## All Posts

## BOOK: The Mindfulness Approach

## BOOK: The Disturbance Theory

## BOOK: Education in Information Age

## Remedial Math

## A Critique of Scientology Philosophy

.

Where Eastern thought meets Western technology

.

.

This is continuation of the examination of Einstein’s postulates underlying his theory of Relativity, specifically, how these postulates were translated into his mathematics.

.

Einstein takes up a system of coordinates in which equations of Newtonian mechanics hold well. These he calls inertial frames in which a body remains at rest or moves with constant linear velocity unless acted upon by forces. This property of a body is called inertia.

**Inertia represents the resistance to change in motion of a body in space. When this resistance is overcome there is acceleration. We have assumed all along that space is completely permeable to matter. This is not so as evidenced by inertia.**

Therefore, matter is ‘stationary’ relative to space when there is no acceleration. All inertial frames in “uniform motion” are actually stationary relative to space. This we identified earlier as the space reference frame (SRF).

A particle is essentially a disturbance propagating through space. This particle of disturbance has a configuration. As the complexity of this configuration increases, the inertia of the particle also increases, and its speed of propagation decreases. A light particle has the simplest configuration and its speed of propagation is ‘c’. An electron is a particle of complex configuration, whose speed is less than 1% of the speed of light. A neutron is a still more complex particle whose speed is thousand times still less.

Einstein’s “material point” refers to a matter particle that has a configuration more complex than that of a neutron. In its most complex configuration a matter particle shall have a speed that is infinitesimal compared to ‘c’. Euclidean geometry and Cartesian co-ordinates apply only to this extreme case of a matter particle. They do not apply to light particles.

All motion considered by Einstein is in reference to matter. This we identified earlier as the material reference frame (MRF). MRF represents a limiting case of a more general SRF that addresses a much wider range of particle configurations.

The natural speed of propagation in space then depends on the complexity of configuration of a disturbance as particle. This we perceive as motion that is balanced by the inertia of the particle. Any change in this balance is perceived as acceleration. Acceleration implies presence of force.

Motion is described by the property of TIME. Time essentially describes the sequence of change. A change is referred back to the previous step in the sequence. Thus, time lies in the continuity of a sequence, and it is unique to the configuration of that sequence.

To compare two time sequences in terms of simultaneity they must have comparable configurations. This is reflected in comparability in terms of inertia of the particles. The property of time shall then be a function of inertia. The “time” that we are used to is tied with the material level of inertia. In other words, our experience of time depends on the inertial characteristic of MRF (material reference frame).

The “time” associated with light shall depend on the configuration of the light particle or its inertia. To consider simultaneity of time for matter and light particles, their relative inertia shall have to be taken into account.

The “time characteristics” of particles of different inertia shall be measurable from a “particle” that has no inertia. Such a particle may be postulated as “undisturbed space”. We can then assess the “simultaneity” of two particles by determining their “time characteristics” in terms of their inertia.

The complexity of configuration, and thus the inertia of a particle may be measured in terms of “disturbance levels” as described earlier in *The Disturbance Theory**.* On this scale* *the disturbance level of zero is a frequency of 1. The disturbance level of 77.6 represents a neutron. All higher disturbance levels represent matter. Earth has a disturbance level of about 235.

At the disturbance levels of matter the wavelength, period and speed become infinitesimal; and the sinusoidal variations in time and space become imperceptible. Time and space then acquire an appearance of constancy that does not exist at electrodynamic and quantum levels.

The idea of observer basically represents the characteristics of the reference frame that is being used to interpret motion. The time measured by Einstein’s clocks follows the inertial characteristics of matter. To combine the velocity of light with material velocity would be equivalent to assuming light to have same inertial characteristics as matter. Any mathematics that combines the velocity of light with material velocity using simple addition or subtraction shall lead to erroneous results. It would be like adding a penny to a dollar and calling it two coins of same magnitude.

Unfortunately, Einstein’s mathematics does just that in the rest of this section. We shall skip this mathematics and focus on those aspects of Einstein’s theory that make correct predictions of physical phenomena. Hopefully, a closer look at such aspects will provide better insight into Einstein’s thinking.

.

.

