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The World of Atom (Part VII)

ReferenceA Logical Approach to Theoretical Physics



Chapter 37: The “Thomson” Atom – J. J. Thomson (1856 – 1940)
An Arrangement of Corpuscles in the Atom. The electrons are assumed to be corpuscles because their charges are quantized.

Chapter 38: The Determination of Avogadro’s Number – Jean Perrin (1870 – 1942)
Brownian Motion and Molecular Reality. It suggests that every fluid is formed of elastic molecules, animated by a perpetual motion.

Chapter 39: The Alpha-Particle and Helium – Ernest Rutherford (1871 – 1937)
The Nature of the Alpha-Particle from Radioactive Substance. Direct proof that alpha-particles are indeed ionized helium atoms

Chapter 40: Atoms of Electricity – Robert Andrews Millikan (1868 – 1953)
The Atomic Nature of Electricity. Direct experimental measurements to show the constancy of charge and its value.


Unlike the material particles, the sub-atomic particles are fuzzy.


Multiverse and Universe

All reality is part of a single system. We call this system “the universe”. We tend to think that each person lives in his own universe. Even some scientists are talking about “multiverses”. But these “multiverses” have their basis in subjective mathematics. Science has always assumed that the universe is, as its name implies, a vast single system.

Mathematically, “multiverses” are discrete units. But, no matter how discrete the forms are on the surface, they are continuous at a fundamental level. Whole numbers, which appear to be discrete, are connected by fractions and irrational numbers on a continuous number line. Thus, it is very likely that there is continuity among discrete “multiverses” at some level. They all are part of an overall set of UNIVERSE.


MULTIVERSE (Subjective): There are many universes as viewed by different people.

UNIVERSE (Objective): The universe, as its name implies, is a vast single system.

Exercise: Something Missing

Reference: A Scientific Approach to Meditation

If something is missing, then recognize that it is missing. Do not imagine something in its place. If someone asks you a question and no answer come up in your mind, then do not feel obliged to make up an answer. Accept that you do not have an answer.

Meditation Exercise:

Something Missing


To discern the influence of something missing on the perception of what there is.


Complete Exercise: Assumptions.


In this exercise you simply become aware of something missing that could influence your observation. You may do this exercise while sipping coffee in a café or strolling along a river. You may even find a place where you can sit comfortably for a while without being disturbed. Then patiently observe the world go by.

Notice something that is puzzling, and about which full understanding is missing. Do not feel obliged to accept the explanations given; as the explanation could be wrong. For example, you see an empty lion’s cage in the zoo. Explanation given is that lion is out to lunch. The explanation is still more puzzling.

Carefully consider the broad context of the scene, and the purpose of the activity that you are observing. Narrow down to something specific that does not make sense. Examine it closely including your viewpoint with respect to it. Observe your mind imagining reasons to fill the uncomfortable gap in understanding. Notice the impulse to come up with an answer. If there is no answer, then acknowledge the fact. Do not make up an answer. Simply become aware that the right answer is missing and move on to the next observation.

Expand your span of attention and let the physical and mental perceptions pour in.

Continue this exercise for at least 20 minutes. You may repeat this exercise as many times as you wish.

End of Exercise:

When you can discern the influence of something missing on your perceptions, then this exercise is passed.

NOTE 1: At any point you may return to a previous exercise if you feel that you need to complete it.


The Dimension of “Mass”

ReferenceA Logical Approach to Theoretical Physics

A quantum was, at first, proposed as a mathematical concept by Max Planck that explained the distribution of the Black body radiation. It was a groundbreaking concept in the sense that it expressed energy as a function of frequency instead of amplitude of the waveform.

Einstein, in his groundbreaking paper on Light quanta, was able to show that the entropy of monochromatic radiation follows the same rules as the entropy of a perfect gas. Einstein thus showed that Planck’s postulate of energy quanta was more than a mathematical device. Light quanta had actual substantiality like a gas molecule.

A quantum of light has substantiality. That indicates mass of certain concentration.


Classical to the Quantum View

Newton’s corpuscular theory viewed light as having substance. The wave theory changed this view to light being energy of a wave traveling through a stationary aether. In wave theory the particles of medium oscillate about a stationary location and do not move with the wave. The energy of the wave is proportional to the square of the amplitude of the wave.

But this view encountered a major setback with Einstein’s theory of Light Quanta. Einstein showed that light approximated particle behavior, therefore, the medium of stationary aether was not required. The light energy was more like the kinetic energy of a particle—a function of mass and velocity. In the case of light, however, that “mass” was determined by a variable “frequency”.

