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Humans and True Reality!

 

Speed measurements are accomplished over finite interval of time or distance moved.  It is the average speed that is measured and for sure it is not the instantaneous speed.  Physicists introduced fictitious method of measurement of objects instantaneous speed by means of mathematical limits.  Such method reflects the limit of series of average speeds computed for smaller and smaller time intervals.  But during the time interval where two physical particles collide, physicists found that discontinuities exist in their velocities, which means each velocity described motion would fail to provide exact measurement of the instant velocity.  Therefore, the idea of applying the necessity condition is violated. 

 

Classical physics usually avoids dealing with physical discontinuities, but mostly rejects the expression that relates cause and effect.  It assumes smooth, continuous, and incremental change.  Although it permits certain types of discontinuities, but it mostly provides a crude process of the change process description, especially related to velocity measurements.  Classical physics insists that particles mechanics do not provide a true picture of the total physical universe.  Therefore, physicists conceptualized additional theories.  For example, they introduced the field theory, which considers particles to be squashy substance and each is surrounded by a field whose major effect is to prevent sharp collisions with other particles.  Classical physics replaces discontinuities with rapid and smooth acceleration and decelerations, while employing mathematical limits, which allow instant property change to be redefined, including temperature, pressure, velocities, energy, mass, and other substance properties.

 

In Physics in general, energy is regarded to be carried by both particles and their fields.  Physicists theorized the existence of a dualism form of energies: the first related to fields, which assumed to carry vibrating energy frequencies that spreads such energy through out the substance particle surrounding space; and the second, energy is assumed to be embodied in the substance particle with localized energies.  They emphasized equilibrium must be established using the two types of energies, field and particle.  Albert Einstein early papers of 1905 presented the idea of quanta or ‘bundles of localized energy’ that is energy represented in fields, and referred to it as, ‘photo-electric’ effects while explaining specific experimental results.  He expressed the radiated energy as particles of light, or photons, and assumed the process of energy change, which appears through emission and absorption of light to take place at finite amounts. 

 

Einstein used Blanck’s ad hoc hypothesis of an idealized glowing body radiated spectrum and established that quantum radiated energy is proportional to its frequency.  The word frequency reflects the energy wave oscillation number in time, providing a new universal constant, h, also known as Blanck’s constant, where the total radiated energy of a given frequency depends upon the quanta in the beam.  Max Blanck discovery meant actually the quantization of energy forces physicists to accept discontinuity existence in physics.  Therefore, the assumption of smooth, continuous, and incremental change could not be valid.  Discontinuity, especially at localized subatomic level of a particle or wave-particle substance might generate strange and unpredictable effects.

 

Many processes were found requiring discontinuous change on the atomic scale, but the atomic solar system theory related to the radiated electrons predicted that it would spiral into the nucleus after very short time duration.  In 1913, Neils Bohr postulated the orbital electrons rotational momentum is quantized, which only allows electrons to jump from one orbital level to another when emitting a quantum of radiation, or photon.  Actually, Bohr’s model placed discontinuity beyond human imagination, while his postulate of instantaneous orbital jumps violated the idea of smooth, continuous, and incremental change in space, it might have violated it also in time.  Such thought ran deeper than physical property substances change, and the wave theory opened Panadora’s box.

 

Louis de Burglie was the first to argue that particles like electrons could be represented as wave-packets.  He showed that the distances from the nucleus at which electrons would form stable patterns could be determined in Bohr’s orbital atomic model.  Empirically, the wave-particle duality appeared to constitute matter fundamentals, but it is hard for physicists to make sense of it.  The wave-particle paradoxical character became clear during the two-slit experiment related to interference fringes for it contradicted Einstein’s theory of localized stream photons.  Positivists argued submicroscopic phenomenalism, and space and time quanta were named as ‘hadons’ and ‘chorons’ respectively.

 

Bohr applied the complementarily principle, and argued that experiments that detect particle like characteristics would preclude simultaneous wave-like characteristics.  The holistic character of quantum mechanics solidified mystics, especially Eastern religion believers position of dichotomy of subject and object.  They claimed, their bliss resides in the unity of awe and wonder similar to the holy.  In Bohr’s sense, such experiences are neither of the same reality nor of any external reality.  But positivism made it clear that the meaning of any scientific hypothesis must be reflected in its observational cash-value. 