This examination of Einstein’s 1905 paper on relativity (see the link above) is being carried out to see if Einstein’s original postulates can be modified to bring better consistency among the Theory of Relativity and Newtonian Mechanics.

.

This introductory paragraph from the paper mentions asymmetry observed in the relative motion between a magnet and a conductor. This asymmetry occurs in the reference frame of the lab, which results in different interpretation of the same phenomenon.

This “asymmetry” disappears when we use the magnetic lines of force, which are attached to the magnet, as the reference frame. The conductor moves relative to these lines of force the same way in either case producing the same result.

This paragraph states that no motion of the earth relatively to the “light medium” has been discovered. This is incorrect because the very fact of radial acceleration due to inertia is a proof of motion relatively to the “light medium”.

This “light medium” is the space itself as established by Maxwell’s equations. The very fact that the speed of light is determined exclusively by the permeability and permittivity of space establishes space as the “light medium”. Light is a disturbance in space.

It was assumed that space could not be a medium because it could not be rigid to electromagnetic waves, while being completely permeable to matter. It was not realized that space puts up resistance to motion relative to it in the form of inertia. Thus space is not completely permeable to matter. Space resists the motion of matter. This resistance shows up as inertia.

Any motion relative to space requires force and it is accompanied by acceleration. Moons are always accelerating toward their planets. Planets are always accelerating toward their stars. Stars are always accelerating toward the center of their galaxies and so on. There may appear to be no acceleration in the direction tangential to an orbit. But there is always a radial acceleration toward some center. When there is no force or acceleration, there is no motion relative to space.

There is no uniform motion without acceleration that travels in straight line. All Newtonian or Einstenian inertial frames are actually a single frame, which is at rest relative to space. This nicely explains the Principle of Relativity.

Any motion in this single frame is resisted by inertia. A fixed velocity in this frame shall result from a balance between acceleration and inertia. The velocity of light is finite and constant because there is a balance between an electromagnetic push of disturbance and the inertia of disturbed space.

If a Michelson-Morley experiment is conducted to compare the speed of light in the direction tangential to earth’s orbit and also normal to it, it is likely to observe a difference due to the centripetal acceleration of earth. Einstein’s assumption that there is no motion of the earth relative to the “light medium” is not fully justified.

An absence of inertia may be used as an absolute rest point from which to measure motion. Any motion relative to space will manifest some force due to inertia as acceleration.

**The phenomena of electrodynamics as well as of mechanics, has inertia as a property common between them that can be referenced from the idea of undisturbed space. **

Einstein postulates as the Principle of Relativity: *“The same laws of electrodynamics and optics will be valid for all frames of reference for which the equations of mechanics hold good.”*

This postulate assumes that light has same inertial characteristics as matter. This assumption is not justified.

Einstein makes another postulate: “Light is always propagated in empty space with a definite velocity c which is independent of the state of motion of the emitting body.”

This postulate assumes that there is no property shared by light with the body that emits it, which control their respective velocities. This assumption is also not justified because the velocities of light and the emitting body are related by their respective inertia relative to space.

Essentially, Einstein uses RIGID MATTER as its reference frame. We may call it the Material Reference Frame or MRF. This reference frame does not properly account for the inertia associated with light and sub-atomic particles. It actually considers inertia of light particle (photon) to be zero.

The proper reference frame would however be SPACE. We may call it the Space Reference Frame or SRF. This reference frame shall account for the inertia associated with light and sub-atomic particles. It would not represent space by rigid coordinates. The SRF coordinate system shall take into account the varying characteristics of inertia of the particles being considered.

.

.

On June 9^{th}, 1952, Einstein stated in the preface of the 15^{th} edition of his “Relativity–The Special and General Theory”,

“In this edition I have added, as a fifth appendix, a presentation of my views on the problem of space in general and on the gradual modifications of our ideas on space resulting from the influence of the relativistic viewpoint. I wished to show that space-time is not necessarily something to which one can ascribe a separate existence, independently of the actual objects of physical reality. Physical objects are notin space, but these objects arespatially extended. In this way the concept of “empty space” loses is meaning.”

