Category Archives: Physics

The Whirlpool Model

ReferenceA Logical Approach to Theoretical Physics

I recently answered the following question on Quora: How are protons and neutrons arranged within the nucleus?

Protons and neutrons differ primarily because of the presence of charge on the proton. Charge exists because of the high density gradient at the interface between the nuclear and electronic regions.

In my opinion, the nucleus is a continuum of dense substance, whereas the electronic region is a continuum of much lesser density. These two regions exist in equilibrium with each other. Charge is the force that exist at the interface because of the large density difference between these two regions.

Protons and neutron are “energy particles”. They are not segregated as particles within the nucleus. From Particle, Continuum and Atom:

The “energy particle” is defined by an interaction. It refers to the amount of the substance involved in an interaction. It is not the amount existing in space by itself. A quantum of light is the amount of light involved in an interaction within the detector. A quantum of light is different for different interactions. This is similar to a chemical agent reacting in different amounts in different chemical reactions.

An ENERGY PARTICLE is the amount of substance participating in an interaction.

A light quantum is created out of a continuum of light. Such energy particle is always discrete because the interactions can be counted. This is what happens in the photoelectric phenomenon. Discrete interactions do not necessarily imply that light is discrete and indivisible in space. Light is a continuum and infinitely divisible in space in space though its interactions are discrete and “indivisible”.

A quantum is an energy particle. It has a specific value determined from how it interacts, but that value is part of a continuum.

A QUANTUM is a discrete amount drawn from a continuum by an interaction at the atomic level.

Protons and neutrons are “energy particles” They are quanta. They are made up of discrete amount drawn from the nuclear continuum for the interactions that detects them. Within the nuclear region there is no difference between the proton and neutron as they are part of a continuum.

The charge that differentiates proton simply represent a density gradient that appears in the interaction, which detects the proton.

This is a novel view, but it comes about naturally from A Logical Approach to Theoretical Physics.

Overall, the atom is a whirlpool of fast-moving continua of substance that is gradually condensing toward the center. It is also slowing down as it approaches the center. The nucleus is the densest part of this whirlpool at the center of the atom. This whirlpool is flat much like the whirlpool of the galaxy.

This is the WHIRLPOOL MODEL of the atom.

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The Lorentz Transformation

ReferenceA Logical Approach to Theoretical Physics

From Wikipedia,

“Historically, the transformations were the result of attempts by Lorentz and others to explain how the speed of light was observed to be independent of the reference frame, and to understand the symmetries of the laws of electromagnetism.”

The null results from Michelson-Morley’s experiment in 1887 led to the belief that the speed of light is the same in all inertial frames. For example, light is observed to have the same speed, c = 3 x 108 meters/second, relative to the earth and also to the sun, even when earth is moving at a speed 3 x 104 meters/second relative to the sun.

But, Earth and Sun, together as a system on a larger scale, are moving at the same velocity with respect to light. The anomaly, therefore, is local and not universal. Logically, it means that space and time characteristics, which determine the speed of light, maintain a constant relationship on a universal basis, while their individual characteristics may vary locally.

We know that the space and time characteristics are intrinsic to substance. As summarized in The Universal Frame of Reference, space is tied to the extents of substance, and time is tied to the duration of substance. Therefore, space and time are tied to the density of substance. As density changes, the space-time characteristics change accordingly, but in a constant relationship.

Mathematically, this constant space-time relationship leads to the Lorentz transformation (see Special Relativity explained at Khan Academy).

Lorentz transformation, however, transforms space and time coordinates from one local frame to another, considering that the speed of light is the same in both frames of references. The mathematics provides the following relationships.

When c is infinite, βc reduces to v, β reduces to 0, and γ reduces to 1. Lorentz transformation reduces to Galilean transformation. This means that Galilean transformation is valid in the universal frame of reference, and our task is to scale the motion in the local frame of reference to motion in the universal frame of reference. This is done by β. The resulting change in γ is the correction factor that needs to be applied to the Galilean transformation.

