Category Archives: Physics

The Uniform Velocity in Space

ReferenceA Logical Approach to Theoretical Physics

Terms, such as, force, mass, velocity and energy acquire their meaning from the mathematical formulations of Newtonian mechanics. The system created from this Newtonian “particles in void” framework is, however, unable to explain “action at a distance”. Therefore, we must evaluate its terms carefully beyond their narrow mathematical meanings.

Newton states in his Principia 1,

DEFINITION III: The vis insita, or innate force of matter, is a power of resisting, by which every body, as much as in it lies, continues in its present state, whether it be of rest, or of moving uniformly forwards in a right line.

Force constitutes the very power of matter. We perceive matter based on its effect on our senses as force. Force is the primary concept. Other concepts, such as inertia, mass and energy are derived from force.

Faraday looked at force as the “power of substance” where substance includes not only the “mass” of matter, but also the “energy” of radiative phenomena. Faraday’s concept of force goes beyond the mathematical description of force as “mass x acceleration”. Faraday’s principle of conservation of force includes the conservation of mass, energy and motion (momentum). Faraday says 2,

There is no question which lies closer to the root of all physical knowledge, than that which inquires whether force can be destroyed or not. The progress of the strict science of modern times has tended more and more to produce the conviction that “force can neither be created nor destroyed,” and to render daily more manifest the value of the knowledge of that truth in experimental research. To admit, indeed, that force may be destructible or can altogether disappear, would be to admit that matter could be uncreated; for we know matter only by its forces: and though one of these is most commonly referred to, namely gravity, to prove its presence, it is not because gravity has any pretension, or any exemption amongst the forms of force, as regards the principle of conservation; but simply that being, as far as we perceive, inconvertible in its nature and unchangeable in its manifestation, it offers an unchanging test of the matter which we recognize by it.

Therefore, Faraday insisted that the principle of conservation of force be included in every hypothesis, theory or definition, because unless this principle is satisfied, no study can be considered complete.

Supposing that the truth of the principle of the conservation of force is assented to, I come to its uses. No hypothesis should be admitted nor any assertion of a fact credited, that denies the principle. No view should be inconsistent or incompatible with it. Many of our hypotheses in the present state of science may not comprehend it, and may be unable to suggest its consequences; but none should oppose or contradict it.

As an example, we may apply this conservation principle of Faraday to the following anomaly in Newtonian Mechanics 1:

When a force is applied to a body, it accelerates. When the force is removed there is no more acceleration, but the body continues to move with the increased velocity.

What keeps the body moving at the higher velocity?

This question arises specifically in the case when the body is drifting in space light minutes away from the bodies influencing it through their gravitational fields. Let us consider the following example:

When a constant force is applied to an object it starts to accelerate at a constant rate. Its velocity starts to increase. The force is constant and so is the acceleration, then what is converting into increased velocity and kinetic energy?

Per Newton’s definition,

DEFINITION II: The quantity of motion is the measure of the same arising from the velocity and quantity of matter conjointly.

To conserve the motion, as the velocity increase, the mass (inertia) must reduce. The mass reduces by converting into kinetic energy. The decrease in mass (inertia) would, however, be extremely small and imperceptible to cause a significant and perceptible increase in velocity.

Furthermore, when the force is removed the acceleration goes away. But if the object continues to move at a higher speed, it must mean that its inertia stays reduced. We may, therefore, conclude:

The velocity of an object drifting in space is a function of its mass (inertia). As its velocity increases, its mass decreases commensurately.

Theoretically, a body in space can be at absolute rest if its mass is infinite. Its inertia would be so large that the gravitational forces cannot push it around. But as its mass decreases it gets pushed around and it acquires a velocity inversely proportional to its mass. A body of near zero mass shall have a velocity of near infinity. We observe this phenomenon with the velocity of light, where the mass is zero and the velocity is extremely large. Light has some inertia due to quantization, which makes its velocity finite.

Newton did not discount absolute velocities as he says 1,

But we may distinguish rest and motion, absolute and relative, one from the other by their properties, causes and effects. It is a property of rest, that bodies really at rest do rest in respect to one another. And therefore as it is possible, that in the remote regions of the fixed stars, or perhaps far beyond them, there may be some body absolutely at rest; but impossible to know, from the position of bodies to one another in our regions whether any of these do keep the same position to that remote body; it follows that absolute rest cannot be determined from the position of bodies in our regions.

That remote body absolutely at rest could be at the center of our milky way. Therefore, we may determine the absolute velocity of a body in terms of its mass (inertia).

