Absolute Rest, Inertia & Motion

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Reference: Disturbance Theory

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

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

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THE MICHELSON-MORLEY EXPERIMENT

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

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

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THE POSTULATES OF EINSTEIN

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

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

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

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

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ANALYSIS OF MICHELSON-MORLEY EXPERIMENT

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

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

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

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

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ANALYSIS OF EINSTEIN’S POSTULATES

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

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

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

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

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

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

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THE MATERIAL DOMAIN

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

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

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SUMMARY

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

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

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Inertial frame of reference (Wikipedia)

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Reference: Disturbance Theory

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Parts from Wikipedia article are quoted in black. My comments follow in bold color italics.

Inertial frame of reference – Wikipedia

An inertial frame of reference, in classical physics, is a frame of reference in which bodies, whose net force acting upon them is zero, are not accelerated, that is they are at rest or they move at a constant velocity in a straight line. In analytical terms, it is a frame of reference that describes time and space homogeneously, isotopically, and in a time-independent manner. Conceptually, in classical physics and special relativity, the physics of a system in an inertial frame have no causes external to the system. An inertial frame of reference may also be called an inertial reference frame, inertial frame, Galilean reference frame, or inertial space.

As described in the paper, The Electromagnetic Cycle, “The electromagnetic cycles collapse into a continuum of very high frequencies in our material domain, which provides the absolute and independent character to the space and time that we perceive.”

The “inertial frame of reference” of classical physics describes only the space and time occupied by matter. It does not describe the space and time that is not occupied by matter.

All inertial frames are in a state of constant, rectilinear motion with respect to one another; an accelerometer moving with any of them would detect zero acceleration. Measurements in one inertial frame can be converted to measurements in another by a simple transformation (the Galilean transformation in Newtonian physics and the Lorentz transformation in special relativity). In general relativity, in any region small enough for the curvature of spacetime and tidal forces to be negligible, one can find a set of inertial frames that approximately describe that region.

As described in the paper, The Problem of Inertia, “The uniform drift velocity results naturally from the innate acceleration of disturbance balanced by its inertia. The higher is the inertia, the smaller is the velocity. Matter may be looked upon as a “disturbance” of large inertia. Therefore, black holes of very large inertial mass shall have almost negligible velocity. On the other hand, bodies with little inertial mass shall have higher velocities.”

These inertial frames are valid for the material domain only. They are described by the Newton’s Laws of motion. The velocities in this domain are extremely small compared to the velocity of light. These material velocities are described in relation to each other by simple Galilean transformations. Acceleration applied to a body changes its velocity only for the duration of that acceleration. In the absence of acceleration the original velocity restores itself if the inertia of the body has not changed.

In a non-inertial reference frame in classical physics and special relativity, the physics of a system vary depending on the acceleration of that frame with respect to an inertial frame, and the usual physical forces must be supplemented by fictitious forces. In contrast, systems in non-inertial frames in general relativity don’t have external causes, because of the principle of geodesic motion. In classical physics, for example, a ball dropped towards the ground does not go exactly straight down because the Earth is rotating, which means the frame of reference of an observer on Earth is not inertial. The physics must account for the Coriolis effect—in this case thought of as a force—to predict the horizontal motion. Another example of such a fictitious force associated with rotating reference frames is the centrifugal effect, or centrifugal force.

An accelerating non-inertial frame is changing in inertia. Therefore, additionalforces appear in that frame to balance that additional inertia.

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Introduction

The motion of a body can only be described relative to something else—other bodies, observers, or a set of space-time coordinates. These are called frames of reference. If the coordinates are chosen badly, the laws of motion may be more complex than necessary. For example, suppose a free body that has no external forces acting on it is at rest at some instant. In many coordinate systems, it would begin to move at the next instant, even though there are no forces on it. However, a frame of reference can always be chosen in which it remains stationary. Similarly, if space is not described uniformly or time independently, a coordinate system could describe the simple flight of a free body in space as a complicated zig-zag in its coordinate system. Indeed, an intuitive summary of inertial frames can be given as: In an inertial reference frame, the laws of mechanics take their simplest form.