The Disturbance Theory is based on the postulate that space, when disturbed, breaks into electric and magnetic fields. In other words, when space and time come together they transform into energy of disturbance. This transition is seamless, meaning that space, time and energy are intimately related. They show up as wavelength, period and frequency of the disturbance.

The electromagnetic spectrum represents increasing state of disturbance, which ranges from low frequency radio waves to high frequency gamma rays. The disturbance starts to condense in the range of gamma rays until it transforms into matter. In this sense, space, time, energy and matter are fundamentally related.

All stages of the electromagnetic spectrum may be found in the structure of an atom, if we consider the atomic boundary to extend all the way to space. The most condensed disturbance forms the nucleus of the atom.

**Atoms may be looked upon as tiny whirlpools in the sea of electromagnetic field of disturbed space.**

The above shows that not only space, time and energy are intimately related, the energy appears as mass at very high disturbance levels.

.

The undisturbed space has no bounds or form. It acquires a form only when it is disturbed. The disturbance appears as a dynamic electromagnetic field that has gradients of disturbance levels. A gradient of disturbance levels has the form of acceleration, force or gravity. Within a uniform disturbance level there is stillness or constant velocity.

The disturbance levels are defined by their wavelength, period and frequency. The wavelength and period maintain a constant ratio ‘c’. The frequency is the inverse of period. This may be shown symbolically as

*λ / T = c*

*f = 1/T*

*Where, λ is the wavelength associated with space;*

* T is the period associated with time;*

* c is a universal constant referred to as speed of light;*

* and, f is the frequency associated with energy*

The electromagnetic spectrum covers a large range of frequencies as radio and micro waves, infra-red, visible and ultra-violet light, X and Gamma ionizing radiation, and subatomic particles. These frequencies may be expressed more conveniently on a logarithmic scale of base 2. The logarithmic form of frequency is referred to as Disturbance Level (D).

*D = log _{2} (f)*

**So we have a fundamental relationship among space, time, energy and matter.**

By equating space-time with energy-mass, the Disturbance Theory hopes to bring about an interpretation that makes the theory of relativity consistent with quantum mechanics and Newton’s theory of motion.

.

We live on a material plane, and so we view space, time and energy from the viewpoint of matter. Our reality is the fact of matter.

Matter appears at the upper end of the electromagnetic spectrum. It is highly condensed disturbance. If we look at the wavelength of disturbance as the unit of space, it is infinitesimal at the level of matter. Similarly, the unit of time as period of disturbance is also infinitesimal at the level of matter. This makes the calculus of space and time possible. But this is so at the level of matter only and not at other parts of the electromagnetic spectrum. There is continuity at disturbance levels lower than matter but it is of a different sort. At these parts of the electromagnetic spectrum the wavelength and period is finite and the reality can be very different, but we do not get to experience it ordinarily.

We live on earth. We are connected to matter all the time. Therefore, we perceive space and time in infinitesimal increments. This brings smoothness of continuity to our physical senses. It forms the basis of our knowledge. Euclidean geometry and Newtonian mechanics has its basis in it.

But how is it out in the interstellar space? How does one experience space and time away from matter—even away from the matter of the spaceship that carried us there, or away from the matter that constitutes our bodies? What is space and time like when its units in terms of wavelength and period are no longer infinitesimal?

How do we visualize an electromagnetic field spread over vast interstellar space in which finite wavelength, period and frequency are changing dynamically. Here the gradients in frequencies bring about the sense of acceleration, force or gravity. It is like living within Faraday’s lines of force that come together, and then spread out in an eternal cosmic dance.

Like a blurred vision, the location in space and time gets blurred far from material surface of a planet. A location can be defined with pin-point precision on a material surface only. The GPS signals that travel to a satellite and back require relativistic correction. This is because the location of satellite is a bit blurred relative to the locations on earth.

**The theory of relativity gets it right about the blurring of the very nature of space and time.**

Dark energy and matter in the interstellar space has no reasonable explanation at the moment. The concept of disturbed space might be able to provide an explanation.

.

Relativistic mathematics of Einstein is based on MRF (material reference frame). The Disturbance Theory proposes mathematics based on SRF (space reference frame). SRF math is yet to be developed. It should lead to similar space-time correction.