The exact relationship of absolute velocity to mass still remains to be determined, but it is likely to be inversely proportional.

It is possible that the constant of proportionality, if it exists, may turn out to be a universal constant. The application of the Faraday’s principle of Conservation of Force thus fixes the uncertainty associated with the uniform velocity of a body drifting in space.

Hopefully Faraday’s principle of Conservation of Force shall lead us to a better understanding of the nature of the particles and void.


1 Newton’s Principia” (1686) Translation by Andrew Motte, American edition of 1846, p. 73
2 On the Conservation of Force” by Michael Faraday (1857), Proceedings of the Royal Institution, Vol. II, p. 352


The “Particles in Void” Framework

ReferenceA Logical Approach to Theoretical Physics

Here is an interesting commentary on the logical framework of physics 1.

Several early Greek philosophers, including Democritus, imagined the universe as consisting of a multitude of irreducible particles moving in an empty void. On the other hand, Aristotle (c. 350 BC) denied the existence of a “void” (a region of space containing no substance), believing instead that the universe is filled continuously with substance… From this point of view it’s possible for a continuous substance to possess variable density, so the compressibility of air does not imply the existence of empty spaces.

The modern physics is based on the “particles in void” framework. It does not believe that the universe is filled continuously with substance.

“Particles” represent isolated bits of matter that are separated by void. Therefore, there is no continuity among the particles. They are never directly in contact.

Particles have properties that we may perceive. But void is perceived only as a gap among particles. Void has no properties of its own that may be perceived.

There is nothing that continues across the boundary between a particle and void except for geometry. The measures of geometry exist even when there is no substance to measure. Therefore, any possibility of continuum of substance is replaced by geometry in the “particles in void” framework.

Common to particles and void is the mathematical abstraction of geometry.



Astronomy considers stars and planets as point particles in the sky separated by vast distances. The obvious relationship among them is provided by Geometry. The other consideration is the motion of the moon around the earth, and planets around the sun, which requires the presence of some kind of force between them.

The success of Newton’s universal law of gravity raised the importance of geometry and mathematics, and established “particles in void” as the logical framework of physics. But with this framework arose the problem of “action at a distance”. It required the presence of some mechanism in the void.

This revived the concept of aether as the substance, which permeated the void. Newton wrote 2,

A most subtle spirit which pervades all bodies…by the force and action of which spirit the particles of bodies mutually attract one another, at near distances, and cohere, if contiguous; and electric bodies operate at greater distances, as well repelling as attracting the neighbouring corpuscles; and light is emitted, reflected, refracted, inflected and heats bodies; and all sensation is excited, and the members of animal bodies move at the command of the will, namely, by the vibrations of this spirit, mutually propagated along the solid filaments of the nerves, from the outward organs of sense to the brain, and from the brain into the muscles.

But the possibility of aether and its actual nature was yet to be corroborated with reality.

Geometry alone could not explain how force got communicated across the void. It then led to the postulate of aether as a substance permeating the void.


Electricity and Magnetism

The phenomena of electricity and magnetism were being studied extensively during the 18th and 19th centuries. During this period the atomic theory was being used to explain the chemical structure of matter. The phenomena of electricity and magnetism seemed to explain how force was communicated through the void between atoms.

From his experimental investigation into electricity and magnetism, Faraday formed the view 3 that an atom is not a supposed little hard particle separate from the powers around it. An atom is constituted of the powers it has, and it extends as far as its powers extend.

… where is there the least ground (except in a gratuitous assumption) for imagining a difference in kind between the nature of that space midway between the centres of two contiguous atoms and any other spot between these centres? a difference in degree, or even in the nature of the power consistent with the law of continuity, I can admit, but the difference between a supposed little hard particle and the powers around it I cannot imagine…

Hence matter will be continuous throughout, and in considering a mass of it we have not to suppose a distinction between its atoms and any intervening space. The powers around the centres give these centres the properties of atoms of matter; and these powers again, when many centres by their conjoint forces are grouped into a mass, give to every part of that mass the properties of matter. In such a view all the contradiction resulting from the consideration of electric insulation and conduction disappears.

Thus, in matter the atoms touch each other and there is no void among them.

But is there a similar situation with the bodies in the heavens? Do these bodies touch each other with their power of gravity that is extended as aether?


Light and Gravity

The phenomena of light and gravity were studied extensively by Newton himself in the 17th century. This study was carried forward in 18th and 19th centuries, but no connection was ever made between light and gravity.