If v = 3 x 104 m/s is the velocity of the Earth relative to the Sun, we are scaling it down by the speed of light, c = 3 x 108 m/s in the universal frame of reference by β = v/c = 10-4. For this value of β, we may calculate γ = 1 + 5 x 10-9.

This means that a local velocity of v = 3 x 104 m/s provides a small correction factor of 5 x 10-9 to the Galilean transformation.

It is to be understood that a velocity differential in free space equates to a density differential (see The Universal Frame of Reference). Therefore, we may interpret the above numbers to mean that an increase in velocity of v = 3 x 104 m/s may equate to decrease in density by a factor of 5 x 10-9.

It should be noted that Lorentz transformation provides a very general correction for the material domain, and it may not account for finer details, such as, the Earth’s velocity is not linear relative to the Sun. In the material domain v is much smaller than c because the inertia (density), in general, is very high.

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Einstein’s Paper on Light Quanta

ReferenceA Logical Approach to Theoretical Physics

In his very first paper published in 1905 Einstein establishes the concept of “energy quantum” or “light quantum”. The energy of light quantum (photon) is proportional to frequency that becomes more pronounced as one moves up the electromagnetic spectrum. Here is a summary of Einstein’s 1905 paper on Light Quantum followed by some comments.

SECTION 0: Introduction

Einstein says,

The energy of a ponderable body cannot be split into arbitrarily many, arbitrarily small parts, while the energy of a light ray, emitted by a point source of light is according to Maxwell’s theory (or in general according to any wave theory) of light distributed continuously over an ever increasing volume.

In other words, Einstein observes that atoms are not infinitely divisible, but the electromagnetic radiation is treated as a continuum and infinitely divisible.

Einstein says,

“In fact, it seems to me that the observations on “black-body radiation”, photoluminescence, the production of cathode rays by ultraviolet light and other phenomena involving the emission or conversion of light can be better understood on the assumption that the energy of light is distributed discontinuously in space.”

In other words, Einstein proposes that the creation and conversion of light may not be continuous.

SECTION 1. On a Difficulty in the Theory of “Black-body Radiation’’

In this section Einstein sets up a thought experiment. He assumes electrons to be particles that are colliding like gas molecules. There are bound “resonator electrons” that emit and absorb electromagnetic waves with definite periods. The average kinetic energy of a resonator electron must equal the average kinetic energy corresponding to the translational motion of a gas molecule under dynamic equilibrium. Similarly, it should also equal the energy of interaction with radiation present in space.

Einstein says,

“This relation, which we found as the condition for dynamic equilibrium does not only lack agreement with experiment, but it also shows that in our picture there can be no question of a definite distribution of energy between aether and matter. The greater we choose the range of frequencies of the resonators, the greater becomes the radiation energy in space…”

This was famously known as the ultraviolet catastrophe.

SECTION 2. On Planck’s Determination of Elementary Quanta

In this section Einstein shows that “determination of elementary quanta given by Mr. Planck is, to a certain extent, independent of the theory of “black-body radiation” constructed by him.”

Using mathematics to back up his argument, Einstein concludes:

“The higher the energy density and the longer the wavelengths of radiation, the more usable is the theoretical basis used by us; for short wavelengths and low radiation densities, however, the basis fails completely.”

In other words, the radiation appears continuous per Maxwell’s theory at lower frequencies, but not at higher frequencies.

SECTION 3. On the Entropy of the Radiation

In this section Einstein presents Wien’s consideration that entropy of radiation may be determined completely from black body radiation law when the radiation energy is given for all frequencies.

SECTION 4. Limiting Law for the Entropy of Monochromatic Radiation for Low Radiation Density

In this section Einstein uses Wien’s approximation (valid for higher frequencies of black body radiation) to derive an equation for the entropy of radiation.

Einstein writes:

“This equation shows that the entropy of a monochromatic radiation of sufficiently small density varies with volume according to the same rules as the entropy of a perfect gas or of a dilute solution.”

Thus, Einstein proves that the energy distribution of radiation becomes particle-like at high frequencies. This is an ingenious way of arriving at this conclusion.