 

The precise articulation of quantum theory actually stands in clear contrast to the mystics attempt to explain their unexplained annihilated state.  Why? It could not be considered a source of scientific theory because it fails all laws of logic, which according to Aristotle: statements are either true or false and there can be intermediate condition in between.  Mystics actually proposed such middle condition, where a state might exist oscillating between reality and imagination or truthfulness and falsehood.  Such thought implies that the discourse of science is similar to the discourse of religions, and if that is the case, then science could not survive new thoughts and innovations.  This means that if the predicted result is not-true, then it might nevertheless be not-false.  Islam rejects innovations totally for they exist they must be measured by ‘Al-Qustass Al-Mustaqeem’ or they Holy Qur’an and they were found to contradict it the innovations are rejected.  Any book that claim other gods beside the Creator are innovations and must be rejected.  Therefore, one may conclude that all religious innovations that contradict their original revelations must be rejected, especially those of the Eastern religious mystical doctrines of incarnation, and generation of other gods with the Creator contradict their original revelations as presented in ***, they do contradict logic, and must be rejected. 

 

The original revelation books clearly specify the Oneness of the Creator, especially at the Western three religions of Islam, Christianity and Judaism.  The Oneness of the Creator is the main theme of the Holy Qur’an, and it is stated as the first commandment in the Holy Bible, which both Christianity and Judaism adhere to it.  Therefore, any innovation related to the generation of other gods must be rejected.  For example,  the Cabala Jewish cult books starting with the Zohar and all the rest contradict the creation as it is described in Genesis; the Christian and non-Christian doctrines that negates the Oneness of the creator through the introduction of innovations such as: ‘the son of god’ which is an idea copied from the Greek mythology of their god,  Zeus and his encounter with an immortal woman called Alchamine to give birth to a mythical god son named Hercules.  such idea implies mixing the Creator with humans through begotten and elevates humans to the level of the Creator; the idea of ‘incarnation’ of Krisna, Buddha, and Christ is another innovative idea that generates other gods elevating by humans to the level of the Creator; in addition, the Eastern, the pagan, and the Christian thought of trinity assembles another innovation for the trinity contradicts the Oneness of the Creator; and finally the negation of the Creator existence thought in general, as advocated by atheism or by the believers of the pantheistic thought who generated from their imaginative mind the thought of a single consciousness.  All these thoughts represent mystical intermediate suspension and allow the existence of a middle condition or a state exists oscillating between reality and imagination or truthfulness and falsehood.  True scientists reject mystical intermediate suspension, and every innovative human addition related to describing the True Reality.

 

One type of delusional innovations penetrated into Islam after Muslims had encountered other monotheistic religions during early Islam in Syria, Iraq, and Egypt, in addition to the Eastern religions of Hinduism in India and the rest of Asia.  A delusion expresses the knowledge of Allah through mystical union in Him could be achieved, that is copying the pantheistic thought to be conceived as an end in itself.  A delusion in which the human personality is extinguished for ever reaching the Nirvana state of godly existence.  They put aside the Holy Qur’an verse (40:62) translated as, “Call unto Me (Allah) and I will answer you.”  Such verse removes the veil between humans Allah while they are awake and completely conscious.  In addition the connection between humans and Allah during sleep or being out of conscious is continuous as the Holy Qur’an verse (**:**) states, “** when human are asleep, their souls reverts to Allah.  Then, He sends back the souls of those who are alive, and keeps the souls of those who died in their sleep ***.”  The veil between humans and Allah is always removed, during consciousness or not, for Allah makes it clear in verse (50:16) translated as, “Allah is nearer to us (humans) than our neck-vain.” 