It is not true that the motion of a body can only be described relative to something else. A body’s absolute motion may be described in terms of its inertia. In the absence of externally applied forces, the velocities of two bodies differ because of difference in their inertia. The velocities become equal when the difference in inertia is balanced by externally applied forces.

The motion of any non-accelerating body may be chosen as a frame of reference. Another body with the same motion will appear at rest in this frame of reference. Such arbitrary frames of references provide fictitious motion on a relative basis. Absolute motion may be perceived only in a frame of zero inertia.

In an inertial frame, Newton’s first law, the law of inertia, is satisfied: Any free motion has a constant magnitude and direction. Newton’s second law for a particle takes the form…

All observers agree on the real forces, F; only non-inertial observers need fictitious forces. The laws of physics in the inertial frame are simpler because unnecessary forces are not present.

In an inertial frame, a body has no acceleration. Its absolute motion is determined by its inertia. Its apparent velocity and direction is determined by the frame of reference being used. The body is imparted acceleration by a force. The acceleration is proportional to the force applied. The proportionality constant is called the “mass” of the body.

The “mass” of the body is an aspect of its inertia. It shows how “pinned” the body is in space. We know from experience that any rotating motion pins a body in space. Therefore, the “mass” of a body may be looked upon as representing some rotating frame of reference.

In Newton’s time the fixed stars were invoked as a reference frame, supposedly at rest relative to absolute space. In reference frames that were either at rest with respect to the fixed stars or in uniform translation relative to these stars, Newton’s laws of motion were supposed to hold. In contrast, in frames accelerating with respect to the fixed stars, an important case being frames rotating relative to the fixed stars, the laws of motion did not hold in their simplest form, but had to be supplemented by the addition of fictitious forces, for example, the Coriolis force and the centrifugal force. Two interesting experiments were devised by Newton to demonstrate how these forces could be discovered, thereby revealing to an observer that they were not in an inertial frame: the example of the tension in the cord linking two spheres rotating about their center of gravity, and the example of the curvature of the surface of water in a rotating bucket. In both cases, application of Newton’s second law would not work for the rotating observer without invoking centrifugal and Coriolis forces to account for their observations (tension in the case of the spheres; parabolic water surface in the case of the rotating bucket).

The fixed stars represent a reference frame of infinite inertia. The absolute motion of such a reference frame is almost zero. An object with lesser inertia will be seen to be in motion in this reference frame. The lesser is the inertia of an object the greater shall be its motion. A rotating frame of reference shall also be rotating with respect to the fixed stars. In that rotating frame of reference there will be inertial forces that are not fictitious, but real, such as, parabolic water surface in the case of the rotating bucket.

As we now know, the fixed stars are not fixed. Those that reside in the Milky Way turn with the galaxy, exhibiting proper motions. Those that are outside our galaxy (such as nebulae once mistaken to be stars) participate in their own motion as well, partly due to expansion of the universe, and partly due to peculiar velocities. The Andromeda galaxy is on collision course with the Milky Way at a speed of 117 km/s. The concept of inertial frames of reference is no longer tied to either the fixed stars or to absolute space. Rather, the identification of an inertial frame is based upon the simplicity of the laws of physics in the frame. In particular, the absence of fictitious forces is their identifying property…

The identification of an inertial frame is based upon the absence of unexplained force or acceleration.

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Background

A brief comparison of inertial frames in special relativity and in Newtonian mechanics, and the role of absolute space is next.

A set of frames where the laws of physics are simple

According to the first postulate of special relativity, all physical laws take their simplest form in an inertial frame, and there exist multiple inertial frames interrelated by uniform translation:

Special principle of relativity: If a system of coordinates K is chosen so that, in relation to it, physical laws hold good in their simplest form, the same laws hold good in relation to any other system of coordinates K’ moving in uniform translation relatively to K.
— Albert Einstein: The foundation of the general theory of relativity, Section A, §1

The special principle of relativity seems to consider the inertial frames of references in material domain only.

