Category Archives: Physics Book

Einstein’s Theory of Quantum

Qunatum Mechanics

Reference: Disturbance Theory

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The Fundamentals

In 1900 when Planck was trying to find a relationship between the intensity of the electromagnetic radiation emitted by a black body and the frequency of the radiation, he could not come up with a theory using the classical approach that explained the experimentally observed black-body spectrum. In desperation he took a statistical approach, making an arbitrary postulate that energy of the emitted radiation is proportional to its frequency. This provided a curve that fitted the experimental data. [See Black-body radiation (Notes)]. Since frequency has a discrete nature, it meant that energy was discontinuous for radiation. This went against the classical notion of Maxwell’s theory that electromagnetic energy is a continuous function in space. Planck looked at his proportionality postulate as a mathematical convenience. He did not believe in the quantum interpretation of his postulate.

About this time Einstein was investigating the factors underlying the atomic phenomena. He was impressed by the success of statistical mechanics in this area, especially with kinetic theory of gases. He decided to apply statistical approach to the atomic theory to derive other material properties. Einstein estimated the accuracy of his assumptions by using them to calculate the Avogadro’s number. He thus verified his theoretical approach to the determination of viscosity (molecular attraction) and distribution coefficient in liquids. This approach has since been found very useful by molecular physicists and chemists.

Einstein was thus testing his assumptions as they applied to the yet theoretical domain of atoms and molecules through the calculation of Avogadro’s number. He then analyzed the Brownian motion of microscopic particles suspended in liquid, which appeared to be “self-induced”. He developed an original statistical approach to determine the relationship between the mean square fluctuation of suspended particles and the distribution coefficient of liquid. Once again, Einstein confirmed his assumptions by calculating the Avogadro’s number. This time his work was immediately verified experimentally. This helped establish the physical reality of atoms and molecules for scientists who were very skeptical before.

Simultaneously, Einstein looked into the distribution of energy density in the blackbody radiation. He analyzed the work of Planck and Wien and showed mathematically that the energy density of radiation, which appeared to be continuous at lower frequencies, became particle-like at higher frequencies. The postulate of Maxwell’s theory that the energy of radiation was a continuous function in space was valid at lower frequencies only. At higher frequencies the behavior of energy density of radiation could be compared to the results from kinetic theory of gases. Einstein thus verified Planck’s postulate that energy of radiation was proportional to its frequency. But Einstein then did something more. He proposed the idea of “light quanta” based on Planck’s postulate and used it to explain the photoelectric effect. He proposed an energy equation for the photoelectric effect that could determine the Planck’s constant experimentally. (See Einstein’s Conception of Light Quanta).

Robert A. Millikan, who vehemently disagreed with the idea of “light quanta”, spent some ten years testing Einstein equation and he did the most exacting experiments. He found that “Einstein’s photoelectric equation · · · appears in every case to predict exactly the observed results.” This turned Planck’s theoretical idea of “energy quanta” into the physical reality of “light quanta”, which came to be known later as “photon”. Einstein also established equivalence between energy and matter that later gave rise to the harvesting of nuclear energy.

In 1905 Einstein published these researches in four different papers. He basically established a relationship between energy and matter. It showed that energy of electromagnetic radiation coagulated with increasing frequency. Thus light became particle-like at higher frequencies, and at the upper reaches of frequency spectrum the limiting condition appeared to be matter. This conclusion supported the idea of particles, such as electrons, in the Gamma range of the electromagnetic spectrum. Thus electromagnetic field was a more fundamental substance than matter. Einstein thus established the fundamentals of the quantum theory.

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The Theory of Relativity

It was the increasing frequency that coagulated energy into matter. Therefore, Einstein’s fifth paper in 1905 investigated the fundamentals of motion. The obvious questions were, “Is there an absolute rest point? What happens to electromagnetic radiation as frequency reduces to zero? What is the limiting condition then?”

In Newtonian Mechanics the absolute rest point was assumed to be the stars fixed in the firmament. Maxwell’s theory also declared the velocity of light to be absolute, and this was confirmed by most exacting experimental evidence. Material velocities did not seem to add or subtract to the velocity of light. When the velocity of light was taken to be an absolute constant, the Lorentz transformations showed that the very characteristics of space and time were affected.

Einstein observed that the simultaneity of time could not be maintained when there were vast differences in the velocities, such as those between light and matter. In his view time could not be treated as absolute. He gave up on the idea of an absolute rest point and advance a theory of relativity based on the following postulates.