SECTION 5. Molecular-Theoretical Investigation of the Volume-dependence of the Entropy of Gases and Dilute Solutions

In this section Einstein shows that, when applied to a large number of discrete particles, the use of “statistical probability” is compatible with macroscopic laws of physics.

SECTION 6. Interpretation of the Expression for the Volume-dependence of the Entropy of Monochromatic Radiation according to Boltzmann’s Principle

In this section, Einstein uses mathematical arguments to conclude:

“Monochromatic radiation of low density behaves—as long as Wien’s radiation formula is valid—in a thermodynamic sense, as if it consisted of mutually independent energy quanta of magnitude Rßv/N.”

Each quantum is the energy of one interaction. Einstein mathematically determines the theoretical value of a quantum.

SECTION 7. On Stokes’ Rule

In this section Einstein uses the new idea of “energy quanta” to explain the Stokes’ Rule for photoluminescence and indicates new possibilities.

SECTION 8. On the Production of Cathode Rays by Illumination of Solids

In this section Einstein brilliantly verifies the calculated value of energy quanta from the experimental value obtained from the study of photoelectricity. Here we have the conclusive evidence that energy of light is made up of frequency (kinetic energy) and not amplitude (wave energy).

SECTION 9. On the Ionization of Gases by Ultraviolet Light

In this section Einstein tests his ideas to explain the existing experimental observations and further proves the viability of the idea of “energy quantum” or “light quantum”.

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Comments

Einstein’s concept of quantum is based on energy. From the phenomenon of photoelectricity, it can be seen that this energy is kinetic (based on frequency) and not that of a wave (based on amplitude). Light carries this energy with it. This means light is a fast-moving substance.

The kinetic energy depends on relative velocity between two things. Therefore, this energy is visible only when there is interaction between two things, such as, light and electron. Einstein is mathematically comparing this interaction to collisions among gas molecules in the kinetic theory of gases.

Therefore, quantum is tied to the energy of interaction. If there is no interaction, the energy, or the quantum, cannot be perceived. The very perception of quantum requires an interaction. Interactions are discrete. Therefore, quantum is discrete also, but only as energy of interaction. This is what Einstein is thinking about when he says, The energy of a ponderable body cannot be split into arbitrarily many, arbitrarily small parts…”

In the kinetic theory of gases, not only the interactions are discrete, but the interacting gas molecules are discrete also. The molecules are discrete because they have individual centers of mass. This is not the case with light because light has no centers of mass. Therefore, light “particles” cannot be distinguished from each other. Light forms a continuum in space even when its interactions are discrete.

Einstein disagreed with Maxwell treating energy of light as a continuous function across the spectrum; but he did agree with Maxwell for energy being continuous at the lower end of the spectrum. Maxwell treated light as a wave, which is not really the case. There is no stationary aether through which light is moving as a disturbance. Therefore, a continuous energy function at lower frequencies can only mean that energy interactions are so frequent that they appear continuous.

Thus, as the frequency reduces, light starts to act as a continuum in terms of energy interactions also. This can be used as an argument to support the observation that, fundamentally, light is infinitely divisible. As frequency increases, the energy interactions become increasingly differentiable.

Electrons also form a continuum in space similar to light, but their frequency is much higher. When light interacts with electrons in the photoelectric phenomenon, it is two continuums of very different frequencies interacting with each other, and not two particles. Any interaction shall only be in terms of partial resonance, and not as an impact between two billiard balls.

Much seems to be unknown about the nature of this interaction between light and electron.

The frequency of light may best be understood as the density of its continuum. The higher is the frequency, the greater is the density of light. There appears to be a high-density gradient from the electronic region to the nucleus within the atom. This is where the charge appears and the center of mass forms. This is an area of transition where radiation appears to be in equilibrium with matter.

Much seems to be unknown about this area of transition from electronic region to nucleus of atom.

In conclusion, let us look at the following assumption made by Einstein in this paper:

According to the assumption considered here, when a light ray starting from a point is propagated, the energy is not continuously distributed over an ever increasing volume, but it consists of a finite number of energy quanta, localized in space, which move without being divided and which can be absorbed or emitted only as a whole.