MRF math uses the concept of velocity, which is applicable only for a specialized view of space and time near the surfaces of planets.

**SRF math shall use the concept of disturbance levels, instead of velocity. **

The concept of disturbance level is applicable to all locations near or far from planets.

.

.

In 1632, Galileo Galilei first described that in a ship travelling at constant velocity, without rocking, on a smooth sea; any observer doing experiments below the deck would not be able to tell whether the ship was moving or stationary. This is a nice description of an inertial frame.

An inertial frame is one in which Newton’s first law remains true. In other words, in this frame, an object stays either at rest or at a constant velocity unless a force acts on it. A non-inertial frame shall be experienced inside an accelerating rocket. In this frame Newton’s first law will not hold true.

In short, all inertial frames are in a state of constant, straight line motion with zero acceleration. Measurements in one inertial frame can be converted to the measurements in another by a simple transformation.

For example, suppose two cars are moving side by side at the speed of 60 mph in the same direction. The driver of each car will see the other car to be practically still. The speed of a car relative to the other would be the “algebraic difference” of their speeds: 60 – 60 = 0. If the two cars were approaching each other at 60 mph, a driver will see the other car approaching at 120 mph [60 – (–60) = 120].

NOTE: The individual speeds would have to be measured in a common reference frame for the above transformation to be valid.

This simple transformation shall also apply to the relative speed of disturbances moving through a medium. Here the medium stays still while the disturbance moves through it. The speed of the disturbance relative to the medium is determined by the properties of the medium.

For example, suppose a ripple on the surface of water moves at speed, R based on the properties of water. We see two ripples approaching each other, each moving on the surface of water at speed R toward the other. Their relative speed shall be: R – (–R) = 2R. The transformation is the same as in the case of cars in the previous example, because individual speeds are measured in a common reference frame.

Sound travels in dry air at 20°C at a speed of 343 meters per second. If two waves of sound are approaching each other, their relative speed shall be 343 x 2 = 686 meters per second. This is because the medium in which these waves are traveling provides a common reference frame. By no means is this relative speed “supersonic”, because this speed is not relative to the medium.

If two beams of light were approaching each other in a medium that provided a common inertial frame, similar consideration shall apply. In other words, their relative speed shall be “2c” where c is the speed of light. This shall not violate the limit placed by the medium on the speed of light.

In the 19^{th} century a medium called “luminiferous ether” was postulated for light, but it could not be found. The absence of a medium resulted in the assumption that the relative speed of two light beams approaching each other would also be ‘c’ instead of ‘2c’. This resulted in a mathematics that led to the strange ideas of ‘length contraction’ and ‘time dilation’.

Why couldn’t we find any medium for light? Were we looking for the wrong thing?

In 1873, Maxwell’s effort to determine the relationship between electromagnetic theories and the Newton’s theory of motion resulted in the amazing discovery that light was an electromagnetic phenomenon.

Maxwell wrote in the preface to the first edition of his book A TREATISE ON ELECTRICITY AND MAGNETISM:

*“The most important aspect of any phenomenon from a mathematical point of view is that of a measurable quantity… I have therefore thought that a treatise would be useful which should have for its principal object to take up the whole subject in a methodical manner, and which should also indicate how each part of the subject is brought within the reach of methods of verification by actual measurement… before I began the study of electricity I resolved to read no mathematics on the subject till I had first read through Faraday’s Experimental Researches in Electricity.*

*“As I proceeded with the study of Faraday, I perceived that his method of conceiving the phenomena was also a mathematical one, though not exhibited in the conventional form of mathematical symbols. I also found that these methods were capable of being expressed in the ordinary mathematical forms, and thus compared with those of the professed mathematicians.*

*“For instance, Faraday, in his mind’s eye, saw lines of force traversing all space where the mathematicians saw centres of force attracting at a distance: Faraday saw a medium where they saw nothing but distance: Faraday sought the seat of the phenomena in real actions going on in the medium, they were satisfied that they had found it in a power of action at a distance impressed on the electric fluids.*

*“When I had translated what I considered to be Faraday’s ideas into a mathematical form, I found that in general the results of the two methods coincided, so that the same phenomena were accounted for, and the same laws of action deduced by both methods, but that Faraday’s methods resembled those in which we begin with the whole and arrive at the parts by analysis, while the ordinary mathematical methods were founded on the principle of beginning with the parts and building up the whole by synthesis.”*

It is interesting to note that Maxwell finds Faraday’s “lines of force traversing all space” to be mathematically equivalent to other mathematician’s “centers of force attracting at a distance”. Maxwell notes, “Faraday saw a medium where they [other mathematicians] saw nothing but distance”.