  1. All physical laws have the same form in all inertial frames (i.e. frames of references which move rectilinearly with a constant velocity with respect to each other);

  2. The velocity of light is same in all inertial frames.

With these postulates Einstein could derive the Lorentz transformations newly. He then showed that as the difference in velocities between two inertial frames increased, the characteristics of space and time changed in the form of “length contraction” and “time dilation”.

In other words, space and time become “diluted” with increase in relative velocity. 

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The Glitch

Einstein’s theory of relativity was extremely successful in explaining previously unexplained phenomena in the cosmological realm where light interacted with matter. But, when it came to the quantum realm, where light interacted with atomic structure, Einstein could not apply his theory of relativity successfully in spite of a lifelong of efforts. Einstein was very troubled by this failure.

Thus, a new subject of Quantum Mechanics came about that lacked a theoretical basis of physical explanations, and which was based entirely on mathematical relationships.

Theoretical physics seems to be stuck at the postulates that Einstein made to derive his theory of relativity. These postulates must be examined closely.

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Einstein’s 1905 Paper on Light Quanta

Light quanta

Reference: Disturbance Theory

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In his very first paper published in 1905 Einstein establishes the concept of “energy quanta” or “light quanta”. The manifestation of light quantum (photon) becomes more pronounced as the frequency of radiation increases.

Einstein’s original paper translated by D. TER HAAR

Einstein’s original paper with comments

In his paper Einstein analyzes the work done by Wien and Planck on Black Body radiation [see Black-body radiation (Notes)] and makes the following fundamental observations.

  1. According to Maxwell’s theory, the energy must be considered to be a continuous function in space for all purely electromagnetic phenomena, thus also for light.

  2. According to Kinetic Theory of gases, the energy in a volume can be written as a sum of energy of a finite number of particles localized in space, which move without being divided.

  3. The classical treatment of energy as a continuous function in space fails to predict the energy spectrum observed for the black body radiation.

  4. Max Planck’s postulate, “energy is proportional to the frequency of radiation” completely predicts the energy spectrum observed for the black body radiation.

  5. Planck’s equation provides the classical results for low frequencies, showing that radiation energy is a continuous function in space at low frequencies only.

  6. Using Wein’s law that matches experimental observations of black-body radiation at high frequencies, Einstein proves the energy behavior of radiation to be particle-like. From this arises Einstein’s proposal of “energy quanta” or “light quanta”.

  7. Use of “statistical probability” by Boltzmann is compatible with the principles of physics, and they can be used to estimate the magnitude of such energy quanta.

  8. The idea of energy quanta is compatible with the observations made in photoluminescence resulting in the Stoke’s Rule.

  9. The calculated magnitude of “energy quanta” is in line with the experimental data obtained from photoelectricity.

  10. In conclusion, the concept of energy quanta is also compatible with ionization of gases by ultraviolet light.

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The Quantum Phenomena

Quantum

Reference: Disturbance Theory

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The electromagnetic cycles are packed so closely in the nucleus of an atom that they may be considered to be “collapsed”. By “collapsed” we mean that that the electromagnetic cycles have become infinitesimal and they cannot be distinguished one from another. Therefore, these cycles form a continuum within the nucleus.  This condition is identified as “mass”.

The Newtonian mechanics is applicable within the material domain where it treats space and time as absolute and independent of each other.  This is possible because the continuum of mass provides constancy to space and time. Thus, arbitrary material units may be used to measure the distance between two points, and the time interval between two events.

Underlying the material domain is the domain of electromagnetic field. In this domain the frequencies are smaller and the variations in them are depicted as a spectrum (see The Spectrum of Substance ). The cycles of these frequencies may be distinguished from one other and counted. In short, we do not have a continuum in the electromagnetic domain; and no constancy of space and time. The theory of relativity identifies this condition as “length contraction” and “time dilation” from the perspective of the material domain.

The quantum phenomenon arises in the electromagnetic domain due to the absence of continuum.

In the electromagnetic domain, length and time are determined by counting the number of cycles between two points. Thus, each electromagnetic cycle is a quantum entity, and length and time do not exist within the cycle.

The fundamental quantum entity is the electromagnetic cycle.

Since both length and time are “counted” by the number of cycles, they are not independent of each other. They are related by the universal constant “c” known as the speed of light.

This quantum characteristic of the electromagnetic cycle may also explain the phenomenon of quantum entanglement. At very low frequencies, one electromagnetic cycle may extend to hundreds of miles when it is superimposed on the material domain. Any action within the span of this cycle will appear as simultaneous and instantaneous from the perspective of material domain.

Quantum entanglement will then be a phenomenon that will occur at very low frequencies. The lower is the frequency the farther will the effects be observed.