This simplicity manifests in that inertial frames have self-contained physics without the need for external causes, while physics in non-inertial frames have external causes. The principle of simplicity can be used within Newtonian physics as well as in special relativity; see Nagel and also Blagojević.

The laws of Newtonian mechanics do not always hold in their simplest form…If, for instance, an observer is placed on a disc rotating relative to the earth, he/she will sense a ‘force’ pushing him/her toward the periphery of the disc, which is not caused by any interaction with other bodies. Here, the acceleration is not the consequence of the usual force, but of the so-called inertial force. Newton’s laws hold in their simplest form only in a family of reference frames, called inertial frames. This fact represents the essence of the Galilean principle of relativity: The laws of mechanics have the same form in all inertial frames.
— Milutin Blagojević: Gravitation and Gauge Symmetries, p. 4

Only the laws of mechanics have the same form in all inertial frames because they operate on a relative basis in the material domain (the continuum of very high frequencies).

In practical terms, the equivalence of inertial reference frames means that scientists within a box moving uniformly cannot determine their absolute velocity by any experiment (otherwise the differences would set up an absolute standard reference frame). According to this definition, supplemented with the constancy of the speed of light, inertial frames of reference transform among themselves according to the Poincaré group of symmetry transformations, of which the Lorentz transformations are a subgroup. In Newtonian mechanics, which can be viewed as a limiting case of special relativity in which the speed of light is infinite, inertial frames of reference are related by the Galilean group of symmetries.

Absolute motion shall be visible only in a frame of reference of zero inertia. Newtonian mechanics uses light as the reference point of “infinite velocity” for material domain. This is adequate except on cosmological scale where the finite speed of light generates anomalies. Special relativity accounts for the finite velocity of light and explains the cosmological anomalies. Special relativity is adequate except on atomic scale where the finite inertia of light generates anomalies.

Absolute space

Newton posited an absolute space considered well approximated by a frame of reference stationary relative to the fixed stars. An inertial frame was then one in uniform translation relative to absolute space. However, some scientists (called “relativists” by Mach), even at the time of Newton, felt that absolute space was a defect of the formulation, and should be replaced.

As explained in the paper, The Electromagnetic Cycle, space and time may be treated as absolute in the material domain only. The doubts entered only where cosmic dimensions were involved in which light’s finite velocity could not be ignored.

Indeed, the expression inertial frame of reference (German: Inertialsystem) was coined by Ludwig Lange in 1885, to replace Newton’s definitions of “absolute space and time” by a more operational definition. As translated by Iro, Lange proposed the following definition:

A reference frame in which a mass point thrown from the same point in three different (non co-planar) directions follows rectilinear paths each time it is thrown, is called an inertial frame.

A discussion of Lange’s proposal can be found in Mach.

The inadequacy of the notion of “absolute space” in Newtonian mechanics is spelled out by Blagojević:

  • The existence of absolute space contradicts the internal logic of classical mechanics since, according to Galilean principle of relativity, none of the inertial frames can be singled out.
  • Absolute space does not explain inertial forces since they are related to acceleration with respect to any one of the inertial frames.
  • Absolute space acts on physical objects by inducing their resistance to acceleration but it cannot be acted upon.
— Milutin Blagojević: Gravitation and Gauge Symmetries, p. 5

“Absolute space” is actually the reference frame of zero inertia. Newton approximated “absolute space” as the background of fixed stars. But fixed stars provide a reference frame of infinite inertia and not of zero inertia.

The utility of operational definitions was carried much further in the special theory of relativity. Some historical background including Lange’s definition is provided by DiSalle, who says in summary:

The original question, “relative to what frame of reference do the laws of motion hold?” is revealed to be wrongly posed. For the laws of motion essentially determine a class of reference frames, and (in principle) a procedure for constructing them.
— Robert DiSalle Space and Time: Inertial Frames

Inertial frames are frames of constant inertia. Acceleration is always related to change in inertia. The physicists have overlooked the concept of zero inertia

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Newton’s inertial frame of reference

Within the realm of Newtonian mechanics, an inertial frame of reference, or inertial reference frame, is one in which Newton’s first law of motion is valid. However, the principle of special relativity generalizes the notion of inertial frame to include all physical laws, not simply Newton’s first law.