 

Therefore, manufacturing innovative ways that claim to allow humans to remove the veil between Allah and them is direct imitation of Eastern religious nihilism, where it appears that the individual is trying to prove to other humans, he is a Taqi or a pious person but showing off has no place in true Islam.   However, the most revealing words in the Holy Qur’an as for example presented in verse (22:6 and 61) proclaiming that Allah is the True Reality, or “Al-Haqq,” And He alone shall remain where all else shall pass away.  Then, is everything, including light, matter, and antimatter is illusion?  Since everything is changing from matter to light, then to antimatter and vice versa, and the only connection between all things that are passing away and Allah are the human souls. 

 

Human souls are the only preserved things in Allah’s existence.  They are who would be allowed to reemerge or reborn as a (verse 50:15) “second creation” on the Resurrection Day to be judged on Judgment Day.  Therefore, mixing falsehood and the True Reality of Allah through magic similar to the ancient Egyptians who did encounter the True Reality proof in Moses staff’.  It is mainly that humans manufacture ideas and thoughts, which their goal is to distinguish Allah’s light as described through the inner yellow seventh sky region and force human souls to become lost among the passing away things.  Belief and disbelief in the invisible True Reality, Allah whose only His signs could be seen are compared to physical passing away substances all of which made of illusions and must pass away, including light, matter, and antimatter of the universe.

 

Those humans who claim to know the Creator are completely misleading towards falsehood.  For those ignorant people would actually claim that a drop of water that fell into the ocean could claim to know the ocean.  The Dhat of Allah in Islamic theology is clearly stated in the Holy Qur’an as unique who has no like, for Allah’s immanence and Transcendence makes Him beyond definitions.  The Holy Qur’an refers to Allah as the “Most Merciful” but it does not mean he has a quality of mercy that corresponds to similar terms with humans, if He is described and referred to in human terms humans do reduce Him to a created being not the Creator.  Therefore, the attributes referred to in the Holy Qur’an to Allah could not be interpreted or understood and looked upon similar to human terms.  Why?  Speaking in Arabic of “Divine Personality” would not actually mean generating a personality, because it implies “Tashkhes” or drawing a picture or forming a status figure of Allah, which is not only forbidden in Islam but also in all other two monotheistic religions of Christianity and Judaism. 

 

However, not only mystics of all religions fall into such a trap in claiming to acquire heavenly knowledge that they could not explain in physical terms, but also few scientists claimed to acquire mysterious powers similar to the magicians of ancient Egypt.  Those too must come down from their high delusional flight to acknowledge the Oneness of the Creator similar to ancient Egypt magicians.  For example, Einstein claimed ****

 

The simplest atom known is the hydrogen atom.  It is consists of a tiny nucleus with a single electron orbiting it.  The Problem for Bohr was, if the atom as big as it appeared to be, then how could the electron keep a stable orbit?  The planetary model predicts for any planet that gives up energy continuously, it would spiral into the sun; then the electron would crash into the nucleus every time it emitted its light energy.  Therefore, the whole atom would be suddenly deflated and all matter would undergo a rapid collapse.  Gravity would crush the atoms together and matter would be empty and lifeless for light would be gone.  Well, if the electron could not emit continuous energy, then how does it radiate any light? Light emission consumes energy.

 

Bohr postulated when an electron jumped discontinuously from one orbit to another and thought that Blank’s h factor, which could be composed of other units, must be involved in the process in dealing with such discontinuity movement.  Blank’s h is a unit of energy per time, or a unit of momentum per distance, which physicists call action.  Bohr viewed it as a unit of angular momentum, and its observation had a direct bearing on his atomic model.  The angular momentum is the product of ordinary or linear momentum and the radius or distance from the object to the referenced point.  The electron, traveling around the nucleus, seemed to be held by a tether of electrical attraction between the electron and the nucleus.  Then, Bohr thought that could Blank’s constant h be used as a unit of the electron’s angular momentum?  He calculated the orbit size required for an electron for one unit of angular momentum, h, which proved to be the correct size.  The, he tried a new orbit of units of two h to find it is four times larger than the original orbit, and for three unit h, to find it nine times larger than the original orbit. 

