Category Archives: P-Book

The Physics Book.

Force, Substance & Spacetime

folding_space_by_ether

Reference: Disturbance Theory

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According to the postulates of disturbance theory, the universe is a continuum of substance that exists in emptiness. The external characteristics of substance are extension (space) and persistence (time). In emptiness there is neither substance, nor space nor time.

The presence of substance is felt through force to which our perceptions react in terms of touch, sight, hearing, smell and taste. But we are limited in the level of force that we can perceive directly. We then use other tools to perceive indirectly.

When Newton saw force acting between two material objects he explained it in terms of gravity of the masses and the distance between them. But he puzzled about how that force passed from one object to another. He wrote to his friend Richard Bentley:

“That gravity should be innate, inherent, and essential to matter, so that one body may act upon another at a distance, through a vacuum, without the mediation of anything else, by and through which their action and force may be conveyed from one to another, is to me so great an absurdity that I believe no man who has in philosophical matters a competent faculty of thinking, can ever fall into it. Gravity must be caused by an agent, acting constantly according to certain laws; but whether this agent be material or immaterial I have left to the consideration of my readers.”

This gravitational force could be computed without considering any substance filling that space in between. Science continued to develop in this way. It simply treated the space between the objects mathematically according to the Newton’s laws.

Newton’s scientific framework came to be known as “action at a distance” compared to the postulated framework of “continuum of substance”.

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Lines of Force

Starting at the beginning of 19th century, extensive experimental work was done on electricity and magnetism. At the forefront of this work was Michael Faraday. When conducting these experiments, Faraday could see the effects propagating through the intervening space.

In a letter dated Jan 25 1844, “Electric Conduction and the Nature of Matter”, Faraday expressed that matter seemed to extend itself as “force” to fill the space in an atom, such that there was no empty space. This conclusion came from his observations of electric conduction through different materials. Thus, Faraday saw atoms as centers of force from which lines of force originated, and on which they terminated as well.

Faraday theorized space to consist of electromagnetic lines of force.

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Light and Aether

It was supposed that light required a medium to travel, and that medium was aether.

In a letter dated April 15, 1846, “Thoughts on Ray Vibration”, Faraday proposed that the vibrations, which were assumed to account for radiation and radiant phenomena, might be seen as occurring in the lines of force which connect particles. In other words, light, radiation or radiant phenomena were part of the force content of space.

Faraday theorized radiant phenomena, such as, light, to constitute the mysterious aether that filled the space.

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Force and Substance

Newton associated force with acceleration of matter in space. Work was the displacement caused by this force. Energy was the capacity for doing this work.

Faraday saw force as the cause of physical action, and not just the tendency of the body to pass from one place to another. Thus, force formed the very essence of substance for Faraday.  In this sense, it also formed the “inertia” described by Newton as “inner force”.

“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 preserve its present state, whether it be of rest or of moving uniformly forward in a straight line.”

In a lecture dated February 27, 1857, “On the conservation of Force”, Faraday proposed that all force was conserved. Non-conservation of force implied that the phenomenon was not being viewed completely.  In a later addendum, Faraday clarified force as, “the source or sources of all possible changes amongst the particles or materials of the universe.”  To Faraday, changes implied force. But changes also implied substance.

Faraday saw force as the fundamental substance.

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Further Research

When we look at spacetime from the viewpoint of the postulates we find that,

Spacetime is the external characteristic of substance. The internal characteristic is force.

Matter is not the only substance; for example, there is definitely a substance that appears as “empty space”. We shall now examine this substance.

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A Look at Spacetime

Observing space through a telescope

Reference: Disturbance Theory

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Wikipedia article on Spacetime states,

In physics, spacetime is any mathematical model that fuses the three dimensions of space and the one dimension of time into a single four-dimensional continuum. Spacetime diagrams can be used to visualize relativistic effects such as why different observers perceive where and when events occur.

So, spacetime is being perceived as a mathematical abstraction rather than as something real. But spacetime is something real as well.