It appears that quanta are more particle-like only because the density of the continuum has increased.

From Faraday’s perspective, quanta can be represented by thicker lines of force, but those lines are still continuous.

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Einstein’s Relativity

ReferenceA Logical Approach to Theoretical Physics

The null results from Michelson-Morley’s experiment in 1887 initiated a line of research that eventually led to Einstein’s theory of Special Relativity. The expected difference between the speed of light in the direction of movement through the presumed aether, and the speed at right angles, was found not to exist. The special relativity then ruled out a stationary aether.

The difference between the universal motion of light and Earth shall be constant because the difference between their densities is constant. This explains the null result of Michelson-Morley’s experiment.

One may object to the above reasoning by saying, “The earth is orbiting the sun. Therefore, it is constantly accelerating in the radial direction towards the sun, but not in the tangential direction. So, there must be a slight difference in speed in the two directions.”

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Michael-Morley’s Experiment

We may calculate this accuracy required of Michael-Morley’s experiment as follows:

1.    From de Broglie’s relationship the frequency of Earth is about 8 x 1070. The frequency of visible light is about 8 x 1014. Therefore, the ratio of their frequency is of the order of 1056

2.     This means that earth is 1056 times as dense as light.

3.     Then the intrinsic speed of earth is 1056 times slower than the speed of light. Even if we take density to be proportional to the square of speed, the intrinsic speed of Earth shall still be 1028 times slower.

4.     Therefore, the intrinsic speed of earth is about (3 x 108 meters/sec) times (10-28), or of the order of 10-20 m/s.

5.     Then, under best of the scenarios, the Michelson-Morley’s experiment is required to detect a velocity difference of the order of 10-20 m/s.

Michelson-Morley’s experiment was unable to detect the difference in speed of the order of 10-20 m/s. It, therefore, gave a null result. According to Wikipedia, modern experiments indicate that the two-way speed of light is isotropic (the same in every direction) to within 6 nanometres per second.

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The Speed of Light

The null results from Michelson-Morley’s experiment led to the formulation of the Lorentz transformation. Einstein derived the same formulation from the principles of relativity. These principles required that the speed of light be the same in all inertial frames of reference.

From Wikipedia,

In 1905 Einstein postulated from the outset that the speed of light in vacuum, measured by a non-accelerating observer, is independent of the motion of the source or observer. Using this and the principle of relativity as a basis he derived the special theory of relativity, in which the speed of light in vacuum c featured as a fundamental constant, also appearing in contexts unrelated to light. This made the concept of the stationary aether (to which Lorentz and Poincaré still adhered) useless and revolutionized the concepts of space and time.

The speed of light provides the basis of universal motion just like Newton’s fixed stars. The fixed stars may be approximated as infinite density and zero motion; whereas, light may be approximated as zero density and infinite motion. Both work as the basis for universal motion because the scale of universal motion is inverse of the scale of density (see The Universal Frame of Reference).

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The Theory of Relativity

The theory of relativity essentially converts local motion (relative to earth) to universal motion before doing math. That is why it gives more accurate results for Mercury’s orbit (see Newtonian Relativity). It does so through the use of Lorentz Transformation.

The Lorentz transformation reduces to Galilean transformation when ‘c’ is infinite. The speed of light is practically infinite compared to the motion in material domain. This means that Lorentz transformation is essentially “Galilean transformation with a correction factor for using local motion”.  The Newton’s laws of motion remain completely valid because they were originally designed for the universal frame of reference.

Lorentz transformation looks at the characteristics of space and time from the viewpoint of the invariant speed of light. Space and time actually represent the “extents” and “duration” of the substance respectively. Thus, space-time relates to the intrinsic properties (density and intrinsic motion) of substance.

The theory of relativity is applying the universal frame of reference in looking at the density and intrinsic motion of substance in the material domain.

We shall be looking at the mathematics of Lorentz transformation in the next chapter.