Newton viewed the first law as valid in any reference frame that is in uniform motion relative to the fixed stars; that is, neither rotating nor accelerating relative to the stars. Today the notion of “absolute space” is abandoned, and an inertial frame in the field of classical mechanics is defined as:

An inertial frame of reference is one in which the motion of a particle not subject to forces is in a straight line at constant speed.

An inertial frame of reference has its true basis in zero inertia of EMPTINESS, and not in the infinite inertia of fixed stars.

Hence, with respect to an inertial frame, an object or body accelerates only when a physical force is applied, and (following Newton’s first law of motion), in the absence of a net force, a body at rest will remain at rest and a body in motion will continue to move uniformly—that is, in a straight line and at constant speed. Newtonian inertial frames transform among each other according to the Galilean group of symmetries.

In material domain, the level of inertia is so high that compared to it, the differences in inertia of material bodies, and its effect on their velocities can be ignored.

If this rule is interpreted as saying that straight-line motion is an indication of zero net force, the rule does not identify inertial reference frames because straight-line motion can be observed in a variety of frames. If the rule is interpreted as defining an inertial frame, then we have to be able to determine when zero net force is applied. The problem was summarized by Einstein:

The weakness of the principle of inertia lies in this, that it involves an argument in a circle: a mass moves without acceleration if it is sufficiently far from other bodies; we know that it is sufficiently far from other bodies only by the fact that it moves without acceleration.
— Albert Einstein: The Meaning of Relativity, p. 58

The weakness here is the implicit assumption that the relative uniform motion remains constant in the absence of external forces. This assumption ignores the influence of inertia on motion.

There are several approaches to this issue. One approach is to argue that all real forces drop off with distance from their sources in a known manner, so we have only to be sure that a body is far enough away from all sources to ensure that no force is present. A possible issue with this approach is the historically long-lived view that the distant universe might affect matters (Mach’s principle). Another approach is to identify all real sources for real forces and account for them. A possible issue with this approach is that we might miss something, or account inappropriately for their influence, perhaps, again, due to Mach’s principle and an incomplete understanding of the universe. A third approach is to look at the way the forces transform when we shift reference frames. Fictitious forces, those that arise due to the acceleration of a frame, disappear in inertial frames, and have complicated rules of transformation in general cases. On the basis of universality of physical law and the request for frames where the laws are most simply expressed, inertial frames are distinguished by the absence of such fictitious forces…

A source of “force” is body’s inertia, from which the body cannot be separated. We cannot assume all inertial frames to have the same inertia.

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Separating non-inertial from inertial reference frames

Theory

Inertial and non-inertial reference frames can be distinguished by the absence or presence of fictitious forces, as explained shortly.

The effect of this being in the noninertial frame is to require the observer to introduce a fictitious force into his calculations….
— Sidney Borowitz and Lawrence A Bornstein in A Contemporary View of Elementary Physics, p. 138

The presence of fictitious forces indicates the physical laws are not the simplest laws available so, in terms of the special principle of relativity, a frame where fictitious forces are present is not an inertial frame:

The equations of motion in a non-inertial system differ from the equations in an inertial system by additional terms called inertial forces. This allows us to detect experimentally the non-inertial nature of a system.
— V. I. Arnol’d: Mathematical Methods of Classical Mechanics Second Edition, p. 129

Bodies in non-inertial reference frames are subject to so-called fictitious forces (pseudo-forces); that is, forces that result from the acceleration of the reference frame itself and not from any physical force acting on the body. Examples of fictitious forces are the centrifugal force and the Coriolis force in rotating reference frames…

The “fictitious” forces are essentially due to the inertia of the reference frame. The influence of inertia can be fully accounted only in a frame of reference of zero inertia.