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Newton, Einstein & Quantum Mechanics

Newton-Einstein
Reference: Disturbance Theory

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The scientific method represents only part of what defines scientific thinking. It covers the research into the physical aspects of the universe only. When it comes to researching both physical and mental aspects of the universe, it requires mindfulness. The criterion of mindfulness is the establishment of continuity, harmony and consistency in what is observed. This is the establishment of objectivity. The scientific method is a “sub set” of mindfulness.

The scientific method limits objectivity to physical phenomena. Mindfulness, as defined above, extends objectivity to all phenomena. This difference is clearly accentuated in how Einstein and Descartes looked at space. Einstein’s approach characterizes the scientific method, whereas, Descartes approach characterizes mindfulness. Please see, The Problem of “Empty Space”.

Einstein tried to address the mental aspects through his “thought experiments” but it fell short of mindfulness. Einstein did make great strides with his thought experiments but he failed to connect the finite speed of light with light having a finite amount of inertia. His theory of relativity addresses material systems only using light as a reference point of “zero” inertia. This approach works for material systems but fails for the atomic region for which the inertia of light cannot be ignored. The lack of understanding of the concept of inertia is the basis of the lack of unification among Newton, Einstein and Quantum mechanics. Please see, The Problem of Inertia.

Here is my take on gravitation from the viewpoint of mindfulness. A force exists in a field because of a frequency gradient. Electromagnetic forces exist due to frequency gradients in the lower gamma region, which is the region of electrons. Nuclear forces exist due to frequency gradients in the upper gamma region, which is the region of neutrons and protons. Thus, the nature of force depends on the area of the spectrum where the frequency gradient occurs. Please see, The Spectrum of Substance.

Matter approximates the very high frequency at the upper end of the electromagnetic spectrum, and space approximates the very low frequency at the bottom. The frequency gradient stretches with distance in space, and this appears as the force of gravitation.

The above explanation follows from a classical reasoning. In this approach mass comes about due to the collapse of very high frequencies in the nucleus of the atom. This represents the gradient at the upper end of the electromagnetic spectrum.

The above reasoning also explains space as a very low frequency electromagnetic field that dilutes the overall frequency gradient, which expresses itself as gravitational force.

The Higgs Mechanism is a product of a mathematical approach that lacks an underlying physical theory.

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Absolute Rest, Inertia & Motion

2017-105-6-344-1-natural

Reference: Disturbance Theory

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In the Newtonian model, any change in motion of a body is innately resisted. This property is called INERTIA. As a result, the body is naturally endowed with a certain uniform motion. This uniform motion can be changed only when the body’s inertia is overcome by an external force. The state of absolute rest is postulated by Newton to be the reference frame of fixed stars. Motion then takes place in the “absolute space” as determined by fixed stars.

Maxwell’s equations describe electromagnetic theory and predict that electromagnetic waves will travel with the speed c = 1/√(μ0ε0) = 3 x 108 m/s. This speed is referenced from the “absolute space” of fixed stars as postulated by Newton. Any other observer moving with respect to this absolute space would find the speed of light to be different from c. Since light is an electromagnetic wave, it was felt by 19th century physicists that a medium must exist through which the light propagated. Thus it was postulated that the “aether” permeated all of absolute space.

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THE MICHELSON-MORLEY EXPERIMENT

If aether exists, then an observer on the earth moving through the aether should notice an “aether wind.” An apparatus with the sensitivity to measure the earth’s motion through the hypothesized aether was developed by Michelson in 1881, and refined by Michelson and Morley in 1887. The outcome of the experiment was that no motion through the ether was detected.

The postulate of a mechanical aether treats light to be the same substance as matter. But light has no mass and it does not follow the same laws of mechanics as matter does. Therefore, the idea of a mechanical aether was rejected by Einstein.

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THE POSTULATES OF EINSTEIN

Einstein’s guiding idea, which he called the Principle of Relativity, was that all nonaccelerating observers should be treated equally in all respects, even if they are moving (at constant velocity) relative to each other.   This principle can be formalized as follows:

Postulate 1:  The laws of physics are the same (invariant) for all inertial (nonaccelerating) observers.

Newton’s laws of motion are in accord with the Principle of Relativity, but Maxwell’s equations together with the Galilean transformations are in conflict with it. Einstein could see no reason for a basic difference between dynamical and electromagnetic laws.  Hence his

Postulate 2:   In vacuum the speed of light as measured by all inertial observers is c = 1/√(μ0ε0) = 3 x 108 m/s independent  of  the motion of  the source.