 

By restricting the electron to the special or quantized orbits, Bohr successfully predicted the correct scale and size of the atom.  But why the electron was not radiating energy while it is whirling in its orbit, or why the atom is stable?  Bohr asserted that the rule for a quantized electron whirling around the nucleus could only exist with whole unit of h’s, such as 1h, 2h, 3h, etc., but not with a fraction of it.  By using Blank’s energy E = h * f formula, he predicted the frequencies of the light observed whenever an electron made an orbital jump.  In 1880, Johann Balmer observed that the light coming out of a hydrogen gas did not exhibit a continuous spread of colors, for missing colors were found when it passed through a prism.  The produced spectra appeared as a horizontal strip containing several vertical lines, like teeth in a comb, but few are missing. 

 

Bohr thought from Balmer’s experiment that he could also calculate the radiated energy of the electron when it changed orbits.  Since there were certain orbits for the electron, then there had to be certain frequencies for the light, which must depend on the difference in energies of the electron involved in the quantum jump.  The picture Bohr could draw was that of a quantum jump, a leap from one place to another, which negates continuity in classical mechanics.  The time to abandon Newton second law had not arrived, after all Bohr’s idea of fixed orbits is planted in Newton’s cosmology of planet rotation around the sun.  According to Newton, a force is acting on the electron pulling it into a circular orbit, which changes the electron orbit.  And there must be electron acceleration because it is a charged particle, which must give out energy when it accelerates.  Bohr noticed that his rule of allowed and forbidden jump depends upon on the size of the quantum jump.  For example, a jump from the second to the first orbit, the size change is tiny, but a sizable change on the scale of the first orbital diameter.  He calculated the radiation from a change in orbits to find the results are in agreement with classical predicted results.  In other words, the smaller the relative result change is found to be the more continuous and classical seemed to be, which is called the Principle of Correspondence.  The universe appears to be continuous even though it is fundamentally discontinuous which is based on quantum jumping.  To Bohr the rule became a question of the relative scale, where discontinuity is the fundamental truth.  The believers of continuity found themselves that had to give up the idea of particles of matter in their attempt to rid themselves of quantum jumps.

 

Physicists found that some lines of the spectra are missing in atoms that contain more than one electron.  They explained the missing lines by either the transition between quantum states is weak or the theory of quantum states has something wrong.  By invoking modern atomic physics and molecular spectroscopy to conclude that something about the state vectors would make the transition a forbidden one.  In 1925, Wolfgang Pauli proposed his exclusion principle to explain the missing lines in the atomic helium spectra.  The principle stated that no two electrons posses the same set values of the four quantum numbers, and an atom orbital could only hold a maximum of two paired electrons, one spins upward and the other downward.

 

Physicists found that at the heart of all quantum particles lies indistinguishability, where fermions differ from bosons in their many particle state vectors.  Indistinguishability is a property that is intrinsically linked to the wave-particle in quantum mechanics as seen in electrons.  Each electron has a three-dimensional shape of delocalized quantities.  Such indistinguishability is explained in terms of state vectors.  Physicists left unanswered the question, ‘where does the collapse of the wave function take place?’  John Bell wrote of the ‘shifty split’ between measured and perceived objects.  To avoid this ‘shifty split’ physicists introduced an element, which assures the wave function collapse at the early stage of amplification. At that instant of wave function collapse measurements become invalid.  Many theories were proposed but the property itself has not yet been detected, that is which might explain how photons vary from existence possibilities into actualities at the moment of the collapse.  Why?  Humans measuring devices are large objects like a photomultiplier and do not have the ability to measure the collapse of the wave functions at their early process stages. 

 

How does the wave function collapse arise?  Well, unless the collapse occurred during the measurement process, observers would be stuck with infinite regress with animate objects suspended in superposition states of life and death.  Von Neumann provided an explanation as follows, ‘the wave function collapses when it interacts with conscious observer.’  He argued that, ‘photons scattered from the pointer and its scale enter the observer’s eye, and interacts with his retina in a quantum process.  The signal passes or does not pass through the observer’s optic nerve, which in principle is represented in terms of a linear superposition.  Then, only when the signal enters the observer’s brain, where it encounters a system that is not subjected to the quantum theory laws, the human conscious interpret the wave function collapse.