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The Reality of Spacetime

Material objects have extension in three dimensions. We call these extensions length, width and height for an object, such as, a box. Such extensions in three dimensions are the characteristic of space.  The material object and its spatial dimensions are also persisting. Such persistence is the characteristic of time.

For a material object, the characteristics of space and time appear together. So, such characteristics may be called spacetime.

All material objects are four-dimensional “spacetime” entities.

But are these characteristics present in the absence of material objects?

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“Empty” Space

There is space inside an empty box. But this space does not define the property of some visible material. Let’s say this box is filled with air. Can this space be defined as the spacetime characteristics of a material substance, such as, air? What happens to this space when we remove the box?

Air exists close to earth only. Beyond earth there is less and less material even as atoms of air, but space seems to acquire much greater extent. This raises doubt about spacetime being the characteristics of material objects or substance.

How can there be “spacetime” empty of matter?

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The Mystery of Aether

Spacetime appears as the characteristics of matter. Descartes said that there is no such thing as empty space because space represents the extensions of substance. Then space, which is empty of matter, must provide the characteristics of some other substance.

Ancients speculated upon such substance, and called it “aether”. Newton speculated on the existence of aether in the Third Book of Opticks (1718):

“Doth not this aethereal medium in passing out of water, glass, crystal, and other compact and dense bodies in empty spaces, grow denser and denser by degrees, and by that means refract the rays of light not in a point, but by bending them gradually in curve lines?”

But no such substance could be found. What then is the spacetime empty of matter?

Is spacetime (empty of matter) something mathematical only?

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Further Research

We shall examine the reality of spacetime from the viewpoint of The Postulates.

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Faraday & Maxwell

Faraday Maxwell

Reference: Disturbance Theory

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Faraday’s prime concern was resolution of the problem of gravitation. The explanation for gravity given by Newton in terms of distance did not fully explain the generation and disappearance of gravitational force as two bodies were moved.

Faraday saw “lines of force” as the substance that filled space with varied substantialness. He was looking for a way to explain gravitation with his concept of force as “the source of all possible changes amongst the particles of the universe.”

But this concept was not fully understood by Maxwell, who saw force merely as “the tendency of the body to pass from one place to another”. Maxwell then went on to formulate the concept of electromagnetic field that was based on a mechanical view of force. But he never addressed the problem of gravitation that Faraday was trying to resolve through the principle of conservation of force.

Here is Faraday’s original paper, On the Conservation of Force that he sent to Maxwell.  Here is Maxwell’s response, followed by Faraday’s answer.

This correspondence is presented below with my comments in colored text.

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 TO PROFESSOR FARADAY

129 Union Street,

Aberdeen, 9th November 1857.

 

DEAR SIR—I have to acknowledge receipt of your papers on the Relations of Gold to Light, and on the Conservation of Force. Last spring you were so kind as to send me a copy of the latter paper, and to ask what I thought of it.

That question silenced me at that time, but I have since heard and read various opinions on the subject, which render it both easy and right for me to say what I think. And first I pass over some who have never understood the known doctrine of conservation of force, and who suppose it to have something to do with the equality of action and reaction.

Conservation of force is not the same thing as Newton’s third law of motion, which says, “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.”

Now, first, I am sorry that we do not keep our words for distinct things more distinct, and speak of the “Conservation of Work or of Energy” as applied to the relations between the amount of “vis viva” and of “tension” in the world; and of the “Duality of Force” as referring to the equality of action and reaction.

“Vis viva” (from the Latin for “living force”) is a historical term used for the first (known) description of what we now call kinetic energy in an early formulation of the principle of conservation of energy.

Maxwell thinks that, to be clearer, the title of Faraday’s paper should be more like “Conservation of Work or Energy”. He doesn’t see that the use of the word “Force” by Faraday is much deeper because it includes the substance of space and matter in the equation of conservation. Maxwell excludes space and matter from the equation of conservation.

Energy is the power a thing has of doing work arising either from its own motion or front the “tension” subsisting between it and other things.

Force is the tendency of a body to pass from one place to another, and depends upon the amount of change of “tension” which that passage would produce.