Applications

Inertial navigation systems used a cluster of gyroscopes and accelerometers to determine accelerations relative to inertial space. After a gyroscope is spun up in a particular orientation in inertial space, the law of conservation of angular momentum requires that it retain that orientation as long as no external forces are applied to it. Three orthogonal gyroscopes establish an inertial reference frame, and the accelerators measure acceleration relative to that frame. The accelerations, along with a clock, can then be used to calculate the change in position. Thus, inertial navigation is a form of dead reckoning that requires no external input, and therefore cannot be jammed by any external or internal signal source…

The “inertial space” is set by the orientation of spinning gyroscopes.

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Newtonian mechanics

Classical mechanics, which includes relativity, assumes the equivalence of all inertial reference frames. Newtonian mechanics makes the additional assumptions of absolute space and absolute time. Given these two assumptions, the coordinates of the same event (a point in space and time) described in two inertial reference frames are related by a Galilean transformation…

Newtonian mechanics applies only to the material domain of very high inertia, where differences in the inertia of material bodies can be ignored.

Special relativity

Einstein’s theory of special relativity, like Newtonian mechanics, assumes the equivalence of all inertial reference frames, but makes an additional assumption, foreign to Newtonian mechanics, namely, that in free space light always is propagated with the speed of light c0, a defined value independent of its direction of propagation and its frequency, and also independent of the state of motion of the emitting body. This second assumption has been verified experimentally and leads to counter-intuitive deductions including:

  • time dilation (moving clocks tick more slowly)
  • length contraction (moving objects are shortened in the direction of motion)
  • relativity of simultaneity (simultaneous events in one reference frame are not simultaneous in almost all frames moving relative to the first).

These deductions are logical consequences of the stated assumptions, and are general properties of space-time, typically without regard to a consideration of properties pertaining to the structure of individual objects like atoms or stars, nor to the mechanisms of clocks…

From this perspective, the speed of light is only accidentally a property of light, and is rather a property of spacetime, a conversion factor between conventional time units (such as seconds) and length units (such as meters).

Incidentally, because of the limitations on speeds faster than the speed of light, notice that in a rotating frame of reference (which is a non-inertial frame, of course) stationarity is not possible at arbitrary distances because at large radius the object would move faster than the speed of light.

As described in the paper, The Electromagnetic Cycle“The electromagnetic cycles collapse into a continuum of very high frequencies in our material domain, which provides the absolute and independent character to the space and time that we perceive.

“This is the Newtonian domain of space and time. Einsteinian length contraction and time dilation does not occur in this Newtonian domain. It occurs at much lower electromagnetic frequencies.”

Special relativity allows frames of references that are outside the material domain. The error is to consider them equivalent to those in material domain.

 

General relativity

General relativity is based upon the principle of equivalence:

There is no experiment observers can perform to distinguish whether an acceleration arises because of a gravitational force or because their reference frame is accelerating.
— Douglas C. Giancoli, Physics for Scientists and Engineers with Modern Physics, p. 155.

General relativity acknowledges inertia in the context of a field.

This idea was introduced in Einstein’s 1907 article “Principle of Relativity and Gravitation” and later developed in 1911. Support for this principle is found in the Eötvös experiment, which determines whether the ratio of inertial to gravitational mass is the same for all bodies, regardless of size or composition. To date no difference has been found to a few parts in 1011. For some discussion of the subtleties of the Eötvös experiment, such as the local mass distribution around the experimental site (including a quip about the mass of Eötvös himself), see Franklin.

Inertial and gravitational mass are equivalent.

Einstein’s general theory modifies the distinction between nominally “inertial” and “noninertial” effects by replacing special relativity’s “flat” Minkowski Space with a metric that produces non-zero curvature. In general relativity, the principle of inertia is replaced with the principle of geodesic motion, whereby objects move in a way dictated by the curvature of spacetime. As a consequence of this curvature, it is not a given in general relativity that inertial objects moving at a particular rate with respect to each other will continue to do so. This phenomenon of geodesic deviation means that inertial frames of reference do not exist globally as they do in Newtonian mechanics and special relativity.