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ANALYSIS OF MICHELSON-MORLEY EXPERIMENT

As stated above light is not the same substance as matter. Light has no mass and, therefore, it does not follow the same laws of mechanics as matter does. The only thing common to both light and matter is the property of inertia.

Newton used fixed stars as the reference for absolute rest. This makes sense if we associate the concept of infinite inertia with fixed stars. It is only when a body has infinite innate resistance that it would become incapable of motion. This means that a lessening of innate resistance from an infinite value allows motion. The lesser is the inertia the greater is the motion. Light moves at a near infinite velocity, so its inertia must be close to zero. Since light has finite velocity, it must have a very small amount of inertia.

We may construct a scale of inertia on which zero inertia shall represent no innate resistance to motion; and infinite inertia shall mean total innate resistance to motion. On this scale light shall appear very near the bottom and matter shall appear very close to the top. In between we shall have the electromagnetic spectrum, the sub-atomic and atomic particles. There shall be a certain motion associated with each frequency and mass according to its inertia.

Michelson-Morley’s experiment failed to detect any aether wind because it was not comparing a characteristic common to both light and earth. It did not use the common background of fixed stars. The proper comparison can occur only in the form of absolute motion due to inertia. The inertia of light does not change with change in the direction of earth; and the inertia of earth is so large that any change in it with change in directions is imperceptible.

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ANALYSIS OF EINSTEIN’S POSTULATES

Einstein essentially replaces the concept of a mechanical aether by frames of references that have inertial characteristics of matter. Einstein justifies this in his paper, Relativity and the Problem of Space.

So far, our concept of space has been associated with the box. It turns out, however, that the storage possibilities that make up the box-space are independent of the thickness of the walls of the box. Cannot this thickness be reduced to zero, without the “space” being lost as a result? The naturalness of such a limiting process is obvious, and now there remains for our thought the space without the box, a self-evident thing, yet it appears to be so unreal if we forget the origin of this concept. One can understand that it was repugnant to Descartes to consider space as independent of material objects, a thing that might exist without matter.  (At the same time, this does not prevent him from treating space as a fundamental concept in his analytical geometry.) The drawing of attention to the vacuum in a mercury barometer has certainly disarmed the last of the Cartesians. But it is not to be denied that, even at this primitive stage, something unsatisfactory clings to the concept of space, or to space thought of as an independent real thing…
When a smaller box s is situated, relatively at rest, inside the hollow space of a larger box S, then the hollow space of s is a part of the hollow space of S, and the same “space”, which contains both of them, belongs to each of the boxes. When s is in motion with respect to S, however, the concept is less simple. One is then inclined to think that s encloses always the same space, but a variable part of the space S. It then becomes necessary to apportion to each box its particular space, not thought of as bounded, and to assume that these two spaces are in motion with respect to each other…
The concept of space as something existing objectively and independent of things belongs to pre-scientific thought, but not so the idea of the existence of an infinite number of spaces in motion relatively to each other.

Einstein’s Principle of Relativity treats all inertial frames of reference to be the same in all respects. In other words, it assumes that the inertial characteristics of all frames of reference are the same in comparison to the inertia of light.

This assumptions works only for the frames of reference restricted to the top of the scale of inertia.  Light is at the bottom of the scale of inertia, and the difference between the inertia at the top and bottom of the scale is so large that compared to it any local differences in the inertial characteristics of  frames at the top are negligible.

Einstein’s Principle of Relativity then cannot be applied to other parts of the scale of inertia that deals with the gamma range of electromagnetic spectrum, the sub-atomic and atomic particles, etc. because the their inertia is much closer to the inertia of light.

Newton’s laws of motion are in accord with the Principle of Relativity because they both apply only to the top of the scale of inertia. Maxwell’s equations are in conflict because they apply to the bottom of the scale of inertia.

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THE MATERIAL DOMAIN

Matter is stopped motion. Mass is a measure of how much stopped that motion is. Any motion in the material domain is due to force. A uniform motion is due to a balance of forces. A car moves at a uniform speed only when its engine is providing just enough force to overcome the resistance on the surface of earth.

The motion of earth, sun, stars and other planets is determined by their inertia. They do not move in an absolute vacuum. They move within a background of electromagnetic field.  Inertia represents the resistance that this field presents to the motion of material bodies. Thus there is a balance of forces here too that maintains their uniform speeds. The problem of gravitation lies therein.

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SUMMARY

It has not been possible to formulate physical theories for the area of Quantum mechanics because the relationship of inertia with motion has not been worked out fully, so that it could be applied throughout the scale of inertia.

The understanding of inertia remains the greatest challenge for the theoretical physics today.

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