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Newtonian Relativity

ReferenceA Logical Approach to Theoretical Physics

Newtonian relativity is an expansion upon Galilean relativity, which states that the laws of motion are the same in all inertial frames. Galileo Galilei first described this principle in 1632 using the example of a ship traveling at constant velocity, without rocking, on a smooth sea; any observer doing experiments below the deck would not be able to tell whether the ship was moving or stationary.

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Inertial Frame of Reference

Newton considered the background of stars, which was at absolute rest, as the basis of all motion. According to Newton, all frames of reference, that are neither rotating nor accelerating, are in a state of constant, rectilinear motion with respect to one another. In other words, the first law of motion applies equally to these frames. Such a frame is called inertial frame of reference. Measurements in one inertial frame can be converted to measurements in another by a simple Galilean transformation.

In an inertial frame of reference, a body does not accelerate unless force is applied to it. In the absence of force, the body either stays at rest or moves at a constant speed in a straight line. Conceptually, the physics of a system in an inertial frame have no causes external to the system.

The inertial frame of reference operates from the perspective of MATERIAL-VOID duality. There is only matter that is homogeneous and isotropic throughout. The matter moves in the void with its space. The is no free space (see Matter, Void and Space).

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Newton’s Assumptions

Newton assumes that matter can move at different uniform velocities independent of density. This assumption is valid for the material region since the velocities are so small that their variation has negligible effect on density.

Newton also assumes that the Laws of Motion (and the Galilean transformation) apply to objects on Earth for motions relative to the Earth. This assumption is valid because Earth adds the same motion to these objects relative to the fixed stars.

Newton also assumes that the Laws of Motion (and the Galilean transformation) apply to the motion of planets of the solar system, when Earth, or the Sun, is used as the basis of motion (instead of the fixed stars). This assumption is generally valid as long as the variations in densities are negligible (see The Universal Frame of Reference).

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Mercury’s Orbit

Error occurs in calculating the precession of the perihelion of Mercury’s orbit because the variation in the densities involved is considerable. Mercury is 12 times as dense as the Sun, and 4 times as dense as the Earth. Therefore, neither Earth nor the Sun can be used as the basis of motion in lieu of the fixed stars.

Einstein resolved this problem through his theory of special relativity (SR), by using the speed of light as the basis of motion. This basis is just as workable as the basis of fixed stars because the speed of light is an intrinsic motion relative to fixed stars (see The Universal Frame of Reference).

Einstein says in The Evolution of Physics:

We really have no choice. We tried to save the Galilean relativity principle by assuming that systems carry the ether along in their motion, but this led to a contradiction with experiment. The only way out is to abandon the Galilean relativity principle and try out the assumption that all bodies move through the calm ether-sea.

The phrase “systems carry the ether along in their motion” seems to refer to the inertial frame operating from the perspective of MATERIAL-VOID duality (see above). Einstein seems to think that the problem is with the Galilean relativity principle.

The truth is that the problem arises because Earth and Sun are being used as the basis of motion instead of the fixed stars.

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Local and Universal Motion

Newton’s Laws of Motion, and the Galilean transformation, apply to motion relative to fixed stars. The fixed stars are assumed to have an intrinsic motion of zero. The intrinsic motion is a characteristic that is inherent to the substance and it does not depend on anything outside of the moving body. We refer to intrinsic motion as universal motion because it is the same throughout the universe like other intrinsic properties, such as, mass.

Therefore, the fixed stars provide the zero of a scale, relative to which we can measure intrinsic or universal motion.

In contrast to universal motion we have local motion, which is measured relative to a local body, such as, the Earth or the Sun. Working with local motion is like working with unlike quantities that require conversion to like quantities before adding and subtracting. Therefore, local motion must be converted to universal motion before Galilean transformation can be applied, especially if the densities of the moving bodies are different.

Current physics uses the terms relative and absolute motion. This is confusing because relative motion exists on the absolute scale also. By absolute motion we really mean intrinsic, or universal motion.

Therefore, the terms local and universal motion are more useful than the terms relative and absolute motion.

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