 

If things that human sense and know their governing laws do not reflect true reality, and if other things that humans could not sense and might not know their governing laws do exist as real, then what is real and what is imaginary?  How could humans decide that this thing is real and that is imaginary?  Assuming humans investigate external stimuli only and do not consider internal mental stimuli that might emerge from dream-like thoughts.

 

With this explanation, humans reached the basic dualism of matter and conscious mind.  In 1961 Eugene Wagner used in his experiment a friend as the conscious mind.  He argued that the wave function collapsed when it interacts with the first conscious mind it encounters, which appears to violate the physical laws of inanimate objects.  It is in the observer’s conscious where the influence of external matter had effect over the conscious mind is balanced by the influence of mind interpretations over matter.  Interpretations of such appeared or perceived reality might lead to physical effects.  The problem becomes, ‘it is not only what the human conscious had observed but it is what the conscious mind interpreted and perceived to have observed would influence their actions and reactions.

 

Assume humans are able to differentiate between external and internal dream like stimuli and observers eliminate hallucination and internal imaginative dreams.  Strange mixture of effects would exist between human conscious and observed perceived matter provides a fogy cloud in differentiating between reality and imagination.  Question presents itself, ‘Does the externally observed physical shape represent actual reality or a figment of the human imagination?’  The human consciousness interpretation related to the observed physical shaped object, which might appear ‘out of thin air,’ such as mirages and flying saucers.  Such types of phenomena not only could be explained physically with the use of mathematical equations and their solutions would allow humans to explain them and their effects.  Therefore, there are spectra lines humans could not observe, but they are part of the True Reality of the universe, and there are imaginary objects that could be seen but they reflect human imaginative interpretations.  Human perception of the reality could not be differentiated

 

On the one hand, ample examples exist where things are real but they could not be seen or detected by human senses; such as: the earth rotation around itself, and lately the utilization of the unseen light to carry multimedia files through fiber optic lines, and other usages.  Yet humans believe of their existence and utilize them to their benefits.  Humans have no ability to sense, measure, and detect, or understand the governing laws of unseen stuff like energy colored quanta similar to the colors appear in a rainbow.   On the other hand, humans sense and at times explain and understand the governing laws of imaginary things physically and mathematically like mirage, and three dimensional flying saucers.

 

Before introducing difficult physical subjects related to measurements and detections of quantum mechanics and string theories with their contradiction with Einstein’s concept of mixing space and time, it is important to explain physically and mathematically how and why do rainbows, mirages, and flying saucers appear from thin air?

 

Therefore, mathematical equations and their solutions alone cannot prove True Reality; physical observations alone cannot prove True Reality; and human sensual detection of physical shapes and other things, especially things that fall out of thin air and register as false sensual substances.  The three major tracks of analysis related to human perception of True Reality help differentiate between True Reality and imagination, but they all fail in relation to the missing lines of the spectra of atoms.  Why? Light is composed out of two opposite and conjugate substances; they are matter and antimatter, each substance wave function had spun in the opposite direction of the other.  Then, when similar and opposite wave functions of matter and antimatter meet their two wave functions appears to annihilate each other and emitting light while passing through each other; when they completely pass each other they emerge in the same of different form but directed with an angle. 

 

The light emitted could be photon or other wave-particle and usually takes place in a finite length of time.  How does the emitted light, photon or other wave-particle distribute its physical quanta sub-particles in the surrounding space?  Does time influence quanta distribution?  It is possible that humans have the ability to influence in laboratory setting the interaction between matter and antimatter at a microscopic level.  But could the action between matter and antimatter be influenced at a cosmological macroscopic level?

 

There are three tracks of analysis that must be perused in studying and understanding the True Reality in relation to human perception of reality.  The first is based on scientific measurements, and the second must be based on mathematical solutions of formulated equations because language fail to explain ……  .  However, the third must be based on the true and real revelations that were not manipulated and changed by humans through out the centuries, that is the Holy Qur’an alone.

