift and blur. As the frequency of photons is increased, the transferred momentum increases increasing the shift and blur of the density pattern. When the shifted point reaches about the nearest minimum, there are hardly any correlated trajectories causing the interference-like pattern to about disappear. At this point, the trajectories AC” and BC” are uncorrelated and must be considered independent monotonic trajectories. Passage around Hole in Space Chambers realization of the Aharonov-Bohm experiment is depicted in Figure 5, which is the same arrangement as of Figure 1 of [8], where the pertaining discussion is also available.
In Figure 5, S is the source of electrons, A and B are the reflectors, the enclosed magnetic flux is shown by the circle, X is the central location on the observation screen and X’ is an arbitrary observation point. Classically, the electrons travel along the straight lines: SAX(X’) and SBX(X’), which constitute a non-monotonic trajectory SAX(X’)BS. If this is a physical trajectory, all physical trajectories are concentrated about it. The assigned gauges at S, A, X(X’) and B are different from one, but they are effectively equal to one as each of these points is common to and physically equivalent for the pairs of two relevant pieces. Passage through Barrier Figure 6, which is the same system as Figure 2 of [8], shows one-dimensional motion of a particle that encounters a potential barrier of finite extension. S is the source. Classically, the particle travels along SA encountering the barrier at A; if the strength of the potential is less than the energy of particle, it passes through traveling along AE; and if the strength is more than the energy, it is reflected along AF. AF is along AS; it is shown here separate for clarity.
Now consider the motion according to the action gauge principle taking the assigned gauges into account. Properties of this system are stated here omitting the technical details to indicate the basic argument. First consider the case when the potential strength is less than the particle energy and thus, classically, the particle would be transmitted. The action in this case increases along SAE, although the rate of increase is lower along AD. Thus, the trajectory SAE is monotonic. Since A and D are in the interior of a continuing trajectory with no imbalance in the gauge, assigned gauges there become ineffective and the gauges at S, E are inconsequential for the argument. Entanglement System of two entangled particles is shown in Figure 7, which is the same as Figure 3 of [8], where further details are available. Two particles, A and B, which are entangled though some conserved quantities, e.g., momentum and relative position, disintegrate at x and travel in opposite directions. EPR argument is that measurement of the momentum of A determines that of B without disturbing it; hence it must be “real;” but quantum mechanics cannot describe it. Also, position of B determines that of A. Thus both, the momentums and positions of both particles are determined exactly simultaneously. Since, the uncertainty principle prohibits this, it is violated. The argument is based on the assumption of locality.
Since the theory being considered in the present section is non-local, as is clear from the above discussions, EPR argument is invalidated. Present formulation differs from the earlier one conceptually in that it is the trajectories that are entangled, instead of the particles, which in this case are Ax and Bx. Such trajectories can be considered a non-monotonic trajectory with the point of inflexion being the correlation point, common to the two monotonic segments. For the EPR system depicted in Figure 7, the trajectory AB is non-monotonic with the action decreasing from A to x and increasing from x to B. The assigned gauge at the inflection point x, which is fixed, is ineffective. This system is essentially the same as the double slit experiment except that there the point of inflexion changes due to interruption, while here it is fixed. Schrödinger’s Cat Realistic depiction of Schrödinger’s thought experiment is given in Figure 4 of [8]; the corresponding essential schematic is given in Figure 8 below. In Figure 8, S is the radioactive material, T is the triggering mechanism, which releases the poison P to reach the cat C; the observer O observes the cat.
Emission of a particle from S is essentially the same as the radiation from any other source, e.g., in the double slit experiment, which is modeled as stochastic processes. This part is in fact not essential element contributing to the “paradox.” In the present context, the emission activity is represented by an assigned gauge at S and the detection of particle by gauge at T. Triggering mechanism and release of poison, as well as its interaction with the cat are bulk activities; their details are not clear. The process can be represented by a trajectory from T to C with different assigned gauges at T and C. The assigned gauge at T as the terminal point of ST is different from that at T as the initial point of TC for the interactions are different. Then the observation process, e.g. photon from C to O, can be considered along a trajectory CO with different values of the assigned gauge at end points. The trajectories shown here are straight lines. Concluding Remarks
Counterintuitive behavior of the physical systems, although described successfully by the rules of calculation of quantum mechanics, necessitated its various interpretations for an understanding of its epistemological underpinnings. Rather surprisingly, about the weakest among them, the Copenhagen interpretation; has been most widely accepted most of the times although at times, it has lost ground to the many worlds view. Another major interpretation, the pilot wave, has had its own following. |
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13-Jul-2014 |
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