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Perceptions of physical reality - 10 |
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by Dr. Raj Vatsya |
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Supplementary Comments
Physics together with metaphysics developed in an attempt to understand the “workings of nature.” An overview of the way such an understanding evolved from ancient times to the present was provided in the first article of the series, “Perceptions of physical reality,” available here in the Education section. Elemental issues:
Regarding the nature of interaction between the nature and observer, two basic approaches developed from the early times: Modern theories in physics include two distinct eras: The classical, from the time of Galileo to the end of the nineteenth century, and the quantum, from 1900 to date. The present article outlines the physical reality as perceived in these theories. Some supplementary material is also discussed.
In the pre-relativistic classical, Galileo-Newtonian, physics, motion of a particle is described by its location in space with respect to time, the space being defined by the relative positions of material bodies and time, by the order of events. Space was assumed to be equipped with the Euclidean geometry and time served as an independent parameter. Newton’s laws stated in terms of “force” naturally suggested a simple mathematical framework, which describes the particle motion along a definite trajectory.
Newton’s laws are supposed to hold in the
Nature and magnitude of the forces were determined by the response of particles acted upon by them, which were gravitational, electric and magnetic. Later, the concept of force was replaced by that of the field.
Waves, e.g., on the surface of water, arose out of the oscillations of particles of the medium supporting a wave. Light and thus, electromagnetic waves can travel in vacuum upsetting this view. Ether, the “substance that the vacuum was made of,” was postulated to maintain the prevailing concept of the waves. However, the efforts at detecting something like ether only revealed its nonexistence. Experiments also revealed that the
In all of the above, physical reality was perceived in mechanical terms. A significant adjustment to this view resulted from Einstein’s formulation of gravitation in terms of the geometrical concepts spurred by Galileo’s observation of equivalence of the inertial and gravitational masses. The
In spite of periodic major adjustments to the descriptions,
Although it was not fully appreciated at the time, realism, determinism and locality suffered a severe setback with Weyl’s suggestion that the
( So)Shut up and Calculate …. — David Mermin
Quantization of the electromagnetic waves was introduced in Planck’s description of the black body radiation, but was not considered genuine. However, the concept took hold as it successfully described specific heat of solids and the photoelectric effect also; and coupled with Rutherford’s model of atom, spurred the formulation of Bohr`s quantized orbits. Dual nature of light, particle and wave, was already well established, although not understood. De Broglie proposed the dual nature for material bodies also. Arguments used were scientifically tenuous inspiring its dubbing as the French Comedy. However, observations in the double slit experiment confirmed this dual nature of all such entities. Each individual entity registers as a particle but a large number of them collected together, exhibit wave characteristics of each entity;
In an empirical formulation of quantum mechanics that followed, the
Multiple path formulations of quantum mechanics were developed in time. The first one among them, Feynman’s, assumes that
Although a significant improvement over the original empirical formulation of quantum mechanics, the essential content of Feynman’s path integral formulation is the same. The multiple path formulation in its final form, which is formally quite similar to Feynman’s, radically altered the content of quantum mechanics. Firstly; this formulation is based on purely particle picture eliminating the concept of wave-particle duality. The wavefunction appears as an aggregate in the framework of the Weyl geometry. Then, the wavefunction appears as a representative of a class of systems, being the same for all assigned gauges, which is the same as the one with assigned gauge being equal to one everywhere, not the representative of a specific physical system. To determine the wavefunction for a specific state, it is required that the assigned gauge be introduced by additional considerations. In this formulation, the Although described correctly by quantum mechanics, some of the observations in experiments involving microscopic systems are counterintuitive and anomalous in terms of the classical thinking. The first one, behavior of the entities in the double slit experiment, discussed in article #7, which Feynman considered the only anomaly, spurred the development of quantum mechanics including its multiple path formulations. Some of the others are discussed in the article #8, namely: Passage around a hole in space; Passage through a barrier; Entanglement; and Schrödinger’s cat. In case of the passage around a hole, two beams of electrons from a common source, neither passing through a magnetic field but enclosing it, are affected by the field when observed on the other side. In case of a barrier, a particle can penetrate a classically forbidden barrier and reflected from a penetrable one. Behavior of the entangled particles is peculiar in that a measurement on one particle affects the other separated from it. In case of Schrödinger’s cat, it is both dead and alive until observed.