 

Jonathan Powers, Philosophy of Physics, Nethuen, NY, 1982

 

 

Energy is the fuel of life

 

What is energy? No one has seen or ever handled energy.  It is defined by mathematical equations expressing changes in matter and is quantitatively determined mathematically.    No matter what intervening machinery is used to transform the energy, it appears after the work is done in the form of heat.   The heat amount is constant no matter the path of change had been utilized. Since matter is an interchangeable form of energy, neither one separately, but it is their sum is rigorously constant.  Conclusive metamorphoses between matter and energy occur, but under what conditions?  Humans succeeded in splitting the atom nucleus and convert it into energy, but they fail to generate, form or manufacture a single quark, open or closed.  The first law of thermodynamics, conservation of energy holds for all systems, including living systems.  A gram of sugar is burned (a chemical reaction with oxygen) into carbon dioxide, water and emits 3,800 calories, but if it is split to lactic acid it produces only 380 calories.  The heat amount liberated by burning sugar directly is the same amount when it is burned in a human body.  When an object emits heat, its energy becomes less.

 

Degradation of energy is dealt with in the second law of thermodynamics, any form of energy can be converted completely into heat, but heat cannot be converted into other forms except under special conditions.  It exists only when a difference between two objects, then heat passes through the stage of chemical, electromagnetic, or other form of energy, but once the two bodies reach the same temperature, no further work can be obtained.  The second law of thermodynamics essence is that entropy of any mass object increases; then within human experience and visualization, entropy always goes forward or increases.  On the other hand, Maxwell keen observation provided the argument,

  

 

Suppose Maxwell’s infinitesimal demon was utilized to close a frictionless shutter every time a molecule approaches from the left rebounding from the shutter, but it opens every time a molecule approaches from the right allowing it to pass.  Then, without any work done, the energy has increased.  Similarly, a living cell acts as if resides in it Maxwell’s demon, the membrane of cells allows certain molecules and ions to pass but not others.  Does living things transcend the second law of thermodynamics?  The probabilities are strong especially when one is dealing with a zygote or multiple cells that would form a fetus in the womb, which is not our concern for the time being, for a zygote membrane acts similar to any other singular cell in searching for food and a location to connect to the mother’s blood in becoming a leach like. 

 

However, living cells sort out ions, build structure, and increase complexity and they achieve this by acquiring free energy obtained from other sources.  The whole web of life is a struggle for acquiring free energy.  One must be able to differentiate between light and heat.  The sunlight radiant energy is entangled by the chlorophyll in plant cells, which together reduce the carbon into compounds that serve as fuel of life.  Similar to bacteria, chlorophyll obtain energy from sunlight because they have colored enzymes, for light energy is caught only when the light is absorbed.  If all sunlight wavelengths reaching the chlorophyll are absorbed, it would be black; if all were reflected, it would be colorless or whitish; however, if specific wavelengths were absorbed and others passed on, then the emerging light would be white minus red, green or blue as the case might be.  One can Experiment by letting sunlight rays pass, say through a prism, and allowing the spectrum to shine on an algae filament under a microscope, the red light is absorbed and photosynthesis occurs in the cell at the location of the red light; as a product, oxygen gas is released into the surrounding water. Then, chlorophyll reduces carbon monoxide and water into sugar, which is a necessary step in the manufacturing of other carbohydrates, fats, proteins, which the plants make for their protoplasm and ours.  A potato plant that hoards red light energy packets turns them into starch replenishing the fuel that drives all living processes.  

 

When a female egg continues slowly to burn up its stored fat and other contents until it stales and dies, but if it is pricked by a sperm cell it embarks upon a fascinating adventure of growth and division, leading through a labyrinthine chemical trail to another being, its enzymes must take.  Every cell as its enzymes must dictate its path, but the enzymes are affected by accelerators, adjuvant, and inhibitors; they could be changed from an inactive to an active condition and vice versa by ions, oxygen or other chemical means by being allowed access to or held restrained from their substrates using physical barriers.  How are enzymes formed?  The protein is built into them, which is fabricated within the protoplasm by progressive linking together with amino acids, which is allowed to enter through the surface of the cell.  The splitting of proteins is performed by enzymes.   