Space is not “nothing” because it has the electromagnetic properties of permittivity and permeability. These properties of space determine the speed of light per Maxwell’s equations. This fact alone should be enough to convince that space is the medium through which light travels.

Why is space not considered to be the medium of light? Why can’t the mysterious ether be space itself?

The answer to this question seems to be tied with the mystery of inertia. Neither space nor light seem to exhibit the property of inertia. Therefore, we cannot apply the considerations of the inertial frame to space and light.

Let’s make the following postulate. It is a reasonable postulate.

**“Space, when disturbed, breaks into electric and magnetic fields.”**

This is similar to the observation that water, when disturbed breaks into peaks and valleys; or air, when disturbed, breaks into high and low pressure areas.

In case of the ripple in water we see the movement of peaks and valleys, but not that of water. In case of sound we see the movement of high and low pressure, but not that of air. We may say that in case of light we see the movement of electric and magnetic fields but not that of space itself.

How does this compare with the 19^{th} century consideration of “luminiferous ether”?

The “luminiferous ether” was assumed to be rigid to electromagnetic wave of light. If light were a disturbance in space, we can see this disturbance to propagate when changing electric field generates a magnetic field, and a changing magnetic field generates an electric field. The problem of ether being rigid to electromagnetic wave of light is thus resolved.

The “luminiferous ether” was also assumed to be completely permeable to matter. Is this true? Doesn’t matter encounter resistance when pushed through space? What is inertia?

By light, we don’t just mean the visible light. It refers to the whole electromagnetic spectrum from low frequency radio waves to very high frequency gamma rays. We may understand the nature of this spectrum better by looking at the structure of atom.

Gamma rays are produced in the disintegration of the nucleus of an atom. This nucleus is surrounded by electrons. Beyond these electrons is electromagnetic field, and beyond that field is space. From space to the nucleus of an atom we seem to have the whole electromagnetic spectrum.

The electromagnetic spectrum represents an increasingly disturbed space. The nucleus of an atom then represents a highly disturbed state of space that appears as mass.

We can now see that the movement of mass through space shall require undisturbed space to suddenly go to a highly disturbed space. This would create a resistance. This resistance may explain the mystery of inertia. The higher is the mass, the greater would be this resistance, and the greater is inertia.

**Space is not completely permeable to matter. The resistance of space to matter is observed as inertia.**

There is an illusion of space being permeable to matter because we see matter gliding through space. But matter is “gliding through space” only when it is either still or moving at a constant velocity relative to other matter. The fact is matter “gliding through space” is not moving through space. It is moving through space only when it is accelerating.

Matter may be conceived to be moving at the velocity of light relative to a light wave; but if matter is not accelerating, it is actually standing still relative to space.

When we look at space as the medium of light we no longer need the relativistic math developed by Einstein. We can apply the classical inertial frame to understand that two light beams approaching each other shall have the relative velocity of ‘2c’; and this shall not violate the limit on ‘c’ as the universal constant.

The universal constant ‘c’ may be seen as the ratio of the wavelength of light to its period. This connects space to time in the domain of electromagnetic field. This is true even in the domain of matter, but it not so obvious because wavelength and period of “disturbed space” are both infinitesimal in that domain. Thus space and time appear to be absolute and independent in the domain of matter but that is not really the case.

**The inertial frame of Galileo and Newton represents a special case of a more general inertial frame where space and time are related by the universal constant ‘c’.**

The inertial frame of Galileo and Newton identifies matter as the basis of the observer. It may be referred to as the Material Reference Frame (MRF). The more general inertial frame identifies space as the basis of the observer. We may refer to it as the Space Reference Frame (SRF).

The general inertial frame (SRF) is consistent with all of physics. It also provides a much more elegant explanation for INERTIA.

.