As mentioned above, in the quantum mechanical formulation, the state function is expressed as a superposition of many “pure” states but a measurement reveals it in one of the states with a probability attached to it. Earliest “explanation” of this occurrence was the
Understanding of the structure of space-time progressed from the absolute independent rigid entities in the non-relativistic classical thinking to a composite 4-dimensional Minkowskian spacetime in the relativistic formulation. Quantum concept did not alter these pictures. Weyl’s radical departure from these concepts by abandoning the rigidity of intervals under parallel transport with length conforming to the underlying geometry of spacetime, has been incorporated in the path-integral formulation of quantum mechanics with a significant impact. Some recent investigations in the framework of multiple path formulations have affected the earlier understanding of space-time, together with a novel formulation of quantum fields. These concepts are discussed in brief below referring specifically to the electromagnetic fields for simplicity, which has all the essential ingredients for the treatment of the other gauge fields.
As discussed before, classical electromagnetic field is a collection of infinitely many oscillators. The field is quantized by replacing the classical oscillators by the quantum oscillators. This formulation has been very successful in describing the quantum electromagnetic phenomena, except for one problem as follows. Minimum energy of a classical oscillator is zero but minimum energy of a quantum oscillator is strictly positive implying that
Consider a trajectory in a free 3-Dimensional Euclidean manifold, which can be parameterized by its arclength, instead of an external parameter; i.e., coordinates of a moving body with respect to the distance travelled specifies the path completely. This enables one to determine the “velocities” and “accelerations” with respect to this parameter, arclength. Now, one can use the action principle to determine the classically prescribed path for a particle; the resulting trajectory is a straight line, regardless of its mass. Clearly, the distance travelled, i.e., the shortest distance between its end points, along a straight line is equal to its arclength, i.e., the particle travels with unit velocity. The magnitude of the velocity of light is equal to one in natural units. Thus,
In the multiple path formulations, all physical trajectories passing through a point can facilitate the passage of a particle from the corresponding initial points to that point. Arclength of each trajectory at the point under consideration is different from the other, in general. Thus, arclegth acquires significance as a parameter independent of the trajectories. In article #4, just as the musings of a mathematician, this parameter was attached to the 3-dimensional Euclidean space as an added dimension and all 3-dimensional trajectories were described in this 4-dimensional manifold. This naturally yielded the light cone together with the 4-dimensional Minkowski manifold with the parameter arclength identified with time. The straight lines in 3-dimensional space are mapped on the surface of the cone and the curved ones in its interior. Exterior of the cone accommodates the trajectories with arclength less than the shortest distance between the points, i.e., the tachyons in the relativistic formulation. It should be clarified that the trajectories are mapped, not copied in the 4-dimensional structure. However, if two sets can be mapped into each other in a one to one manner both ways, then mathematically they are essentially equivalent. Now consider the other, curved, trajectories which are mapped in the interior by decomposing it in its components: A straight line and its arclength. The same particle as considered above moving along a curved path has the corresponding trajectory in the interior of cone, which have velocities less than one. Now, the action principle applied to the Minkowski space constructed above assigns a trajectory to this particle, which has its curved counterpart in the Euclidean base. Some simple manipulations show that the particle acquires a rest mass equal to the photon energy. With the underlying space being Minkowskian, the results of special relativity are the natural outcome, without its usual assumptions.
Multiple path formulation yields a wavefunction. By translating the initial points along the trajectories, one can generate a one parameter family of wavefunctions, translation parameter being the defining parameter. When the translation is equal to one elemental on each trajectory, the wavefunction is again the same as the original one. Thus, this family is periodic with respect to the translation parameter. Since the translation is along the arclengths, it is identified with the parameter arclength. This together with the equation it satisfies, the periodic family is identified with the electromagnetic potential with the arclength parameter identified with time. The quantized Maxwell’s field equations are easily deduced from the equation for the potential and the photon is understood as the quantum of this field. The Repeating the above program in the Minkowski manifold with the massive particle, both generated in the process, one obtains the classical particle description, which is relativistic; quantum particle description; and its quantum field description; generating in the process a 5-dimensional Minkowskian manifold and a massive-like particle in it. The process continues ad infinitum.
This article presents an outline of the modern theories of physics, which were covered in detail in the earlier articles of this series. In addition, a recently developed understanding of time together with that of the quantized fields is briefly described. In this new understanding, Answer to the question: How the particle came where it is spotted; would be: We do not know. All theories are conjectures, i.e., essentially they are postulates, assumptions. Based on such postulates, we deduce some results. In mathematics, deduced results are just what the assumptions imply; they do not have any more essential content than the original assumptions; process of deductions is just to delineate the contents of the assumptions. The action principle and all the other elements of the theory are basically our assumptions. Thus, a straight line path for a particle in a free 3-dimensional space and other similar results are the implications of our assumptions. Same is the case with the other theories. Thus, the above manifestations of the behavior of particles are the outcomes of certain assumptions that we use to develop suitable mathematical frameworks to describe our observations.
With the above background:
Yet again, the thought springs to mind: Perhaps I leave it to the reader to decide what our perception of physical reality is. |
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03-Aug-2014 |
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rdashby08/06/2014 20:51 PM
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