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Perceptions of Physical Reality  8 

by Dr. Raj Vatsya  
Quantum Theories – Anomalies
Through every rift of discovery some seeming anomaly drops out of darkness Quantum mechanics was formulated to accommodate certain observations that were at variance with the classical expectations. Observations in the double slit experiment were about the most intriguing ones, which delineated peculiar behavior of the entities observed, which was interpreted to be due to their dual nature, wave and particle. These observations were described in some detail in the article, “Perceptions of physical reality  7.” In turn, quantum mechanics predicted some phenomena that were unexpected in the classical thinking. Almost all of such predictions have been confirmed experimentally, but they present some quite unsettling conceptual issues; major ones are discussed in the present article. As for the “chain of order,” thinkers search forever. Passage around Hole in Space If there is seeing without perceiving, there is also perceiving without seeing. If Ruby B were invisible we could infer her presence from your anomalous wobbling. Brown dwarfs and black holes, though hidden from sight, can be inferred from the anomalies they cause in their seeable neighbors. – Amy Leach in Things that are
As discussed in the article, “Perceptions of physical reality  4,” electromagnetic potentials were introduced as mathematical auxiliaries to streamline the classical formulation of electromagnetism. Although the fields were deduced from the potentials and thus, they acquired mathematically secondary position, electromagnetism was still considered to be described adequately and completely by the fields. This changed after Aharonov and Bohm noticed, in 1959, that the quantum mechanics predicted some electromagnetic phenomena, which could not be adequately described in terms of the fields and concluded that the potentials have a physical significance.
In Figure 1, the beams shown are classical, piecewise straight line paths. As discussed in the article, “Perceptions of physical reality  7,” an electron has multitude of trajectories available to it, which although not classical, are concentrated about the classical ones. The AharonovBohm argument is applicable to arbitrary trajectories. Since the cylinder is long and the experiment is conducted near one of its ends, it mimics a point magnetic monopole, enclosed by the beams. While the field is enclosed by the trajectories SAX and SBX, they do not pass through it. Extra care is taken in shielding the beams from the field. Geometrically, the field punctures a hole in space, i.e., a closed curve encircling the hole and remaining outside it cannot be shrunk to a point. In comparison, a closed curve in the complement of the hole and not enclosing it can be shrunk to a point. Passage through Barrier Consider a beam of particles travelling from left to right that encounters a potential barrier as shown in Figure 2. Classically, if the potential strength is more than the energy of each individual particle, the particles would be reflected; if it is less, then they would pass through the barrier. Quantum mechanics predicts that in both cases, in fact in all cases, some particles would be reflected and some would be transmitted; difference would only be in the fractions transmitted and reflected.
Again, one can imagine a parallel scenario: A hunter is chasing a cat; the cat finds a wall thick enough that the energy of the bullets is not sufficient to penetrate it classically; and hides behind the wall. The hunter cannot jump over the wall like the cat but keeps firing. Quantum mechanically, some bullets would pass through the wall to strike the cat. This effect is called the tunneling effect, which has been exploited in some major technological advances. Tunneling can also be understood in terms of a wave phenomenon. Entanglement In an attempt to show incompleteness of quantum mechanics, Einstein, Podolsky and Rosen (EPR) in 1935 devised a thought experiment. To avoid technicalities, the basic argument is illustrated below with a concrete example. Consider a system in spin zero state, e.g., a pion, which disintegrates in two subsystems, electronpositron pair. In Figure 3, the pion at X disintegrates in two particles, A and B, one of them being an electron and the other, positron. The component of spin of an electron along one axis, say xaxis, can have two values, half and negative half, termed spin up and spin down; same is the case with positron. In a measurement of the spin of one particle, probabilities of the result being spin up and down are equal. Spin is a conserved quantity. Therefore, if the spin of electron along xaxis is measured to be up, the spin of positron in x direction must be down, since the total spin, that of the composite system pion, is equal to zero; and thus the electronpositron pair is entangled.