The inertial frames of general relativity acknowledge the differences in their inertia and start to account for it.

However, the general theory reduces to the special theory over sufficiently small regions of spacetime, where curvature effects become less important and the earlier inertial frame arguments can come back into play. Consequently, modern special relativity is now sometimes described as only a “local theory”. The study of double-star systems provided significant insights into the shape of the space of the Milky Way galaxy. The astronomer Karl Schwarzschild observed the motion of pairs of stars orbiting each other. He found that the two orbits of the stars of such a system lie in a plane, and the perihelion of the orbits of the two stars remains pointing in the same direction with respect to the solar system. Schwarzschild pointed out that that was invariably seen: the direction of the angular momentum of all observed double star systems remains fixed with respect to the direction of the angular momentum of the Solar System. These observations allowed him to conclude that inertial frames inside the galaxy do not rotate with respect to one another, and that the space of the Milky Way is approximately Galilean or Minkowskian.

Special relativity uses light as its reference frame. This is different from a reference frame of zero inertia. This introduces an error that is carried forward into General relativity.

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The Electromagnetic Cycle

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Reference: Disturbance Theory

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Electromagnetism is described by Maxwell’s equations. It describes how electric field E, and magnetic field B, influence each other and are created by charges and currents:

  1. ∇⃗⋅ E = ρ/ϵ0
  2. ∇⃗⋅ B = 0
  3. ∇⃗× E = −∂B /∂t
  4. ∇⃗× B = c−2E /∂t + μ0J

∇⃗ ⋅” is the divergence operator. The divergence is a measure of the flow of a vector field.

∇⃗ ×” is the curl operator. The curl is a measure of the rotation of a vector field.

The Maxwell’s equations may be interpreted as follows:

  1. Electrical lines of force flow forward due to charge (misalignment in the field).

  2. The magnetic lines of force appear as circles around the electrical lines of force.

  3. The flow of electrical lines of force slows as it converts into rotating magnetic lines of force.

  4. The rotation overshoots the point of equilibrium and starts unwinding as forward flow again.

This is like an oscillation taking place in the field in the form of electric flow and magnetic rotation under the influence of some charge. The charge may be perceived as a misalignment of frequency gradient, which then drives this back and forth interchange.

An electromagnetic cycle is then an oscillation of electric flow and magnetic rotation. Such electromagnetic cycles are in equilibrium with the atomic harmonic oscillators of the blackbody in the blackbody radiation.

We may consider the electric flow and magnetic rotation of electromagnetic cycle to correspond to the kinetic and potential energies of harmonic oscillators respectively.

The electric flow then has a kinetic aspect of forward motion through SPACE. It seems to provide the idea of wavelength, and a sense of extension. On the other hand, the magnetic rotation has a potential aspect of holding motion through TIME. It seems to provide the idea of period, and a sense of duration. Thus, it seems that,

There is a back and forth conversion of flowing space and stored time in the electromagnetic cycle. The universal constant ‘c’, or the speed of light, then provides a basic relationship between space and time.

When there is extremely low frequency, space and time appear to be infinite and almost indistinguishable. However, as the frequency increases, space and time subdivide into increasingly smaller segments and intervals. We then start to get an increasingly defined sense of space and time.

The greater is the frequency the more defined are space and time.

In the material domain, the frequency of electromagnetic cycle is so high that the segments of space and the intervals of time are practically infinitesimal. The ‘discrete’ frequency collapses into a ‘continuum’ of mass. The extensions of space and durations of time are made of infinitely refined bits and clearly defined. This refinement of space and time has a constancy because it is no longer affected by changes in frequency.

In the material domain, the very high frequency of electromagnetic cycles collapses into the continuum of  mass. This provides an absolute and independent feel to space and time.

This is the Newtonian domain of space and time. Einsteinian length contraction and time dilation occurs at much lower electromagnetic frequencies than those in the Newtonian doman.