Faraday, however, stated the following 4:

The view which I am so bold to put forth considers, therefore, radiation as a kind of species of vibration in the lines of force which are known to connect particles and also masses of matter together. It endeavors to dismiss the aether, but not the vibration …

The aether is assumed as pervading all bodies as well as space: in the view now set forth, it is the forces of the atomic centres which pervade (and make) all bodies, and also penetrate all space. As regards space, the difference is, that the aether presents successive parts of centres of action, and the present supposition only lines of action; as regards matter, the difference is, that the aether lies between the particles and so carries on the vibrations, whilst as respects the supposition, it is by the lines of force between the centres of the particles that the vibration is continued.

According to Faraday, there was no separate substance, such as, aether. Matter itself extended as lines of force filling all space between the material bodies. Radiation was the vibrations in these lines of force.

Faraday looked at radiation, such as, light, to be the extension that carried the force of matter.

In short, the idea of “void” was unsustainable. First, the theoretical concept of “aether”, and then, a more realistic idea of “force carrying radiation” were simply the attempts to discover the nature of “space”, which was thought to be void of matter.


1Continuity and the Void” by Kevin Brown
2Newton’s Principia” (1686) Translation by Andrew Motte, American edition of 1846, p. 26
3 A speculation touching Electrical Conduction and the Nature of Matter” by Michael Faraday (1844), Philosophical Magazine and Journal of Science, Vol. XXIV, p. 136
4 Thoughts on Ray Vibrations”, Lecture by Michael Faraday (1846),  Experimental Researches in Electricity, Vol III, M. Faraday, p447-452


Preface (Approach to Physics)

ReferenceA Logical Approach to Theoretical Physics

It has been a while since any major contribution has been made to physical sciences in terms of fundamental theoretical research. It has not been easy to examine physical phenomena at the atomic levels. More mathematics is being demanded in modern scientific investigations in lieu of objective reality.

Newton used mathematics to “describe” the void, which could not be realistically described. Maxwell used mathematics to “describe” a postulated aether. Einstein used mathematics to “describe” space as some abstract substance. Similar use of mathematics in quantum mechanics and particle physics has only served to further lose touch with reality.

Although Newtonian mechanics, the Electromagnetic theory, the theory of Relativity, and now Quantum mechanics and Particle physics predict remarkably verifiable results in selected areas, they cannot be reconciled with each other.

The very fact that the fundamental theories of physics cannot be reconciled means that some basic assumption underlying all physics is inconsistent with reality.

The common denominator of the physical theories above is the “particles in void” approach. This approach considers the physical universe to be made up of matter and void only. Material particles are separated by void. The contact between material particles cannot be defined. The “action at a distance” problem, which arose with Newton’s theory of gravity, is still unresolved. Therefore, much confusion follows the concepts of “particle” and “void”.

This book is written on the premise that the “particles in void” framework that underlies current physics is inconsistent and it needs to be examined thoroughly to discover the missing truth,


Substance, Motion and Inertia

Reference: A Logical Approach to Theoretical Physics

With the discovery of quantization, the concept of substance expands. We see quantization as thickening of substance, which, ultimately congeals as matter. This is supported by the correspondence principle.  This may be visualized as happening within the atom.

Force seems to be the very characteristic of substance. The concept of substance expands beyond matter to radiation and raw force. The concepts of motion and inertia shall change with the quantization of substance.

The following and subsequent quotes are from NEWTON’S PRINCIPIA:

Definition I: The quantity of matter is the measure of the same, arising from its density and bulk conjunctly.

Thus, quantity of matter is the product of its density and volume.

The quantity of radiation may be described analogously as the product of its quantization level (frequency) and intensity.

Definition II: The quantity of motion is the measure of the same, arising from the velocity and quantity of matter conjunctly.

For a material body, the quantity of motion is the product of its velocity and the quantity of matter. This is also called momentum.

For radiation, the quantity of motion is the product of its frequency and the quantity of radiation.

Definition III: The vis insita, or innate force of matter, is a power of resisting, by which every body, as much as in it lies, endeavours to persevere in its present state, whether it be of rest, or of moving uniformly forward in a right line.

For a material body, a change in motion means a change in velocity because matter changes little. Resistance to this change in velocity is called inertia of the material body. Inertia keeps the motion (velocity) of the material body uniform in space.

For radiation, a change in motion means a change in frequency because velocity changes little. Resistance to this change in frequency may be called
quantization. The quantization of radiation is very small, but it keeps the motion (frequency) of radiation uniform in space.