A measurement can be carried out on one of the particles when the particles are separated by so large a distance that the measurement can be carried out in lesser time than light would take to travel from one particle to the other; i.e., there is no impact of this measurement on the other. According to special relativity, no signal, information, can travel faster than light. According to the EPR argument, one can determine the spin of positron along xaxis by a single measurement of the electron spin without in any way disturbing the positron. Therefore, the positron spin along xaxis must have had that value all along, i.e., it is physically real. Similarly, the spins along y, z axes must be real. Since quantum mechanics cannot determine the spin values, a physically real observable, quantum mechanics is incomplete and fundamentally inadequate. Now, according to the uncertainty principle, the spin along xaxis and along any other axis cannot be determined with certainty simultaneously as is the case with the momentumposition pair. However, the spin along one direction can be determined exactly if that in the other directions is left completely undetermined. Thus, an exact determination of the spin of electron along xaxis renders its spin along say, yaxis completely undetermined. But one can measure the spin of positron along yaxis, and by the conservation property, determine that of the electron and thus can determine the spin of electron exactly along x as well as y direction simultaneously violating the uncertainty principle. In their original treatment, EPR considered momentum and position instead of the spin. Momentum of the EPR composite system and thus, of the pair of particles, is equal to zero; and the relative distance of the two particles is a nonzero constant; both of these are conserved quantities, entangling the particles. Relevant properties of the EPR particles and the spin properties of the system considered here are the same: According to the uncertainty principle, the momentum and position of a particle cannot be measured with complete precision simultaneously, but one of them can be with complete precision if the other one is left completely undetermined. In the example cited above, the spins in different directions cannot be measured with certainty simultaneously, but in one direction it can be determined with certainty if the other one is left completely undetermined. Now the argument can be transposed exactly from the above case to the momentumposition pair of observables, to show that they are both physically real, which quantum mechanics cannot determine and each one can be determined experimentally exactly simultaneously violating the uncertainty principle. The argument of EPR is based on the assumption that no signal, information, from one particle to the other can travel faster than light, as dictated by the special relativity. Alternatively, if some nonlocal effects exist in nature, then this argument is invalid, but nonlocality, equivalently action at a distance, was unacceptable to these authors. However, existence of nonlocal effects in nature has been experimentally verified validating the pertaining quantum rules of calculations predicting the experimental outcomes. Initially, there were some technical difficulties with this verification with the momentumposition pair, i.e., with the original EPR system. For the spin observable, the verification was found to be easier, which was done. Since then the original EPR experiment has also been realized confirming the existence of nonlocal effects. As an alternative to nonlocality, it has been suggested that each particle carries the information coded in it at the time of disintegration, i.e., remembers its history; which would transfer the entanglement to the code rendering them independent but different from its bare form; i.e., the particle together with the coded information defines it in its completeness at the moment of disintegration. However, one would not know the coded information without measurement. EPR argument was described to be the “bolt out of the blue,” when it was presented initially. Confirmation of the nonlocal effects was done after Einstein’s death. It was said then that “Einstein must be turning in his grave,” at verifications of existence of nonlocal effects. In any case, the entanglement phenomenon presents some puzzling situations, e.g., a measurement on one of the partners in an entangled system at any time anywhere in the universe would impact upon the other partner. Schrödinger’s Cat Furthering the discussion about the EPR argument, Schrödinger devised another thought experiment, also in 1935. In this arrangement, a cat is encased in a chamber as shown in the top Figure 4, with some radioactive material and a flask containing poisonous gas. There is also a mechanism that triggers a hammer breaking the flask releasing the gas and killing the cat as a particle is emitted from the radioactive material. The matter to decide is whether the cat is alive or dead at a given time.
As illustrated in Figure 4, if the radioactive material has not decayed yet, i.e., has not released a particle, the cat must be alive; if it has decayed, then the cat must be dead. However, from the quantum mechanical rules, one can only compute the wavefunction representing the state of system, which is a superposition of “pure” states. The wavefunction can be used to calculate the probability of emission of a particle in certain time and thus, of the cat being alive after that much time, yielding also the probability of the cat being dead, both between zero and one. But if one looks into the chamber, which can be assumed to have a glass window, the cat would be found either dead or alive, not both. Concluding Remarks
While the first two examples described above, passage around a hole and through a barrier, are counterintuitive in the framework of the classical thinking, they do not pose any “paradoxical” situations except the waveparticle duality, which is the fundamental premise of quantum mechanics. Once the waveparticle duality and the resulting formalism of quantum mechanics are accepted, these effects are successfully described. 

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29Jun2014  
More by : Dr. Raj Vatsya  
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