 

Therefore, energy packets could take the form of sustenance to be consumed by living cells, or they could be utilized for observations and measurements to acquire knowledge related to an object.

 

Before leaving thermodynamics, it is important to introduce the third law.  Sontag et. al. wrote, (p.580), “

 

 

 

 

Crystals:

 

Crystal axial character (pp.133-

Uniaxial crystals have one optic axis, a one direction along a light traveling with same velocity.  Crystals of the tetragonal and hexagonal are uniaxial.  Most colored uniaxial crystals show differential absorption of transmitted light related to vibration direction associated with ε and ω.  Absorption is defined as the difference in intensity of light in the two principal directions of vibration.  In uniaxial crystals there are two principal vibration directions.  Then, there are two principal associated colors. The recognition of color absorption depends upon the color intensity, which depends upon the thickness of the section. Minerals experimental data refer to section of 0.03 mm thickness unless noted otherwise.  Absorption requires the principal direction O, white and E, black for diachronic grains to be associated and identified with the principal indices of ε and ω in polarized light without crossed polars and the absorption formula is E > O. Assemblage observed where the grain do not change color on stage rotation without crossed polars have basal sections and their color must be O.  Crystals that have ε greater than ω have by definition a positive optic sign, and those of ε less than ω have negative. 

 

Fletcher defined the indicatrix of a uniaxial crystals by a geometrical figure based on indices of refraction.  The indicatrix is an ellipsoid of revolution see figure 7.1 (p.113). The axis of revolution has length 2ε and is the direction of vibration of the E, black ray at ε maximum. The ellipsoid diameter has length of 2ω and is the direction of vibration of the O, white ray.  Any vector from the origin to the ellipsoid surface has the magnitude of a refractive index. Light for which the crystal has that refractive index vibrates parallel to the vector and is propagated normal to the vector.  There is a circular section of radius ω; the direction normal to this circular section is the optic axis.  Because the velocities of the O, white, and E, black rays along the optic axis are equal, both rays are called ω.  Light propagated along the optic axis is not resolve into two unlike components; it is not plane polarized and vibrations normal to the optic axis is in all directions.

 

The orientation of optical or indictrix direction in a crystal must always be consistent with morphological crystal symmetry, since both are manifestations of the structural symmetry.  The optic axis of a uniaxial crystal, which is the rotational axis of the indicatrix ellipsoid, is the c crystallographic axis, which coincides with the E, black ray vibration direction for which ε is a limit.  Light propagates normal to the c axis, it has refractive index ε; but if it vibrates parallel to c, it has refractive index ω.  For negative crystals, the ellipsoid short axis is the axis of the rotation and it is oblate ellipsoid; but for positive crystals, the ellipsoid long axis is the axis rotation and it is prolate ellipsoid.  Larson and Berman stated (p.28) that tabulated minerals have 6.8% uniaxial positive and 13.8% uniaxial negative.

 

 

Biaxial crystal optics

They have two optic axes along which light propagates with the same velocity.  In every other wave propagation direction there exist two plane polarized components at right angles to each other and to the propagation direction; they have unequal velocities.  There are three principal indices of refraction, α alpha, β beta, and γ gamma.  Beta is the index associated with light propagated along the optic axis; it is analogous to ω of uniaxial crystals.  Humans consider that α, β, and γ are the least, intermediate and the greatest refraction indices of the crystal respectively.  The principal refractive indices α, β, and γ are associated with the directions X, Y, and Z respectively.

 

 

 

CRYSTALS: 

 

Richard E. Stoiber and Stearns A. Morse, Microscopic Identification of Crystals, Robert E. Krieger Publishing Company, Malabar, Fl., 1981

L. Fletcher, The Optical Indicatrix and the transmission of light in crystals, H. Frowde London, 1892.

E. S. Larson and H. Berman, The Microscopic determination of the non – opaque minerals, 2nd ed., U.S. Geol. Surv. Bull. 848, 1934

 

 