In his letter Maxwell defines force as, “the tendency of a body to pass from one place to another”. This is not what Faraday meant. In his desire to interpret Faraday mathematically, Maxwell did not quite understand what Faraday was saying.

Now, as far as I know, you are the first person in whom the idea of bodies acting at a distance by throwing the surrounding medium into a state of constraint has arisen, as a principle to be actually believed in. We have had streams of hooks and eyes flying around magnets, and even pictures of them so beset; but nothing is clearer than your descriptions of all sources of force keeping up a state of energy in all that surrounds them, which state by its increase or diminution measures the work done by any change in the system. You seem to see the lines of force curving round obstacles and driving plump at conductors, and swerving towards certain directions in crystals, and carrying with them everywhere the same amount of attractive power, spread wider or denser as the lines widen or contract.

Maxwell did not see force as the source of all possible changes in the universe. He saw force only in limited mechanical terms as described by Newton. Thus he interpreted Faraday’s ideas as a force field of a mechanical nature filling the space. He did not see the effect taking time to travel through the medium as Faraday saw.

You have also seen that the great mystery is, not how like bodies repel and unlike attract, but how like bodies attract (by gravitation). But if you can get over that difficulty, either by making gravity the residual of the two electricities or by simply admitting it, then your lines of force can “weave a web across the sky,” and lead the stars in their courses without any necessarily immediate connection with the objects of their attraction.

The lines of Force from the Sun spread out from him, and when they come near a planet curve out from it, so that every planet diverts a number depending on its mass from their course, and substitutes a system of its own so as to become something like a comet, if lines of force were visible.

Lines of Force

The lines of the planet are separated from those of the Sun by the dotted line. Now conceive every one of these lines (which never interfere but proceed from sun and planet to infinity) to have a pushing force instead of a pulling one, and then sun and planet will be pushed together with a force which comes out as it ought, proportional to the product of the masses and the inverse square of the distance.

Maxwell’s force field does seem to act as a substance filling the space, but it is assumed to be of mechanical nature. This is pretty much the same idea as that of aether, which was prevalent at that time. Faraday did not agree with the idea of mechanical aether, because his idea of force was not mechanical.

The difference between this case and that of the dipolar forces is, that instead of each body catching the lines of force from the rest, all the lines keep as clear of other bodies as they can, and go off to the infinite sphere against which I have supposed them to push.

Maxwell supposed the lines of force going around the bodies and pushing against an infinite sphere; but Faraday saw lines of force originating and terminating at each atom.

Here then we have conservation of energy (actual and potential), as every student of dynamics learns, and besides this we have conservation of “lines of force” as to their number and total strength, for every body always sends out a number proportioned to its own mass, and the pushing effect of each is the same.

Maxwell saw mechanical force field filling the space, while Faraday saw substance of varying force (inertia) extending out from the bodies.

All that is altered when bodies approach is the direction in which these lines push. When the bodies are distant the distribution of lines near each is little disturbed. When they approach, the lines march round from between them, and come to push behind each, so that their resultant action is to bring the bodies together with a resultant force increasing as they approach.

Maxwell’s lines of force push two objects towards each other from behind, with the resultant force increasing as they approach each other. Faraday saw substance of the bodies extending toward each other and thickening as the two bodies approached.

 Now the mode of looking at Nature, which belongs to those who can see the lines of force, deals very little with “resultant forces,” but with a network of lines of action of which these are the final results, so that I, for my part, cannot realise your dissatisfaction with the law of gravitation, provided you conceive it according to your own principles. It may seem very different when stated by the believers in “forces at a distance,” but there can be only differences in form and conception, not in quantity or mechanical effect, between them and those who trace force by its lines.

Maxwell could not comprehend Faraday’s dissatisfaction with the law of gravitation. He saw lines of forces as a mathematical device that provided an alternative explanation to action at a distance, but nothing more.

But when we face the great questions about gravitation—Does it require time? Is it polar to the “outside of the universe” or to anything? Has it any reference to electricity? or does it stand on the very foundation of matter, mass or inertia? — then we feel the need of tests, whether they be comets or nebulæ, or laboratory experiments, or bold questions as to the truth of received opinions.