The frequency of light represents a “mass concentration” that becomes denser as frequency increases.


Quanta as “Mass Particle”

A variable mass concentration based on frequency was a revolutionary concept, because matter has a constant mass concentration in terms of atoms. Einstein had difficulty in accepting the variability of mass concentration. He proposed a mass-energy equivalence as E = mc2 and declared quantum to be an “energy particle”. For Einstein, light did not have mass, because it did not have the same “mass concentration” as that in a material particle.

Einstein concludes in his 1905 paper on light quanta:

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.

But a particle can be treated as discrete in space only when it can be viewed as a point particle. A material particle can be viewed as a point particle because its mass can be treated as being concentrated at a center. That is called the center of mass. The uncertainty principle essentially says that a quantum particle does not have a center of mass because its location cannot be pinned down. In other words, as particles are continued to be divided, they lose their center of mass beyond a certain limit, and they merge into each other forming a fluid-like continuum.

Einstein’s conclusion about discreteness of quanta was based on the assumption of “constant concentration of mass” Einstein did not become aware of the inconsistency of his assumption because he conflated energy with mass. It is true that quantum can have discrete energy interactions, and that the concentration of mass could be so low that its significance can be appreciated in energy units only. But it is also true that there can be no concept of energy without an underlying concept of substance.

Unlike matter, quanta has variable “mass concentration”. It is a fluid-like continuum with rapid intrinsic motion.


Variable Mass Concentration

In matter, mass has a concentration that we find in a neutron or a proton. These particles have a certain volume, but they may be treated as point particles because of their center of mass property. This property arises because of their rigid structure.

Mass is 1840 times less concentrated in an electron that makes the size of the electron about 1840 times larger than the size of the proton. An electron is no longer rigid, it does not have the center of mass property and it flows like a fluid. An electron cannot be treated like a point particle.

Mass is still less concentrated in a photon, and its size may be considered much larger than an electron. It flows more like a fluid without center of mass. Richard Feynman, in his book QED: The Strange Theory of Light and Matter, shows calculations that treats light as such a fluid. Feynman, however, thinks of those calculated values as “probabilities” because he thought of photon as a “point particle”.

Matter, as it loses its rigidity of high concentration, becomes a field of much lesser mass concentration. The field does not have a center of mass. It is fluid with rapid motion. Field is not just a mathematical reality as considered by Maxwell and Einstein. This is an actual reality as visualized by Faraday with his lines of force. There is no limit to which the concentration of mass can be diluted as a field. The ultimate limit may be the gravitational field as “space”.

Current physics does not acknowledge the dimension of “mass” that exists at every location in space due to varying concentrations.


Einstein 1920: Simple Derivation of the Lorentz Transformation

Reference: Einstein’s 1920 Book

This paper presents Appendix 1 from the book RELATIVITY: THE SPECIAL AND GENERAL THEORY by A. EINSTEIN. The contents are from the original publication of this book by Henry Holt and Company, New York (1920).

The paragraphs of the original material (in black) are accompanied by brief comments (in color) based on the present understanding.  Feedback on these comments is appreciated.

The heading below is linked to the original materials.


Simple Derivation of the Lorentz Transformation

Please see Appendix 1 at the link above.



The math of Lorentz transformation is based on the consideration that the velocity of light is constant regardless of the velocity of the observer. This means that the space-time characteristics of the observer must change depending on his velocity, such that, from the viewpoint of light the velocity of the observer is zero. This produces the following equations.

When the velocity of the observer is negligible compared to the velocity of light, we have the familiar Galilean transformation. But when the velocity becomes a sizable fraction of the velocity of light the denominator in the above equations becomes less than 1, and the space-time characteristics expand.

When the velocity of the observer is very close to the velocity of light, the space time characteristics have expanded to near infinite. We may relate this to the electromagnetic spectrum. At the frequencies of light, the space-time characteristics are really magnified. At the frequency of electron inside the atom, the space-time characteristics have shrunk. When one reaches the frequency of the nucleus of atom, we have solidity due to extreme shrinkage of space-time characteristics. This is the frequency we are most familiar with. It is the frequency of the material universe.

The frequency spectrum extends from light to matter. It is a spectrum of substance that is manifested in the dimension of inertia. Inertia is how substantive the substance is. It is measured as the “duration” of substance. This is the fourth dimension and not some abstract notion of time.

The Lorentz transformation was not interpreted this way. The special theory of relativity hinted at it but did not relate it to the electromagnetic spectrum. But now we can say that the greatest contribution of the special theory of relativity is to bring this dimension of inertia to our awareness.