Definition IV: An impressed force is an action exerted upon a body, in order to change its state, either of rest, or of moving uniformly forward in a right line.

A force must be impressed upon the body to change its motion over the resistance of inertia.  This inertia makes the change in velocity (acceleration) of the body proportional to the force applied. As mass of the body increases, so does its inertia, which makes it increasingly  difficult to accelerate the body.

Theoretically, a body of infinite mass shall have infinite inertia, and it would be impossible to accelerate. We may consider such a body to be absolutely fixed in space. The body becomes less fixed as its mass decreases. When mass decreases to zero the substance reduces to radiation, and inertia sharply reduces to quantization, making it barely fixed in space.

NOTE: We may define space here as “radiation” of zero quantization.

LAW I: Every body perseveres in its state of rest, or of uniform motion in a right line, unless it is compelled to change that state by forces impressed thereon.

LAW II: The alteration of motion is ever proportional to the motive force impressed; and is made in the direction of the right line in which that force is impressed.

LAW III: To every action there is always opposed an equal reaction: or the mutual actions of two bodies upon each other are always equal, and directed to contrary parts.

The motion is changed through force, where force can be applied only through contact. As an example, contact occurs between radiation and matter in photoelectric phenomenon. If radiation applies force to matter then the matter must apply force back to radiation. This may result in a visible increase in the frequency of radiation, increasing its quantization level. If the increased quantization is maintained then it must be accompanied by a decrease in velocity, no matter how imperceptible.

A substance, as radiation and matter, is fixed in space to the degree it is substantial. As radiation the substance is not very substantial and it is barely fixed. The substantiality of radiation increases slowly with quantization. The substantiality, however, increases very sharply when radiation transitions into matter. This transition occurs within the atom at the interface between the electronic and nuclear regions. Even as matter it continues to quantize into denser matter.

The characteristic of substantiality or fixedness of substance determines its inertia. This inertia is very low throughout the region of radiation, and it is comparatively very high throughout the domain of matter.

The speed seems to change sharply with the level of inertia. The speed is very high throughout the region of radiation (known as the speed of light), and it is comparatively very low throughout the domain of matter.

Because of inertia, the change in motion is proportional to the force impressed. For matter, the proportionality factor is the mass, and the change in motion appears as change in speed. The mass represents inertia.

For radiation, the proportionality factor appears to be the speed of light, and the change in motion appears as change in frequency. The frequency represents the quantization.

To summarize, motion appears as velocity for matter, but as frequency for radiation. Inertia is represented by mass in case of matter, and by quantization in case of radiation. With these considerations taken into account Newton’s laws may be applied to radiation.


Einstein 1920: General Results

Reference: Einstein’s 1920 Book

This paper presents Part 1, Chapter 15 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.


General Results of the Theory

NOTE: These comments are temporary as more work is required. Better results are expected if velocity is replaced by acceleration, kinetic energy is replaced by force, and potential energy and mass are replaced by inertia.

It is clear from our previous considerations that the (special) theory of relativity has grown out of electrodynamics and optics. In these fields it has not appreciably altered the predictions of theory, but it has considerably simplified the theoretical structure, i.e. the derivation of laws, and —what is incomparably more important —it has considerably reduced the number of independent hypotheses forming the basis of theory. The special theory of relativity has rendered the Maxwell-Lorentz theory so plausible, that the latter would have been generally accepted by physicists even if experiment had decided less unequivocally in its favour.

The theory of relativity has grown out of the effort to align the laws of electrodynamics with the laws of mechanics. This goes back to Einstein’s paper on light quanta, from which it may be inferred that radiation is a substance that quantizes into matter. The laws of electrodynamics apply to radiation, whereas, the laws of mechanics apply to matter.

The special theory of relativity has succeeded in explaining the observed motions better than classical mechanic, by somehow accounting for inertia. Classical mechanics assumes inertia to be uniform because velocity is uniform. This is not so because velocity can be different while uniform, and so can inertia. Not accounting of inertia in classical mechanics is causing the error that is being corrected by special theory of relativity.

Classical mechanics required to be modified before it could come into line with the demands of the special theory of relativity. For the main part, however, this modification affects only the laws for rapid motions, in which the velocities of matter vare not very small as compared with the velocity of light. We have experience of such rapid motions only in the case of electrons and ions; for other motions the variations from the laws of classical mechanics are too small to make themselves evident in practice. We shall not consider the motion of stars until we come to speak of the general theory of relativity. In accordance with the theory of relativity the kinetic energy of a material point of mass m is no longer given by the well-known expression


but by the expression

mc2 / √(1 – v2/c2).