Wahlstrom defined in, Optical Crystallography, (pp. 205– 6) the following terms related to waves, “A light wave is a single pulse of energy and, in a linearly polarized wave, is a combination of forward motion and the simple–harmonic vibration of a light vector specified for a phase change of 0 to 360 degrees (0 to 2π radians).  A ray is the path followed by a wave or a succession of waves in traveling from one point to another in a medium.  A succession of waves moving along a ray constitutes a wave train.  The wave–front normal, or, more briefly, the wave normal, is perpendicular to the wave front, at the same time, according to the electromagnetic wave theory, perpendicular to the direction of vibration of the light vectors in the light waves forming a wave front. The ray velocity is the velocity of movement of a light wave along a ray, as opposed to the velocity of movement of a wave front in the direction of the wave normal.  The confusing and the widespread use of the term wave to describe the sum of all energy advancing in a wave front is specifically avoided in the following treatment.  Advance of a wave front is regarded as a group phenomenon involving the in–phase advance of the total energy in a family of electromagnetic waves.” 

 

He wrote (p.207), “If the velocity of the component vibrating parallel to the c axis is less than the velocity of the component vibrating perpendicular to the c axis, the crystal is said to exhibit positive birefringence and is described as optically positive.  The reverse situation produces negative birefringence.”  He added, “In crystals with positive birefringence the electric vector parallel to the c axis vibrates parallel to linear or planer elements of crystal structure, and in crystals with negative birefringence the electric vector parallel to the c axis is vibrating transversely to linear elements and has a velocity of transmission greater than than that for light waves vibrating parallel to linear or planar elements.

 

For each color of light, uniaxial crystals have two principal indices of refraction.  Light of particular color (frequency) traveling in any direction except the direction of the optic axis consistes of two sets of waves with different velocities but the same frequency.  The change of refractive index with the direction of light propagation or vibration may be visualized by use of a uniaxial indicatrix, a three–dimensional geometric figure showing the vibration of the indices of refraction of a crystal for monochromatic light waves in their directions of vibration.  Each radius vector represents a vibration direction whose length measures the index of refraction of the crystal for waves vibrating parallel to the direction.”

 

Wahlstrom (p.220–221) wrote that wave surfaces “are defined in the same manner that ray – velocity surfaces are defined.” He added, “A difficult concept to grasp is the fact that, in most directions in uniaxial (and biaxial) crystals, the direction of propagation of light waves along extraordinary ray does not coincide with the direction of the associated wave normal.” He continued, “Determination of wave front velocities in the direction of the wave normals for all possible rays yields an ovaloid outside of the ray–velocity ellipse and, in three dimensions, an ovaloid of revolution whose axis coincides with the optic axis.  For the ordinary waves, similar constructions yield, in three dimensions, a sphere that coincides with the spherical ray–velocity surface for the ordinary waves.  The ovaloid of revolution and the sphere showing the wave – front velocities in all directions in three dimensions are designed either as wave–normal–velocity surfaces or, wave–front–normal–velocity–surfaces.”

 

He added, “By using Huygenian constructions it is possible to trace the paths pf refracted polarized light waves and wave fronts through a crystal for light of any angle of incidence.  Huygenian constructions are usually drawn in planes of optical symmetry, because in these planes the paths followed the light may be presented graphically in two dimensions.  Huygenian constructions not in a plane of symmetry require three–dimensional drawings that are difficult to construct.”  He assumed that “the ray–velocity surfaces are derived from a uniaxial positive indicatrix in which nO =1.5, nE = 2.0.  the drawings are made in a principal section, and the optic axis is parallel to the surface of a crystal plate on which the light is incident.  In figure 9-14A (p.222) normally incident nonpolarized light, upon entering the crystal, is resolved into two components vibrating mutually perpendicular planes.  One component, the E component contains waves vibrating in the principal section that pass through the crystal with a velocity proportional to 1/nE = 1/2.0.  The other component, the O component, contains waves vibrating in a plane perpendicular to the plane of the drawing and having a velocity proportional to 1/nO = 1/1.5.   The rays and the normals coincide, and the ray velocities are the same as the wave–normal velocities.”

   

Ernest E. Wahlstrom, Optical Crystallography, fifth ed., John Wiley and Sons, NY,

1979

 

Hindash