But Maxwell did agree with Faraday in terms of greater questions that needs to be resolved in the understanding of inertia, mass, electricity, magnetism, etc., and effect taking time to travel, and that would require more experimentation, and could not be resolved by lines of force.

I have now namely tried to show you why I do not think gravitation a dangerous subject to apply your methods to, and that it may be possible to throw light on it also by the embodiment of the same ideas, which are expressed mathematically in the functions of Laplace and of Sir W. R. Hamilton in Planetary Theory.

Maxwell resolved the issue of aether in electromagnetic terms but he couldn’t come up with the explanation for gravitation that was missing per the principle of Faraday’s conservation of force.

But there are questions relating to the connection between magneto-electricity and certain mechanical effects which seems to me opening up quite a new road to the establishment of principles in electricity, and a possible conformation of the physical nature of magnetic lines of force. Professor W. Thomson seems to have some new lights on this subject.

I can see how Faraday must have been disappointed by this response from Maxwell.

—Yours sincerely,

JAMES CLERK MAXWELL.

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FARADAY TO MR. CLERK MAXWELL

Royal Institution: November 13, 1857

 

My dear Sir,—If on a former occasion I seemed to ask you what you thought of my paper, it was very wrong, for I do not think anyone should be called upon for the expression of their thoughts before they are prepared and wish to give them. I have often enough to decline giving an opinion, because my mind is not ready to come to a conclusion, or does not wish to be committed to a view that may by further consideration be changed. But having received your last letter, I am exceedingly grateful to you for it; and rejoice that my forgetfulness of having sent the former paper on conservation has brought about such a result. Your letter is to me the first intercommunication on the subject with one of your mode and habit of thinking. It will do me much good, and I shall read and meditate on it again and again.

Faraday is disappointed at not being understood by Maxwell on his principle of the conservation of force. Nevertheless, he seems pleased to hear back from a mathematician like Maxwell.

I dare say I have myself greatly to blame for the vague use of expressive words. I perceive that I do not use the word “force” as you define it, “the tendency of a body to pass from one place to another.” What I mean by the word is the source or sources of all possible actions of the particles or materials of the universe, these being often called the powers of nature when spoken of in respect of the different manners in which their effects are shown.

Faraday was an experimentalist and not a theoretician versed in mathematics. He struggled to get his ideas across that were based on experiments only. Maxwell interpreted Faraday’s intent as conservation of work and energy, which was limited to a mechanical interpretation only. Much later, only Einstein could see that Faraday’s ideas went beyond a simple mechanical interpretation.

In a paper which I have received at this moment from the “Phil. Mag.,” by Dr. Woods, they are called the forces, “such as electricity, heat, &c.” In this way I have used the word “force” in the description of gravity which I have given as that expressing the received idea of its nature and source, and such of my remarks as express an opinion, or are critical, apply only to that sense of it. You may remember I speak to labourers like myself; experimentalists on force generally who receive that description of gravity as a physical truth, and believe that it expresses all and no more than all that concerns the nature and locality of the power,—to these it limits the formation of their ideas and the direction of their exertions, and to them I have endeavored to speak, showing how such a thought, if accepted, pledged them to a very limited and probably erroneous view of the cause of the force, and to ask them to consider whether they should not look (for a time, at least), to a source in part external to the particles. I send you two or three old printed papers with lines marked relating to this point.

Faraday explains further that he was speaking of the ‘force of gravity’ in a broad sense and not in a local sense as implied by the inverse square law. He wanted other experimentalists to consider if the source of gravity could be broader than just being limited to material particles.

 To those who disown the definition or description as imperfect, I have nothing to urge, as there is then probably no real difference between us.

Faraday intuitively felt that reality went beyond the mechanical view of Newton, but he struggled to express it clearly.