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Remedial Math Level 2A

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Middle School Review 2A

Lesson 1: Factoring

For exercise: Factoring Problems from Dubb

For certification solve 3 randomly selected problems each

(1) From Article 87 (1 to 21) in 5 minutes.

(2) From Article 88 (1 to 22) in 5 minutes.

(3) From Article 89 (1 to 35 – 1 word problem) in 10 minutes.

(4) From Article 90 (1 to 37 – 1 word problem) in 10 minutes.

(5) From Article 91 (1 to 21 – 1 word problem) in 10 minutes.

Lesson 2: Fractions

For exercise: Fraction Problems from Dubb

For certification solve 3 randomly selected problems each

(1) From Article 103 (1 to 20) in 10 minutes.

(2) From Article 104 (1 to 30) in 10 minutes.

(3) From Article 105 (1 to 30) in 10 minutes.

(4) From Article 106 (1 to 25) in 10 minutes.

(5) From Article 107 (1 to 30) in 10 minutes.

(6) From Article 108 (1 to 40) in 10 minutes.

(7) From Article 108 GCD (1 to 12) in 10 minutes.

(8) From Article 108 LCM (1 to 12) in 10 minutes.

(9) From Article 111 (1 to 34 – 1 word problem) in 10 minutes.

(10) From Article 114 (1 to 38 – 1 word problem) in 10 minutes.

(11) From Article 115 (1 to 21) in 10 minutes.

(12) From Article 118 (1 to 35) in 10 minutes.

(13) From Article 119 (1 to 42 – 1 word problem) in 10 minutes.

(14) From Article 120 (1 to 20) in 10 minutes.

(15) From Article 121 (1 to 14) in 10 minutes.

(16) From Article 122 (1 to 20) in 10 minutes.

(17) From Article 129 (1 to 102) in 10 minutes.

Lesson 3: Decimals

For exercise: Decimal Problems from Dubb

For certification solve 3 randomly selected problems each

(1) From Article 135 (1 to 50) in 5 minutes.

(2) From Article 136 (1 to 18) in 5 minutes.

(3) From Article 141 (1 to 31) in 10 minutes.

(4) From Article 142 (1 to 30) in 10 minutes.

(5) From Article 143 (1 to 20 – one word problem) in 10 minutes.

(6) From Article 144 (1 to 30 – one word problem) in 10 minutes.

(7) From Article 147 (1 to 35 – one word problem) in 10 minutes.

(8) From Article 150 (1 to 37 – one word problem) in 10 minutes.

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OLDER VERSIONS

MS B3 Factors

MS B4 Frac Props

MS B5 Frac Ops

MS B6 Decimals

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Inertia of EM Field

background1
Reference: Disturbance Theory

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In my opinion, quantum physics lacks a basic explanation because it has no definition for “physical substance” or inertia.

A definition of physical substance cannot be arrived at in the absence of the fundamental postulate of EMPTINESS (no substance, no space, no time).

The awareness of substance comes from its property of inertia. The theoretical concept of EMPTINESS is a state of zero inertia.

A substance more basic than matter is the electromagnetic field. For this field the inertia may be defined as,

Inertia = momentum x frequency

This means that if there is a frequency, then there is also inertia. Therefore, light has a finite amount of inertia.

Einstein assumed the inertia of light to be zero. This assumption works when dealing with matter, or material systems, because the inertia of matter is very high and the inertia of light can be ignored.

However, that assumption does not work for quantum particles because in that case the inertia of light cannot be ignored.

Thus, inertia provides a sense of physical substance, and a precise mathematical definition.

This concept of inertia or “substance” is lacking in quantum physics. Please see

The Problem of Inertia

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Addition (1/10/2018)

Inertia is “innate force” per Newton. The unit of inertia is more like the unit of force. Since, Force = Energy/distance, we may write inertia for the EM field as

Inertia = energy / wavelength = hf/λ

Its unit will be something like electron volt per angstrom.

Therefore, inertia increases as
… Energy increases
… Wavelength decreases
… Momentum increases
… Frequency increases

Inertia goes to zero as frequency goes to zero. Therefore, we can express inertia in absolute terms.

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