Velocity is different for different reference-bodies, and it can be chosen arbitrarily. This makes kinetic energy dependent on the reference-body too. This arbitrary dependency goes away when acceleration is chosen in place of velocity;  force is chosen in place of kinetic energy, and inertia is chosen in place of potential energy and mass.

This expression approaches infinity as the velocity vapproaches the velocity of light c. The velocity must therefore always remain less than c, however great may be the energies used to produce the acceleration. If we develop the expression for the kinetic energy in the form of a series, we obtain

Each velocity seems to represent a certain “potential force”, or inertia that is in balance. This is the case with both v and c. The value of c is very high because the inertia in balance is very small.

When v2/c2 is small compared with unity, the third of these terms is always small in comparison with the second, which last is alone considered in classical mechanics. The first term mc2 does not contain the velocity, and requires no consideration if we are only dealing with the question as to how the energy of a point-mass depends on the velocity. We shall speak of its essential significance later.

The first term (mc2) is more representative of the inertia of the body. The second term seems to be more representative of force in some manner.

The most important result of a general character to which the special theory of relativity has led is concerned with the conception of mass. Before the advent of relativity, physics recognised two conservation laws of fundamental importance, namely, the law of the conservation of energy and the law of the conservation of mass; these two fundamental laws appeared to be quite independent of each other. By means of the theory of relativity they have been united into one law. We shall now briefly consider how this unification came about, and what meaning is to be attached to it.

Faraday had combined the two conservation laws of mass and energy into one single law of the conservation of force. In Faraday’s framework mass corresponds to inertia. Active energy corresponds to force.

The principle of relativity requires that the law of the conservation of energy should hold not only with reference to a co-ordinate system K, but also with respect to every co-ordinate system K’ which is in a state of uniform motion of translation relative to K, or, briefly, relative to every “Galileian” system of co-ordinates. In contrast to classical mechanics, the Lorentz transformation is the deciding factor in the transition from one such system to another.

Lorenz transformations somehow account for the difference in inertia, when velocities are different.

By means of comparatively simple considerations we are led to draw the following conclusion from these premises, in conjunction with the fundamental equations of the electrodynamics of Maxwell: A body moving with the velocity v, which absorbs 1 an amount of energy E0 in the form of radiation without suffering an alteration in velocity in the process, has, as a consequence, its energy increased by an amount

E0 / √(1 – v2/c2).

1 E0 is the energy taken up, as judged from a co-ordinate system moving with the body.

This is more like an increase in inertia with the absorption of radiation force.

In consideration of the expression given above for the kinetic energy of the body, the required energy of the body comes out to be

Thus the body has the same energy as a body of mass (m + E0/c2) moving with the velocity v. Hence we can say: If a body takes up an amount of energy E0, then its inertial mass increases by an amount E0/c2; the inertial mass of a body is not a constant, but varies according to the change in the energy of the body. The inertial mass of a system of bodies can even be regarded as a measure of its energy. The law of the conservation of the mass of a system becomes identical with the law of the conservation of energy, and is only valid provided that the system neither takes up nor sends out energy. Writing the expression for the energy in the form

we see that the term mc2, which has hitherto attracted our attention, is nothing else than the energy possessed by the body 2 before it absorbed the energy E0.

2 As judged from a co-ordinate system moving with the body.

The special theory of relativity interprets mass as the configuration of substance formed from an equivalent amount of energy. In the relationship E0 = m0c2 , however, c cannot be taken to its limiting value of infinity. A finite solution must exists when c is taken to infinity.

A direct comparison of this relation with experiment is not possible at the present time, owing to the fact that the changes in energy E0to which we can subject a system are not large enough to make themselves perceptible as a change in the inertial mass of the system. E0/c2 is too small in comparison with the mass m, which was present before the alteration of the energy. It is owing to this circumstance that classical mechanics was able to establish successfully the conservation of mass as a law of independent validity.

Let me add a final remark of a fundamental nature. The success of the Faraday-Maxwell interpretation of electromagnetic action at a distance resulted in physicists becoming convinced that there are no such things as instantaneous actions at a distance (not involving an intermediary medium) of the type of Newton’s law of gravitation. According to the theory of relativity, action at a distance with the velocity of light always takes the place of instantaneous action at a distance or of action at a distance with an infinite velocity of transmission. This is connected with the fact that the velocity c plays a fundamental rôle in this theory. In Part II we shall see in what way this result becomes modified in the general theory of relativity.