I hang on to your words, because they are to me weighty; and where you say, “I, for my part, cannot realise your dissatisfaction with the law of gravitation, provided you conceive it according to your own principles,” they give me great comfort. I have nothing to say against the law of the action of gravity. It is against the law which measures its total strength as an inherent force that I venture to oppose my opinion; and I must have expressed myself badly (though I do not find the weak point), or I should not have conveyed any other impression. All I wanted to do was to move men (not No. 1, but No. 2), from the unreserved acceptance of a principle of physical action which might be opposed to natural truth. The idea that we may possibly have to connect repulsion with the lines of gravitation-force (which is going far beyond anything my mind would venture on at present, except in private cogitation), shows how far we may have to depart from the view I oppose.

Faraday had no problem with the law of action of gravity as expressed by Newton. He only objected to the fact that this law did not fully explain the total measure of inherent forces involved. He simply wanted others to see that something was missing from the natural truth.

There is one thing I would be glad to ask you. When a mathematician engaged in investigating physical actions and results has arrived at his own conclusions, may they not be expressed in common language as fully, clearly, and definitely as in mathematical formula? If so, would it not be a great boon to such as we to express them so—translating them out of their hieroglyphics that we also might work upon them by experiment. I think it must be so, because I have always found that you could convey to me a perfectly clear idea of your conclusions, which, though they may give me no full understanding of the steps of your process, gave me the results neither above nor below the truth, and so clear in character that I can think and work from them.

Faraday feels that mathematical results should be expressed in clear and useful working terms so that non-mathematicians can understand and work with them experimentally.

If this be possible, would it not be a good thing if mathematicians, writing on these subjects, were to give us their results in this popular useful working state as well as in that which is their own and proper to them?

It seems that Faraday’s purpose was to inspire Maxwell to look beyond ‘action at a distance’ as coded in the inverse square law. Maxwell did just that as his life’s work. What a wonderful teamwork.

Ever, my dear Sir, most truly yours,

M. Faraday.

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Newton: Basic Concepts

Isaac's Apple

Reference: Disturbance Theory

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From Newton’s Principia for the Common Reader we have the following basic concepts:

Definitions

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

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

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.

DEFINITION IV: An impressed force is an action exerted upon a body, in order to change its state, either of rest, or of uniform motion in a right line.

DEFINITION V: A centripetal force is that by which bodies are drawn or impelled, or any way tend, towards a point as to a centre.

DEFINITION VI: The absolute quantity of a centripetal force is the measure of the same, proportional to the efficacy of the cause that propagates it from the centre, through the spaces round about.

DEFINITION VII: The accelerative quantity of a centripetal force is the measure of the same, proportional to the velocity which it generates in a given time.

DEFINITION VIII: The motive quantity of a centripetal force is the measure of the same, proportional to the motion which it generates in a given time.

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Laws of Motion

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

LAW II: The change of motion is 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.

Newton is describing the motion resulting from the action of force impressed upon material objects using the geometry of space. This geometry is used to determine the center of gravity and its motion.

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Maxwell’s Reformulation

Maxwell reformulated the first two laws of motion as follows:

Law I – The centre of mass of the system perseveres in its state of rest, or of uniform motion in a straight line, except in so far as it is made to change that state by forces acting on the system from without.

Law II – The change of momentum of the system during any interval of time is measured by the sum of the impulses of the external forces during that interval.

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The Newtonian Principle of Relativity

The Principle of Relativity of Galileo and Newton:

  • Inertial frames are undistinguished: any frame will serve as equally as any other.

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The Property of Inertia

Newton defines inertia as an innate force of matter (see Definition III above). This property is so fundamental that it establishes the very nature of matter. Here matter refers to any substance. For Newton, light was made up of fine particles and , therefore, it had substance. We may, therefore, define inertia as the measure of “substantialness” of a substance. Therefore,

Any resistance to change in motion means that there is substance.

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The Inertia of Light

The following conclusion may be derived from the basic concepts stated above.

  • This uniform motion of a body implies a balance between gravitational forces in space and the innate forces of inertia.

  • Any attempt to change this uniform motion immediately activates, per Law III, an inertial force to balance the applied external force. Any excess external force generates acceleration.

  • The “inertial force plus acceleration” is equivalent to the external force at any point. A constant acceleration represents a new state of uniform motion. The acceleration, thus, represents an increase in the inertia of the body. 

  • The acceleration is relative to the body itself and not to some other body or observer. Thus the uniform motion may be described in terms of inertia of the body irrespective of the “velocity” of some external observer.

  • The greater is the acceleration of a body, the harder it is to increase that acceleration further. In other words, the greater is the inertia of a body, the more difficult it is to move it.

  • When a body has infinite inertia it may be impossible to move it. Its “uniform motion” may then be identified as “absolute rest”.

  • The magnitude of the uniform motion of a body thus increases as inertia reduces from an infinite magnitude.

  • The large but constant velocity of light implies that it has a very small but finite inertia. This inertia is so small that it could not be detected through the Michelson-Morley’s experiment.

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Inertia, Geometry & Quantization

Geometry of space

Reference: Disturbance Theory

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The Space Reference frame (SRF) highlights the dimension of inertia. Newton defines inertia as follows,

“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 preserve its present state, whether it be of rest or of moving uniformly forward in a straight line.”

The status quo of a body is defined here in terms of rest or uniform motion in a straight line. But a “straight line” only means near zero curvature, which is approached as the radius approaches an infinitely large value.

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Geometry & Inertia

Straight line relates to geometry of space.  Space is a property of substance. It expresses the extension of substance.  The fundamental substance is an electromagnetic cycle.  Per The Problem of Field,

“Something called “charge” triggers the electromagnetic cycle. This cycle is an oscillation between electrical flow and magnetic rotation. The electrical flow winds up as magnetic rotation. The magnetic rotation then unwinds back as electrical flow.”

The electric flow has the kinetic aspect of forward motion, which provides a sense of extension, or SPACE. The magnetic rotation has the potential aspect of holding motion in place, which provides a sense of duration, or TIME. Thus,

“The electromagnetic cycle consists of an oscillation between the “flow” of space and “rotation” of time. The relationship between space and time would depend on the frequency of oscillation. We perceive the ratio of space to time of an electromagnetic cycle as ‘c’ the speed of light.”

As frequency goes to zero space would seem to stretch out with its curvature approaching zero. The reverse seems to occur as frequency increases. In other words, the curvature of space seems to increase with frequency. Since frequency contributes to the substantial-ness, or inertia, of the electromagnetic substance, it seems that

The curvature of space increases with increase in inertia.

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Inertia & Quantization

In the electromagnetic spectrum, space represents the extensions of the electromagnetic substance. The curvature of this space approaches zero towards the bottom of the electromagnetic spectrum. But as we move up the electromagnetic spectrum it starts to become very conspicuous towards the top. This is the basis of quantization.

The greater is the inertia of substance, the more quantized it appears.

This, in a way, was the subject of Einstein’s very first paper in 1905 on light quanta [see Einstein’s Paper on Light Quanta (1905)].

This phenomenon of quantization has been debated as the duality of wave and particle properties of electromagnetic substance. Even though the quantization appears to be particle-like, there is always an underlying continuity. Even a material particle of very high inertia has some degree of continuity with the space around it.

Underlying quantization there is always continuity of substance from higher to lower inertia.

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Empty Space & Substance

“Empty space” is empty of matter only. When there is no matter, there is electromagnetic substance, which is not easily visible. But if the electromagnetic substance is not there, there won’t be empty space either. We may say that the electromagnetic substance is visible as empty space.

This may shed some light on the concepts of “dark energy” and “dark matter”. Any presence of dark energy and matter shall be accompanied by invisible curvatures in space. The curvatures shall change as the inertia of the electromagnetic substance changes.

Higher levels of inertia means more condensed regions. Therefore, regions of higher inertia shall appear inside the regions of lower inertia, just as higher elevations on a surface appear within lower elevations. Thus,

Contour maps of different inertial levels may be created within the “empty space”.

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Further Research

Heavenly bodies are like regions of very high inertia that exist within with the regions of very low inertia of space. Very high gradients of inertia shall exist at the interface of matter with space, where continuity must exist.

Further research in this area may lead to a better understanding of gravity beyond the mathematical symbols that are often very confusing.

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